From f301352cdfb857603c157159d48c33a5ba433e81 Mon Sep 17 00:00:00 2001 From: Francisco Bernardo Date: Mon, 19 May 2025 14:18:33 +0100 Subject: [PATCH 01/14] added wave_to_current method to basedWDF and corrected Short and Open circuit impedance/conductance calculation --- pywdf/core/wdf.py | 24 ++++++++++++++++++------ 1 file changed, 18 insertions(+), 6 deletions(-) diff --git a/pywdf/core/wdf.py b/pywdf/core/wdf.py index d159af2..4c41351 100644 --- a/pywdf/core/wdf.py +++ b/pywdf/core/wdf.py @@ -4,7 +4,11 @@ class baseWDF: def __init__(self) -> None: - self.a, self.b = 0, 0 + self.a = 0.0 + self.b = 0.0 + # Added default values for impedance and admittance + self.r = 1.0e-9 # impedance + self.g = 1.0 / self.r # admittance self.parent = None def connect_to_parent(self, parent: baseWDF) -> None: @@ -19,7 +23,11 @@ def impedance_change(self) -> None: self.parent.impedance_change() def wave_to_voltage(self) -> float: - return (self.a + self.b) / 2.0 + return (self.a + self.b) * 0.5 + + # Added base class method to convert wave to current according to WDF parametric definition + def wave_to_current(self) -> float: + return (self.a - self.b) * 0.5 * self.g def reset(self) -> None: self.a, self.b = 0, 0 @@ -54,8 +62,10 @@ def __init__(self): self.calc_impedance() def calc_impedance(self) -> None: - self.Rp = 0 - self.G = 1e16 + # self.Rp = 0 + # self.G = 1e16 + self.Rp = 1e-16 # short circuit has zero resistance, here we set it to a very small value + self.G = 1.0 / self.Rp # set the conductance to a very large value def accept_incident_wave(self, a: float) -> None: self.a = a @@ -74,8 +84,10 @@ def __init__(self): self.calc_impedance() def calc_impedance(self) -> None: - self.Rp = 0 - self.G = 1e16 + # self.Rp = 0 + # self.G = 1e16 + self.Rp = 1e16 # open circuit has infinite resistance, here we set it to a very large value + self.G = 1.0 / self.Rp # set the conductance to a very small value def accept_incident_wave(self, a: float) -> None: self.a = a From 056f8bbbbfba115c92f458d68fab96380eca6a14 Mon Sep 17 00:00:00 2001 From: Francisco Bernardo Date: Tue, 24 Jun 2025 01:25:13 +0100 Subject: [PATCH 02/14] added chua --- README.md | 5 + pywdf/__init__.py | 7 +- pywdf/core/circuit.py | 143 +- pywdf/core/solver/__init__.py | 1 + pywdf/core/solver/newton_raphson.py | 38 + pywdf/core/solver/runge_kutta.py | 57 + pywdf/core/wdf.py | 199 ++- pywdf/examples/__init__.py | 1 + pywdf/examples/capacitor.py | 91 ++ pywdf/examples/chua_circuit.py | 182 +++ pywdf/examples/diodeclipper.py | 10 +- pywdf/examples/inductor.py | 104 ++ pywdf/examples/lc_oscillator.py | 33 +- pywdf/examples/passive_apf.py | 10 +- .../{passivelpf.py => passive_lpf.py} | 9 +- pywdf/examples/rc_highpass.py | 28 +- .../examples/{rclowpass.py => rc_lowpass.py} | 28 +- pywdf/examples/resistor.py | 61 + ...voltagedivider.py => resistor_parallel.py} | 5 + pywdf/examples/resistor_series.py | 69 + pywdf/examples/voltage_divider.py | 64 + pywdf/figures/diode_clipper_transient.png | Bin 0 -> 68611 bytes .../figures/diode_clipper_transient_anal.png | Bin 81258 -> 0 bytes pywdf/figures/hat_res_IR.png | Bin 36169 -> 33392 bytes pywdf/figures/mk2_sef_lpf_knob.png | Bin 200759 -> 182528 bytes pywdf/figures/voltage_divider_IR.png | Bin 0 -> 19498 bytes pywdf/figures/voltage_divider_transient.png | Bin 0 -> 56331 bytes test.py | 33 +- tests/chua_ac_analysis.png | Bin 0 -> 70082 bytes tests/chua_impulse_response.png | Bin 0 -> 55941 bytes tests/data/rk4_example1_results.csv | 22 + tests/data/rk4_example2_results.csv | 1259 +++++++++++++++++ tests/plots/capacitor.png | Bin 0 -> 76947 bytes tests/plots/chua_ac_analysis.png | Bin 0 -> 70082 bytes tests/plots/chua_circuit_440Hz.png | Bin 0 -> 42227 bytes tests/plots/chua_circuit_signal.png | Bin 0 -> 76799 bytes tests/plots/chua_impulse_response.png | Bin 0 -> 55941 bytes tests/plots/lc_oscillator_440Hz.png | Bin 0 -> 43538 bytes tests/plots/lc_oscillator_signal.png | Bin 0 -> 18685 bytes tests/plots/newton_raphson_visualization.png | Bin 0 -> 182626 bytes tests/plots/rc_highpass_ac_analysis.png | Bin 0 -> 65410 bytes tests/plots/rc_highpass_freqz.png | Bin 0 -> 42593 bytes tests/plots/rc_highpass_freqz_list.png | Bin 0 -> 131288 bytes tests/plots/rc_highpass_impulse_response.png | Bin 0 -> 19009 bytes tests/plots/rc_lowpass_ac_analysis.png | Bin 0 -> 70542 bytes tests/plots/rc_lowpass_freqz.png | Bin 0 -> 42557 bytes tests/plots/rc_lowpass_freqz_list.png | Bin 0 -> 100201 bytes tests/plots/rc_lowpass_impulse_response.png | Bin 0 -> 18394 bytes tests/plots/resistor.png | Bin 0 -> 40991 bytes tests/plots/resistor_series.png | Bin 0 -> 43013 bytes tests/plots/rk4_example1_plot.png | Bin 0 -> 128816 bytes tests/plots/rk4_example2_plot.png | Bin 0 -> 412594 bytes tests/plots/voltage_divider.png | Bin 0 -> 43013 bytes tests/test_newton_raphson.py | 101 ++ tests/test_runge_kutta.py | 155 ++ 55 files changed, 2675 insertions(+), 40 deletions(-) create mode 100644 pywdf/core/solver/__init__.py create mode 100644 pywdf/core/solver/newton_raphson.py create mode 100644 pywdf/core/solver/runge_kutta.py create mode 100644 pywdf/examples/capacitor.py create mode 100644 pywdf/examples/chua_circuit.py create mode 100644 pywdf/examples/inductor.py rename pywdf/examples/{passivelpf.py => passive_lpf.py} (87%) rename pywdf/examples/{rclowpass.py => rc_lowpass.py} (64%) create mode 100644 pywdf/examples/resistor.py rename pywdf/examples/{voltagedivider.py => resistor_parallel.py} (81%) create mode 100644 pywdf/examples/resistor_series.py create mode 100644 pywdf/examples/voltage_divider.py create mode 100644 pywdf/figures/diode_clipper_transient.png delete mode 100644 pywdf/figures/diode_clipper_transient_anal.png create mode 100644 pywdf/figures/voltage_divider_IR.png create mode 100644 pywdf/figures/voltage_divider_transient.png create mode 100644 tests/chua_ac_analysis.png create mode 100644 tests/chua_impulse_response.png create mode 100644 tests/data/rk4_example1_results.csv create mode 100644 tests/data/rk4_example2_results.csv create mode 100644 tests/plots/capacitor.png create mode 100644 tests/plots/chua_ac_analysis.png create mode 100644 tests/plots/chua_circuit_440Hz.png create mode 100644 tests/plots/chua_circuit_signal.png create mode 100644 tests/plots/chua_impulse_response.png create mode 100644 tests/plots/lc_oscillator_440Hz.png create mode 100644 tests/plots/lc_oscillator_signal.png create mode 100644 tests/plots/newton_raphson_visualization.png create mode 100644 tests/plots/rc_highpass_ac_analysis.png create mode 100644 tests/plots/rc_highpass_freqz.png create mode 100644 tests/plots/rc_highpass_freqz_list.png create mode 100644 tests/plots/rc_highpass_impulse_response.png create mode 100644 tests/plots/rc_lowpass_ac_analysis.png create mode 100644 tests/plots/rc_lowpass_freqz.png create mode 100644 tests/plots/rc_lowpass_freqz_list.png create mode 100644 tests/plots/rc_lowpass_impulse_response.png create mode 100644 tests/plots/resistor.png create mode 100644 tests/plots/resistor_series.png create mode 100644 tests/plots/rk4_example1_plot.png create mode 100644 tests/plots/rk4_example2_plot.png create mode 100644 tests/plots/voltage_divider.png create mode 100644 tests/test_newton_raphson.py create mode 100644 tests/test_runge_kutta.py diff --git a/README.md b/README.md index bfed375..98bedfe 100644 --- a/README.md +++ b/README.md @@ -35,6 +35,11 @@ The core directory contains the main source code of the repository. ## Usage +``` +python3 -m debugpy --wait-for-client --listen 5678 pywdf/examples/chua_circuit.py +``` + + ```python from pywdf import RCA_MK2_SEF, DiodeClipper, TR_808_HatResonator diff --git a/pywdf/__init__.py b/pywdf/__init__.py index 8132810..6d32c8b 100644 --- a/pywdf/__init__.py +++ b/pywdf/__init__.py @@ -1,13 +1,14 @@ from .core.circuit import * from .core.rtype import * from .core.wdf import * +from .core.solver import * from .examples.tr_808_hatresonator import TR_808_HatResonator from .examples.bassmantonestack import BassmanToneStack from .examples.baxandalleq import BaxandallEQ, UnadaptedBaxandallEQ from .examples.diodeclipper import DiodeClipper from .examples.lc_oscillator import LCOscillator -from .examples.passivelpf import PassiveLPF +from .examples.passive_lpf import PassiveLPF from .examples.rca_mk2_sef import RCA_MK2_SEF -from .examples.rclowpass import RCLowPass -from .examples.voltagedivider import VoltageDivider +from .examples.rc_lowpass import RCLowPass +from .examples.voltage_divider import VoltageDivider diff --git a/pywdf/core/circuit.py b/pywdf/core/circuit.py index 2dec46e..6641a6c 100644 --- a/pywdf/core/circuit.py +++ b/pywdf/core/circuit.py @@ -22,6 +22,7 @@ def __init__(self, source: baseWDF, root: rootWDF, output: baseWDF) -> None: self.root = root self.output = output + def process_sample(self, sample: float) -> float: """Process an individual sample with this circuit. @@ -38,6 +39,40 @@ def process_sample(self, sample: float) -> float: self.root.next.accept_incident_wave(self.root.propagate_reflected_wave()) return self.output.wave_to_voltage() + + + def process_sample_i_v(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.source.set_voltage(sample) + self.root.accept_incident_wave(self.root.next.propagate_reflected_wave()) + self.root.next.accept_incident_wave(self.root.propagate_reflected_wave()) + + return ( self.output.wave_to_voltage(), self.source.wave_to_current(), self.output.wave_to_current() ) + + + def process_i_v_signals(self, signal: np.array) -> np.array: + """Process an entire signal with this circuit. + + Args: + signal (np.array): incoming signal to process + + Returns: + (i,v) tuples list: processed signal + """ + self.reset() + l = [ self.process_sample_i_v(sample) for sample in signal] + return l + + def process_signal(self, signal: np.array) -> np.array: """Process an entire signal with this circuit. @@ -48,7 +83,10 @@ def process_signal(self, signal: np.array) -> np.array: np.array: processed signal """ self.reset() - return np.array([self.process_sample(sample) for sample in signal]) + + return np.array([ self.process_sample(sample) for sample in signal ]) + + def process_wav(self, filepath: str, output_filepath: str = None) -> np.array: fs, x = wavfile.read(filepath) @@ -67,8 +105,14 @@ def __call__(self, *args: any, **kwds: any) -> any: elif hasattr(args[0], "__iter__"): return self.process_signal(args[0]) + + + + + def get_impulse_response(self, delta_dur: float = 1, amp: float = 1) -> np.array: - """Get circuit's impulse response + """ + Get circuit's impulse response Args: delta_dur (float, optional): duration of Dirac delta function in seconds. Defaults to 1. @@ -81,6 +125,34 @@ def get_impulse_response(self, delta_dur: float = 1, amp: float = 1) -> np.array d[0] = amp return self.process_signal(d) + + + + + def plot_signal( + self, + signal: np.array, + n_samples: int = 500, + outpath: str = None, + title: str = "Signal", + ) -> None: + + plt.figure(figsize=(9, 5.85)) + plt.plot(signal[:n_samples]) + plt.xlabel("Sample [n]") + plt.ylabel("Amplitude [V]") + plt.title(title) + + plt.grid() + if outpath: + plt.savefig(outpath) + plt.show() + + + + + + def plot_impulse_response( self, n_samples: int = 500, @@ -120,14 +192,23 @@ def reset(self) -> None: if isinstance(self.__dict__[key], baseWDF): self.__dict__[key].reset() + + + + def compute_spectrum(self, fft_size: int = None) -> np.ndarray: x = self.get_impulse_response() N2 = int(fft_size / 2 - 1) H = fft(x, fft_size)[:N2] return H + + + + def plot_freqz(self, outpath: str = None, fft_size: int = None): - """Plot the circuit's frequency response + """ + Plot the circuit's frequency response Args: outpath (str, optional): filepath to save figure. Defaults to None. @@ -171,6 +252,9 @@ def plot_freqz(self, outpath: str = None, fft_size: int = None): plt.savefig(outpath) plt.show() + + + def plot_freqz_list( self, values: list, @@ -241,6 +325,59 @@ def plot_freqz_list( plt.show() + + + + + def i_v_analysis( + self, + freq: float = 1000, + amplitude: float = 1, + t_ms: float = 5, + outpath: str = None, + ): + """Plot transient analysis of Circuit's response to sine wave + + Args: + freq (float, optional): frequency of sine wave. Defaults to 1000. + amplitude (float, optional): amplitude of sine wave. Defaults to 1. + t_ms (float, optional): time in ms of sine wave. Defaults to 5. + """ + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + + n_samples = int(t_ms * self.fs / 1000) + n = np.arange(0, 2, 1 / self.fs) + x = np.sin(2 * np.pi * freq * n) * amplitude + + y = self.process_i_v_signals(x) + + v, ii, io = zip(*y) + + v, ii, io = np.array(v), np.array(ii) * 100, np.array(io) * 0.01 + + ax.plot(x[:n_samples], label="input signal") + ax.plot(v[:n_samples], label="voltage out", alpha=0.75) + ax.plot(ii[:n_samples], label="current source through", alpha=0.75) + ax.plot(io[:n_samples], label="current output through", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("amplitude") + ax.set_yscale('log') + ax.set_ylim(0, 1000000) + + ax.set_title(loc="left", label="output signal vs input signal waveforms") + ax.grid(True) + ax.legend() + + if outpath: + plt.savefig(outpath) + + plt.show() + + + + + + def AC_transient_analysis( self, freq: float = 1000, diff --git a/pywdf/core/solver/__init__.py b/pywdf/core/solver/__init__.py new file mode 100644 index 0000000..2885088 --- /dev/null +++ b/pywdf/core/solver/__init__.py @@ -0,0 +1 @@ +__all__ = ['newton_raphson', 'runge_kutta'] \ No newline at end of file diff --git a/pywdf/core/solver/newton_raphson.py b/pywdf/core/solver/newton_raphson.py new file mode 100644 index 0000000..eae5169 --- /dev/null +++ b/pywdf/core/solver/newton_raphson.py @@ -0,0 +1,38 @@ +import math + +def newton_raphson(f, df, x0, tolerance=1e-10, max_iterations=100): + """ + Find the root of a function using the Newton-Raphson method. + + Parameters: + f: function whose root we want to find + df: derivative of the function f + x0: initial guess + tolerance: convergence criterion (default: 1e-10) + max_iterations: maximum number of iterations (default: 100) + + Returns: + root: approximate root of the function + iterations: number of iterations performed + """ + x = x0 + + for i in range(max_iterations): + fx = f(x) + dfx = df(x) + + # Check if derivative is too close to zero + if abs(dfx) < 1e-15: + raise ValueError(f"Derivative too close to zero at x = {x}") + + # Newton-Raphson formula: x_new = x - f(x)/f'(x) + x_new = x - fx / dfx + + # Check for convergence + if abs(x_new - x) < tolerance: + return x_new, i + 1 + + x = x_new + + raise ValueError(f"Failed to converge after {max_iterations} iterations") + diff --git a/pywdf/core/solver/runge_kutta.py b/pywdf/core/solver/runge_kutta.py new file mode 100644 index 0000000..e75341c --- /dev/null +++ b/pywdf/core/solver/runge_kutta.py @@ -0,0 +1,57 @@ +import numpy as np + +def rk4_step(f, t, y, h): + """ + Single step of fourth-order Runge-Kutta method + + Parameters: + f: function that defines dy/dt = f(t, y) + t: current time + y: current value of y + h: step size + + Returns: + y_next: next value of y + """ + k1 = h * f(t, y) + k2 = h * f(t + h/2, y + k1/2) + k3 = h * f(t + h/2, y + k2/2) + k4 = h * f(t + h, y + k3) + + y_next = y + (k1 + 2*k2 + 2*k3 + k4) / 6 + return y_next + +def rk4_solve(f, t_span, y0, h): + """ + Solve ODE using RK4 method + + Parameters: + f: function that defines dy/dt = f(t, y) + t_span: tuple (t_start, t_end) + y0: initial condition (scalar or array) + h: step size + + Returns: + t_values: array of time points + y_values: array of solution values + """ + t_start, t_end = t_span + t_values = np.arange(t_start, t_end + h, h) + + # Handle both scalar and vector initial conditions + y0 = np.asarray(y0) + if y0.ndim == 0: # Scalar case + y_values = np.zeros(len(t_values)) + else: # Vector case + y_values = np.zeros((len(t_values), len(y0))) + + # Initial condition + y_values[0] = y0 + + # Apply RK4 method + for i in range(len(t_values) - 1): + y_values[i + 1] = rk4_step(f, t_values[i], y_values[i], h) + + return t_values, y_values + + diff --git a/pywdf/core/wdf.py b/pywdf/core/wdf.py index 4c41351..cb92b48 100644 --- a/pywdf/core/wdf.py +++ b/pywdf/core/wdf.py @@ -3,12 +3,15 @@ class baseWDF: + ''' + The base one port object from which all wave digital elements will inherit. + ''' def __init__(self) -> None: self.a = 0.0 self.b = 0.0 # Added default values for impedance and admittance - self.r = 1.0e-9 # impedance - self.g = 1.0 / self.r # admittance + self.Rp = 1.0e-9 # impedance + self.G = 1.0 / self.Rp # admittance self.parent = None def connect_to_parent(self, parent: baseWDF) -> None: @@ -27,7 +30,7 @@ def wave_to_voltage(self) -> float: # Added base class method to convert wave to current according to WDF parametric definition def wave_to_current(self) -> float: - return (self.a - self.b) * 0.5 * self.g + return (self.a - self.b) * 0.5 * self.G def reset(self) -> None: self.a, self.b = 0, 0 @@ -43,6 +46,11 @@ def __str__(self) -> str: class rootWDF(baseWDF): + ''' + The rootWDF class is a subclass of baseWDF that represents the root element in a WDF circuit. + It inherits from baseWDF but overwrites the connection of an element to a parent + and throws an error should this be attempted. + ''' def __init__(self, next: baseWDF) -> None: baseWDF.__init__(self) self.next = next @@ -144,9 +152,20 @@ def set_capacitance(self, new_C: float) -> None: self.impedance_change() def calc_impedance(self) -> None: + ''' + Local discretisation of capacitor using the warped bilinear transform method. + + 1 + Z_C = -------------- + 2 * C * f_s + + where f_s is the sampling frequency and C the capacitance. + ''' + self.Rp = 1.0 / (2 * self.C * self.fs) self.G = 1.0 / self.Rp + def accept_incident_wave(self, a: float) -> None: self.a = a self.z = self.a @@ -165,6 +184,9 @@ def reset(self) -> None: class Inductor(baseWDF): def __init__(self, L: float, fs: int) -> None: + ''' + TODO: Why does inductor have a different constructor than capacitor? + ''' self.fs = fs self.L = L self.z = 0 @@ -312,8 +334,41 @@ def propagate_reflected_wave(self) -> float: #################################################################################### +class SeriesVoltage(baseWDF): + + def __init__(self, p1: baseWDF) -> None: + baseWDF.__init__(self) + p1.connect_to_parent(self) + self.p1 = p1 + self.calc_impedance() + + def calc_impedance(self) -> None: + self.Rp = self.p1.Rp + self.G = 1.0 / self.Rp + + def set_voltage(self, new_V: float) -> None: + self.Vs = new_V + + def accept_incident_wave(self, a: float) -> None: + self.a = a + self.p1.accept_incident_wave( -a + -self.Vs ) # Incident wave is the negative of the voltage source + + def propagate_reflected_wave(self) -> float: + self.b = 0 - self.p1.propagate_reflected_wave() + -self.Vs + return self.b + + + +#################################################################################### + + class IdealVoltageSource(rootWDF): def __init__(self, next: baseWDF) -> None: + ''' + IdealVoltageSource is a subclass of rootWDF and not of baseWDF. + This is because there is delay free loop in the reflected wave and therefore + we can only use an ideal voltage source at the root of a connection tree, not as a leaf node. + ''' rootWDF.__init__(self, next) self.Vs = 0 self.calc_impedance() @@ -332,8 +387,35 @@ def propagate_reflected_wave(self) -> float: #################################################################################### +class IdealCurrentSource(rootWDF): + def __init__(self, next: baseWDF) -> None: + ''' + IdealCurrentSource is a subclass of rootWDF and not of baseWDF. + This is because there is delay free loop in the reflected wave + therefore we can only use an ideal current source at the root of a connection tree, not as a leaf node. + ''' + rootWDF.__init__(self, next) + self.Is = 0 + # self.Vs = 0 + self.calc_impedance() + + def set_current(self, new_I: float) -> None: + self.Is = new_I + + def accept_incident_wave(self, a: float) -> None: + self.a = a + + def propagate_reflected_wave(self) -> float: + self.b = 2.0 * self.Is + self.a + return self.b + + +#################################################################################### + + class ResistiveVoltageSource(baseWDF): - def __init__(self, Rval: float = None): + # def __init__(self, Rval: float = None): + def __init__(self, next: baseWDF = None, Rval: float = None) -> None: baseWDF.__init__(self) self.Rval = Rval if Rval else 1e-9 self.Vs = 0 @@ -359,14 +441,115 @@ def propagate_reflected_wave(self) -> None: #################################################################################### + +class ChuaDiode(rootWDF): + """ + Computes the Chua diode nonlinearity, a piecewise linear active resistance. + This class implements a Chua diode model for Wave Digital Filter (WDF) circuits. + The Chua diode is characterized by a piecewise linear current-voltage relationship. + """ + + def __init__( + self, + next: baseWDF, + g1: float, + g2: float, + v0: float, + r1: float + ) -> None: + """ + Initialize the Chua diode. + + Args: + next_element: The next WDF element in the circuit + g1: Slope of i(v) parameter of the chua diode + g2: Slope of i(v) parameter of the chua diode + v0: Voltage parameter of the chua diode + r1: Resistance value in Ohms + """ + rootWDF.__init__(self, next) + next.connect_to_parent(self) + self.set_Chua_parameters(g1, g2, r1, v0) + + + def set_Chua_parameters( + self, + g1: float, + g2: float, + r1: float, + v0: float + ) -> None: + """ + Sets diode specific parameters. + + Args: + g1: First conductance parameter + g2: Second conductance parameter + r1: Resistance parameter + """ + self.G1 = g1 + self.G2 = g2 + self.R1 = r1 + self.V0 = v0 + + def calc_impedance(self): + """Calculate impedance - implementation depends on specific circuit context""" + # Implementation would depend on the specific WDF framework + # This is a placeholder as the original C++ implementation is empty + pass + + + def incident(self, a: float): + """ + Set the incident wave. + + Args: + a: The incident wave value + """ + self.a = a + + + def propagate_reflected_wave(self) -> float: + """ + Compute the reflected wave using the Chua diode characteristic. + This implements the piecewise linear characteristic of the Chua diode + using the absolute value function to create the nonlinear behavior. + + Args: + a0: The incident wave value + + Returns: + The reflected wave value + """ + # TODO: g1 and g2 do not need to be calculated for every reflected calculation, just a_0 + g1 = (1.0 - self.G1 * self.R1) / (1.0 + self.G1 * self.R1) + g2 = (1.0 - self.G2 * self.R1) / (1.0 + self.G2 * self.R1) + a_0 = self.V0 * (1.0 + self.G2 * self.R1) + + self.b = ( + g1 * self.a + 0.5 * (g2 - g1) * (abs( self.a + a_0 ) - abs( self.a - a_0 ))) + + return self.b + + + +#################################################################################### + + class Diode(rootWDF): def __init__( - self, next: baseWDF, Is: float, Vt: float = 25.85e-3, n_diodes: float = 1 + self, + next: baseWDF, + Is: float, + Vt: float = 25.85e-3, + n_diodes: float = 1 ) -> None: + rootWDF.__init__(self, next) next.connect_to_parent(self) self.set_diode_params(Is, Vt, n_diodes) + def set_diode_params(self, Is: float, Vt: float, n_diodes: float) -> None: self.Is = Is self.n_diodes = n_diodes @@ -419,7 +602,11 @@ def omega4(self, x: float) -> float: class DiodePair(Diode): def __init__( - self, next: baseWDF, Is: float, Vt: float = 25.85e-3, n_diodes: float = 2 + self, + next: baseWDF, + Is: float, + Vt: float = 25.85e-3, + n_diodes: float = 2 ) -> None: Diode.__init__(self, next, Is, Vt, n_diodes) diff --git a/pywdf/examples/__init__.py b/pywdf/examples/__init__.py index b8a1dd0..b842ad6 100644 --- a/pywdf/examples/__init__.py +++ b/pywdf/examples/__init__.py @@ -8,4 +8,5 @@ "rca_mk2_sef", "rclowpass", "voltagedivider", + "chua_circuit", ] diff --git a/pywdf/examples/capacitor.py b/pywdf/examples/capacitor.py new file mode 100644 index 0000000..e5ca088 --- /dev/null +++ b/pywdf/examples/capacitor.py @@ -0,0 +1,91 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + + +class _Capacitor(Circuit): + + def __init__( + self, + sample_rate: int, + cutoff: float + ) -> None: + + self.fs = sample_rate + self.cutoff = cutoff + + self.C = 47e-9 # capacitance in Farads + self.R = 1.0 / (2 * np.pi * self.C * self.cutoff) + self.Vs = ResistiveVoltageSource(self.R) + + self.C1 = Capacitor(self.C, self.fs) + self.S1 = SeriesAdaptor(self.Vs, self.C1) + + super().__init__(self.Vs, self.S1, self.C1) + # super().__init__(self.Vs, self.Vs, self.C1) + + + def process_sample_i_v(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vs.set_voltage(sample) + self.Vs.accept_incident_wave(self.S1.propagate_reflected_wave()) + self.S1.accept_incident_wave(self.Vs.propagate_reflected_wave()) + + return ( self.source.wave_to_voltage(), self.source.wave_to_current(), self.output.wave_to_current() ) + + + + +if __name__ == "__main__": + + fs = 44100 + f = 4 + # duration = .25 + duration = 1.0 + + cap = _Capacitor(fs, 1000) + + # cap.plot_freqz() + # cap.plot_freqz_list(range(1000, 10000, 1000), cap.set_cutoff, param_label="cutoff") + # cap.AC_transient_analysis() + + t = np.linspace(0, duration, int(fs * duration), endpoint=False) + + sine = np.sin(2 * np.pi * f * t) + + y = cap.process_i_v_signals(sine) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + ax.plot(sine, color="r", label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + color = 'tab:blue' + ax2 = ax.twinx() + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + ax2.plot(i, color=color, label="current through", alpha=0.75) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through capacitor C1 ") + ax.legend() + ax2.legend() + ax.grid(True) + + plt.savefig("./tests/capacitor.png") + plt.show() \ No newline at end of file diff --git a/pywdf/examples/chua_circuit.py b/pywdf/examples/chua_circuit.py new file mode 100644 index 0000000..1ecafc2 --- /dev/null +++ b/pywdf/examples/chua_circuit.py @@ -0,0 +1,182 @@ +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class Chua(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.C1_value = 5.5e-9 + self.R2_value = 1.428e3 + self.L3_value = 7.07e-3 + self.C4_value = 49.5e-9 + + self.C1 = Capacitor(self.C1_value, self.fs) # fs, needs local discretization + self.R2 = Resistor(self.R2_value) # no need for discretization + self.L3 = Inductor(self.L3_value, self.fs) # fs, needs local discretization + self.C4 = Capacitor(self.C4_value, self.fs) # fs, needs local discretization + + self.Vs = SeriesVoltage(self.C4) + self.P2 = ParallelAdaptor(self.L3, self.Vs) + self.S1 = SeriesAdaptor(self.R2, self.P2) + self.P1 = ParallelAdaptor(self.C1, self.S1) + + self.g1 = -500.0e-6 + self.g2 = -800.0e-6 + self.v0 = 1.0 + self.R_NL = 1.0 + + self.NL = ChuaDiode( + self.P1, + g1=self.g1, # parameter 1 + g2=self.g2, # parameter 2 + v0=self.v0, # Voltage parameter + r1=self.R_NL, # Resistance in Ohms + ) + + # init and set circuit + super().__init__(self.Vs, self.NL, self.C1) + + + def process_sample( + self, + sample: float + ) -> float: + + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage() + + + def process_sample_chua(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage(), self.C1.wave_to_voltage(), self.L3.wave_to_current() + + + + + def set_params( + self, + frequency: float, + decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + # self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + # self.L1.set_inductance(self.L) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + fs = 48e3 + frequency = 440 + decibels = 0 + + chua_circuit = Chua(fs) + chua_circuit.set_params(frequency, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + + # chua_circuit.plot_freqz( + # out_path + # ) + + # chua_circuit.AC_transient_analysis( + # freq = 1000, + # amplitude = 1, + # t_ms = 5, + # outpath="tests/chua_ac_analysis.png" + # ) + + # chua_circuit.plot_impulse_response( + # outpath="tests/chua_impulse_response.png" + # ) + + + samples = np.zeros((int(500))) + samples[0] = 1.0 # impulse signal + + i_list, v1_list, v2_list = [], [], [] + + for s in samples: + v1, v2, i = chua_circuit.process_sample_chua(s) + i_list.append(i) + v1_list.append(v1) + v2_list.append(v2) + + # Plotting + fig, axes = plt.subplots(1, 3, figsize=(15, 4)) + axes[0].plot(v1_list, label='Amplitude C1 [V]', color='r') + axes[1].plot(v2_list, label='Amplitude C4 [V]', color='g') + axes[2].plot(i_list, label='Amplitude L3 [I]', color='b') + + for ax in axes: + ax.legend() + ax.grid(True) + ax.set_xlabel("Sample [n]") + + axes[0].set_ylabel("Output") + + # Centered title + fig.suptitle("Chua impulse response", fontsize=14) + plt.tight_layout(rect=[0, 0, 1, 0.95]) # Leave space for suptitle + + # Save and show + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + + diff --git a/pywdf/examples/diodeclipper.py b/pywdf/examples/diodeclipper.py index dd2767a..c417831 100644 --- a/pywdf/examples/diodeclipper.py +++ b/pywdf/examples/diodeclipper.py @@ -11,8 +11,12 @@ class DiodeClipper(Circuit): def __init__( - self, sample_rate: int, cutoff: float = 1000, input_gain_db: float = 0, - output_gain_db: float = 0, n_diodes: float = 2 + self, + sample_rate: int, + cutoff: float = 1000, + input_gain_db: float = 0, + output_gain_db: float = 0, + n_diodes: float = 2 ) -> None: self.fs = sample_rate @@ -38,7 +42,7 @@ def __init__( def process_sample(self, sample: float) -> float: sample *= self.input_gain - return -(super().process_sample(sample) * self.output_gain) ### ¡! phase inverted !¡ + return -( super().process_sample(sample) * self.output_gain) ### ¡! phase inverted !¡ def set_cutoff(self, new_cutoff: float) -> None: if self.cutoff != new_cutoff: diff --git a/pywdf/examples/inductor.py b/pywdf/examples/inductor.py new file mode 100644 index 0000000..cb7f957 --- /dev/null +++ b/pywdf/examples/inductor.py @@ -0,0 +1,104 @@ +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class _Inductor(Circuit): + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.L = 1.0e3 + self.twopi = 2 * np.pi + + self.L1 = Inductor(self.L, self.fs) + + self.Vs = ResistiveVoltageSource() + self.S1 = SeriesAdaptor(self.Vs, self.L1) + + # self.SW1 = Switch(self.S1) + + # init and set circuit + super().__init__(self.Vs, self.S1, self.C1) + # super().__init__(self.Vs, self.SW1, self.C1) + self.set_params(self.frequency, self.closed, self.decibels) + + def process_sample(self, sample: float) -> float: + return super().process_sample(sample) * self.gain + + def set_params( + self, frequency: float, switch_closed: bool, decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + self.L1.set_inductance(self.L) + + # update switch status + if switch_closed != self.closed: + self.SW1.set_closed(switch_closed) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + fs = 48e3 + frequency = 440 + decibels = 0 + switch_closed = True + + _inductor = _Inductor(fs) + _inductor.set_params(frequency, switch_closed, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "data" / "plot" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + _inductor.plot_freqz(out_path) + + # generate sinusoid + out = _inductor.process_signal(np.ones((int(fs)))) + out = out - 1 # remove DC offset [0, 2] + + plt.figure(figsize=(10, 4)) + plt.plot(out) + plt.xlim([0, fs]) + plt.title(f"{frequency}Hz sinewave") + plt.tight_layout() + plt.show() + + # estimate pitch using zerocrossing + zero_crossings = np.where(np.diff(np.sign(out)))[0] + T = (zero_crossings[2] - zero_crossings[0]) / fs + f = 1 / T + print(f"T = {T:.6f}[s]\nf = {f:.3f}[Hz]") diff --git a/pywdf/examples/lc_oscillator.py b/pywdf/examples/lc_oscillator.py index 5d37520..e3d2142 100644 --- a/pywdf/examples/lc_oscillator.py +++ b/pywdf/examples/lc_oscillator.py @@ -12,6 +12,7 @@ class LCOscillator(Circuit): + def __init__( self, sample_rate: int, @@ -44,11 +45,22 @@ def __init__( super().__init__(self.Vs, self.SW1, self.C1) self.set_params(self.frequency, self.closed, self.decibels) - def process_sample(self, sample: float) -> float: + + + def process_sample( + self, + sample: float + ) -> float: + return super().process_sample(sample) * self.gain + + def set_params( - self, frequency: float, switch_closed: bool, decibels: float + self, + frequency: float, + switch_closed: bool, + decibels: float ) -> None: # update frequency @@ -83,10 +95,13 @@ def decibels_to_gain(self): lc_oscillator.set_params(frequency, switch_closed, decibels) # update params # plot transfer function - plt_dir = src_dir.parent / "data" / "plot" + plt_dir = src_dir.parent / "tests" / "plots" plt_dir.mkdir(exist_ok=True, parents=True) out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" - lc_oscillator.plot_freqz(out_path) + + lc_oscillator.plot_freqz( + out_path + ) # generate sinusoid out = lc_oscillator.process_signal(np.ones((int(fs)))) @@ -97,10 +112,18 @@ def decibels_to_gain(self): plt.xlim([0, fs]) plt.title(f"{frequency}Hz sinewave") plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) plt.show() + # estimate pitch using zerocrossing - zero_crossings = np.where(np.diff(np.sign(out)))[0] + zero_crossings = np.where( + np.diff( + np.sign(out) + ) + )[0] + T = (zero_crossings[2] - zero_crossings[0]) / fs f = 1 / T print(f"T = {T:.6f}[s]\nf = {f:.3f}[Hz]") diff --git a/pywdf/examples/passive_apf.py b/pywdf/examples/passive_apf.py index 16bf56d..dacee09 100644 --- a/pywdf/examples/passive_apf.py +++ b/pywdf/examples/passive_apf.py @@ -12,7 +12,7 @@ script_dir = Path(__file__).resolve().parent wdf_dir = script_dir.parent -plot_dir = wdf_dir.parent / "data" / "plot" +plot_dir = wdf_dir.parent / "tests" / "plots" # add path to PYTHONPATH sys.path.append(str(wdf_dir)) @@ -283,8 +283,14 @@ def set_cutoff(self, cutoff: float) -> None: if __name__ == "__main__": + apf = PassiveAPF(48000) + apf.plot_freqz() + apf.plot_freqz_list( - [100, 250, 500, 1000, 2000, 4000, 8000], apf.set_cutoff, param_label="cutoff", outpath=plot_dir / "passive_apf-cutoff_list.png" + [100, 250, 500, 1000, 2000, 4000, 8000], + apf.set_cutoff, + param_label="cutoff", + outpath=plot_dir / "passive_apf-cutoff_list.png" ) diff --git a/pywdf/examples/passivelpf.py b/pywdf/examples/passive_lpf.py similarity index 87% rename from pywdf/examples/passivelpf.py rename to pywdf/examples/passive_lpf.py index 99c260f..142ec59 100644 --- a/pywdf/examples/passivelpf.py +++ b/pywdf/examples/passive_lpf.py @@ -37,5 +37,12 @@ def set_cutoff(self, new_cutoff: float) -> None: self.C2.set_capacitance(self.C) if __name__ == '__main__': + lpf = PassiveLPF(44100, 1000) - lpf.plot_freqz_list(range(1000,10000,1000),lpf.set_cutoff,param_label='cutoff') \ No newline at end of file + + lpf.plot_freqz_list( + range(1000,10000,1000), + lpf.set_cutoff, + param_label='cutoff', + outpath="tests/passive_lpf_freqz_list.png" + ) \ No newline at end of file diff --git a/pywdf/examples/rc_highpass.py b/pywdf/examples/rc_highpass.py index d4701ad..dffaf6d 100644 --- a/pywdf/examples/rc_highpass.py +++ b/pywdf/examples/rc_highpass.py @@ -44,7 +44,29 @@ def set_cutoff(self, new_cutoff: float): if __name__ == "__main__": + lpf = RCHighPass(44100, 1000) - lpf.plot_freqz() - # lpf.plot_freqz_list(range(1000, 10000, 1000), lpf.set_cutoff, param_label="cutoff") - # lpf.AC_transient_analysis() + + lpf.plot_freqz( + outpath="tests/rc_highpass_freqz.png" + ) + + lpf.plot_freqz_list( + range(1000, 10000, 1000), + lpf.set_cutoff, + param_label="cutoff", + outpath="tests/rc_highpass_freqz_list.png" + ) + + lpf.AC_transient_analysis( + freq = 1000, + amplitude = 1, + t_ms = 5, + outpath="tests/rc_highpass_ac_analysis.png" + ) + + lpf.plot_impulse_response( + outpath="tests/rc_pass_impulse_response.png" + ) + + print("done") \ No newline at end of file diff --git a/pywdf/examples/rclowpass.py b/pywdf/examples/rc_lowpass.py similarity index 64% rename from pywdf/examples/rclowpass.py rename to pywdf/examples/rc_lowpass.py index 96a2b92..70b3ea4 100644 --- a/pywdf/examples/rclowpass.py +++ b/pywdf/examples/rc_lowpass.py @@ -35,7 +35,29 @@ def set_cutoff(self, new_cutoff: float): if __name__ == "__main__": + lpf = RCLowPass(44100, 1000) - lpf.plot_freqz() - lpf.plot_freqz_list(range(1000, 10000, 1000), lpf.set_cutoff, param_label="cutoff") - lpf.AC_transient_analysis() + + lpf.plot_freqz( + outpath="tests/rc_lowpass_freqz.png" + ) + + lpf.plot_freqz_list( + range(1000, 10000, 1000), + lpf.set_cutoff, + param_label="cutoff", + outpath="tests/rc_lowpass_freqz_list.png" + ) + + lpf.AC_transient_analysis( + freq = 1000, + amplitude = 1, + t_ms = 5, + outpath="tests/rc_lowpass_ac_analysis.png" + ) + + lpf.plot_impulse_response( + outpath="tests/rc_lowpass_impulse_response.png" + ) + + print("done") \ No newline at end of file diff --git a/pywdf/examples/resistor.py b/pywdf/examples/resistor.py new file mode 100644 index 0000000..7fd9483 --- /dev/null +++ b/pywdf/examples/resistor.py @@ -0,0 +1,61 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + +class _Resistor(Circuit): + + def __init__( + self, + fs: int, + R1_val: float + ) -> None: + + self.fs = fs + + self.R1 = Resistor(R1_val) + + self.Vs = IdealVoltageSource(self.R1) + + super().__init__(self.Vs, self.Vs, self.R1) + + def set_R1(self, new_R): + self.R1.set_resistance(new_R) + + # def process_sample(self, sample: float) -> float: + # return super().process_sample_i_v(sample) + + +if __name__ == '__main__': + + r = _Resistor(44100, 1e4) + + vs = np.arange(0.0, 6.0, 0.01) + + y = r.process_i_v_signals(vs) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + ax.plot(v, label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + color = 'tab:blue' + ax2 = ax.twinx() + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + ax2.plot(i, color=color, label="current through output", alpha=0.75) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through resistor R1 ") + ax.grid(True) + ax.legend() + + plt.savefig("./tests/resistor.png") + plt.show() + + diff --git a/pywdf/examples/voltagedivider.py b/pywdf/examples/resistor_parallel.py similarity index 81% rename from pywdf/examples/voltagedivider.py rename to pywdf/examples/resistor_parallel.py index b088db1..b7a182d 100644 --- a/pywdf/examples/voltagedivider.py +++ b/pywdf/examples/resistor_parallel.py @@ -24,6 +24,11 @@ def set_R1(self,new_R): def set_R2(self,new_R): self.R2.set_resistance(new_R) + + def process_sample(self, sample: float) -> float: + # return super().process_sample(sample) + self.R1.wave_to_voltage() + self.C1.wave_to_voltage() + pass + if __name__ == '__main__': vd = VoltageDivider(44100, 1e5, 1e10) vd.plot_freqz() \ No newline at end of file diff --git a/pywdf/examples/resistor_series.py b/pywdf/examples/resistor_series.py new file mode 100644 index 0000000..a00902c --- /dev/null +++ b/pywdf/examples/resistor_series.py @@ -0,0 +1,69 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + + +class ResistorSeries(Circuit): + + def __init__( + self, + fs: int, + R1_val: float, + R2_val: float + ) -> None: + + self.fs = fs + + self.R1 = Resistor(R1_val) + self.R2 = Resistor(R2_val) + + self.S1 = SeriesAdaptor(self.R1, self.R2) + self.I1 = PolarityInverter(self.S1) + self.Vs = IdealVoltageSource(self.I1) + + super().__init__(self.Vs, self.Vs, self.R2) + + def set_R1(self,new_R): + self.R1.set_resistance(new_R) + + def set_R2(self,new_R): + self.R2.set_resistance(new_R) + + +if __name__ == '__main__': + + rs = ResistorSeries(44100, 1e4, 1e4) + + vs = np.arange(0.0, 6.0, 0.01) + + y = rs.process_i_v_signals(vs) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + + # ax.plot(vs, label="voltage across", alpha=0.75) + ax.plot(v, label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + + color = 'tab:blue' + ax2 = ax.twinx() + ax2.plot(i, color=color, label="current through output", alpha=0.75) + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through resistor R1 ") + ax.grid(True) + ax.legend() + + plt.savefig("./tests/resistor_series.png") + plt.show() + + diff --git a/pywdf/examples/voltage_divider.py b/pywdf/examples/voltage_divider.py new file mode 100644 index 0000000..6af0fa8 --- /dev/null +++ b/pywdf/examples/voltage_divider.py @@ -0,0 +1,64 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + + +class VoltageDivider(Circuit): + def __init__(self, fs: int, R1_val: float, R2_val: float) -> None: + self.fs = fs + + self.R1 = Resistor(R1_val) + self.R2 = Resistor(R2_val) + + self.S1 = SeriesAdaptor(self.R1, self.R2) + + self.I1 = PolarityInverter(self.S1) + self.Vs = IdealVoltageSource(self.I1) + + super().__init__(self.Vs, self.Vs, self.R1) + + def set_R1(self,new_R): + self.R1.set_resistance(new_R) + + def set_R2(self,new_R): + self.R2.set_resistance(new_R) + + + def process_sample(self, sample: float) -> float: + # return super().process_sample(sample) + self.R1.wave_to_voltage() + self.C1.wave_to_voltage() + pass + +if __name__ == '__main__': + + vd = VoltageDivider(44100, 1e4, 1e4) + + vd.plot_freqz() + + vs = np.arange(0.0, 6.0, 0.01) + + y = vd.process_i_v_signals(vs) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + ax.plot(v, label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + color = 'tab:blue' + ax2 = ax.twinx() + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + ax2.plot(i, color=color, label="current through output", alpha=0.75) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through resistor R1 ") + ax.grid(True) + ax.legend() + + plt.savefig("voltage_divider.png") + plt.show() \ No newline at end of file diff --git a/pywdf/figures/diode_clipper_transient.png 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z^!u!jYZ8H@Qw6e>6%`&%PEDZpO4zy>&CTiOr#+uv9|t@xLT9mi|1{uTNvGFDZZ3Jf z3piHbx1_tfTU+)pusKn)F6zqa+slML)VJ@_SWp9uu&I-(T(1I8j*O87rSTju)eFE@ z%hl7s>blfuU&+g$$o+MD|A6+AJU%xSSg?48gs z@j+&0W?|}&UYTYs0yc3!%m>cmG8||N@%{>A%3J-^s;@QA&dj_7EG6dZ^vhTV zS(Ut4kl+3dRR6jBjLNvRW#v5GxUJ{rTNb Date: Wed, 1 Oct 2025 17:22:59 +0100 Subject: [PATCH 03/14] add all changes to the library and examples --- README.md | 9 +- pywdf/core/wdf.py | 113 ++++++++-- pywdf/examples/bassmantonestack.py | 3 +- pywdf/examples/chua_ODE.py | 122 ++++++++++ pywdf/examples/chua_circuit.py | 73 +++--- pywdf/examples/chua_circuit_sr.py | 186 ++++++++++++++++ pywdf/examples/chua_minimal.py | 93 ++++++++ pywdf/examples/chua_res_src.py | 208 ++++++++++++++++++ pywdf/examples/chua_switch.py | 204 +++++++++++++++++ pywdf/examples/lc_oscillator.py | 32 +-- pywdf/examples/nl_oscillator.py | 129 +++++++++++ pywdf/examples/rc_highpass.py | 8 +- pywdf/examples/rc_lowpass.py | 8 +- pywdf/examples/rc_lowpass_z.py | 149 +++++++++++++ pywdf/examples/rlc_oscillator.py | 146 ++++++++++++ pywdf/examples/sallenkeyfilter.py | 4 +- tests/plots/chua_2D_projections.png | Bin 0 -> 165626 bytes tests/plots/chua_C1_C2_L.png | Bin 0 -> 223482 bytes tests/plots/chua_RK4.png | Bin 0 -> 165626 bytes tests/plots/chua_WDF_C1v_C4v_L3i.png | Bin 0 -> 107065 bytes tests/plots/chua_WDF_attractor.png | Bin 0 -> 138965 bytes tests/plots/chua_attractor.png | Bin 0 -> 197065 bytes tests/plots/chua_circuit_WDF_attractor.png | Bin 0 -> 177943 bytes tests/plots/chua_circuit_attractor.png | Bin 0 -> 96438 bytes tests/plots/chua_circuit_signal.png | Bin 76799 -> 119392 bytes tests/plots/chua_circuit_signal_4_10.png | Bin 0 -> 84515 bytes tests/plots/chua_circuit_signals.png | Bin 0 -> 76709 bytes tests/plots/chua_circuit_sr_WDF_attractor.png | Bin 0 -> 111992 bytes tests/plots/chua_circuit_sr_signal.png | Bin 0 -> 37632 bytes tests/plots/chua_minimal.png | Bin 0 -> 34447 bytes tests/plots/chua_minimal_chu.png | Bin 0 -> 29188 bytes tests/plots/chua_minimal_signal.png | Bin 0 -> 16682 bytes .../plots/chua_res_src_WDF_attractor-1.5k.png | Bin 0 -> 92472 bytes .../plots/chua_res_src_WDF_attractor-1e-3.png | Bin 0 -> 85258 bytes .../chua_res_src_WDF_attractor-res-source.png | Bin 0 -> 173869 bytes tests/plots/chua_res_src_WDF_attractor.png | Bin 0 -> 95702 bytes tests/plots/chua_res_src_signal-1.5k.png | Bin 0 -> 29043 bytes tests/plots/chua_res_src_signal-1e-3.png | Bin 0 -> 28849 bytes .../plots/chua_res_src_signal-res-source.png | Bin 0 -> 103567 bytes tests/plots/chua_res_src_signal.png | Bin 0 -> 33237 bytes tests/plots/chua_switch_signal.png | Bin 0 -> 62073 bytes tests/plots/lc_oscillator_10Hz.png | Bin 0 -> 47198 bytes tests/plots/lc_oscillator_signal.png | Bin 18685 -> 34734 bytes tests/plots/lc_oscillator_syn_z_1000Hz.png | Bin 0 -> 47230 bytes tests/plots/lc_oscillator_syn_z_100Hz.png | Bin 0 -> 45894 bytes tests/plots/lc_oscillator_syn_z_10Hz.png | Bin 0 -> 44899 bytes tests/plots/lc_oscillator_syn_z_signal.png | Bin 0 -> 116499 bytes tests/plots/rc_lowpass_z_10Hz.png | Bin 0 -> 42557 bytes tests/plots/rc_lowpass_z_signal--.png | Bin 0 -> 59705 bytes tests/plots/rc_lowpass_z_signal-.png | Bin 0 -> 60077 bytes tests/plots/rc_lowpass_z_signal-C1-R.png | Bin 0 -> 63459 bytes tests/plots/rc_lowpass_z_signal-C1-R:2.png | Bin 0 -> 64053 bytes tests/plots/rc_lowpass_z_signal.png | Bin 0 -> 14493 bytes tests/plots/rlc_oscillator_100Hz.png | Bin 0 -> 42998 bytes tests/plots/rlc_oscillator_signal.png | Bin 0 -> 30900 bytes tests/rc_lowpass_ac_analysis.png | Bin 0 -> 70542 bytes tests/rc_lowpass_freqz.png | Bin 0 -> 34290 bytes tests/rc_lowpass_freqz_list.png | Bin 0 -> 100201 bytes tests/rc_lowpass_impulse_response.png | Bin 0 -> 18394 bytes 59 files changed, 1403 insertions(+), 84 deletions(-) create mode 100644 pywdf/examples/chua_ODE.py create mode 100644 pywdf/examples/chua_circuit_sr.py create mode 100644 pywdf/examples/chua_minimal.py create mode 100644 pywdf/examples/chua_res_src.py create mode 100644 pywdf/examples/chua_switch.py create mode 100644 pywdf/examples/nl_oscillator.py create mode 100644 pywdf/examples/rc_lowpass_z.py create mode 100644 pywdf/examples/rlc_oscillator.py create mode 100644 tests/plots/chua_2D_projections.png create mode 100644 tests/plots/chua_C1_C2_L.png create mode 100644 tests/plots/chua_RK4.png create mode 100644 tests/plots/chua_WDF_C1v_C4v_L3i.png create mode 100644 tests/plots/chua_WDF_attractor.png create mode 100644 tests/plots/chua_attractor.png create mode 100644 tests/plots/chua_circuit_WDF_attractor.png create mode 100644 tests/plots/chua_circuit_attractor.png create mode 100644 tests/plots/chua_circuit_signal_4_10.png create mode 100644 tests/plots/chua_circuit_signals.png create mode 100644 tests/plots/chua_circuit_sr_WDF_attractor.png create mode 100644 tests/plots/chua_circuit_sr_signal.png create mode 100644 tests/plots/chua_minimal.png create mode 100644 tests/plots/chua_minimal_chu.png create mode 100644 tests/plots/chua_minimal_signal.png create mode 100644 tests/plots/chua_res_src_WDF_attractor-1.5k.png create mode 100644 tests/plots/chua_res_src_WDF_attractor-1e-3.png create mode 100644 tests/plots/chua_res_src_WDF_attractor-res-source.png create mode 100644 tests/plots/chua_res_src_WDF_attractor.png create mode 100644 tests/plots/chua_res_src_signal-1.5k.png create mode 100644 tests/plots/chua_res_src_signal-1e-3.png create mode 100644 tests/plots/chua_res_src_signal-res-source.png create mode 100644 tests/plots/chua_res_src_signal.png create mode 100644 tests/plots/chua_switch_signal.png create mode 100644 tests/plots/lc_oscillator_10Hz.png create mode 100644 tests/plots/lc_oscillator_syn_z_1000Hz.png create mode 100644 tests/plots/lc_oscillator_syn_z_100Hz.png create mode 100644 tests/plots/lc_oscillator_syn_z_10Hz.png create mode 100644 tests/plots/lc_oscillator_syn_z_signal.png create mode 100644 tests/plots/rc_lowpass_z_10Hz.png create mode 100644 tests/plots/rc_lowpass_z_signal--.png create mode 100644 tests/plots/rc_lowpass_z_signal-.png create mode 100644 tests/plots/rc_lowpass_z_signal-C1-R.png create mode 100644 tests/plots/rc_lowpass_z_signal-C1-R:2.png create mode 100644 tests/plots/rc_lowpass_z_signal.png create mode 100644 tests/plots/rlc_oscillator_100Hz.png create mode 100644 tests/plots/rlc_oscillator_signal.png create mode 100644 tests/rc_lowpass_ac_analysis.png create mode 100644 tests/rc_lowpass_freqz.png create mode 100644 tests/rc_lowpass_freqz_list.png create mode 100644 tests/rc_lowpass_impulse_response.png diff --git a/README.md b/README.md index 98bedfe..88af8bd 100644 --- a/README.md +++ b/README.md @@ -33,13 +33,20 @@ The core directory contains the main source code of the repository. ├── setup.py ``` -## Usage +## Interactive Debugging + ``` python3 -m debugpy --wait-for-client --listen 5678 pywdf/examples/chua_circuit.py ``` + + + + +## Usage + ```python from pywdf import RCA_MK2_SEF, DiodeClipper, TR_808_HatResonator diff --git a/pywdf/core/wdf.py b/pywdf/core/wdf.py index cb92b48..843f276 100644 --- a/pywdf/core/wdf.py +++ b/pywdf/core/wdf.py @@ -1,5 +1,14 @@ from __future__ import annotations import numpy as np +from enum import Enum +import math + +class Transform(Enum): + BILINEAR = 1 + WARPED_BILINEAR = 2 + BACKWARD_EULER = 3 + ALPHA = 4 + MOBIUS = 5 class baseWDF: @@ -131,7 +140,13 @@ def propagate_reflected_wave(self) -> float: class Capacitor(baseWDF): - def __init__(self, C: float, fs: int, tolerance: float = 0) -> None: + def __init__( + self, + C: float, + fs: int, + tolerance: float = 0, + alpha: float = 1.0 # 0.0 – Backward Euler; 1.0 – Bilinear Transform + ) -> None: baseWDF.__init__(self) self.fs = fs @@ -139,8 +154,17 @@ def __init__(self, C: float, fs: int, tolerance: float = 0) -> None: rand_samp = np.random.normal(loc=0, scale=C * tolerance / 2) self.C = C + rand_samp self.z = 0 + self.setAlpha(alpha) self.calc_impedance() + + def setAlpha(self, alpha: float) -> None: + self.alpha = alpha + self.b_coef = (1.0 - alpha) / 2.0 + self.a_coef = (1.0 + alpha) / 2.0 + self.impedance_change() + + def prepare(self, new_fs: int) -> None: self.fs = new_fs self.impedance_change() @@ -151,20 +175,26 @@ def set_capacitance(self, new_C: float) -> None: self.C = new_C self.impedance_change() - def calc_impedance(self) -> None: - ''' - Local discretisation of capacitor using the warped bilinear transform method. + # def calc_impedance(self) -> None: + # ''' + # Local discretisation of capacitor using the warped bilinear transform method. - 1 - Z_C = -------------- - 2 * C * f_s + # 1 + # Z_C = -------------- + # 2 * C * f_s - where f_s is the sampling frequency and C the capacitance. - ''' + # where f_s is the sampling frequency and C the capacitance. + # ''' - self.Rp = 1.0 / (2 * self.C * self.fs) - self.G = 1.0 / self.Rp + # self.G = 1.0 / self.Rp + + def calc_impedance( + self, + ) -> None: + + self.Rp = 1.0 / ( ( 1.0 + self.alpha ) * self.C * self.fs) + self.G = 1.0 / self.Rp def accept_incident_wave(self, a: float) -> None: self.a = a @@ -183,13 +213,20 @@ def reset(self) -> None: class Inductor(baseWDF): - def __init__(self, L: float, fs: int) -> None: + def __init__(self, + L: float, + fs: int, + alpha: float = 1.0 + ) -> None: ''' TODO: Why does inductor have a different constructor than capacitor? ''' self.fs = fs self.L = L - self.z = 0 + self.z = 0.0 + self.alpha = alpha + self.b_coef = (1.0 - alpha) / 2.0 + self.a_coef = (1.0 + alpha) / 2.0 self.calc_impedance() def prepare(self, new_fs: int) -> None: @@ -197,21 +234,33 @@ def prepare(self, new_fs: int) -> None: self.impedance_change() self.reset() + def setAlpha(self, alpha: float) -> None: + self.alpha = alpha + self.b_coef = (1.0 - alpha) / 2.0 + self.a_coef = (1.0 + alpha) / 2.0 + self.impedance_change() + def set_inductance(self, new_L: float) -> None: if self.L != new_L: self.L = new_L self.impedance_change() - def calc_impedance(self) -> None: - self.Rp = 2 * self.L * self.fs - self.G = 1.0 / self.Rp + def calc_impedance( + self + ) -> None: + + self.Rp = (1.0 + self.alpha ) * self.L * self.fs + self.G = 1.0 / self.Rp + def accept_incident_wave(self, a: float) -> None: self.a = a self.z = self.a def propagate_reflected_wave(self) -> float: self.b = -self.z + self.b = self.b_coef * self.b - self.a_coef * self.z + return self.b def reset(self) -> None: @@ -223,7 +272,10 @@ def reset(self) -> None: class ParallelAdaptor(baseWDF): - def __init__(self, p1: baseWDF, p2: baseWDF) -> None: + def __init__(self, + p1: baseWDF, + p2: baseWDF + ) -> None: baseWDF.__init__(self) self.p1 = p1 self.p2 = p2 @@ -334,6 +386,30 @@ def propagate_reflected_wave(self) -> float: #################################################################################### +class SVoltage(baseWDF): + + def __init__(self, p1: baseWDF) -> None: + baseWDF.__init__(self) + p1.connect_to_parent(self) + self.p1 = p1 + self.calc_impedance() + + def calc_impedance(self) -> None: + self.Rp = self.p1.Rp + self.G = 1.0 / self.Rp + + def set_voltage(self, new_V: float) -> None: + self.Vs = new_V + + def accept_incident_wave(self, a: float) -> None: + self.a = a + self.p1.accept_incident_wave( -(a + self.Vs) ) # Incident wave is the negative of the voltage source + + def propagate_reflected_wave(self) -> float: + self.b = -( self.a + self.Vs ) + return self.b + + class SeriesVoltage(baseWDF): def __init__(self, p1: baseWDF) -> None: @@ -526,8 +602,7 @@ def propagate_reflected_wave(self) -> float: g2 = (1.0 - self.G2 * self.R1) / (1.0 + self.G2 * self.R1) a_0 = self.V0 * (1.0 + self.G2 * self.R1) - self.b = ( - g1 * self.a + 0.5 * (g2 - g1) * (abs( self.a + a_0 ) - abs( self.a - a_0 ))) + self.b = ( g1 * self.a + 0.5 * (g2 - g1) * (abs( self.a + a_0 ) - abs( self.a - a_0 ))) return self.b diff --git a/pywdf/examples/bassmantonestack.py b/pywdf/examples/bassmantonestack.py index 4f7e518..1b2084f 100644 --- a/pywdf/examples/bassmantonestack.py +++ b/pywdf/examples/bassmantonestack.py @@ -66,7 +66,8 @@ def _impedance_calc(self,R: RTypeAdaptor): Rb, Rc, Rd, Re, Rf, Rg = R.get_port_impedances() # This scattering matrix was derived using the R-Solver python script (https://github.com/jatinchowdhury18/R-Solver), # invoked with command: r_solver.py --adapt 0 --out ./test_outputs/bassman_test.txt --pywdf ./netlists/bassman_netlist.txt - R.set_S_matrix([[0,-(Rc*Rd + (Rc + Rd)*Re + Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + Rb*Re + (Rb + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Re - Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + (Rb + Rc + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rc*Rd + (Rb + Rc + Rd)*Re)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -1,], + R.set_S_matrix([ + [0,-(Rc*Rd + (Rc + Rd)*Re + Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + Rb*Re + (Rb + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Re - Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + (Rb + Rc + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rc*Rd + (Rb + Rc + Rd)*Re)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -1,], [-(Rb*Rc*Rd + Rb*Rc*Rf + (Rb*Rc + Rb*Rd)*Re)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg), -(Rb*Rb*Rc*Rd*Rd + (Rb*Rb*Rc + Rb*Rb*Rd)*Re*Re + (Rb*Rb*Rc - Rc*Rc*Rd - Rc*Rd*Rd + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re)*Rf*Rf + (2*Rb*Rb*Rc*Rd + Rb*Rb*Rd*Rd)*Re + (2*Rb*Rb*Rc*Rd - Rc*Rc*Rd*Rd + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc - Rc*Rd*Rd + (Rb*Rb - Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb - Rc*Rc)*Rd*Rd + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re*Re + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Rf*Rf - 2*(Rc*Rd*Rd - (Rb*Rb - Rc*Rc)*Rd)*Re - 2*(Rc*Rd*Rd - (Rb*Rb - Rc*Rc)*Rd - (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rb*Rc*Rd*Rd + (Rb*Rb*Rc + Rb*Rb*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf*Rf + (2*Rb*Rb*Rc*Rd + Rb*Rb*Rd*Rd)*Re + (2*Rb*Rb*Rc*Rd + Rb*Rc*Rd*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (2*Rb*Rb*Rc + Rb*Rd*Rd + 3*(Rb*Rb + Rb*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Rd + (Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (Rb*Rb + Rb*Rc + Rb*Rd)*Rf*Rf + (Rb*Rd*Rd + 2*(Rb*Rb + Rb*Rc)*Rd)*Re + (Rb*Rd*Rd + 2*(Rb*Rb + Rb*Rc)*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rb*Rc*Rd*Re + (Rb*Rb*Rc + Rb*Rb*Rd)*Re*Re + (2*Rb*Rb*Rc + Rb*Rc*Rc + 2*Rb*Rc*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf*Rf + (2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (2*Rb*Rb*Rc + Rb*Rc*Rc)*Rd + (3*Rb*Rb*Rc + Rb*Rc*Rc + (2*Rb*Rb + 3*Rb*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Re + (Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (Rb*Rb + Rb*Rc + Rb*Rd)*Rf*Rf + ((Rb*Rb + Rb*Rc)*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rb*Rc*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rc*Rd)*Rf*Rf + (Rb*Rb*Rc*Rd + Rb*Rb*Rd*Rd)*Re - (Rb*Rc*Rc*Rd - Rb*Rc*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc - Rb*Rb*Rd - Rb*Rd*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Rd + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Re + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((2*Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (2*(Rb*Rb + Rb*Rc)*Rd*Rd + (3*Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd)*Re + (2*Rb*Rc*Rd*Rd + (2*Rb*Rb*Rc + Rb*Rc*Rc)*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + 2*Rb*Rd*Rd + (2*Rb*Rb + 3*Rb*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Rd + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Re + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rc*Rd + Rb*Rc*Rf + (Rb*Rc + Rb*Rd)*Re)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg),], [-(Rb*Rc*Rd + Rb*Rc*Re + (Rb*Rc + Rc*Rd)*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg), (Rb*Rc*Rc*Rd*Rd + (Rb*Rc*Rc + Rb*Rc*Rd)*Re*Re + (Rb*Rc*Rc + Rc*Rc*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf*Rf + (2*Rb*Rc*Rc*Rd + Rb*Rc*Rd*Rd)*Re + (2*Rb*Rc*Rc*Rd + Rc*Rc*Rd*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (2*Rb*Rc*Rc + Rc*Rd*Rd + 3*(Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (Rb*Rc + Rc*Rc + Rc*Rd)*Rf*Rf + (Rc*Rd*Rd + 2*(Rb*Rc + Rc*Rc)*Rd)*Re + (Rc*Rd*Rd + 2*(Rb*Rc + Rc*Rc)*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rc*Rc*Rd*Rd + (Rb*Rc*Rc - Rb*Rb*Rd - Rb*Rd*Rd)*Re*Re + (Rb*Rc*Rc + Rc*Rc*Rd - (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re)*Rf*Rf + (2*Rb*Rc*Rc*Rd - Rb*Rb*Rd*Rd)*Re + (2*Rb*Rc*Rc*Rd + Rc*Rc*Rd*Rd - (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rc*Rc - Rb*Rd*Rd - (Rb*Rb - Rc*Rc)*Rd)*Re)*Rf - ((Rb*Rb - Rc*Rc)*Rd*Rd + (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re*Re + (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Rf*Rf + 2*(Rb*Rd*Rd + (Rb*Rb - Rc*Rc)*Rd)*Re + 2*(Rb*Rd*Rd + (Rb*Rb - Rc*Rc)*Rd + (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd*Re + (Rb*Rb*Rc + 2*Rb*Rc*Rc + 2*Rb*Rc*Rd)*Re*Re + (Rb*Rc*Rc + Rc*Rc*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf*Rf + (Rb*Rc*Rc*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (Rb*Rb*Rc + 3*Rb*Rc*Rc + (3*Rb*Rc + 2*Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Re + (Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (Rb*Rc + Rc*Rc + Rc*Rd)*Rf*Rf + ((Rb*Rc + Rc*Rc)*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd)*Rf*Rf + (2*Rb*Rc*Rd*Rd + (Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd)*Re + (2*(Rb*Rc + Rc*Rc)*Rd*Rd + (2*Rb*Rb*Rc + 3*Rb*Rc*Rc)*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + 2*Rc*Rd*Rd + (3*Rb*Rc + 2*Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Rd + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Re + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rc*Rc*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rc*Rd)*Re*Re - (Rb*Rb*Rc*Rd - Rb*Rc*Rd*Rd)*Re + (Rb*Rc*Rc*Rd + Rc*Rc*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc - Rc*Rc*Rd - Rc*Rd*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Rd + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Re + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rc*Rd + Rb*Rc*Re + (Rb*Rc + Rc*Rd)*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg),], [-(Rb*Rd*Re - Rc*Rd*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg), (Rb*Rc*Rd*Rd*Re + (Rb*Rc*Rd + Rb*Rd*Rd)*Re*Re + (2*Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((2*Rb + 3*Rc)*Rd*Rd + (3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + 2*((Rb + Rc)*Rd*Rd*Re + ((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + ((Rb + Rc)*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb + 2*Rb*Rc)*Rd*Rd*Re + (2*Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rc*Rd + Rc*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + (Rb*Rc*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((3*Rb + 2*Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc)*Rd)*Re)*Rf + 2*((Rb + Rc)*Rd*Rd*Re + ((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + ((Rb + Rc)*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb + 2*Rb*Rc)*Rd*Rd*Re + (Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc - Rb*Rd*Rd)*Re*Re - (Rb*Rb*Rc + Rb*Rc*Rc - Rc*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re)*Rf*Rf + ((2*Rb*Rc + Rc*Rc)*Rd*Rd - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re*Re - 2*(Rb*Rb*Rc + Rb*Rc*Rc - (Rb + Rc)*Rd*Rd)*Re)*Rf + (2*(Rb + Rc)*Rd*Rd*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re*Re - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((3*Rb*Rc + 2*Rc*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + ((Rb + 2*Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + 2*Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Re*Re + ((2*Rb*Rb + 3*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + ((2*Rb + Rc)*Rd*Rd + (2*Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rd*Re - Rc*Rd*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg),], diff --git a/pywdf/examples/chua_ODE.py b/pywdf/examples/chua_ODE.py new file mode 100644 index 0000000..4235b44 --- /dev/null +++ b/pywdf/examples/chua_ODE.py @@ -0,0 +1,122 @@ +import numpy as np +from scipy.integrate import solve_ivp +import matplotlib.pyplot as plt + +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +plt_dir = src_dir.parent / "tests" / "plots" +plt_dir.mkdir(exist_ok=True, parents=True) + + +# Parameters +alpha = 15.6 # C2 / C1 +beta = 28 # C2 * R2 / L +gamma = 0.5 # C2R RL /L +m0 = -1.143 +m1 = -0.714 + +# Chua's nonlinearity +def f(x): + return m1 * x + 0.5 * (m0 - m1) * (np.abs(x + 1) - np.abs(x - 1)) + +# Chua's system (ODE) +def chua(t, state): + x, y, z = state + dx = alpha * (y - x - f(x)) # x – Voltage across C1 + dy = x - y + z # y – Voltage across C2 + dz = -beta * y # z – Current through L + return [dx, dy, dz] + +# Simulation +t_span = (0, 300) +t_eval = np.linspace(*t_span, 10000) +initial_state = [0.1, 0.0, 0.0] + +# method='RK45' (default) explicit Runge-Kutta method of order 5(4) +sol = solve_ivp(chua, t_span, initial_state, t_eval=t_eval) + +t = sol.t +x, y, z = sol.y + +# Plot time series of x, y, z +plt.figure(figsize=(12, 8)) + +plt.subplot(3, 1, 1) +plt.plot(t, x, color='blue') +plt.title('x(t) - Voltage across C1') +plt.xlabel('Time') +plt.ylabel('x') +plt.grid(True) + +plt.subplot(3, 1, 2) +plt.plot(t, y, color='green') +plt.title('y(t) - Voltage across C2') +plt.xlabel('Time') +plt.ylabel('y') +plt.grid(True) + +plt.subplot(3, 1, 3) +plt.plot(t, z, color='red') +plt.title('z(t) - Current through L') +plt.xlabel('Time') +plt.ylabel('z') +plt.grid(True) + +plt.tight_layout() + +out_path = plt_dir / f"{script_path.stem}_C1_C2_L.png" +plt.savefig(out_path.with_suffix('.png')) + +plt.show() + +# 3D Phase Portrait +fig = plt.figure(figsize=(8, 6)) +ax = fig.add_subplot(111, projection='3d') +ax.plot(x, y, z, lw=0.5) +ax.set_title("3D Phase Portrait of Chua's Circuit") +ax.set_xlabel("x (V_C1)") +ax.set_ylabel("y (V_C2)") +ax.set_zlabel("z (I_L)") +plt.tight_layout() +out_path = plt_dir / f"{script_path.stem}_attractor.png" +plt.savefig(out_path.with_suffix('.png')) +plt.show() + +# 2D Projections +plt.figure(figsize=(15, 4)) + +plt.subplot(1, 3, 1) +plt.plot(x, y, color='purple') +plt.title('Projection: x vs y') +plt.xlabel('x') +plt.ylabel('y') +plt.grid(True) + +plt.subplot(1, 3, 2) +plt.plot(x, z, color='orange') +plt.title('Projection: x vs z') +plt.xlabel('x') +plt.ylabel('z') +plt.grid(True) + +plt.subplot(1, 3, 3) +plt.plot(y, z, color='teal') +plt.title('Projection: y vs z') +plt.xlabel('y') +plt.ylabel('z') +plt.grid(True) + +plt.tight_layout() + +# plot + +out_path = plt_dir / f"{script_path.stem}_2D_projections.png" +plt.savefig(out_path.with_suffix('.png')) + +plt.show() diff --git a/pywdf/examples/chua_circuit.py b/pywdf/examples/chua_circuit.py index 1ecafc2..a76fafd 100644 --- a/pywdf/examples/chua_circuit.py +++ b/pywdf/examples/chua_circuit.py @@ -1,3 +1,7 @@ +# Chua's Circuit example using WDF following the principles of Meerkotter and Scholz 1989. +# "Digital simulation of nonlinear circuits by wave digital filter principles" + + import matplotlib.pyplot as plt from pathlib import Path import sys @@ -29,7 +33,8 @@ def __init__( # initialize wdf self.C1_value = 5.5e-9 - self.R2_value = 1.428e3 + self.R2_value = 1.3e3 + # self.R2_value = 1.428e3 self.L3_value = 7.07e-3 self.C4_value = 49.5e-9 @@ -38,15 +43,17 @@ def __init__( self.L3 = Inductor(self.L3_value, self.fs) # fs, needs local discretization self.C4 = Capacitor(self.C4_value, self.fs) # fs, needs local discretization + # self.Vs = ParallelVoltage(self.C4) + self.Vs = SeriesVoltage(self.C4) self.P2 = ParallelAdaptor(self.L3, self.Vs) - self.S1 = SeriesAdaptor(self.R2, self.P2) - self.P1 = ParallelAdaptor(self.C1, self.S1) + self.S1 = SeriesAdaptor(self.P2, self.R2) + self.P1 = ParallelAdaptor(self.S1, self.C1) self.g1 = -500.0e-6 self.g2 = -800.0e-6 self.v0 = 1.0 - self.R_NL = 1.0 + self.R_NL = 569.2 self.NL = ChuaDiode( self.P1, @@ -87,9 +94,7 @@ def process_sample_chua(self, sample: float) -> float: self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) - return self.output.wave_to_voltage(), self.C1.wave_to_voltage(), self.L3.wave_to_current() - - + return self.output.wave_to_voltage(), self.C4.wave_to_voltage(), self.L3.wave_to_current() def set_params( @@ -117,50 +122,37 @@ def decibels_to_gain(self): if __name__ == "__main__": # set params - fs = 48e3 - frequency = 440 - decibels = 0 + # fs = 48e3 # doesn't work for this sample rate + # fs = 96e3 + fs = 100e3 chua_circuit = Chua(fs) - chua_circuit.set_params(frequency, decibels) # update params + # chua_circuit.set_params(frequency, decibels) # update params # plot transfer function plt_dir = src_dir.parent / "tests" / "plots" plt_dir.mkdir(exist_ok=True, parents=True) - out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + out_path = plt_dir / f"{script_path.stem}_{fs}Hz.png" - # chua_circuit.plot_freqz( - # out_path - # ) - - # chua_circuit.AC_transient_analysis( - # freq = 1000, - # amplitude = 1, - # t_ms = 5, - # outpath="tests/chua_ac_analysis.png" - # ) - - # chua_circuit.plot_impulse_response( - # outpath="tests/chua_impulse_response.png" - # ) - - - samples = np.zeros((int(500))) - samples[0] = 1.0 # impulse signal + a = np.ones(1) # impulse signal + b = np.zeros(2400) + samples = np.concatenate((a, b)) + i_list, v1_list, v2_list = [], [], [] for s in samples: v1, v2, i = chua_circuit.process_sample_chua(s) - i_list.append(i) v1_list.append(v1) v2_list.append(v2) + i_list.append(i) # Plotting fig, axes = plt.subplots(1, 3, figsize=(15, 4)) - axes[0].plot(v1_list, label='Amplitude C1 [V]', color='r') - axes[1].plot(v2_list, label='Amplitude C4 [V]', color='g') - axes[2].plot(i_list, label='Amplitude L3 [I]', color='b') + axes[0].plot(v1_list, label='C1 [V]', color='r') + axes[1].plot(v2_list, label='C4 [V]', color='g') + axes[2].plot(i_list, label='L3 [I]', color='b') + for ax in axes: ax.legend() @@ -179,4 +171,15 @@ def decibels_to_gain(self): plt.show() - + # 3D Phase Portrait + fig = plt.figure(figsize=(8, 6)) + ax = fig.add_subplot(111, projection='3d') + ax.plot(v1_list, v2_list, i_list, lw=1.0) + ax.set_title("3D Phase Portrait of Chua's Circuit WDF") + ax.set_xlabel("x C1 [V]") + ax.set_ylabel("y C4 [V]") + ax.set_zlabel("z L3 [I]") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_WDF_attractor.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() diff --git a/pywdf/examples/chua_circuit_sr.py b/pywdf/examples/chua_circuit_sr.py new file mode 100644 index 0000000..259a4fb --- /dev/null +++ b/pywdf/examples/chua_circuit_sr.py @@ -0,0 +1,186 @@ +# Chua's Circuit example using WDF following the principles of Meerkotter and Scholz 1989. +# "Digital simulation of nonlinear circuits by wave digital filter principles" + + +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class Chua(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.C1_value = 5.5e-9 + # self.R2_value = 1.215e3 + # self.R2_value = 1.428e3 + self.R2_value = 1.8e3 + self.L3_value = 7.07e-3 + self.C4_value = 49.5e-9 + + self.C1 = Capacitor(self.C1_value, self.fs) # fs, needs local discretization + self.R2 = Resistor(self.R2_value) # no need for discretization + self.L3 = Inductor(self.L3_value, self.fs) # fs, needs local discretization + self.C4 = Capacitor(self.C4_value, self.fs) # fs, needs local discretization + + # self.Vs = ParallelVoltage(self.C4) + + self.Vs = SeriesVoltage(self.C4) + self.P2 = ParallelAdaptor(self.L3, self.Vs) + self.S1 = SeriesAdaptor(self.P2, self.R2) + self.P1 = ParallelAdaptor(self.S1, self.C1) + + self.g1 = -500.0e-6 + self.g2 = -800.0e-6 + self.v0 = 1.0 + self.R_NL = 569.2 + + self.NL = ChuaDiode( + self.P1, + g1=self.g1, # parameter 1 + g2=self.g2, # parameter 2 + v0=self.v0, # Voltage parameter + r1=self.R_NL, # Resistance in Ohms + ) + + # init and set circuit + super().__init__(self.Vs, self.NL, self.C1) + + + def process_sample( + self, + sample: float + ) -> float: + + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage() + + + def process_sample_chua(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage(), self.C4.wave_to_voltage(), self.L3.wave_to_current() + + + def set_params( + self, + frequency: float, + decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + # self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + # self.L1.set_inductance(self.L) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + # fs = 48e3 # doesn't work for this sample rate + # fs = 96e3 + fs = 100e3 + + chua_circuit = Chua(fs) + # chua_circuit.set_params(frequency, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{fs}Hz.png" + + + a = np.ones(1) # impulse signal + b = np.zeros(2400) + samples = np.concatenate((a, b)) + + i_list, v1_list, v2_list = [], [], [] + + for s in samples: + v1, v2, i = chua_circuit.process_sample_chua(s) + v1_list.append(v1) + v2_list.append(v2) + i_list.append(i) + + # Plotting + fig, axes = plt.subplots(1, 3, figsize=(15, 4)) + axes[0].plot(v1_list, label='C1 [V]', color='r') + axes[1].plot(v2_list, label='C4 [V]', color='g') + axes[2].plot(i_list, label='L3 [I]', color='b') + + + for ax in axes: + ax.legend() + ax.grid(True) + ax.set_xlabel("Sample [n]") + + axes[0].set_ylabel("Output") + + # Centered title + fig.suptitle("Chua impulse response", fontsize=14) + plt.tight_layout(rect=[0, 0, 1, 0.95]) # Leave space for suptitle + + # Save and show + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + + # 3D Phase Portrait + fig = plt.figure(figsize=(8, 6)) + ax = fig.add_subplot(111, projection='3d') + ax.plot(v1_list, v2_list, i_list, lw=1.0) + ax.set_title("3D Phase Portrait of Chua's Circuit WDF") + ax.set_xlabel("x C1 [V]") + ax.set_ylabel("y C4 [V]") + ax.set_zlabel("z L3 [I]") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_WDF_attractor.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() diff --git a/pywdf/examples/chua_minimal.py b/pywdf/examples/chua_minimal.py new file mode 100644 index 0000000..27ec94b --- /dev/null +++ b/pywdf/examples/chua_minimal.py @@ -0,0 +1,93 @@ +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + + +class ChuaMinimal(Circuit): + def __init__( + self, + sample_rate: int, + cutoff: float = 1000, + input_gain_db: float = 0, + output_gain_db: float = 0 + ) -> None: + + self.fs = sample_rate + self.cutoff = cutoff + self.input_gain = 10 ** (input_gain_db / 20) + self.input_gain_db = input_gain_db + self.output_gain = 10 ** (output_gain_db / 20) + self.output_gain_db = output_gain_db + + self.R = 2.5e3 # Ohms + + self.R1 = Resistor(self.R) + self.Vs = ResistiveVoltageSource() + + self.S1 = SeriesAdaptor(self.Vs, self.R1) + + # self.C = 1.0e-6 + # self.C1 = Capacitor(self.C, self.fs) + # self.P1 = ParallelAdaptor(self.S1, self.C1) + + self.g1 = -500.0e-6 + self.g2 = -800.0e-6 + self.v0 = 1.0 + self.R_NL = 569.2 + + self.NL = ChuaDiode( + self.S1, + g1=self.g1, # parameter 1 + g2=self.g2, # parameter 2 + v0=self.v0, # Voltage parameter + r1=self.R_NL, # Resistance in Ohms + + ) + + # super().__init__(self.Vs, self.NL, self.C1) + super().__init__(self.Vs, self.NL, self.NL) + + def process_sample(self, sample: float) -> float: + sample *= self.input_gain + return -( super().process_sample(sample) * self.output_gain) ### ¡! phase inverted !¡ + +if __name__ == "__main__": + + fs = 48e3 + frequency = 1000 + + cm = ChuaMinimal(44100, cutoff=5000, input_gain_db=5) + + duration = 1.0 + t = np.linspace(0, duration, int(fs * duration), endpoint=False) + sine = np.sin(2 * np.pi * frequency * t) + + + # out = cm.process_signal(np.ones((int(fs)))) + out = cm.process_signal(sine * 5.0) # Use a sine wave as input signal + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}.png" + + # _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + + + plt.figure(figsize=(10, 4)) + plt.plot(out) + plt.xlim([0, fs]) + plt.title(f"Chua diode output signal at {fs}Hz") + plt.tight_layout() + + plt.savefig(out_path.with_suffix('.png')) + plt.show() diff --git a/pywdf/examples/chua_res_src.py b/pywdf/examples/chua_res_src.py new file mode 100644 index 0000000..3ec285c --- /dev/null +++ b/pywdf/examples/chua_res_src.py @@ -0,0 +1,208 @@ +# Chua's Circuit example using WDF following the principles of Meerkotter and Scholz 1989. +# "Digital simulation of nonlinear circuits by wave digital filter principles" + + +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class Chua(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + self.Vin_prev_i = 0.0 + + # initialize wdf + self.C1_value = 5.5e-9 + self.R2_value = 1.3e3 + + self.R2_value = 1.428e3 + + self.L3_value = 7.07e-3 + self.C4_value = 49.5e-9 + + self.C1 = Capacitor(self.C1_value, self.fs) # fs, needs local discretization + + # self.R2 = Resistor(self.R2_value) # no need for discretization + + self.R2_value = 1e-3 + + self.Vin = ResistiveVoltageSource( None, self.R2_value ) + + self.L3 = Inductor(self.L3_value, self.fs) # fs, needs local discretization + self.C4 = Capacitor(self.C4_value, self.fs) # fs, needs local discretization + + # self.Vs = SeriesVoltage(self.C4) + self.P2 = ParallelAdaptor(self.L3, self.C4) + # self.P2 = ParallelAdaptor(self.L3, self.Vs) + # self.S1 = SeriesAdaptor(self.P2, self.R2) + self.S1 = SeriesAdaptor(self.P2, self.Vin) + self.P1 = ParallelAdaptor(self.S1, self.C1) + + self.g1 = -500.0e-6 + self.g2 = -800.0e-6 + self.v0 = 1.0 + self.R_NL = 569.2 + + self.NL = ChuaDiode( + self.P1, + g1=self.g1, # parameter 1 + g2=self.g2, # parameter 2 + v0=self.v0, # Voltage parameter + r1=self.R_NL, # Resistance in Ohms + ) + + # init and set circuit + super().__init__(self.Vin, self.NL, self.C1) + + + def process_sample( + self, + sample: float + ) -> float: + + # self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage() + + + def process_sample_chua(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vin_prev_i = self.Vin.wave_to_current() + print('i: ', self.Vin_prev_i) + + # self.Vs.set_voltage(0.0) + # self.Vin.set_voltage(sample) + self.Vin.set_voltage( sample + self.Vin_prev_i * 1.428e3 ) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + + + + print('v: ', self.Vin_prev_i * 1.428e3 ) + # self.Vin.set_voltage( self.Vin_prev_i * 1e-3 ) + + return self.Vin.wave_to_voltage(), self.Vin_prev_i, self.L3.wave_to_current() + + # return self.output.wave_to_voltage(), self.C4.wave_to_voltage(), self.L3.wave_to_current() + + + def set_params( + self, + frequency: float, + decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + # self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + # self.L1.set_inductance(self.L) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + # fs = 48e3 # doesn't work for this sample rate + # fs = 96e3 + fs = 100e3 + + chua_circuit = Chua(fs) + # chua_circuit.set_params(frequency, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{fs}Hz.png" + + + a = np.ones(1) # impulse signal + b = np.zeros(2400) + samples = np.concatenate((a, b)) + + i_list, v1_list, v2_list = [], [], [] + + for s in samples: + v1, v2, i = chua_circuit.process_sample_chua(s) + v1_list.append(v1) + v2_list.append(v2) + i_list.append(i) + + # Plotting + fig, axes = plt.subplots(1, 3, figsize=(15, 4)) + axes[0].plot(v1_list, label='C1 [V]', color='r') + axes[1].plot(v2_list, label='C4 [V]', color='g') + axes[2].plot(i_list, label='L3 [I]', color='b') + + + for ax in axes: + ax.legend() + ax.grid(True) + ax.set_xlabel("Sample [n]") + + axes[0].set_ylabel("Output") + + # Centered title + fig.suptitle("Chua impulse response", fontsize=14) + plt.tight_layout(rect=[0, 0, 1, 0.95]) # Leave space for suptitle + + # Save and show + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + + # 3D Phase Portrait + fig = plt.figure(figsize=(8, 6)) + ax = fig.add_subplot(111, projection='3d') + ax.plot(v1_list, v2_list, i_list, lw=1.0) + ax.set_title("3D Phase Portrait of Chua's Circuit WDF") + ax.set_xlabel("x C1 [V]") + ax.set_ylabel("y C4 [V]") + ax.set_zlabel("z L3 [I]") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_WDF_attractor.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() diff --git a/pywdf/examples/chua_switch.py b/pywdf/examples/chua_switch.py new file mode 100644 index 0000000..b6ae3e9 --- /dev/null +++ b/pywdf/examples/chua_switch.py @@ -0,0 +1,204 @@ +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class Chua(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.C1_value = 5.5e-9 + self.R2_value = 1.428e3 + self.L3_value = 7.07e-3 + self.C4_value = 49.5e-9 + + self.C1 = Capacitor(self.C1_value, self.fs) # fs, needs local discretization + self.R2 = Resistor(self.R2_value) # no need for discretization + self.L3 = Inductor(self.L3_value, self.fs) # fs, needs local discretization + self.C4 = Capacitor(self.C4_value, self.fs) # fs, needs local discretization + + # voltage injection with impulse for agitation ang getting oscillations started, given the system will always initialize with zeros, + # vInject(i) = wdf.series_voltage(i, button("impulse")*5 : ba.impulsify); + self.Vs = ResistiveVoltageSource() + # self.S2 = SeriesAdaptor(self.C4, self.Vs) + # self.S2 = SeriesAdaptor(self.Vs, self.C4) + # self.S2 = ParallelAdaptor(self.C4, self.Vs) + self.P2 = ParallelAdaptor(self.L3, self.Vs) + self.S1 = SeriesAdaptor(self.P2, self.R2) + self.P1 = ParallelAdaptor(self.S1, self.C1 ) + + self.g1 = -500.0e-6 + self.g2 = -800.0e-6 + self.v0 = 1.0 + self.R_NL = 569.2 + + self.NL = ChuaDiode( + self.P1, + g1=self.g1, # parameter 1 + g2=self.g2, # parameter 2 + v0=self.v0, # Voltage parameter + r1=self.R_NL, # Resistance in Ohms + ) + + + # self.S2 = SeriesAdaptor(self.C1, self.L1) + # self.Vs = ResistiveVoltageSource() + # self.S1 = SeriesAdaptor(self.Vs, self.S2) + + # self.SW1 = Switch(self.S1) + + # # init and set circuit + # super().__init__(self.Vs, self.SW1, self.C1) + # self.set_params(self.frequency, self.closed, self.decibels) + + # init and set circuit + super().__init__(self.Vs, self.NL, self.C1) + + + def process_sample( + self, + sample: float + ) -> float: + + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage() + + + def process_sample_chua(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage(), self.C4.wave_to_voltage(), self.L3.wave_to_current() + + + + + def set_params( + self, + frequency: float, + decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + # self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + # self.L1.set_inductance(self.L) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + fs = 48e3 + frequency = 440 + decibels = 0 + + chua_circuit = Chua(fs) + # chua_circuit.set_params(frequency, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + + # chua_circuit.plot_freqz( + # out_path + # ) + + # chua_circuit.AC_transient_analysis( + # freq = 1000, + # amplitude = 1, + # t_ms = 5, + # outpath="tests/chua_ac_analysis.png" + # ) + + # chua_circuit.plot_impulse_response( + # outpath="tests/chua_impulse_response.png" + # ) + # num_impulses = 4 # number of impulses to generate + # impulse_frequency = 10 # duration of impulse signal in samples + # # samples = np.zeros((int(impulse_frequency * fs / 1000))) # 500 ms impulse signal + # samples = np.zeros((int(impulse_frequency * num_impulses))) # 500 ms impulse signal + # samples[::impulse_frequency] = 1.0 # impulse signal + + a = np.ones(1) # impulse signal + b = np.zeros(500) + samples = np.concatenate((a, b)) + + + i_list, v1_list, v2_list = [], [], [] + + for s in samples: + v1, v2, i = chua_circuit.process_sample_chua(s) + i_list.append(i) + v1_list.append(v1) + v2_list.append(v2) + + # Plotting + fig, axes = plt.subplots(1, 3, figsize=(15, 4)) + axes[0].plot(v1_list, label='Amplitude C1 [V]', color='r') + axes[1].plot(v2_list, label='Amplitude C4 [V]', color='g') + axes[2].plot(i_list, label='Amplitude L3 [I]', color='b') + + for ax in axes: + ax.legend() + ax.grid(True) + ax.set_xlabel("Sample [n]") + + axes[0].set_ylabel("Output") + + # Centered title + fig.suptitle("Chua impulse response", fontsize=14) + plt.tight_layout(rect=[0, 0, 1, 0.95]) # Leave space for suptitle + + # Save and show + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + + diff --git a/pywdf/examples/lc_oscillator.py b/pywdf/examples/lc_oscillator.py index e3d2142..4136d52 100644 --- a/pywdf/examples/lc_oscillator.py +++ b/pywdf/examples/lc_oscillator.py @@ -35,14 +35,17 @@ def __init__( self.C1 = Capacitor(self.C, self.fs) self.L1 = Inductor(self.L, self.fs) self.S2 = SeriesAdaptor(self.C1, self.L1) + # self.S2 = ParallelAdaptor(self.C1, self.L1) self.Vs = ResistiveVoltageSource() self.S1 = SeriesAdaptor(self.Vs, self.S2) + # self.S1 = ParallelAdaptor(self.Vs, self.S2) self.SW1 = Switch(self.S1) # init and set circuit super().__init__(self.Vs, self.SW1, self.C1) + self.set_params(self.frequency, self.closed, self.decibels) @@ -52,9 +55,15 @@ def process_sample( sample: float ) -> float: - return super().process_sample(sample) * self.gain + # self.Vs.set_voltage(sample) + # self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + # self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + # return self.output.wave_to_voltage() + return super().process_sample(sample) * self.gain + def set_params( self, @@ -87,7 +96,7 @@ def decibels_to_gain(self): # set params fs = 48e3 - frequency = 440 + frequency = 10 decibels = 0 switch_closed = True @@ -103,27 +112,20 @@ def decibels_to_gain(self): out_path ) + a = np.ones(1) # impulse signal + b = np.zeros(24000) + samples = np.concatenate((a, b)) + # generate sinusoid - out = lc_oscillator.process_signal(np.ones((int(fs)))) + out = lc_oscillator.process_signal(samples) out = out - 1 # remove DC offset [0, 2] plt.figure(figsize=(10, 4)) plt.plot(out) plt.xlim([0, fs]) - plt.title(f"{frequency}Hz sinewave") + plt.title(f"LC Oscillator {frequency}Hz sinewave") plt.tight_layout() out_path = plt_dir / f"{script_path.stem}_signal.png" plt.savefig(out_path.with_suffix('.png')) plt.show() - - # estimate pitch using zerocrossing - zero_crossings = np.where( - np.diff( - np.sign(out) - ) - )[0] - - T = (zero_crossings[2] - zero_crossings[0]) / fs - f = 1 / T - print(f"T = {T:.6f}[s]\nf = {f:.3f}[Hz]") diff --git a/pywdf/examples/nl_oscillator.py b/pywdf/examples/nl_oscillator.py new file mode 100644 index 0000000..5aa6dcf --- /dev/null +++ b/pywdf/examples/nl_oscillator.py @@ -0,0 +1,129 @@ +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class NLOscillator(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.C = 1.0e-6 + self.L = 1.0e3 + self.twopi = 2 * np.pi + + self.C1 = Capacitor(self.C, self.fs) + self.L1 = Inductor(self.L, self.fs) + self.S2 = SeriesAdaptor(self.C1, self.L1) + + self.Vs = ResistiveVoltageSource() + self.S1 = SeriesAdaptor(self.Vs, self.S2) + + self.SW1 = Switch(self.S1) + + # init and set circuit + super().__init__(self.Vs, self.SW1, self.C1) + self.set_params(self.frequency, self.closed, self.decibels) + + + + def process_sample( + self, + sample: float + ) -> float: + + return super().process_sample(sample) * self.gain + + + + def set_params( + self, + frequency: float, + switch_closed: bool, + decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + self.L1.set_inductance(self.L) + + # update switch status + if switch_closed != self.closed: + self.SW1.set_closed(switch_closed) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + fs = 48e3 + frequency = 440 + decibels = 0 + switch_closed = True + + nl_oscillator = NLOscillator(fs) + nl_oscillator.set_params(frequency, switch_closed, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + + nl_oscillator.plot_freqz( + out_path + ) + + # generate sinusoid + out = nl_oscillator.process_signal(np.ones((int(fs)))) + out = out - 1 # remove DC offset [0, 2] + + plt.figure(figsize=(10, 4)) + plt.plot(out) + plt.xlim([0, fs]) + plt.title(f"LC Oscillator {frequency}Hz sinewave") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + + # estimate pitch using zerocrossing + zero_crossings = np.where( + np.diff( + np.sign(out) + ) + )[0] + + T = (zero_crossings[2] - zero_crossings[0]) / fs + f = 1 / T + print(f"T = {T:.6f}[s]\nf = {f:.3f}[Hz]") diff --git a/pywdf/examples/rc_highpass.py b/pywdf/examples/rc_highpass.py index dffaf6d..f510954 100644 --- a/pywdf/examples/rc_highpass.py +++ b/pywdf/examples/rc_highpass.py @@ -47,9 +47,7 @@ def set_cutoff(self, new_cutoff: float): lpf = RCHighPass(44100, 1000) - lpf.plot_freqz( - outpath="tests/rc_highpass_freqz.png" - ) + lpf.plot_freqz( outpath="tests/rc_highpass_freqz.png" ) lpf.plot_freqz_list( range(1000, 10000, 1000), @@ -65,8 +63,6 @@ def set_cutoff(self, new_cutoff: float): outpath="tests/rc_highpass_ac_analysis.png" ) - lpf.plot_impulse_response( - outpath="tests/rc_pass_impulse_response.png" - ) + lpf.plot_impulse_response( outpath="tests/rc_pass_impulse_response.png" ) print("done") \ No newline at end of file diff --git a/pywdf/examples/rc_lowpass.py b/pywdf/examples/rc_lowpass.py index 70b3ea4..ca4ca10 100644 --- a/pywdf/examples/rc_lowpass.py +++ b/pywdf/examples/rc_lowpass.py @@ -38,9 +38,7 @@ def set_cutoff(self, new_cutoff: float): lpf = RCLowPass(44100, 1000) - lpf.plot_freqz( - outpath="tests/rc_lowpass_freqz.png" - ) + lpf.plot_freqz( outpath="tests/rc_lowpass_freqz.png" ) lpf.plot_freqz_list( range(1000, 10000, 1000), @@ -56,8 +54,6 @@ def set_cutoff(self, new_cutoff: float): outpath="tests/rc_lowpass_ac_analysis.png" ) - lpf.plot_impulse_response( - outpath="tests/rc_lowpass_impulse_response.png" - ) + lpf.plot_impulse_response( outpath="tests/rc_lowpass_impulse_response.png" ) print("done") \ No newline at end of file diff --git a/pywdf/examples/rc_lowpass_z.py b/pywdf/examples/rc_lowpass_z.py new file mode 100644 index 0000000..2a147d6 --- /dev/null +++ b/pywdf/examples/rc_lowpass_z.py @@ -0,0 +1,149 @@ + +import sys +from pathlib import Path +import matplotlib.pyplot as plt +import numpy as np + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class RCLowPass(Circuit): + + def __init__( + self, + sample_rate: int, + cutoff: float + ) -> None: + + self.fs = sample_rate + self.cutoff = cutoff + self.gain = 1 + + self.previous_i = 0 + + self.C = 1e-6 + # self.R = 1.0 / (2 * np.pi * self.C * self.cutoff) + self.R = 1.0 + + # self.R1 = Resistor(self.R) + + self.R1 = ResistiveVoltageSource(None, Rval=self.R) + # self.R1 = ResistiveVoltageSource(None, Rval=self.R*.5) + + self.C1 = Capacitor(self.C, self.fs, alpha=0.0) # Alpha transform param (0.0 Backward Euler; 1.0 Bilinear Transform) + + self.S1 = SeriesAdaptor(self.R1, self.C1) + self.I1 = PolarityInverter(self.S1) + self.Vs = IdealVoltageSource(self.I1) + + super().__init__(self.Vs, self.Vs, self.C1) + # super().__init__(self.Vs, self.Vs, self.R1) + + + + def set_cutoff(self, new_cutoff: float): + if self.cutoff != new_cutoff: + self.cutoff = new_cutoff + self.R = 1.0 / (2 * np.pi * self.C * self.cutoff) + self.R1.set_resistance(self.R) + + + def process_sample( + self, + sample: float + ) -> float: + + print('i: ', self.previous_i) + self.previous_i = self.R1.wave_to_current() + + # self.R1.set_voltage( self.previous_i * self.R*.5 ) # works well + self.R1.set_voltage( self.previous_i * 10 ) #  + # self.R1.set_voltage( self.previous_i * 100 ) # blows up !!! + # self.R1.set_voltage( sample + self.previous_i * self.R ) # returns 0.0s + + self.previous_i = self.R1.wave_to_current() + + # self.R1.set_voltage(sample) + # print('s: ', sample) +# + return super().process_sample(sample) + + # return ( + # super().process_sample(sample), + # self.previous_i, + # self.R1.wave_to_current(), + # ) + + + +if __name__ == "__main__": + + # set params + fs = 100e3 + frequency = 500 + decibels = 0 + switch_closed = True + + lpf = RCLowPass(fs, 1000) + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + + # lpf.plot_freqz( + # outpath="tests/rc_lowpass_freqz.png" + # ) + + # lpf.plot_freqz_list( + # range(1000, 10000, 1000), + # lpf.set_cutoff, + # param_label="cutoff", + # outpath="tests/rc_lowpass_freqz_list.png" + # ) + + # lpf.AC_transient_analysis( + # freq = 1000, + # amplitude = 1, + # t_ms = 5, + # outpath="tests/rc_lowpass_ac_analysis.png" + # ) + + # lpf.plot_impulse_response( + # outpath="tests/rc_lowpass_impulse_response.png" + # ) + + + # a = np.ones(1) # impulse signal + # b = np.zeros(24000) + # samples = np.concatenate((a, b)) + + duration = .05 # sec + t = np.linspace(0, duration, int(fs * duration), endpoint=False) # 1 period, 48000 points + samples = np.sin(2 * np.pi * frequency * t) # 1 period of samples of a f sign + + # lpf.set_cutoff(500) + + # generate sinusoid + out = lpf.process_signal(samples) + # out = out - 1 # remove DC offset [0, 2] + + # x, y, z = zip(*out) + + plt.figure(figsize=(10, 4)) + # plt.plot(x, y, z) + plt.plot(out ) + plt.xlim([0, 2400]) + plt.title(f"LPF {frequency}Hz sinewave") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + print("done") \ No newline at end of file diff --git a/pywdf/examples/rlc_oscillator.py b/pywdf/examples/rlc_oscillator.py new file mode 100644 index 0000000..997b8b2 --- /dev/null +++ b/pywdf/examples/rlc_oscillator.py @@ -0,0 +1,146 @@ +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class LCOscillator(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.n_sample = 0.0 + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.C = 1.0e-6 + self.L = 1.0e3 + self.twopi = 2 * np.pi + + self.C1 = Capacitor(self.C, self.fs) + self.L1 = Inductor(self.L, self.fs) + self.S2 = SeriesAdaptor(self.C1, self.L1) + # self.S2 = ParallelAdaptor(self.C1, self.L1) + + self.Vs = ResistiveVoltageSource() + self.S1 = SeriesAdaptor(self.Vs, self.S2) + # self.S1 = ParallelAdaptor(self.Vs, self.S2) + + self.SW1 = Switch(self.S1) + + # init and set circuit + super().__init__(self.Vs, self.SW1, self.C1) + # self.set_params(self.frequency, self.closed, self.decibels) + + + + def process_sample( + self, + sample: float + ) -> float: + + # if self.n_sample == 24000: + # self.Vs.set_resistance(1) + + + + + # # self.Vs.set_voltage(sample) + # self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + # self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + # return self.output.wave_to_voltage() + + self.n_sample += 1 + + return super().process_sample(sample) * self.gain, self.Vs.wave_to_current(), self.Vs.wave_to_voltage() + + + + def set_params( + self, + frequency: float, + switch_closed: bool, + decibels: float + ) -> None: + + self.Vs.set_resistance(100) # + # self.Vs.set_resistance(1) + # self.Vs.set_resistance(1e-3) + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + self.L1.set_inductance(self.L) + + + + # update switch status + if switch_closed != self.closed: + self.SW1.set_closed(switch_closed) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + + +if __name__ == "__main__": + + # set params + fs = 48e3 + frequency = 100 + decibels = 0 + switch_closed = True + + lc_oscillator = LCOscillator(fs) + lc_oscillator.set_params(frequency, switch_closed, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + + lc_oscillator.plot_freqz( + out_path + ) + + a = np.ones(1) # impulse signal + b = np.zeros(48000) + samples = np.concatenate((a, b)) + + # generate sinusoid + out = lc_oscillator.process_signal(samples) + out = out - 1 # remove DC offset [0, 2] + + plt.figure(figsize=(10, 4)) + plt.plot(out) + plt.xlim([0, fs]) + plt.title(f"LC Oscillator {frequency}Hz sinewave") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() diff --git a/pywdf/examples/sallenkeyfilter.py b/pywdf/examples/sallenkeyfilter.py index 597f555..6062fb4 100644 --- a/pywdf/examples/sallenkeyfilter.py +++ b/pywdf/examples/sallenkeyfilter.py @@ -48,7 +48,9 @@ def __impedance_calc(self, R: RTypeAdaptor) -> float: Ro = 1.0e-1 Rb, Rc, Rd = R.get_port_impedances() - R.set_S_matrix ([ [ 0, -(Rc * Rd + ((Ag + 1) * Rc + (Ag + 1) * Rd) * Ri - Rc * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), -(Rb * Rd + ((Ag + 1) * Rb - Ag * Rd) * Ri - (Rb + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), (((Ag + 1) * Rb + Ag * Rc) * Ri - (Rb + Rc + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro) ], + + R.set_S_matrix ([ + [ 0, -(Rc * Rd + ((Ag + 1) * Rc + (Ag + 1) * Rd) * Ri - Rc * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), -(Rb * Rd + ((Ag + 1) * Rb - Ag * Rd) * Ri - (Rb + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), (((Ag + 1) * Rb + Ag * Rc) * Ri - (Rb + Rc + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro) ], [ -(Rb * Rc * Rd - Rb * Rc * Ro + ((Ag + 1) * Rb * Rc + Rb * Rd) * Ri) / (Rb * Rc * Rd + ((Ag + 1) * Rb * Rc + (Ag + 1) * Rb * Rd) * Ri - (Rb * Rc + (Rb + Rc) * Rd + (Rc + Rd) * Ri) * Ro), -(Rb * Rb * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rd) * Ri * Ri + (Rb * Rb * Rc - (Rc + Rd) * Ri * Ri + (Rb * Rb - Rc * Rc) * Rd - (Rc * Rc + 2 * Rc * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rb * Rc * Rd + (Ag + 1) * Rb * Rb * Rd * Rd) * Ri - (2 * Rb * Rb * Rc * Rd + (Rb * Rb - Rc * Rc) * Rd * Rd - ((Ag + 1) * Rc * Rc + (Ag + 2) * Rc * Rd + Rd * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rb * Rc - 2 * Rc * Rd * Rd + (2 * (Ag + 1) * Rb * Rb - (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (Rb * Rb * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + Ag * Rb * Rd * Rd + ((2 * Ag * Ag + 3 * Ag + 1) * Rb * Rb + (Ag * Ag + Ag) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + 2 * (Rb * Rb + Rb * Rc) * Rd + (Rb * Rc + 2 * Rb * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rb * Rc * Rd + ((2 * Ag + 1) * Rb * Rb + Ag * Rb * Rc) * Rd * Rd) * Ri - (2 * Rb * Rb * Rc * Rd + 2 * (Rb * Rb + Rb * Rc) * Rd * Rd + ((Ag + 1) * Rb * Rc + (2 * Ag + 1) * Rb * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * Rb * Rd * Rd + ((4 * Ag + 3) * Rb * Rb + 3 * (Ag + 1) * Rb * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (((Ag - 1) * Rb * Rb * Rc + Ag * Rb * Rc * Rc) * Rd * Ri + ((Ag * Ag - 1) * Rb * Rb * Rc + (Ag * Ag + Ag) * Rb * Rc * Rc - ((Ag + 1) * Rb * Rb - Ag * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + Rb * Rc * Ri) * Ro * Ro - (((Ag - 1) * Rb * Rc - Rb * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * Ag * Rb * Rb * Rc + (2 * Ag + 1) * Rb * Rc * Rc - Rb * Rb * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) ], [ -((Ag + 1) * Rb * Rc * Ri + Rb * Rc * Rd - (Rb * Rc + Rc * Ri) * Ro) / (Rb * Rc * Rd + ((Ag + 1) * Rb * Rc + (Ag + 1) * Rb * Rd) * Ri - (Rb * Rc + (Rb + Rc) * Rd + (Rc + Rd) * Ri) * Ro), (Rb * Rc * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rd) * Ri * Ri + (Rb * Rc * Rc + 2 * (Rb * Rc + Rc * Rc) * Rd + (Rc * Rc + 2 * Rc * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rc * Rc * Rd + (Ag + 1) * Rb * Rc * Rd * Rd) * Ri - (2 * Rb * Rc * Rc * Rd + 2 * (Rb * Rc + Rc * Rc) * Rd * Rd + ((Ag + 1) * Rc * Rc + (Ag + 1) * Rc * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rc * Rc + 2 * Rc * Rd * Rd + (3 * (Ag + 1) * Rb * Rc + (2 * Ag + 3) * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), -(Rb * Rc * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc - (Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rd - (Ag + 1) * Rb * Rd * Rd) * Ri * Ri + (Rb * Rc * Rc - Rd * Ri * Ri - (Rb * Rb - Rc * Rc) * Rd + (Rc * Rc - 2 * Rb * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rc * Rc * Rd - (Ag + 1) * Rb * Rb * Rd * Rd) * Ri - (2 * Rb * Rc * Rc * Rd - (Rb * Rb - Rc * Rc) * Rd * Rd + ((Ag + 1) * Rc * Rc - 2 * (Ag + 1) * Rb * Rd - Rd * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rc * Rc - 2 * Rb * Rd * Rd - (2 * (Ag + 1) * Rb * Rb - (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (((Ag + 1) * Rb * Rb * Rc + (Ag + 2) * Rb * Rc * Rc) * Rd * Ri + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 3 * Ag + 2) * Rb * Rc * Rc + 2 * (Ag + 1) * Rb * Rc * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + Rc * Ri * Ri + (2 * Rb * Rc + Rc * Rc) * Ri) * Ro * Ro - ((2 * (Ag + 1) * Rb * Rc + (Ag + 2) * Rc * Rc + 2 * Rc * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + (2 * Ag + 3) * Rb * Rc * Rc + (3 * Rb * Rc + 2 * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) ], [ ((Ag + 1) * Rb * Rd * Ri - ((Rb + Rc) * Rd + Rd * Ri) * Ro) / (Rb * Rc * Rd + ((Ag + 1) * Rb * Rc + (Ag + 1) * Rb * Rd) * Ri - (Rb * Rc + (Rb + Rc) * Rd + (Rc + Rd) * Ri) * Ro), -((Ag + 1) * Rb * Rc * Rd * Rd * Ri + ((Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rd + (Ag * Ag + 2 * Ag + 1) * Rb * Rd * Rd) * Ri * Ri - (Rc * Rd * Ri + (Rb * Rc + Rc * Rc) * Rd) * Ro * Ro + ((Rb * Rc + Rc * Rc) * Rd * Rd - ((Ag + 1) * Rc * Rd + (Ag + 1) * Rd * Rd) * Ri * Ri + ((Ag + 1) * Rc * Rc * Rd - ((Ag + 1) * Rb + Ag * Rc) * Rd * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (((Ag + 1) * Rb * Rb + 2 * (Ag + 1) * Rb * Rc) * Rd * Rd * Ri + ((Ag * Ag + 3 * Ag + 2) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + 2 * (Ag * Ag + 2 * Ag + 1) * Rb * Rc) * Rd) * Ri * Ri + ((2 * Rb + Rc) * Rd * Ri + Rd * Ri * Ri + (Rb * Rb + Rb * Rc) * Rd) * Ro * Ro - ((Rb * Rb + Rb * Rc) * Rd * Rd + ((Ag + 2) * Rd * Rd + 2 * ((Ag + 1) * Rb + (Ag + 1) * Rc) * Rd) * Ri * Ri + (((Ag + 3) * Rb + (Ag + 2) * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 1) * Rb * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), -(((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd * Ri + (Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd - ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc - (Ag + 1) * Rb * Rd * Rd) * Ri * Ri - (Rb * Rb * Rc + Rb * Rc * Rc + Rc * Ri * Ri + (2 * Rb * Rc + Rc * Rc) * Ri) * Ro * Ro - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd - (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc - Rd * Rd) * Ri * Ri - 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc - (Rb + Rc) * Rd * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) ] ]) diff --git a/tests/plots/chua_2D_projections.png b/tests/plots/chua_2D_projections.png new file mode 100644 index 0000000000000000000000000000000000000000..5a4df69008a2a6fdd15a5db1e29f7eab69b1ddf2 GIT binary patch literal 165626 zcmcG#b97$qw>BEvwwlIjY&B|Q+qP{sMw7IS)yB51#%XNZc5>F!_uc#K-#+L2^UFv_ 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