import sys import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt from PyQt5.QtWidgets import ( QApplication, QMainWindow, QVBoxLayout, QWidget, QSlider, QLabel, QComboBox, QHBoxLayout, ) from PyQt5.QtCore import Qt from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas from matplotlib.patches import FancyArrowPatch, Arc plt.rcParams.update( { "text.usetex": True, "font.family": "EB Garamond", "axes.labelsize": "x-large", "xtick.labelsize": "x-large", "ytick.labelsize": "x-large", } ) plt.rcParams["figure.facecolor"] = "w" mpl.rc("text.latex", preamble=r"\usepackage{xcolor}\usepackage{amsmath}") def compute_Q(R, L, C): if R == 0 or C == 0: return np.inf return 1 / R * np.sqrt(L / C) class RCFilterWidget(QWidget): def __init__(self): super().__init__() # Initial values self.R = 1.0 self.L = 1.0 self.C = 1.0 self.init_w = 1 / (self.R * self.C) self.w = np.linspace(0, 10 * self.init_w, 500) self.init_ui() def get_transfer_functions(self): R, L, C = self.R, self.L, self.C return { "RC (C voltage)": lambda w: 1 / (1 + 1j * w * R * C), "RC (R voltage)": lambda w: 1j * w * R * C / (1 + 1j * w * R * C), "RL (R voltage)": lambda w: R / (R + 1j * w * L), "RL (L voltage)": lambda w: 1j * w * L / (R + 1j * w * L), "RLC (C voltage)": lambda w: 1 / (1 - w**2 * L * C + 1j * w * R * C), "RLC (R voltage)": lambda w: (1j * w * R * C) / (1 - w**2 * L * C + 1j * w * R * C), "RLC (L voltage)": lambda w: (w**2 * L * C) / (1 - w**2 * L * C + 1j * w * R * C), } def init_ui(self): layout = QVBoxLayout(self) # Matplotlib Figure self.fig, self.axs = plt.subplots(1, 3, figsize=(15, 5)) self.fig.subplots_adjust(bottom=0.18) self.canvas = FigureCanvas(self.fig) layout.addWidget(self.canvas) # Complex plane ax0 = self.axs[0] unit_circle = plt.Circle((0, 0), 1, color="gray", fill=False, linestyle="--") ax0.add_artist(unit_circle) ax0.axhline(0, color="black", lw=1) ax0.axvline(0, color="black", lw=1) ax0.set_xlim(-1.2, 1.2) ax0.set_ylim(-1.2, 1.2) ax0.set_aspect("equal") ax0.set_title("Amplitude complexe") ax0.set_xlabel("Re") ax0.set_ylabel("Im") # Initial transfer function self.current_tf = list(self.get_transfer_functions().keys())[0] H_func = self.get_transfer_functions()[self.current_tf] H_vals = H_func(self.w / self.init_w) modulus = np.abs(H_vals) argument = np.angle(H_vals) # Arrow for complex amplitude H_init = H_func(self.init_w / self.init_w) self.vector = FancyArrowPatch( (0, 0), (np.real(H_init), np.imag(H_init)), color="#d62626", arrowstyle="->", mutation_scale=20, lw=3, ) ax0.add_patch(self.vector) # Arc for phase angle_init = np.angle(H_init) angle_init_deg = np.degrees(angle_init) if angle_init_deg >= 0: theta1_init = 0 theta2_init = angle_init_deg else: theta1_init = angle_init_deg theta2_init = 0 self.arc = Arc( (0, 0), 0.6, 0.6, angle=0, theta1=theta1_init, theta2=theta2_init, color="#2e8b73", lw=2, ) ax0.add_patch(self.arc) # Initial position for arrow tip arrow_tip_x = np.real(H_init) arrow_tip_y = np.imag(H_init) self.arrow_text = ax0.text( arrow_tip_x, arrow_tip_y, r"$\underline{H}(x)$", color="#733bb3", fontsize=14, va="center", ha="left", ) # Initial position for arrow middle self.middle_text = ax0.text( arrow_tip_x / 2, arrow_tip_y / 2, r"$G(x)$", color="#d62626", fontsize=14, va="bottom", ha="right", ) # Initial position for arc label (place at middle of arc) arc_angle = np.angle(H_init) arc_radius = 0.4 arc_label_x = arc_radius * np.cos(arc_angle / 2) arc_label_y = arc_radius * np.sin(arc_angle / 2) self.arc_text = ax0.text( arc_label_x, arc_label_y, r"$\Delta\varphi_{s/e}(x)$", color="#2e8b73", fontsize=14, va="center", ha="left", ) # Modulus plot ax1 = self.axs[1] (self.mod_line,) = ax1.plot( self.w / self.init_w, modulus, ls="-", color="#d62626" ) ax1.set_title("Gain selon pulsation") ax1.set_xlabel(r"$x = \displaystyle\frac{\omega}{\omega_0}$") ax1.set_ylabel(r"$G(x)$") ax1.grid(True) (self.mod_point,) = ax1.plot( [self.init_w / self.init_w], [np.abs(H_init)], "ko" ) # Argument plot ax2 = self.axs[2] (self.arg_line,) = ax2.plot( self.w / self.init_w, argument, ls="-", color="#2e8b73" ) ax2.set_title("Déphasage selon pulsation") ax2.set_xlabel(r"$x = \displaystyle\frac{\omega}{\omega_0}$") ax2.set_ylabel(r"$\Delta\varphi_{s/e}(x)$ (rad)") ax2.grid(True) (self.arg_point,) = ax2.plot( [self.init_w / self.init_w], [np.angle(H_init)], "ko" ) # Slider self.slider_label = QLabel( "Pulsation ($\\omega/\\omega_0$): {:.2f}".format(self.init_w / self.init_w) ) layout.addWidget(self.slider_label) self.slider = QSlider(Qt.Horizontal) self.slider.setMinimum(0) self.slider.setMaximum(1000) self.slider.setValue(100) self.slider.setTickInterval(1) layout.addWidget(self.slider) self.slider.valueChanged.connect(self.update_plot) # Dropdown for transfer function selection self.dropdown = QComboBox() self.dropdown.addItems(list(self.get_transfer_functions().keys())) layout.addWidget(self.dropdown) self.dropdown.currentIndexChanged.connect(self.change_transfer_function) # R, L, C sliders param_layout = QHBoxLayout() self.r_label = QLabel(f"R = {self.R:.2f}") self.r_slider = QSlider(Qt.Horizontal) self.r_slider.setMinimum(1) self.r_slider.setMaximum(1000) self.r_slider.setValue(int(self.R * 100)) self.r_slider.valueChanged.connect(self.change_params) param_layout.addWidget(self.r_label) param_layout.addWidget(self.r_slider) self.l_label = QLabel(f"L = {self.L:.2f}") self.l_slider = QSlider(Qt.Horizontal) self.l_slider.setMinimum(1) self.l_slider.setMaximum(1000) self.l_slider.setValue(int(self.L * 100)) self.l_slider.valueChanged.connect(self.change_params) param_layout.addWidget(self.l_label) param_layout.addWidget(self.l_slider) self.c_label = QLabel(f"C = {self.C:.2f}") self.c_slider = QSlider(Qt.Horizontal) self.c_slider.setMinimum(1) self.c_slider.setMaximum(1000) self.c_slider.setValue(int(self.C * 100)) self.c_slider.valueChanged.connect(self.change_params) param_layout.addWidget(self.c_label) param_layout.addWidget(self.c_slider) layout.addLayout(param_layout) # Q display self.q_label = QLabel(f"Q = {compute_Q(self.R, self.L, self.C):.2f}") layout.addWidget(self.q_label) def update_plot(self, value): puls_ratio = value / 100.0 puls = puls_ratio * self.init_w H_func = self.get_transfer_functions()[self.dropdown.currentText()] H_val = H_func(puls / self.init_w) self.slider_label.setText( "Pulsation ($\\omega/\\omega_0$): {:.2f}".format(puls_ratio) ) # Arrow update self.vector.set_positions((0, 0), (np.real(H_val), np.imag(H_val))) # Points update self.mod_point.set_data([puls_ratio], [np.abs(H_val)]) self.arg_point.set_data([puls_ratio], [np.angle(H_val)]) # Arc update angle = np.angle(H_val) angle_deg = np.degrees(angle) if angle_deg >= 0: self.arc.theta1 = 0 self.arc.theta2 = angle_deg else: self.arc.theta1 = angle_deg self.arc.theta2 = 0 # Arrow tip position arrow_tip_x = np.real(H_val) arrow_tip_y = np.imag(H_val) self.arrow_text.set_position((arrow_tip_x, arrow_tip_y)) # Middle tip position self.middle_text.set_position((arrow_tip_x / 2, arrow_tip_y / 2)) # Arc label position (middle of arc) arc_angle = np.angle(H_val) arc_radius = 0.4 arc_label_x = arc_radius * np.cos(arc_angle / 2) arc_label_y = arc_radius * np.sin(arc_angle / 2) self.arc_text.set_position((arc_label_x, arc_label_y)) self.canvas.draw_idle() def change_transfer_function(self, index): H_func = self.get_transfer_functions()[self.dropdown.currentText()] H_vals = H_func(self.w / self.init_w) modulus = np.abs(H_vals) argument = np.angle(H_vals) self.mod_line.set_ydata(modulus) self.arg_line.set_ydata(argument) # Autoscale self.axs[1].relim() self.axs[1].autoscale_view() self.axs[2].relim() self.axs[2].autoscale_view() self.update_plot(self.slider.value()) self.canvas.draw_idle() def change_params(self, value): self.R = self.r_slider.value() / 100.0 self.L = self.l_slider.value() / 100.0 self.C = self.c_slider.value() / 100.0 self.r_label.setText(f"R = {self.R:.2f}") self.l_label.setText(f"L = {self.L:.2f}") self.c_label.setText(f"C = {self.C:.2f}") self.q_label.setText(f"Q = {compute_Q(self.R, self.L, self.C):.2f}") # Update frequency axis and transfer function self.init_w = 1 / (self.R * self.C) self.w = np.linspace(0, 10 * self.init_w, 500) H_func = self.get_transfer_functions()[self.dropdown.currentText()] H_vals = H_func(self.w / self.init_w) modulus = np.abs(H_vals) argument = np.angle(H_vals) self.mod_line.set_xdata(self.w / self.init_w) self.mod_line.set_ydata(modulus) self.arg_line.set_xdata(self.w / self.init_w) self.arg_line.set_ydata(argument) # Autoscale self.axs[1].relim() self.axs[1].autoscale_view() self.axs[2].relim() self.axs[2].autoscale_view() self.update_plot(self.slider.value()) self.canvas.draw_idle() class MainWindow(QMainWindow): def __init__(self): super().__init__() self.setWindowTitle("RC/RLC Filter Transfer Function Animation") self.widget = RCFilterWidget() self.setCentralWidget(self.widget) if __name__ == "__main__": app = QApplication(sys.argv) window = MainWindow() window.show() sys.exit(app.exec_())