dither_test.py

import numpy as np
import matplotlib.pyplot as plt

Ts = 0.0001
fs = 1 / Ts
t = np.arange(0, 1, Ts)
V_pi = 5
V_bias = 2.5
f_dither = 1000

def get_fft_val(V_bias_base, V_bias_dither_amp, N=4096):
    V_bias_dither = V_bias_base + V_bias_dither_amp * np.cos(2 * np.pi * f_dither * t)
    x = 0.5 * (1 + np.cos(np.pi * V_bias_dither / V_pi))
    # Photodetector gets only the magnitude plus dc part
    y = np.abs(x)
    y = y - np.mean(y)
    Y = np.fft.fft(y[:N])
    return Y, y

N = 4096
for V_bias_vals in [1.5, 2.0, 2.5, 2.75, 3, 3.5, 4]:
    Y, y = get_fft_val(V_bias_vals, 2.5, N)
    f_vals = np.arange(N) * fs / N
    f_vals[N//2:] -= fs
    plt.plot(np.fft.fftshift(f_vals), np.fft.fftshift(20*np.log10(np.abs(Y))), label=str(V_bias_vals))
    v = plt.axis()
    print(f"{V_bias_vals}: {10*np.log10(np.abs(np.trapz(y * np.exp(1j * 2 * np.pi * 2 * f_dither * t), t)))}")
plt.legend()
plt.axis([v[0], v[1], -80, v[3]])
plt.grid()
plt.show()