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"""
Emulation: average output of a phase detector (XOR) vs a phase-frequency
detector (tri-state PFD) when the two inputs differ in frequency.

Setup (open loop, no feedback):
    input A = reference square wave at f_a = 1
    input B = "VCO" square wave at f_b = f_a - df

Claims demonstrated:
  1. XOR PD: time-average -> 0 for every df != 0, identical for +df and -df

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"""
Inductive shunt peaking: bandwidth, peak frequency, and peaking gain
as functions of m = R^2 * C / L.

All frequencies are normalized to 1/RC (i.e. the plotted value is omega * RC).
Smaller m  <=>  larger inductor L.

Impedance:  Z(s)/R = (1 + s L/R) / (1 + s R C + s^2 L C)
With u = (omega * RC)^2 and m = R^2 C / L:
    |Z/R|^2 = (1 + u/m^2) / ((1 - u/m)^2 + u)

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"""
Quantization noise of a sinusoid: harmonic coefficients A_p, noise power,
and the impact of the bit count n.

Model: uniform quantizer, step Delta, input x(t) = A*sin(w t).
The quantization error expands into ODD harmonics only:

    e(t) = sum_{p odd} A_p sin(p w t)

For a mid-tread quantizer  y = Delta*round(x/Delta)  the error e = y - x has

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# modified from https://github.com/wulffern/aic2023/blob/main/ex/q.py

#!/usr/bin/env python3

import numpy as np
import matplotlib.pyplot as plt


#- Enable hanning window
hann = True

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"""Plot statistical and empirical eye diagrams from the smoke test fixtures."""

import os
import sys

import matplotlib
# matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np

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"""
Overlay: OSR=1 (FOH inactive), OSR=16 (FOH active), nd*sinc^2 ideal FOH at
OSR=16, and target nd.  noise_gen.va verification.
"""

import numpy as np
import matplotlib
# matplotlib.use("Agg")
import matplotlib.pyplot as plt

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%% Complex-conjugate poles of a 2nd-order system vs. quality factor Q
%  H(s) ~ 1 / ( s^2 + (w0/Q) s + w0^2 )
%  Poles:  s = -w0/(2Q) +/- w0*sqrt(1/(4Q^2) - 1)
%  For Q > 0.5 the poles are complex conjugates on a circle of radius w0.

clear; clc; close all;

w0 = 1.0;                              % natural frequency (normalized)

% Discrete Q values to mark with 'x'

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clear; clc; close all;

% Parameters
wp = 1;   % rad/s

% Frequency axis
w = logspace(-2, 2, 1000);

s = 1j*w;