从 TI 参考设计看 IEPE 压电传感器

       ┌──────────────┐
       │   压电晶体   │
       └─────┬────────┘
             │ 电荷信号
             ▼
         内置放大器 (FET)
             │
   ┌─────────┴──────────┐
   │  供电 + 信号输出端 │ ←—— 单线输出
   └────────────────────┘

IEPE 输出 (~10 V DC + ±5 V AC)
     │
     │  交流耦合电容 (C耦)
     ▼
  电阻分压器 (10:1) — 将 ±10 V 降至 ±1 V
     ▼
  同相缓冲 OPA2320（增益 2）
     ▼
  全差分放大 THS4551（增益 2）
     ▼
  ADC (ADS127L11) ±4.096 V 满量程

        +24 V 电源
             │
             │
       ┌─────────────┐
       │ 3.5 mA 恒流源│ ← TLV431B + OPA4187
       └──────┬──────┘
              │
              │ (同轴电缆)
      +-------┴-------------------+
      |       IEPE 传感器         |
      |  内置放大器 + 偏置电路     |
      +----------------------------+
              │
        输出 ≈ 10V ± AC
              │
         │ 交流耦合电容
              ▼
         信号调理前端

       IEPE 三轴加速度计 (4525-B)
          |     |     |
          X     Y     Z
          |     |     |
          +-----+-----+
                │
          四针密封接头
                │
     ┌──────────┴──────────┐
     │ WB-1453 三轴IEPE电源 │
     └──────────┬──────────┘
                │
           3×BNC 输出
                │
           数据采集系统

(0.15915494309189535,
 np.float64(2.2179179043082584),
 np.float64(2.502283215402552),
 np.float64(2.212134951473059))

# Simulate IEPE (4525-B-001) accelerometer output and front-end chain
# Assumptions (typical):
# - Sensitivity S = 100 mV/g
# - Bias ~ 12.5 V
# - Noise floor ~ 0.5 mg_RMS
# - Useful flat response ~ 1 Hz – 10 kHz
#
# Signal chain modeled:
# IEPE sensor (bias + AC) → AC coupling (RC high-pass) → 10:1 divider → buffer → THS4551 (G=2) → ADC input (differential)
#
# Outputs:
# - Time-domain waveforms at key nodes
# - Magnitude spectra (dBFS relative to ADC full-scale assumed ±4.096 V diff)

import numpy as np
import matplotlib.pyplot as plt

# Sampling parameters
fs = 200_000  # 200 kS/s, enough for 0–20 kHz BW
T = 0.25      # 250 ms duration
t = np.arange(int(T*fs)) / fs

# Sensor & chain parameters
S = 0.100  # V/g (100 mV/g)
Vbias = 12.5  # V
noise_g_rms = 0.0005  # 0.5 mg RMS
# Synthetic acceleration: combination of tones + slow drift + burst
a_g = (0.3*np.sin(2*np.pi*50*t) +
       0.1*np.sin(2*np.pi*1200*t) +
       0.02*np.sin(2*np.pi*6000*t) +
       0.07*np.sin(2*np.pi*8*t))  # g

# Add a short transient burst
burst = ((t>0.120) & (t<0.135)).astype(float) * 1.0 * np.sin(2*np.pi*350*t)
a_g = a_g + burst

# Add sensor noise (white)
rng = np.random.default_rng(42)
a_g = a_g + rng.normal(0, noise_g_rms, size=a_g.shape)

# IEPE raw output (with DC bias)
v_iepe = Vbias + S * a_g  # V

# Analog AC coupling (single-pole HPF)
# Choose Cin=10 uF, Rin=100 kΩ => fc ≈ 0.159 Hz (within 1 Hz – 10 kHz flatness with negligible droop)
Cin = 10e-6
Rin = 100e3
fc_hp = 1/(2*np.pi*Rin*Cin)

# Discrete-time HPF via bilinear transform
# Analog H(s)= sRC/(1+sRC); bilinear s = 2*fs*(1 - z^-1)/(1 + z^-1)
K = 2*fs*Rin*Cin
b0 =  K/(1+K)
b1 = -K/(1+K)
a1 =  (1-K)/(1+K)
x = v_iepe
y_hpf = np.zeros_like(x)
x1 = 0.0
y1 = 0.0
for n in range(len(x)):
    y = b0*x[n] + b1*x1 - a1*y1
    y_hpf[n] = y
    x1, y1 = x[n], y

# 10:1 divider
v_div = y_hpf / 10.0

# Buffer (unity) then THS4551 fully differential driver with gain = 2 (single-ended to differential magnitude ~2x)
G_ths = 2.0
v_adc_diff = G_ths * v_div  # differential peak-to-peak modeled as 2x single-ended

# Assume ADC full-scale differential ±4.096 V => Vfs = 4.096 V
Vfs = 4.096
# dBFS magnitude helper
def dbfs(v):
    # Use RMS referenced to full-scale sine RMS (Vfs/sqrt(2)). For spectrum bins, use |FFT| normalized to Vfs.
    return 20*np.log10(np.maximum(np.abs(v)/(Vfs), 1e-20))

# Plot 1: Time-domain (IEPE raw with bias) - show a short window to see details
Nwin = int(0.02*fs)  # 20 ms
start = int(0.10*fs)
end = start + Nwin

plt.figure(figsize=(8,4))
plt.plot(t[start:end]*1000, v_iepe[start:end])
plt.xlabel("时间 (ms)")
plt.ylabel("IEPE 原始输出电压 (V)")
plt.title("IEPE 原始输出（含偏置约 12.5 V） — 局部 20 ms 窗口")
plt.tight_layout()
plt.show()

# Plot 2: Time-domain overlay of key nodes (AC-coupled, divider, ADC input diff) same window
plt.figure(figsize=(8,4))
plt.plot(t[start:end]*1000, y_hpf[start:end], label="AC 耦合后 (HPF)")
plt.plot(t[start:end]*1000, v_div[start:end], label="10:1 分压后")
plt.plot(t[start:end]*1000, v_adc_diff[start:end], label="THS4551 (G=2) → ADC差分")
plt.xlabel("时间 (ms)")
plt.ylabel("电压 (V)")
plt.title("信号链各节点的瞬时波形（同一时窗）")
plt.legend()
plt.tight_layout()
plt.show()

# Plot 3: Full-length time trace at ADC input (to see burst)
plt.figure(figsize=(8,3.5))
plt.plot(t*1000, v_adc_diff)
plt.xlabel("时间 (ms)")
plt.ylabel("ADC 差分输入 (V)")
plt.title("ADC 输入差分波形（含 350 Hz 瞬时突发）")
plt.tight_layout()
plt.show()

# Plot 4: Spectrum at ADC input
# Windowing and FFT
from numpy.fft import rfft, rfftfreq
w = np.hanning(len(v_adc_diff))
V = rfft((v_adc_diff)*w)
freqs = rfftfreq(len(v_adc_diff), 1/fs)
# Amplitude spectrum normalized to Vfs
mag = np.abs(V)/ (np.sum(w)/2)
mag_dbfs = 20*np.log10(np.maximum(mag/Vfs, 1e-20))

plt.figure(figsize=(8,4))
plt.semilogx(freqs[1:], mag_dbfs[1:])
plt.xlim(10, 50_000)
plt.ylim(-160, 0)
plt.xlabel("频率 (Hz)")
plt.ylabel("幅度 (dBFS)")
plt.title("ADC 输入差分端的幅度谱")
plt.grid(True, which='both', linestyle='--', alpha=0.4)
plt.tight_layout()
plt.show()

# Print some quick numeric summaries
import numpy as np
rms_adc = np.sqrt(np.mean(v_adc_diff**2))
pk_adc = np.max(np.abs(v_adc_diff))
drift = np.mean(v_adc_diff)
fc_hp, rms_adc, pk_adc, drift