Design Goals

Design Description

This design amplifies a 1.3-mV signal between the frequency band of 10Hz to 10kHz. The output of the charge amplifier signal is filtered from the resonance frequency of the sensor and amplified for the expected stable output of ±500mV (1G shock). The common-mode voltage is half of the power supply, noted as VREF. The design implements a charge sensor amplifier intended to detect excessive force or shock, such as what occurs when an object is dropped or exposed to mechanical shock. The output of the detector can be acquired with an ADC and sampled by a controller to initiate the necessary protective steps.

Design Notes

1. Use the op amp in a linear operating region. Linear output swing is usually specified under the A_OL test conditions.
2. Select a high feedback resistor (Rf) to minimize noise impact. Signal conditioning for piezoelectric sensors may be referenced for further information.
3. Sensor sensitivity increases with higher capacitance and in turn increases the op amp voltage noise gain. This trade-off must be kept in mind when selecting a sensor. The Murata PKGS-00GXP1-R sensor has the following characteristics: 0.35 pC/G sensor sensitivity, 390-pF capacitance, 31-kHz resonance frequency.
4. An amplifier with low input voltage noise and low input current noise is preferred to minimize signal to noise ratio (SNR).
5. Low input bias current and high input impedance will minimize offset error and provide a suitable sensor interface. The output should swing from rail-to-rail to allow simple biasing and large output voltage swing with a low single supply voltage.

Design Steps

1. Select the highest value resistor for R_f to minimize noise impact:
   $R_f=240 M\Omega$
2. Calculate C_f for low frequency cutoff (f_low) of 10Hz.
   $C_f=\frac{1}{2{\mathrm{\pi R}}_f{f}_{clow}}=\frac{1}{2\pi \left(240\mathrm{M\Omega }\right)\left(10\mathrm{Hz}\right)}=66.3pF \cong 68pF (S\tan dard Value)$
3. Calculate R_in for high frequency cutoff (f_high) of 10kHz with sensor capacitance.
   $R_{in}=\frac{1}{2{\mathrm{\pi C}}_{\mathrm{sensor}}{f}_{\mathrm{chigh}}}=\frac{1}{2\pi \left(390\mathrm{pF}\right)\left(10\mathrm{kHz}\right)}=40.8k\Omega \cong 39.2k\Omega (S\tan dard Value)$
4. Compute the expected output of the charge amplifier:
   $V_{out}=\frac{Q}{C_f}=\frac{0.35\frac{ pC}{G}}{68pF}=5.14mV$
5. To avoid resonance from the sensor, which has a resonance frequency of 31kHz, place a Twin-T Notch filter with a stop band at 31kHz. For simplicity, assume all three capacitors are equal 1nF (C1, C2, C3).
   $R_1=7.5k\Omega , R_2=7.5k\Omega , R_3=1.8k\Omega$
6. Use a second op amp in a noninverting configuration to scale Vout to ±500mV. Select R₄=110Ω
   $R_5=\left(\frac{Vo}{Vi}-1\right)\times R_4=\left(\frac{500mV}{5.14mV}-1\right)\times 110\Omega =11k\Omega (S\tan dard Value)$
7. Add a high-pass filter on the output with a center frequency of 10 Hz, select a low capacitor value, C4 = 0.1μF.
   $R_6=\frac{1}{2{\mathrm{\pi C}}_4{f}_{\mathrm{low}}}=\frac{1}{2\pi \left(0.1\mathrm{uF}\right)\left(10\mathrm{Hz}\right)}=159.15k\Omega \cong 158k\Omega (S\tan dard Value)$

Design Results

AC Simulation Results

Transient Simulation Results

References:

1. Analog Engineer's Circuit Cookbooks
2. SPICE Simulation File SBOMBX8
3. TI Precision Labs

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