The Physics: Charge, Not Voltage
The piezoelectric effect occurs when mechanical deformation shifts the crystal lattice of a material (like PZT ceramic or PVDF film), generating a surface charge. Electrically, the sensor acts as a capacitor ($C_p$) in parallel with a charge source ($Q$). The open-circuit voltage is theoretically $V = Q / C_p$. Because the internal capacitance of a typical disc is tiny (often 1nF to 5nF), even a modest tap generates a massive voltage spike. However, this is a high-impedance source; it cannot supply meaningful current.
Because the output is fundamentally a charge packet rather than a sustained voltage, the signal will collapse almost instantly as the charge leaks through the sensor's internal dielectric resistance or your measurement circuit. To measure dynamic force, vibration, or impact accurately, you must convert this high-impedance charge into a low-impedance voltage using a charge amplifier. If you only need simple "knock" detection (like an electronic drum trigger), a 1MΩ bleed resistor across the terminals is sufficient, but it sacrifices all linear scaling capabilities.
| Part Number | Material / Type | Capacitance ($C_p$) | Resonant Freq | Charge Sensitivity | Typical Application |
|---|---|---|---|---|---|
| LDT0-028K (TE) | PVDF Film | 2.1 nF | N/A (Broadband) | ~15 pC/N | Dynamic strain, vibration |
| 7BB-20-6L0 (Murata) | PZT Ceramic | 4.5 nF | 6.0 kHz | ~35 pC/N | Knock sensors, audio pickups |
| PKI-402 (PIEZO SYS) | PZT-5H Ceramic | 12.0 nF | 4.2 kHz | ~110 pC/N | Precision force measurement |
| AB2112B (PUI Audio) | PZT Bending | 18.0 nF | 2.1 kHz | ~85 pC/N | Impact triggers, acoustic |
Front-End Circuit & ESP32 Wiring
To measure actual physical units (Newtons or Gs), we will build an inverting charge amplifier using the LMC6062. Standard op-amps like the LM358 or MCP6001 have input bias currents that are too high; they will drain the piezo's charge before the ADC can sample it. The LMC6062 is a precision CMOS op-amp with an input bias current of just 0.05 pA, making it ideal for high-impedance piezo nodes. We power the op-amp at 5V to allow for a 2.5V virtual ground bias, keeping the signal well within the ESP32's 0-3.3V ADC range.
| Component / Pin | Connection | Notes & Supply Range |
|---|---|---|
| Piezo Terminal 1 | LMC6062 Pin 2 (Inverting Input) | Keep trace as short as possible (<10mm) |
| Piezo Terminal 2 | System Ground (0V) | Use shielded coaxial cable if >2 inches |
| LMC6062 Pin 3 (Non-Inv) | Voltage Divider (10kΩ/10kΩ) | Biases output to 2.5V (mid-supply) |
| Feedback Capacitor ($C_f$) | Between Pin 2 and Pin 1 (Output) | 1nF C0G/NP0 ceramic (sets gain) |
| Feedback Resistor ($R_f$) | Parallel with $C_f$ | 10MΩ (prevents DC saturation) |
| LMC6062 Pin 1 (Output) | ESP32 GPIO 34 (ADC1_CH6) | Add 100Ω series resistor + 10nF to GND |
| LMC6062 VCC (Pin 8) | 5V Supply | Op-amp requires 4.5V - 5.5V for rail specs |
The ESP32's internal 12-bit ADC is notoriously non-linear near the 0V and 3.3V rails. By biasing the op-amp output to 2.5V (using a 5V op-amp supply and a voltage divider on the non-inverting pin), your resting state sits at ~2.5V. Impacts will swing the voltage down toward 0V and up toward 3.3V, keeping you out of the worst non-linear zones. For production, always use the
esp_adc_cal component to apply eFuse calibration values.Assembly Steps
- Prep the Sensor: Solder 24AWG shielded twisted pair to the piezo disc. Use low-temperature solder (or a heat sink clip) to avoid depolarizing the PZT ceramic, which occurs around 150°C-300°C depending on the grade.
- Build the Bias Network: Connect two 10kΩ 1% resistors in series between 5V and GND. Tie the midpoint to LMC6062 Pin 3. Add a 10µF bypass capacitor from the midpoint to GND to filter power supply noise.
- Install Feedback Components: Solder the 1nF C0G capacitor and 10MΩ resistor directly between Pin 2 and Pin 1. Do not use X7R or Y5V capacitors for $C_f$; their capacitance changes with applied voltage, ruining your linearity.
- Route to ESP32: Run the op-amp output through a 100Ω resistor to GPIO 34, with a 10nF capacitor to GND at the ESP32 pin to form a low-pass filter cutting off at ~160kHz, eliminating RF interference.
The Math: Converting ADC Counts to Newtons
In a charge amplifier, the output voltage is determined strictly by the feedback capacitor ($C_f$) and the input charge ($Q$), independent of the sensor's internal capacitance or cable length. The governing equation is:
V_out = -(Q / C_f)
Because we biased the non-inverting pin to 2.5V, the actual voltage seen by the ESP32 is V_adc = 2.5V + V_out. Let's convert a raw 12-bit ADC reading into Force (Newtons).
Worked Example
Assume we are using the PKI-402 sensor (Charge Sensitivity $S_q$ = 110 pC/N) and a $C_f$ of 1nF (1000 pF).
- Calculate Voltage per Newton:
V_per_N = S_q / C_f = 110 pC/N / 1000 pF = 0.11 V/N. - Read the ESP32 ADC:
Assume a resting reading of 3106 (which is 2.5V on a 12-bit scale where 4095 = 3.3V). An impact occurs, and the ADC reads2400. - Find the Delta Voltage:
Delta_Counts = 3106 - 2400 = 706 counts.
Delta_Voltage = (706 / 4095) * 3.3V = 0.568V. - Calculate Peak Force:
Force = Delta_Voltage / V_per_N = 0.568V / 0.11 V/N = 5.16 Newtons.
In C++, this translates to a highly efficient floating-point operation:
const float V_REF = 3.3;
const int ADC_MAX = 4095;
const float BIAS_COUNTS = 3106; // Calibrate this at rest
const float V_PER_N = 0.11; // (Sensor_pC_per_N / Feedback_C_pF)
float get_force_newtons(int raw_adc) {
float delta_v = ((BIAS_COUNTS - raw_adc) / ADC_MAX) * V_REF;
return delta_v / V_PER_N;
}Defeating Noise: Interference & Calibration
Piezo front-ends are notoriously susceptible to environmental noise because the inverting input node is extremely high impedance. If you are seeing 50/60Hz mains hum or random baseline wandering, check these three interference sources:
- Electromagnetic Interference (EMI): The high-Z node acts as an antenna. Fix: Enclose the front-end circuit in a grounded metal project box. Use coaxial cable for the piezo connection, and tie the cable shield to circuit ground only at the op-amp end to prevent ground loops.
- Triboelectric Noise: When standard insulated cables flex, the dielectric rubs against the conductor, generating static charge that the amplifier reads as a signal. Fix: Use specialized low-noise coaxial cable (like Belden 8214) or secure the cable firmly so it cannot vibrate near the sensor.
- Surface Leakage Currents: Humidity and flux residue on the PCB can create high-impedance paths that drain the feedback capacitor. Fix: Clean the PCB with isopropyl alcohol and apply a conformal coating. For ultimate precision, implement a guard ring—a copper trace surrounding the high-Z input pin, driven by a low-impedance buffer at the exact same 2.5V bias potential.
Calibration Protocol
Factory charge sensitivity values ($S_q$) have a tolerance of ±20%. To calibrate your specific assembly, perform a drop-test. Drop a steel ball of known mass (e.g., 50g) from a known height (e.g., 10cm) directly onto the sensor's center. Calculate the theoretical impulse force, record the peak ADC delta, and adjust your V_PER_N constant in software until the calculated output matches the physical input. For continuous vibration monitoring, mount the piezo element alongside a reference MEMS accelerometer (like the ADXL345) on a shaker table and map the frequency response.
