Piezoelectric Sensor Front Ends: Choose Charge or Voltage Readout Before Changing Cable Length

System boundary

A passive piezoelectric charge-output sensor, cable and separately designed analog receiver. The ceramic thick-film circuit may provide feedback or bias resistors, but is not itself assumed to be a piezoelectric sensing element or an integrated sensor product.

Integration interfaces

Integration risks

Identify the electrical quantity entering the receiver

A passive piezoelectric sensor can be represented, over an appropriate operating range, as generated charge with parallel capacitance and leakage. Its charge sensitivity comes from the selected sensor and mechanical mounting, not from a generic ceramic substrate label. Record whether the connected receiver observes the sensor voltage or maintains a controlled summing node to collect charge.

An internally buffered sensor is a different interface. Its cable may be driven by active electronics rather than connected directly across the sensing capacitance. Do not apply the passive source equations to that product without its electrical model. Similarly, a ceramic resistor network used beside the sensor does not establish a piezoelectric material, charge coefficient or acceleration rating for the supplied circuit.

Include cable capacitance in the voltage-mode denominator

For a charge change Q applied rapidly enough that leakage is negligible, the voltage across an unloaded capacitive source is Q divided by total capacitance. In a high-impedance voltage receiver, that total includes sensor capacitance, cable capacitance and relevant amplifier or fixture input capacitance. A subsequent fixed voltage gain multiplies this already divided signal.

Assume the sensor contributes 1 nanofarad, the cable contributes 1 nanofarad and the remaining input capacitance is negligible for the example. A 100 picocoulomb charge change produces 50 millivolts. Replacing the cable with one contributing 2 nanofarads raises total capacitance to 3 nanofarads and reduces the voltage to about 33.33 millivolts. The unchanged mechanical charge now appears one third smaller without any resistor changing.

Move the principal conversion into a feedback capacitor

In an ideal inverting charge amplifier, the active circuit holds the summing node at its reference while charge enters the feedback capacitor Cf. The output change is minus Q divided by Cf. Because the input node changes negligibly, cable capacitance does not absorb the charge through a significant voltage change in this ideal model. The sign follows the defined input current and amplifier polarity.

Using an assumed Cf of 1 nanofarad, the same 100 picocoulomb charge change gives a minus 100 millivolt output change. Increasing cable capacitance from 1 to 2 nanofarads does not alter that ideal conversion. This comparison concerns topology, not a claim that real cables have no influence. A parallel feedback resistor, finite amplifier response and input protection all limit the useful charge-conversion range.

Check the loop-gain cost of added input capacitance

The virtual summing node is an approximation maintained by feedback. For a simplified capacitive model with total input capacitance Ct and feedback capacitance Cf, let the amplifier obey Vout = minus A times the summing-node voltage. Charge balance gives Vout/Q = minus A divided by Ct plus Cf times one plus A. This expression shows directly why a finite A makes cable capacitance relevant again.

Relative to the ideal minus one over Cf conversion, the factor is A divided by A plus one plus Ct/Cf. The quantities can be complex and frequency-dependent in a real amplifier; an open-loop gain magnitude alone does not establish phase margin. Use the expression as a circuit-model check, then evaluate the selected amplifier, feedback resistor and input components over the required band.

Keep feedback recovery separate from cable sensitivity

A practical feedback resistor provides a DC path and returns the output toward its baseline. Its product with Cf controls a low-frequency decay in the simple parallel-RC model. Making that resistor larger can extend a charge-observation interval, but it does not automatically increase loop gain or remove the dynamic effect of input capacitance. These are different design controls.

Use the dedicated charge-pulse recovery calculation to set the allowed collection loss, event spacing and accumulated tail. This page's cable comparison does not replace that work. A configuration that preserves charge amplitude over one event may still saturate during repeated events, while a rapidly recovering configuration may lose part of a slowly delivered charge. Keep those timing requirements in the same circuit package without treating them as a cable calibration constant.

Do not reduce the cable to capacitance alone

Cable motion can generate charge, insulation leakage can divert current, and shielding or ground connections can introduce interference. A charge-mode topology does not distinguish unwanted generated charge from sensor charge merely because both arrive at the summing node. Use the cable construction and mounting appropriate to the actual sensor application, and retain the reference connection when comparing replacements.

Input series resistance, protection capacitance and sensor capacitance can also shape the high-frequency response. Do not delete protective components to recover amplitude without an approved circuit review. Long cables may need a distributed model beyond the lumped approximation used here. State the frequency range over which the capacitance measurement and simplified transfer represent the installed assembly.

Change capacitance without changing the mechanical stimulus

Begin with an approved low-energy electronics test that supplies a defined charge change at the receiver input, independent of the mechanical sensor. Compare the receiver with the characterized cable capacitances or controlled equivalent capacitors while keeping the injected charge and observation time fixed. Preserve the generator connection so a changed source termination does not change the delivered charge.

Then repeat the relevant sensor test with the same mechanical fixture and stimulus. Record cable type, routing, motion and grounding together with raw output waveforms. A voltage-mode amplitude change consistent with total capacitance is different from a charge-mode response that rings or settles slowly after adding capacitance. A simple gain adjustment should not hide instability, overload or a new noise source.

Specify the receiver topology before ordering the network

Provide the sensor source model, intended cable family, capacitance range, charge range and required observation band. Identify whether the resistor network supplies bias, feedback decay or subsequent voltage gain. Include the feedback capacitor and active-device model because the passive resistor drawing alone cannot establish charge sensitivity or cable independence.

For a custom thick-film signal-conditioning circuit, ChipSimple can review the defined resistor and interconnect functions by drawing. The sensor and analog owners establish mechanical sensitivity, receiver stability and the complete calibration. Treat a cable replacement as an electrical interface change where appropriate, and retain the topology-specific calculation so service teams know when a gain recalibration is meaningful and when the receiver architecture needs review.