Piezoelectric measurement chain: A force transducer has charge sensitivity 20 pC/N. The combined transducer + charge amplifier gain is 50 mV/N. Determine the amplifier gain in mV/pC.

Introduction / Context:
Piezoelectric force sensors generate electric charge proportional to applied force. A charge amplifier converts this charge to a voltage with a known charge-to-voltage gain. Understanding how to relate sensor charge sensitivity and amplifier gain to the overall volts-per-newton factor is central to instrument calibration.

Given Data / Assumptions:

• Charge sensitivity of transducer: 20 pC/N.
• Total chain gain: 50 mV/N at the output.
• Charge amplifier is linear, so V_out = (gain) * Q.

Concept / Approach:

The overall volts-per-newton response is the product of the sensor’s charge-per-newton and the amplifier’s volts-per-coulomb. Therefore, gain_amp (mV/pC) = (overall mV/N) / (pC/N). This simple ratio directly yields the charge amplifier's gain independent of force magnitude used for calibration.

Step-by-Step Solution:

Verification / Alternative check:

Check units: (mV/N) divided by (pC/N) → mV/pC, correct. Try a sample: 10 N produces Q = 200 pC; with G = 2.5 mV/pC, V_out = 200 * 2.5 = 500 mV = 0.5 V; also 10 N * 50 mV/N = 0.5 V—consistent.

Why Other Options Are Wrong:

• 1, 1.5, 4, 0.25 mV/pC do not satisfy the product required to achieve 50 mV/N with 20 pC/N charge sensitivity.

Common Pitfalls:

• Multiplying instead of dividing by the charge sensitivity.
• Missing unit consistency when moving between pC, mV, and N.

Final Answer:

2.5 mV/pC