SaM - Charge Amplifier

Remeber:

This is the circuit for a “charge amplifier”:

• ==An operational amplifier with capacitive feedback==.

• If we ignore $R_f$:$V_{out}=-\frac{Q}{C_f}$
• If we consider $R_f$:$V_{out}=-\frac{Q}{C_f}\cdot e^{-\frac{t}{\tau }}$Where: $\tau =R_f\cdot C_f$.
• Source: Wikipedia

Take for example the output of a piezoelectric ultrasonic transducer, it’s a charge:$Q_p=Kdx$Described in “piezoelectric actuators” and “ultrasonic tranducers”. This charge is then converted to a voltage. To aid to this conversion, some special kind of amplifiers, called charge amplifiers where developed: ==“A charge amplifier is an electronic current integrator, that produces a voltage output proportional to the integrated value of the input current”==. This is effectevely a measurement of the electrical input charge:$V_{out}=-\frac{q_{in}}{C_f}=-\frac{Kdx}{C_f}$Source: Youtube.

Advantages of a charge amplifier:

• The output voltage is proportional to the charge produced by the piezoelectric transducer.
• The amount of charge present is not affected by the cable capacitance.
• The sensititivity as well as the time constant are independent of the capacitance of the crystal, and aslo that of the connecting cables.

Disadvantages of a charge amplifier:

• The signal to noise ratio (SNR) tends to be small.
• The natural frequency of the transducer is reduced due to loss of stiffness caused by what amounts to a short circuit across the crystall.

Source: Youtube.

A charge amplifier is often used with a piezoelectric sensor. Here’s a simple scheme: (Source: Wikipedia)

• The sensor is a piezoelectric one
• $C_C$ is the “cable capacitance”.
• $C_{\text{inp}}$ is the “inpedance capacitance”, we described it as $Z_{eq}$ for the AT-cut quartz.
• $C_f$ and $R_f$ are the “feedback impedance”.
• $q_{in}$ and $q_f$ input charge and feedback charge, also: $q_f=-q_{in}$.
• The output formula is:$V_{out}=-\frac{q_{in}}{C_f}$Where: $q_{in}$ depends on: the sensor, and the capacitances $C_C$ and $C_{inp}$.
• The feedback resistor $R_f$ discharges the capacitor.
  Without  $R_f$  the DC gain would be very high so that even the tiny DC input offset current of the operational amplifier would appear highly amplified at the output.
• $R_f$ and  $C_f$ set the lower frequency limit of the charge amplifier:$f_{\min }=\frac{1}{2\pi R_f{C}_f}$

Here’s another version of the same circuit: (Source: Youtube)

• This version is more similar to how we discribed the AT-cut quartz, and the electric circuit for a piezoelectric accelerometer.

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