handbook of modern sensors

5.2 Amplifiers 163
Fig. 5.11. An equivalent circuit of a current-generating sensor.
(A)
(B)
Fig. 5.12. Noninverting current-to-voltage converter (A) and resistance multiplier (B).
be proportional to the magnitude of the current. Fig. 5.10B shows a basic current-tovoltage
converter where the current-generating sensor is connected to the inverting
input of an OPAM, which serves as a virtual ground; that is, voltage at the inverting
input is almost equal to that at the noninverting input, which is grounded. The sensor
operates at nearly zero voltage across its terminals and its current is represented by
the output voltage of the OPAM:
V out =−iR. (5.13)
A resistor, r ≪ R is often required for the circuit stability. At high frequencies, the
OPAM would operate near the open-loop gain, which may result in oscillations. This
is especially true when the sensor has reduced leakage resistance. The advantage of the
virtual ground is that the output signal does not depend on the sensor’s capacitance.
The circuit produces a voltage whose phase is shifted by 180 ◦ with respect to the
current. The noninverting circuit shown in Fig. 5.12A can convert and amplify the
signal; however, its speed response depends on both the sensor’s capacitance and the
converting resistor R 1 . Thus, the response to a step function in a time domain can be
described by
(
V out = iR b 1 + R )
2
(1 − e −t/rC ). (5.14)
R 1