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Question & solution around the trans impedance opamp circuit

(a) The circuit of FIGURE 2 (attached) is known as a trans-impedance circuit used for the measurement of very small currents. Derive the relationship between the output voltage V and the input current I; i.e. if V = kI find k in terms of R1, R2 and Rf.

(b) Calculate the current I if Rf =10 mOhm (milli-Ohms), R1 = 90 kOhm, R2=10 kOhm, and V= 0.1 V.


Solution Preview

For the Ideal Op-Amp, the virtual earth theorem applies, meaning that the potential at both the + and - terminals is ~ 0 V. We can thus determine the potential at point A as that due to the potential divider formed by Rf parallel with R2 in turn in series with R1. So

R2 || Rf = R2*Rf/(R2 + Rf)

Hence by voltage divider ...

Solution Summary

A relationship is derived between the input current and the measured output voltage for the transimpedance Opsamp circuit in terms of the resistances R1, R2 and Rf. Values of R1 = 90 kOhm, R2 = 10 kOhm, Rf = 10 mOhm with Vout = 0.1V and the input current value is derived