Prove that op-amp can be used as current to voltage converter.
1 Answer

Photocell, photodiode and photovoltaic cell give an output current that is proportional to an incident radiant energy or light. The current through these devices can be converted to voltage using a current to voltage converter and thereby the amount of light or radiant energy incident of the photo device can be measured.

Figure 1 shows an op-amp used as I to V converter. Since the (-) input terminal is at virtual ground, no current flows through $R_S$ and current $i_S$ flows through the feedback resistor $R_f$.

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Apply KCL at inverting terminal, $$I_S = I_{BI} + I_F$$ Input impedance of op-amp is very large $I_{B1}$ ≈ 0 , hence $I_S$ = $I_F$


$$I_F = \frac{V_1 - V_0}{R_F} = I_S.......(1)$$

For non saturated output $V_O$ = $AV_{id}$, i.e $A = V_O / AV_{id}$

A is large $V_{id}$ ≈ 0 , $V_1- V_2$ = 0, i.e $V_1= V_2$

$V_2$ is at zero potential $V_1$ is also at zero potential. Hence Equation (1) becomes,

$$\frac{-V_0}{R_F} = I_S$$ $$\boxed{V_0 = -I_SR_F}$$

From the above expression it is included that output voltage can vary by varying input current hence the circuit is known as transresistance amplifier.

The resistor $R_F$ is sometimes shunted with a capacitor $C_F$ to reduce high frequency noise and the possibility of oscillations.

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