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Prove that op-amp can be used as current to voltage converter.
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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 $I_S$ = $I_F$

But,

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

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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