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Transimpedance amplifier with parallel RC

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Consider this circuit.enter image description here

Since a constant current source is present, the output voltage will always be $$V_o=i_sR_f$$

However, you can also drive $$i_s=i_c+i_R=C\frac{dv_c}{dt}+v_c/R$$

Then you can say that the output voltage is a function of capacitor voltage and is an exponential function.

The two approaches seem contradictory. Which one is correct? Is the output voltage constant or not? Why?


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