Consider the transconductance amplifier shown in Figure P12.55. Assume the op-amp is ideal. (a) Derive the expression

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Consider the transconductance amplifier shown in Figure P12.55. Assume the op-amp is ideal.

(a) Derive the expression for the transconductance function \(A_{g f}=I_{o} / V_{i}\).

(b) If the circuit is designed such that \(R_{F} / R_{1}=\) \(R_{3} / R_{2}\), show that \(I_{o} / V_{i}=-1 / R_{2}\).

(c) Design the circuit such that \(I_{o} / V_{i}=-0.5 \mathrm{~mA} / \mathrm{V}\).

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