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Two port feedback analysis of shunt-shunt amplifier with unity feedback

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To consider the effect of loading in a shunt-shunt amplifier that is being analyzed with two port analysis, we short the feedback network at the input/output to calculate loading at the amplifier output/input.

Also, inverting amplifier topologies are often analyzed as shunt-shunt configurations after a Norton transformation is applied at the input.

Consider the following switched-capacitor (SC) integrator below. The input is sampled onto C1 during one clock phase (even-numbered switches closed) and integrated onto the feedback capacitor during the second clock phase (odd-numbered switches closed).

How would I model the open loop amplifier with feedback network loading during the sampling phase? If SW2 is closed, and I short the feedback network at the amplifier input to consider loading at the amplifier output, then the amplifier output is shorted. This would predict 0 loop gain for the circuit in the sampling phase, which I do not think is true.

schematic

simulate this circuit– Schematic created using CircuitLab


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