The forward scattering parameters of an amplifier based on a dc superconducting quantum interference device are directly measured at 4.2K as functions of the applied magnetic flux. These parameters are equivalent to the real and imaginary components of the input impedance and forward gain of the amplifier. The results can be described using an equivalent circuit model of the fundamental resonance of the microstrip resonator which forms the input of the amplifier. The circuit model is used to determine the series capacitance required for critical coupling of the microstrip to the input circuit.
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Kinion et al. (2008) studied this question.
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