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The theory of the parametric amplifier has been reformulated to permit the prediction of noise temperature and pump power in terms of the physical parameters of the nonlinear element and circuit. The results of this analysis are supported by careful experiments at S-band using a gold-bonded germanium semiconductor diode. They can be summarized as follows. 1) Performance of a parametric amplifier using semiconductor diodes with respect to noise temperature and pump power can be accurately predicted, once the diode and circuit parameters have been measured. 2) It is shown that the ultimate limitation on noise temperature depends simply on the product of the diode cutoff frequency and the normalized capacitance swing. 3) The derived figure of merit for the diode can serve as a basis for optimum design of the semiconductor parameters.