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A genetic circuit amplifier is designed using an electronic inverting amplifier as a starting point. Two simulation methods are used to analyze circuit performance in terms of the impulse and sinusoidal responses of electrical engineering. The first method is an exact stochastic simulation based on a kinetic model of the circuit. The second method incorporates statistical thermodynamic analysis. The simulations are used to analyze amplifier performance in response to classical systems analysis stimuli: impulses and sine waves. Degradation reactions, analogous to leakage off circuit capacitors, are found to have considerable impact on circuit response. For the nonlinear gain element used in our exemplary circuit, the selection of bias level based on controlling protein degradation rate plays an important role in determining circuit behavior. A parameter without electronic analog, the circuit plasmid copy number, is crucial to circuit operation. These simulations suggest that the copy number must be less than 50 for desired circuit operation.