Methods and formulas for determining the integral nonlinearity of solid-state amplifiers

Two computer simulation techniques were developed for determining the closed-loop nonlinearity for nonperiodic signals in negative feedback amplifiers with memory. Both of these techniques use computer time efficiently. One of the two computer techniques linearizes the feedback loop which allows closed-loop nonlinearity to be evaluated analytically. This linearized model can be used to empirically understand closed-loop linearity performance. The other simulation technique is slightly more accurate. Both of the simulation techniques use first-order approximations and the accuracy of these models depends on the magnitude of the nonlinearity. The fractional value of the error in simulating the nonlinearity is generally less than the fractional value of the open-loop nonlinearity.

The computer simulation techniques were used to find the integral nonlinearity of several negative feedback amplifiers, each of which had an integrating element in the forward plant. This type of feedback amplifier closely approximates most operational amplifiers. The results of several simulations indicate that the closed-loop nonlinearity at the output of such feedback amplifiers is differentiated with respect to time. For spectroscopy type pulses, the nonlinearity is going through zero at approximately the time that the pulse peaks.