An Analysis of Certain Errors in Electronic Differential Analyzers I-Bandwidth Limitations

When a differential analyzer or analog computer is set up to solve a given equation, certain errors are introduced into the solution because the components of the computer are not perfect. Stated another way, the computer produces the solution to an equation, called the "machine equation," which differs from the given equation. In this paper the computer imperfections considered are 1) operational amplifier frequency response, 2) capacitor leakage resistance, and 3) stray capacitance in summing and integrating amplifier circuits. It is shown that when the given equation is a system of one or more linear differential equations with constant coefficients, the machine equation can be expressed approximately as an equation of the same degree as the given equation and with constant coefficients which are functions of the coefficients of the given equation and of the computer imperfections.