ABSTRACT
Laplace Transfer Functions. We have defined and used since early in the book the concepts of operational and sinusoidal transfer functions. Suppose we Laplacetransform a set of simultaneous differential equations, take all the initial conditions to be zero, and then reduce the set down to single algebraic equations in single unknowns. If we now form the ratio of any output quantity to any input quantity, this ratio will be a function of s and is defined as the Laplace transfer function relating that pair of output/input variables. If we apply this idea to Eqs. (6-35) and (6-36) we see that the pair of equations looks exactly like Eqs. (6-15), except that D's are replaced by s's and the variables are written uppercase rather than lowercase. When we use determinants or other algebraic means to reduce the set of equations to single equations, we will get results like Eqs. (6-18) and (6-19), except we again have s's instead D's.
