Software Makes Transfer Functions

S mall-signal analysis of switching dc-dc converters determines their specific transfer functions, for example, for stability analysis or design of a proper input filter. Transfer functions of interest for switching dc-dc converters are input impedance , output impedance, duty cycle (or control voltage) to output voltage, and input voltage to output voltage. Two pieces of literature about accomplishing small-signal analysis of switching dc-dc converters suggests two fundamental methods: 1. The state-space averaging method, by Dr. Middlebrook et al, employs algebraic manipulation of a set of state-space equations to derive average model equations of a switching converter topology. Linearizing the averaged model at a dc operating point derives the desired transfer function. With this method, the complete circuit must be averaged and linearized every time the topology is changed. 2. The method of PWM switch model, by Dr. Vorperian, averages and linearizes the dc-dc converter's switch pair, which is its only nonlinear portion, and invariantly uses this model in different topologies. The main advantages of a PWM switch approach are: l The PWM switch model is already averaged and linearized, so no averaging and linearization is necessary, which differs from the state-space averaging method. l As a circuit-oriented approach, it is very convenient for use with numerical or symbolic circuit-analysis software. l The PWM switch model's properties are the same for a given conduction and control mode, so they can be used invariantly from one topology to another. Because of these advantages, particularly that it is circuit oriented, the PWM switch model is best suited for obtaining symbolic and numeric small-signal equations of switching dc-dc converters. The small-signal model of a switching converter with Combining PWM switch models with linear circuit-analysis software and math software creates a fully computer-based approach to obtaining and analyzing the transfer functions of dc-dc converters.