Transfer Functions

Abstract

The transfer function is the operator that takes input to output, in the frequency world! For example, when input is current and output is voltage, the transfer function is referred to as the impedance transfer function. Conversely when input is voltage and output is current then the transfer function is referred to as the admittance function, and so on. In deriving the transfer function it is implicit that the input signal is of the form e ^st; it is also implicit that the output would have the same time dependence, but is scaled by a frequency dependent constant such that output is H(s)e ^st; the H(s) is then the transfer function. There is an intimate relation between the transfer function and the impulse response; the former is the Fourier/Laplace transform of the latter! Sticking in the frequency domain we next demonstrate the transfer function generation on multitude of examples, ranging from the simple RC network to the parallel RLC one. For each case we plot both magnitude and phase of the transfer function, identify and rationalized the rate of change of the magnitude and the phase values, both in terms poles and zeroes; we also rationalize the DC and high-frequency limits.