What is a circuit Transfer Function?

The Transfer Function of a circuit is defined as the ratio of the output signal to the input signal in the frequency domain, and it applies only to linear time-invariant systems. It is a key descriptor of a circuit, and for a complex circuit the overall transfer function can be relatively easily determined from the transfer functions of its sub circuits. Transfer functions are typically denoted with H(s).

Transfer functions are used in the design of electronic systems such as filters, power supplies, and other control systems. Transfer functions are used when we want to analyze how the output of a circuit changes depending on the input. To analyze a circuit, we want to know how its output amplitude and phase compare with the input over frequency. To do this we use the Laplace transform.

Let's formulate how to find the transfer function for a second order RLC circuit shown in figure 1.

Figure 1. Second Order RLC Circuit

We use LTSpice to graph the Gain and Phase of the second order RLC circuit.

Figure 2. Gain and Phase for a Second Order RLC Circuit.

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Model Transfer Functions by Applying the Laplace Transform in LTspice.

The end.