Network Function of a Circuit

The frequency response of a circuit, which characterizes its behavior with varying signal frequency, can be analyzed using the transfer or network function.

This mathematical function defines the ratio of output to input. It is classified into four types: Voltage Gain, Current Gain, Transfer Impedance, and Transfer Admittance.

The circuit's behavior is analyzed in the Laplace domain using the complex variable 's'.

The transfer function of the circuit, in general, can be presented in zeros and poles.

Here, zeros are the roots of the numerator polynomial, and poles are the roots of the denominator polynomial. The transfer function value becomes infinite at the poles and zero at the zeros.

Consider an audio crossover circuit with two capacitors and an inductor that selects high-frequency signals from an amplifier to a tweeter.

The combination of the inductor, resistors, and capacitors provides the circuit impedance.

Applying Ohm's Law, the node voltage is proportional to the input voltage.

Similarly, the output voltage is proportional to the node voltage.

Finally, the transfer function represented by the output-to-input voltage ratio is obtained.