9.1:
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.
9.1:
Network Function of a Circuit
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
Here, zeros are roots of the numerator polynomial, and poles are roots of the denominator polynomial.
As an illustrative example, consider an audio crossover circuit that separates high-frequency signals for a tweeter from an amplifier. The analysis of this circuit concerning signal frequency occurs in the Laplace domain by employing 's' as a complex variable.
Utilizing Ohm's Law, the input voltage relates to the node voltage; subsequently, the output voltage is expressed in terms of the input voltage. This analysis derives the transfer function, which represents the output-to-input voltage ratio.
Frequency response analysis boasts extensive applications, particularly in communication and control systems. Electric filters, utilized in various applications such as radio and television technologies, rely on this analysis to allow the desired signals to pass while suppressing unwanted ones. A comprehensive understanding of transfer functions and frequency responses is pivotal in circuit design and engineering.
As a fundamental tool, the transfer function simplifies the assessment of circuit behavior across diverse frequencies in engineering and electronics.