Frequency Response
The AC circuits concepts presented so far suppose sinusoidal excitation at the constant frequency. It was mentioned that 2 or more signals can be combined by using phasors given that they have same frequency. The response of the linear AC circuit can be examined when excited with the AC signal of constant amplitude but varying frequency thus the term frequency response. These signals are common in the application areas like in a television, radio, and telephone and can be studied by using the frequency response analysis. Additionally filter circuits are introduced and their output response is observed constantly.
To understand the concept of frequency response, consider linear circuit with and output and input voltage signals can be represented by Vi and Vo respectively as shown in the Figure drawn below.
Figure: A two port linear network showing the input and output voltage signals.
If the input amplitude Vi is kept constant while its frequency ω (rad/s) is varied, then it is observed that amplitude and phase of the output signal Vo will change. But, the input and output frequencies remain unaltered. This means that Vo and φ become functions of frequency ω which are represented by Vo(ω) and φ(ω) with Vi being the reference signal. Ratio of the output to input voltage signal can be denoted by H(jω) which is a complex function and can be given mathematically as
here the voltage gain A = |H(jω)| and φ = argH(jω) are both the functions of frequency, ω.
Amplitude Response
The variations recorded in the amplitude gain, A w.r.t. ω is known as amplitude response of the network.
Phase Response
The variations observed in phase, φ of network with respect to ω is called as the phase response.
The amplitude and the phase outputs define frequency response together of a network. In the next chapter, filters are introduced and their response to an input signal with the3 varying frequency is observed. This will further assist to clarify the concepts of frequency response analysis.
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