Frequency Response

At low frequencies, the coupling and bypass capacitors can no longer be replaced by the short-circuit approximation because of the increase in reactance of these elements.

The larger capacitors of a system will have an important impact on the response of a system in the low-frequency range and can be ignored for the high-frequency region.

For the smaller capacitors that come into play due to the parasitic capacitances of the device or network, the frequency range of concern will be the higher frequencies.

The smaller capacitors of a system will have an important impact on the response of a system in the high-frequency range and can be ignored for the low-frequency region.

In the mid-frequency range the effect of the capacitive elements is largely ignored and the amplifier considered ideal and composed simply of resistive elements and controlled sources.

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  • Transfer Functions

    The transfer function \(\mathbf{H}(\omega)\) (also called the network function) is a useful analytical tool for finding the frequency response of a circuit. The frequency response of a circuit is the plot of the circuit’s transfer function \(\mathbf{H}(\omega)\) versus \(\omega\), with \(\omega\) varying from \(\omega = 0\) to \(\omega = \infty\).

    To obtain the transfer function \(\mathbf{H}(\omega)\), first obtain the frequency-domain equivalent of the circuit by replacing resistors, inductors, and capacitors with their impedances. Then use any circuit techniques to obtain the transfer function. The frequency response of the circuit can be obtained by plotting the magnitude and phase of the transfer function as the frequency varies.

  • Bode Plots

    The frequency range required in frequency response is often so wide that it is inconvenient to use a linear scale for the frequency axis. For these reason, it has become standard practice to plot the transfer function on a pair of semilogarithmic plots: The magnitude in decibels is plotted against the logarithm of the frequency; on a separate plot, the phase in degrees is plotted against the logarithm of the frequency.

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