Bode Plot - Example

Example

A passive (unity pass band gain) lowpass RC filter, for instance has the following transfer function expressed in the frequency domain:

$H(jf) = \frac{1}{1+j2\pi f R C}.$

From the transfer function it can be determined that the cutoff frequency point f_c (in hertz) is at the frequency

$f_\mathrm{c} = {1 \over {2\pi RC}}$

or (equivalently) at

$\omega_\mathrm{c} = {1 \over {RC}}$ where is the angular cutoff frequency in radians per second.

The transfer function in terms of the angular frequencies becomes:

$H(j\omega) = {1 \over 1+j{\omega \over {{\omega_\mathrm{c}}}}}.$

The above equation is the normalized form of the transfer function. The Bode plot is shown in Figure 1(b) above, and construction of the straight-line approximation is discussed next.

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