Approximate Bode Plots
The advantage of using Bode plots is the easiness through which they can be sketched by using a simple graphical technique which is very useful for complicated transfer functions. In this method, numerator and denominator polynomials are factorised which are then treated individually. Asymptotic plots are drawn for each 1st and second order factors by the following some simple rules. The resultant Bode plot can be obtained by simply adding all individual plots. This is another rationale of employing logarithmic units as log(AB) = logA + logB.
Consider the voltage transfer function of the electric circuit in factored form as follows
here K is a constant gain and T1, T2 and T3 are the 3 time constants. The factor in numerator is a zero whereas the 2 denominator factors are called as poles. The term jω in denominator is a 2nd order integrator.
Let A1∠φ1,A2∠φ2 and A3∠φ3 represents the magnitudes and phases of single 0 and 2 poles of H(jω) respectively. Then the combined amplitude and phase can be written in the polar form as
Therefore the individual plots can be simply added to find resultant amplitude response. In the following, some rules are outlined to draw the approximate or asymptotic Bode amplitude and phase plots.
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