The poles are sometimes called the cutoff frequencies of the network.
For simpler expressions, we substitute s for frequency: j w = s.īecause the quantities being plotted are plotted on a logarithmic scale, the curves belonging to the different terms of the product can be added. Here’s a summary of the important principles of Bode plots, and the rules for sketching them. The 3 dB point on a Bode plot is special, representing the frequency at which the amplitude has increased from a constant value by 3 dB. The –3 dB point implies that A is 1/1.41 = 0.7.Ī typical transfer function looks like this: Converting from A in dB to A in volts/volt, we solve 3 dB = 20 log10 A and obtain log10 A = 3/20 and hence. Now we will see how transfer functions like the ones above can be quickly sketched (transfer function gain in dB versus frequency in Hz). Because the vertical axis is represented in dB, it is a logarithmic scale. Remembering that the product of terms in the transfer function will be seen as the sum of terms in the logarithmic domain, we will see how to sketch the individual terms separately and then add them graphically to obtain the final result. The curve of the absolute value of a first order term s has a 20 dB/decade slope crossing the horizontal axis at w = 1. The phase of this term is 90 ° at any frequency. The curve of K* s also has a 20 dB/decade slope but it crosses the axis at w = 1/K i.e., where the absolute value of the product ½ K* s ½ = 1. Similarly, the absolute value of the term K/ s has a -20 dB/decade slope the phase is -90 ° at any frequency but it crosses the w axis at w = K, where the absolute value of the fraction The next first order term (in the second example), s -1 = 1/s, is similar: its absolute value has a -20 dB/decade slope its phase is -90 ° at any frequency and it crosses the w -axis at w = 1. The next first order term to sketch is 1+sT. The amplitude plot is a horizontal line until w 1 = 1/T, after which it slopes upward at 20 dB/decade. The phase equals zero at small frequencies, 90 ° at high frequencies and 45 ° at w 1 = 1/T. A good approximation for phase is that it is zero until 0.1* w 1 = 0.1/T and is nearly 90 ° above 10* w 1 = 10/T.
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