buddypoor
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Hi raj,
At first, I completely agree with Ricky's explanation. Secondly, there may be some confusion using the term "zero". Therefore, I'll try to give my explanation:
Taking your simple example H(s)=(1+sRC)/D(s). This is a transfer function with the complex variable s. I have added a time constant RC due to consistency in units. At s=-1/RC there is a zero, which means that the transfer function output is zero at this "point" (it is not a frequency!). It is simply the negative real part of s. This property of H(s) cannot be measured (it is just a mathematical fiction) because one cannot produce a "frequency" which is a negative constant. Referring to measurements, we can, however,transfer H(s) into a frequency response A(jw) by simply replacing s by jw. And we can ask ourself: What can be measured at a "frequency" that equals the above given "zero": w=1/RC ? As a result, we can compute the magnitude (and phase) for A(jw) and we see that at this frequency the BODE diagram exhibits a change in the slope. Thus, we can conclude that H(s) exhibits a zero at a certain value for the variable s (in our case negative-real). If we, however, interpret this variable as a frequency we see that the frequency response (Bode diagram) at this point changes the slope. The point of confusion is that in both cases we speak of a "zero frequency". Unfortunately, Razavi is not consistent because on page 176 this zero is called "wz" and on page 177 he uses "sz". Thus, on page 176 he implicitely referres to A(jw) and on page 177 he referres to H(s). A similar case exists, of course, for poles. We speak of pole frequencies, thereby knowing that the magnitude of A(jw) goes not up to infinity. This can be observed only in the 3D-plot for H(s). ________________ Regards
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