vivkr
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Hi Sezi,
This is just a basic concept, but many people get confused about it. If you are familiar with basic Laplace transforms and bode plots, then this should be enough. Otherwise, try reading any book on signals or controls. There are several of these by Oppenheim, Kuo etc.
But no book will really discuss this matter. Just consider the following examples:
Imagine a linear system with N zeros and M poles
H(s) = (s-z1)(s-z2)....(s-zN)/(s-p1)(s-p2)...(s-pM)
Now, if the value of 's' were to be equal to any of the zi, then H(s)=0, and thus the zi values are called zeros of the system.
Conversely, for the case where 's' equals any of the pi values, the denominator is zero and H(s) tends to infinity.
Remember that in the discussion above, I allow 's' to assume some values.
If s = a + j*w, then all real-world frequencies can be found by setting a=0, and sweeping w.
If you now consider the 2 systems shown below:
Hreal(s) = (s-z1)/(s-p1), where z1 and p1 are real numbers, say z1=1, p1=-2
and Himag(s) =(s-z21)(s-z22)/(s-p2)(s-p22), where z21= 0+j1, z22=0-j1 , p21=0-j2, p22=0+j2.
Now try to calculate H(jw) for both the systems by setting s=0+jw. You will get the answer to your questions.
The respective pole and zero magnitudes are same for both cases, but the location is different. Hreal(s) has real poles and zeros, while Himag(s) has imaginary poles and zeros. This makes all the difference.
Regards Vivek
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