What do you mean by poles and zeroes of a system?
Answers
Think of POLEs and ZEROs as INFINITY's and ZEROs.
*** At ZEROs, the system produces ZERO output ... At POLEs, the system produces INFINITE output ... Obviously, you cannot produce infinite voltage with any electronics :) So, it means that, the output will be unbounded (in theory) and SATURATED AT THE HIGHEST POSSIBLE VALUE (in practice).
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Now, let's talk about a specific case: The TRANSFER FUNCTION can be the IMPEDANCE of a filter, it will be zero (short circuit) at zeros, and INFINITY (open circuit) at poles ...
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EXAMPLE: Take an inductor and a capacitor, and connect them in parallel. Their impedances are Ls and 1/Cs ... So, the parallel inductor and capacitor will have an impedance of Ls/(1+s^2LC) ... Substitute s=j*2*PI*f. This means that, it has a ZERO at f=0 and a POLE at (2*PI*f)^2=LC (meaning, POLE at f=1/(2*PI*sqrt(LC)).
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It is clear what the ZERO means. It means that, if f=0 (i.e., NO oscillation activity is present or in other words, if you apply a DC voltage to the pins), since the capacitor is open circuit and the inductor is SHORT circuit, inductor will short circuit the capacitor, and the resulting impedance is ZERO. Since our transfer function is the impedance, we have ZERO impedance, and, thus, it corresponds to the ZERO of the transfer function.
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The POLE is a little less obvious. Let's assume that, C=1 microfarad, and L=1 microhenry. So, C=1E-6, L=1E-6. The POLE of the impedance is at f=159,236 Hz.
This means that, if you apply a sine wave of frequency 159 KHz to the pins of the parallel capacitor and resistor, since the impedance is INFINITY at that frequency, the oscillation will be forever sustained and never lost ...
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However, of course, these components will have a little bit of resistance which will make them non-ideal which will eventually kill the oscillation ...