Poles and Zero's

[Arouse1973]

Hi Guys
Does anyone know how to work out the position of the poles and zeros in the s plane of a simple LCR filter. I would like to see a step by step example on how they are derived. The internet does not explain the steps good enough for me. Here is what I understand so far. the transfer function is Vo/Vin =RCs/LCs^2+RCs+1 if this is correct and I think s is sigma+jw and sigma being 1/2RC. How do I use this and break it down to find the complex conjugates of the circuit to plot them on the s plane diagram. Can you also use this to work out the voltage across each component instead of going back into the time domain if so can anyone show me a worked example. I might have this all wrong can someone help.

R = 10R
L = 10mH
C = 1uF
Freq = 1000Hz

Thanks
Adam

 

[Arouse1973]

Oh well, 47 views and no replies, that's a shame

 

[(*steve*)]

We're waiting for Laplace to explain it

 

[Laplace]

Regrettably, the waiting will continue. My preference is to study topics that may prove useful, while pole-zero diagrams seem to mainly be of academic interest, i.e., useful to answer homework problems but little else. Pole-zero diagrams may have once been more useful in the old times to sketch the performance of a transfer function but now it is simpler to get an accurate plot using symbolic algebra software on a personal computer. Did I mention that I got my Bachelor of Engineering degree using a Keuffel & Esser slide rule? Then went to graduate school using an HP-35 calculator. Then worked 40 years as a systems engineer for the Department of Defense. By the time I got my HP-15C programmable calculator with complex number mode making it fairly easy to plot a transfer function, poles and zeroes receded to merely an academic interest.

 

[Arouse1973]

Regrettably, the waiting will continue. My preference is to study topics that may prove useful, while pole-zero diagrams seem to mainly be of academic interest, i.e., useful to answer homework problems but little else. Pole-zero diagrams may have once been more useful in the old times to sketch the performance of a transfer function but now it is simpler to get an accurate plot using symbolic algebra software on a personal computer. Did I mention that I got my Bachelor of Engineering degree using a Keuffel & Esser slide rule? Then went to graduate school using an HP-35 calculator. Then worked 40 years as a systems engineer for the Department of Defense. By the time I got my HP-15C programmable calculator with complex number mode making it fairly easy to plot a transfer function, poles and zeroes receded to merely an academic interest.

Oh dear Laplace.
That's disappointing, Poles and zeros are extensively mentioned in filter design, even up to date text still refer to them and as a visual aid in filter performance. A VNA has a pole zero plot output even the new ones.
But thanks for looking at this anyway. I'll carry on and never you know I might be the one educating people for a change, but I doubt it
Thanks
Guys
Adam