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Intuitively, what makes a resistor/capacitor combination become a pole or zero in around an amplifier system?

My intuition always says that a zero is formed when there is a direct path through a capacitor from input to output. And pole is formed when output has a load that causes output response to diminish in high frequency. However, I feel this is just experience from arbitrary examples.

Is there a more definitive intuition without the mathematics of which is based on calculating transfer function to be 0 at zero and \$\infty\$ at pole to get their locations?

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  • \$\begingroup\$ Poles and zeros are mathematical constructs so, to ask for a non-mathematical definition seems to miss the point. \$\endgroup\$
    – Andy aka
    Dec 26, 2023 at 16:35
  • \$\begingroup\$ scc28, probably start with this answer here on this site and then consider buying and reading Christophe P. Basso's "Linear Circuit Transfer Functions: An Introduction to Fast Analytical Techniques" book. He discusses the work of Dr. Middlebrook (now deceased.) I used to subscribe and read Dr. Middlebrook's regular emails. His wife did what she could after he died for those who followed his writing. But Dr. Basso has done the best of any to keep his flame alive. And it's probably the better answer you can get here. Start there. \$\endgroup\$ Dec 27, 2023 at 7:31

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RC low pass transfer function is 1/(1+sT) and there is a pole at 1/T radians/sec where the magnitude frequency response is half way through its transition from a slope of 0 dB/decade to -20 dB/decade and the phase lag is -45 degrees.

RC high pass filter transfer function is sT/(1+sT) so there is a zero at 0 radians/sec where the magnitude frequency response is half way through its transition from a slope of 0 dB/decade to +20 dB/decade and the phase lead is +45 degrees. But there is also a pole at 1/T where the magnitude frequency response is half way through its transition from +20 dB/decade to 0 dB/decade and the phase lead is also +45 degrees.

So in the case of the RC high pass filter, the increase in the magnitude response gradient and phase lead caused by the low frequency zero is cancelled out by the reduction in the magnitude response gradient and phase lag of the higher frequency pole.

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