1st order RC filters and pole positions?

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Joined Feb 14, 2011
I noticed that for an RC filter, the closer the pole is to the jω axis, the smaller the cutoff frequency is, and conversely the further the pole is from the jω axis, a larger cutoff frequency is produced. However, if you take a look at a 3d model of poles/zeros with the σ, jω, and dB axis combined(with the jω axis highlighted to show the frequency response), then a pole close to the jω axis would leave you to believe that a peaking response could occur(which can only happen in higher order filters with complex poles). My question is, how can we show that a real pole with a large value of σ would relate to a large cutoff frequency along the jω axis(and vice versa) yet still retain the characteristic flat lowpass response?

I found the above image from an app note so if someone knows a free program that can provide this type of graph when given a transfer function, I'd greatly appreciate it :)
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Joined Jul 3, 2008
The response does peak, but it peaks at a frequency of zero. This is what you would expect for a low pass filter. As far as, how fast it rolls off? You can see that the closer the pole is to the origin, the more peaky the response is and the faster the rolloff is. This equates to a lower cutoff frequency.

Note that your plot shows frequency on a linear scale, while you may be used to seeing Bode plots on a logarithmic scale.

If you are a student, I recommend the student version of Matlab. There are free Matlab clones around, if you can't swing the $100. Keep in mind that $100 is buying you over $5000 worth of software, including full unlimited Matlab, Simulink (with 1000 block limit), control system toolbox, signal processing toolbox, symbolic math toolbox etc.
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