Finding R for Negative Pole Frequency Transfer Function

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SUMMARY

The discussion focuses on determining the resistance R in the transfer function H(jω) = RCjωz / (1 + RCjωp) with given values of capacitance C = 47nF and a desired pole frequency of 3.3kHz. The confusion arises from the interpretation of the pole frequency, which is correctly identified as a positive frequency of 20,735 rad/s, despite the negative representation in the complex σ-jω plane. The pole frequency indicates that the circuit's frequency response reaches a level within 3dB of the input at this frequency. The notation used in the transfer function should be clarified for accuracy.

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ElijahRockers
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Homework Statement



I have a transfer function:

H(jw) = RCjwz / (1+RCjwp)

and I'm being asked to find R, if C = 47nF and the desired pole frequency is at 3.3kHz.

what I'm confused about is that the pole frequency is supposed to make the denominator of the transfer function 0, but that would imply that wp should be -1/RC, not 1/RC, right?

This means that the frequency is negative, and that doesn't really make sense...
 
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The pole location on the complex σ-jω plane (the s plane) is at -2π(3.3 KHz) = -20,735 s-1 radian frequency. This does not mean that the frequency itself is negative; it's positive 20,735 rad/s.

In your present example the significance of the pole frequency 3.3 KHz is that the frequency response of your circuit increases with input frequency until at 3.3 KHz the output is within 3dB (0.707) of the input.

(The notation is not really correct. It should be H(jw) = jwRC/(!+jwRC). The p and z subscripts were apparently intended to indicate pole and zero but that is already obvious by the formula above.)
 

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