Finding R for Negative Pole Frequency Transfer Function

[ElijahRockers]

Homework Statement

I have a transfer function:

H(jw) = RCjw_z / (1+RCjw_p)

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 w_p should be -1/RC, not 1/RC, right?

This means that the frequency is negative, and that doesn't really make sense...

 

[rude man]

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.)