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Scaling (example #1)

Scale the low-pass filter so that the corner frequency increases from 1 rad/sec to 200 rad/sec using a 1 microfarad capacitor.

low-pass filter scaling

We are given the following information: ω=200rads,ω=1rads Since both the magnitude (impedance) and the frequency response of the circuit will be modified, we proceed to use equations #6 to calculate the frequency factor: ω=Kfω

Kf=ωω=2001=200

Additionally, we are given the following information: C=1μF,C=1F We again use equations #6 to calculate the magnitude factor: C=(1KmKf)C Km=(1Kf)(CC) =(1200)(11×106)

Km=5000

We now use equations #6 to determine the remaining post-scaled values to the two resistors: R1=KmR1 =5000(1)

R1=5kΩ

R2=KmR2 =5000(2)

R2=10kΩ

The newly scaled circuit will look like the following:

low-pass filter scaling

The resulting corner frequency would be 200 rad\s. Converting to hertz would give us: ωo=200rads=2πfo

fo=2002π=31.8Hz