# Frequency response function

1. Dec 24, 2007

### discombobulated

1. The problem statement, all variables and given/known data
The relationship between the input voltage V(t) and the output voltage across a resistor VR(t) is:-

CR dVR /dt + VR = CR dV/dt

Circuit diagram of a capacitor and resistor with VR(t) in series across V(t)

1. Show that the frequency response function G(iw) (w= omega) is given by G (iw) = iwCR/ (1 + iwCR)

2.Sketch the locus of the frequency response function, G(iw) (w= omega) on the argand diagram.

2. Relevant equations

CR dVR /dt + VR = CR dV/dt

G (iw) = iwCR/ (1 + iwCR)

3. The attempt at a solution

1. I got this G (iw) = iwCR/ (1 + iwCR) by voltage division, from the circuit, but how could I do that from the given equation?

2. By taking the real and imaginary parts; G(iw) = x + iy

x = (wcr)2 /(1 + (wcr)2)
y = wcr/ ( 1 + (wcr)2)

G(iw) = (wcr)2 /(1 + (wcr)2) + iwcr/ ( 1 + (wcr)2)

I'm having trouble eliminating wcr now...

2. Dec 25, 2007

### unplebeian

I thought you'd apply Laplace transform and then subst s= jw to get the steady state solution. Then proceed to find the frequency response. But you arrived at the answer in one step, so why are you simplifying it further?

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