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Homework Statement
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.
Homework Equations
CR dVR /dt + VR = CR dV/dt
G (iw) = iwCR/ (1 + iwCR)
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...