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Quick Impedance Mag Q

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strokebow

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Please, some one refresh my memory.

I want the magnitude and the phase of the input impedance of my circuit.

I have the input impedance, Zin, as:

Zin = (Rs + Rd) * ((1 + s*a*t) / 1 + s*t)

Simply a resistor (Rs) connected to a parallel RC combination (Rd//Cd)
[Also note: s = jω; t = Rd*Cd; a = Rs/(Rs + Rd)]

I want to find |Zin(jω)| and Φ(jω). How do I go about doing this???
 
Please, some one refresh my memory.

I want the magnitude and the phase of the input impedance of my circuit.

I have the input impedance, Zin, as:

Zin = (Rs + Rd) * ((1 + s*a*t) / 1 + s*t)

Simply a resistor (Rs) connected to a parallel RC combination (Rd//Cd)
[Also note: s = jω; t = Rd*Cd; a = Rs/(Rs + Rd)]

I want to find |Zin(jω)| and Φ(jω). How do I go about doing this???

Let Z be the expression Zin with s replaced by jω

Let Z* be the expression Zin with s replaced by -jω; Z* is the conjugate of Z.

Then |Zin(jω)| is SQRT((Z)(Z*))

Multiply the numerator of Z by the conjugate of the denominator of Z. Call this expression X. Let Im() mean Imaginary part () and Re mean Real part ().

Then Φ(jω) = Arctan(Im(X)/Re(X))
 
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