A question in smith chart with s11 parameter

[polirules9]

Hello everybody
I need to answer this question :
After simulate with PUFF software the following circuit:

It's observed a spiral to represent the parameter s11 with the frequency in the Smith chart. Is the module of reflection coefficient constant with frequency? Why this should be done ?

Thanks you.

 

[tyassin]

Hi,

If the question is whether the magnitude of the reflection(S11) is constant with frequency, the answer is no.

I do not understand your last question: "Why this should be done?"

 

[polirules9]

Hi,

If the question is whether the magnitude of the reflection(S11) is constant with frequency, the answer is no.

I do not understand your last question: "Why this should be done?"

Thanks you tyassin. Ok, the magnitude of the reflection (s11) isn't constant with frequency.
I think to be constant, should be a circle. Am I right?
The second question is:

According to the circuit , why the magnitude of the reflection (s11) is not constant with frequency ?

 

[FvM]

The first circuit (transmission line + capacitor) has no losses unless it's a lossy transmission line which should be indicated in the parameters. A lossless one port circuit should always have |S11| = 1, in so far the S11 (spiral) graph doesn't fit.

 

[albbg]

FvM is right. I think the textbook omitted the circuit is terminated on 50 ohm (the spiral is going toward the Smith chart center and is stated Zo=50 ohm).
Under this assumption, the magnitude is not constant because at a frequency --> very low with respect to C and length of the transmission line, the transmission line can be considered just as a wire, while the capacitor as an open circuit so the impedance seen by the port1 is equal to the termination, that is 50 Ohm. Increasing the frequency the transmission line will behave as a transmission line, transforming the output impedance (taht is C in parallel with 50 ohm) into the impedance seen by the port1 using the transmission line equation (lossless in our case):

Zin = Zo*[ZL + jZo*tan(beta*length)]/[Zo + jZL*tan(beta*length)]

Where, in our case Zo = 50ohm, ZL =50//C
beta=2*pi/wavelength