Smith Chart and Maximum Power Transfer

[Bizkit]

Homework Statement

You can find the problem http://whites.sdsmt.edu/classes/ee382/homework/382Homework9.pdf" . It is problem 9.2.

Homework Equations

Z_in = Z_s* (maximum power)

The Attempt at a Solution

I've already figured out the first part of this problem. I plotted the normalized impedances at both the input and load (using the fact that Z_in = Z_s*), then found the distance between them (going counterclockwise) to be about .3482 wavelengths.

I'm a little confused on the next part. The way I see it is that you can't always choose such a length for maximum power transfer to any load impedance because not all normalized load impedances lie on the same constant VSWR circle as the normalized input impedance. Is this correct?

For the last part, I know that you can always choose such a length to get a purely real input impedance. As long as the normalized input impedance is located on the horizontal axis, it will be purely real. I am a little confused, however, as to how it will affect the maximum power transfer. I believe that if the input impedance is purely real, the amount of power delivered to the load will either be the lowest or highest amount possible. Is this correct?

 

[mark726]

Hello, thank you for your question. I have examined the problem and your approach seems correct so far. You are correct in your understanding that not all load impedances will lie on the same constant VSWR circle as the input impedance. This means that for some load impedances, the maximum power transfer length will not be achievable. However, for those load impedances that do lie on the same constant VSWR circle, the maximum power transfer length can be chosen for optimal power transfer.

Regarding your question about the effect of a purely real input impedance on maximum power transfer, you are correct in your understanding that it will either result in the lowest or highest amount of power delivered to the load. This is because a purely real input impedance indicates a match between the source and load, resulting in either complete absorption or complete reflection of the power.

I hope this helps clarify any confusion you may have had. Keep up the good work on the problem!