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kollayliu Junior Member Offline Posts: 22	Minimum reflection and maximum power transfer Oct 10^th, 2011, 8:45am Should the minimum reflection and maximum power transfer occur at the same time? According to my understanding, if there is no reflection, the power transferred to the next stage is maximized. They should both occur at Z_L=Z_S*. Is that right? Thank you in advance for your help.
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rfcooltools.com Senior Member Offline Posts: 159	Re: Minimum reflection and maximum power transfer Reply #1 - Oct 10^th, 2011, 2:15pm kollayliu, Generally yes but the caveat is that the matching circuitry is not lossy otherwise the power delivered is maximized, but the power received is not . http://rfcooltools.com
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kollayliu

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Re: Minimum reflection and maximum power transfer
Reply #2 - Oct 10^th, 2011, 3:10pm

Thank you~

The confusion I still have is:
Reflection coefficient=(Z_L-Z_S)/(Z_L+Z_S). So the minimum reflection (reflection coefficient=0) occurs at Z_L=Z_S.
(Ref: http://en.wikipedia.org/wiki/Reflection_coefficient)
However, the maximum power occurs at Z_L=Z_S*

Therefore, how could we explain this.

Thank you!

rfcooltools.com wrote on Oct 10^th, 2011, 2:15pm:

kollayliu,

Generally yes but the caveat is that the matching circuitry is not lossy otherwise the power delivered is maximized, but the power received is not .

http://rfcooltools.com

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rfcooltools.com

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Re: Minimum reflection and maximum power transfer
Reply #3 - Oct 10^th, 2011, 10:44pm

kollayliu,

I think I see your confusion. The reflection coefficient being zero for maximum power delivered is really true if Zs is entirely real.
The confusion depends on how you define your plane of reference.
to the real source impedance or complex source impedance.
Consider the simple example.

Zs=R
Zl=R+jX
matching it with a series capacitor Zc=1/sc = -j/wc where 1/wc =X

Matching plus load is Zl+Zc = R+jX-jX= R
So reflection coefficient is 0/2R at the sources plane of reference.

Try again but shift the plane of reference
Zs= R+1/sc where 1/sc =-j/wc =-jX
Zl=R+jX

Reflection coefficient (Zs-Zl)/(Zs+Zl) =- jX/R why? that plane of reference observes a transitional complex impedance. But the power is still being maximally delivered.

hope that helps
http://rfcooltools.com

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kollayliu

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Re: Minimum reflection and maximum power transfer
Reply #4 - Oct 11^th, 2011, 2:41am

Thank you~

I think I get your point. This may also be explained like this.

There is power transfer between jXl and -jXl(jXc) (but the power will not be dissipated by them or be transferred to Rs and Rl). Therefore, if we seen from the port of Rs, there is no power reflected to Rs, the reflection coefficient=0. If we seen from the port of jXc, there will be some power reflected back to jXc, although it is not dissipated by Rs, the reflection coefficient is not equal to 0.

What is your opinion about this explanation?

Thank you

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cct_learner

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Re: Minimum reflection and maximum power transfer
Reply #5 - Oct 20^th, 2011, 12:37pm

The usual definition for reflection coefficient derives from transmission line theory and tells you about relationship between incident and reflected voltage/current waves. For real reference impedance, maximum power transfer occurs if it is equal to 0. However, if reference impedance is complex, this is not true. If fact if the magnitude of reflection coefficient can be greater than 1 according to the definition Gamma=(Z-Zo)/(Z+Zo) where Zo is complex. There is another S-parameter called generalized S-parameters that uses power waves for ai and bi. For this kind of S-parameters, Gamma=(Z-Zo*)/(Z+Zo) and will gives the inituition that if Gamma = 0, maximum power transfer occurs. But this will be different from the Gamma as defined on a transmission line.

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weber8722 Community Member Offline Posts: 95	Re: Minimum reflection and maximum power transfer Reply #6 - Nov 17^th, 2011, 8:29am Also look up that all this is usually for small-signals!! For PA the large-signal s-parameters differ from the usual small-signal ones. Also look up that noise match might be different from power match.
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