The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl Design >> RF Design >> Minimum reflection and maximum power transfer https://designers-guide.org/forum/YaBB.pl?num=1318261522 Message started by kollayliu on Oct 10th, 2011, 8:45am |
Title: Minimum reflection and maximum power transfer Post by kollayliu on Oct 10th, 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 ZL=ZS*. Is that right? Thank you in advance for your help. |
Title: Re: Minimum reflection and maximum power transfer Post by rfcooltools.com on Oct 10th, 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 |
Title: Re: Minimum reflection and maximum power transfer Post by kollayliu on Oct 10th, 2011, 3:10pm Thank you~ The confusion I still have is: Reflection coefficient=(ZL-ZS)/(ZL+ZS). So the minimum reflection (reflection coefficient=0) occurs at ZL=ZS. (Ref: http://en.wikipedia.org/wiki/Reflection_coefficient) However, the maximum power occurs at ZL=ZS* Therefore, how could we explain this. Thank you! rfcooltools.com wrote on Oct 10th, 2011, 2:15pm:
|
Title: Re: Minimum reflection and maximum power transfer Post by rfcooltools.com on Oct 10th, 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 |
Title: Re: Minimum reflection and maximum power transfer Post by kollayliu on Oct 11th, 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 |
Title: Re: Minimum reflection and maximum power transfer Post by cct_learner on Oct 20th, 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. |
Title: Re: Minimum reflection and maximum power transfer Post by weber8722 on Nov 17th, 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. ::) |
The Designer's Guide Community Forum » Powered by YaBB 2.2.2! YaBB © 2000-2008. All Rights Reserved. |