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# Conjugate match - RF Cafe Forums

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Below are all of the forum threads, including all the responses to the original posts.

T
Post subject: Conjugate match
Unread post Posted: Sun Jan 16, 2005 4:36 pm

Hello all,

What is the reason of matching a network to a conjugate match?

I know that the conjugate is the inverse of the phase for a given match.

When is there a need to do the matching to the conjugate value?

Thanks,

- T

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Len
Post subject: Conjugate match
Unread postPosted: Sun Jan 16, 2005 6:03 pm

Theoretically, a complex conjugate match results in maximum transfer of power from the source to the load.

Len

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Old Tele man
Post subject:
Unread postPosted: Mon Jan 17, 2005 12:15 am
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Joined: Sun Oct 17, 2004 1:07 am
Posts: 6
Location: Tucson, AZ
maximum power occurs because with a purely RESISTIVE load no energy is "stored" so as to create standing/reflected waves...

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Guest
Post subject:
Unread postPosted: Thu Jan 27, 2005 12:34 am

Why conjugate? If Xsource = -Xload then it is resonant and only the source and load resistances influence power transfer.

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Old Tele man
Post subject:
Unread postPosted: Thu Jan 27, 2005 11:14 pm
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Joined: Sun Oct 17, 2004 1:07 am
Posts: 6
Location: Tucson, AZ
conjugate implies "paired completion"...as: When XL = -XC, the two vectors "cancel" each other, leaving a purely resistive (R) load...and NO energy is "dissipated" in either the capacitive- or inductive-reactance, it ALL goes to the resistive (R) load.

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Devil sez: "...Yes, but it's a DRY heat!"

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Oleg Pozdeev
Post subject: Re: Conjugate match
Unread postPosted: Tue Feb 08, 2005 4:10 pm

Len wrote:
Theoretically, a complex conjugate match results in maximum transfer of power from the source to the load.

Len

I failed to find a thorough prove for conjugate match approach, the one published in school books seems a bit too artificial to me.
I’d suggest an exercise in math.
A passive 2-port is described by Y matrix and on left hand side is connected to source with impedance Zs, while on right hand side is connected to load with impedance Zl.
The power transfer function G(Zs,Zl) can be derived analytically, and takes max value when

dG(Zs,Zl)/dZs=0 and dG(Zs,Zl)/dZl=0 simultaneously.

One can take a step further to check whether the solution relates to max (not a min) value.
Under conjugate match condition there is no reflection between source and 2-port likewise between 2-port and load. The suggested approach gives similar result if and only if a 2-port is a purely reactive one.

Posted  11/12/2012
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