Reflection Coefficient when conjugate matching

[BigBoss]

Microwave Transistor Amplifiers-Analysis and Design.Guillermo Gonzalez
The best book about fundamental of Microwave Engineering ever I have seen, no doubt..
In section 1.7 , the author said ( briefly)" In case of there is no transmission line so characteristic impedance is not defined, travelling voltage and current waves are not applicable( valid) anymore.Instead "Power Waves are used" and added an example for an example of conjugate matching case.
Gamma=Zload-conj(Zsource)/(Zload+Zsource)

So, the definition is coming from existence or nonexistence of a Transmission Line so briefly there is nothing to discuss, it's just terminology presumption.

 

[pancho_hideboo]

Microwave Transistor Amplifiers-Analysis and Design.Guillermo Gonzalez
The best book about fundamental of Microwave Engineering ever I have seen,
no doubt..

This is very famous book.
Keysight recommends this book since MDS(Microwave Design System) Days.
See https://www.edaboard.com/attachment.php?attachmentid=147829&d=1531391256

But this is a text book for specialist not standard.

On the other hand, "Microwave Engineering" Written by David M. Pozar, is a major standard text book which are used world wide.
https://www.amazon.com/Microwave-Engineering-David-M-Pozar/dp/0470631554
**broken link removed**

"Power Wave Formulation" is described even in a major standard text book.

 

[BigBoss]

This is very famous book.
Keysight recommends this book since MDS(Microwave Design System) Days.
See https://www.edaboard.com/attachment.php?attachmentid=147829&d=1531391256
But this is a text book for specialist not standard.

I don't think so..
This is a very well explained , deeply analyzing,comprehensively expressing book.Every Microwave Engineer must have this book at any level, any background.

 

[pancho_hideboo]

Like others mentioned in the linked previous thread https://www.edaboard.com/showthread.php?347861-Network-theory-travelling-waves-vs-power-waves, the terms "power wave" and "power wave reflection coefficient" aren't commonly used in the majority of RF text books.

"Power Wave Formulation" is described even in a major standard text book.
However, "Microwave Engineering" Written by David M. Pozar, is not deep about any topic....

I don't think so..
This is a very well explained,
deeply analyzing,comprehensively expressing book.Every Microwave Engineer must have this book at any level, any background.

I don't think any regular and fundamental courses in university use this book.

 

[mtwieg]

" In case of there is no transmission line so characteristic impedance is not defined, travelling voltage and current waves are not applicable( valid) anymore.Instead "Power Waves are used" and added an example for an example of conjugate matching case.
Gamma=Zload-conj(Zsource)/(Zload+Zsource)

This is why the power wave formulation was attractive to me. I work on RFPAs which connect directly to their load (sometimes with a short coax cable), and without any isolator/circulator. The optimal load/source impedances are not necessarily real-valued, making the distinction between power and travelling waves relevant.

However, I would not suggest that travelling waves are "not applicable" or "invalid" in such a case. It just means that the impedance match condition Γ_V=0 (to borrow pancho_hideboo's notation) is not the same as the conjugate match condition Γ_P=0. So long as we respect the differences between the two, neither are "wrong." But one might be more convenient and yield neater equations.

 

[pancho_hideboo]

[Conclusion]
"Power Wave Formulation" is described even in a major standard text book.

Generalized S-parameters are defined by "Power Wave Formulation" in almost all commercial RF Circuit Simulators.
They give S11=0 at conjugate matched condition.

 

[cariban]

I have a question about the conjugate matching.

When we calculate the reflection coefficient of the circuit, we use Γ=(ZL-Zg)/(ZL+Zg).

What if Zg is conjugate matching we ZL which means Zg=ZL*, and Zg=R+jX, ZL=R-jX?

The Γ is not 0.

I think the conjugate matching make sure that there is no power reflect back to source generator so the Γ should be 0. I know why we need the conjuagate matching. All I need is to solve this math problem.

Thanks

Yes, the one time reflection is not zero. But you forget that the reflection is multiple. The source will reflect as well. At first time you have reflection from the load, but since your source impedance is not ideal as well, so the reflected signal will be reflected by the source again....

(Sounds difficult to understand, just image you stay in the middle of two parallel mirror, you will see a lot of yourself.)

Since the source impedance and load impedance must be referred to the same point (one towards the source, another one towards the load from the same point), there is no time delay between those multi-reflected signals, they will be added together, and finally you will get the maximized power to the load.

 

[pancho_hideboo]

But you forget that the reflection is multiple.
................................................................
and finally you will get the maximized power to the load.

Your appends have no relation to this thread focus, since our focus is steady state response.

Your appends is no more than simple boundary condition problem with termination at both sides.

We can express Green function as two forms, close form and series expansion.

Mutiple reflection can be expressed by Green function of series expansion.

However Green function of close form is enough for this thread.