On a transmission line, why does max power transfer occur at impedance matching and neglecting Zi?

AndrieGnd

Joined Jun 25, 2019
52
Hi guys, we know already from basic electronics that if ZL=ZS then we get maximum power transmitter from source to load.

In transmission line for getting maximum transmitter power from the source to the load, we say ZL=ZO .
not saying (Zi+Z0)=ZL , why is that correct?! isn't the rule for maximum power must be Zs=ZL ? thanks alot.
Zi- is the input resistor impedance.
Zo-Line transmission's impedance.

what's required that maximum power transferred from the source to the load, I already state the answer : Zo=ZL .

I claim according to electronics it must be Z0+Zi = ZL , it seems I'm wrong, but why? anyone please can explain to me why we are getting maximum power at Zo=ZL ? and why we are neglecting Zi ? it would be much appreciated if you explain that by a meaningful analogy because it's confusing me alot.

Attachments

• 21.9 KB Views: 1
• 21.9 KB Views: 1

AndrieGnd

Joined Jun 25, 2019
52
so I conclude that it must be Zi+Z0 = ZL for getting maximum power .. but it's wrong and I don't know why; that's why I posted this question.

nsaspook

Joined Aug 27, 2009
7,586
Transmission lines are EM energy storage devices, they can't be analyzed as simple series circuits.

https://en.wikipedia.org/wiki/Impedance_matching#Maximum_power_transfer_matching
Complex conjugate matching is used when maximum power transfer is required, namely
...
where a superscript * indicates the complex conjugate. A conjugate match is different from a reflection-less match when either the source or load has a reactive component.

Step back, find a good book or video series about AC analysis.

Last edited:

WBahn

Joined Mar 31, 2012
26,141
Hi guys, we know already from basic electronics that if ZL=ZS then we get maximum power transmitter from source to load.

In transmission line for getting maximum transmitter power from the source to the load, we say ZL=ZO .
not saying (Zi+Z0)=ZL , why is that correct?! isn't the rule for maximum power must be Zs=ZL ? thanks alot.
Zi- is the input resistor impedance.
Zo-Line transmission's impedance.

what's required that maximum power transferred from the source to the load, I already state the answer : Zo=ZL .

I claim according to electronics it must be Z0+Zi = ZL , it seems I'm wrong, but why? anyone please can explain to me why we are getting maximum power at Zo=ZL ? and why we are neglecting Zi ? it would be much appreciated if you explain that by a meaningful analogy because it's confusing me alot.

View attachment 180499
You've got a couple of problems with you reasoning.

First, when you have a source with an output impedance and you have no control over either, then the maximum power deliverable to a load is when the load impedance is the complex conjugate of the source impedance.

Second, this rule simply doesn't apply when you have the ability to change the source impedance (and as far as the load is concerned, the transmission line impedance is part of the source impedance). This is because this rule came about by performing an optimization analysis under the constraint that we could change the load impedance but that the source impedance was fixed.

BR-549

Joined Sep 22, 2013
4,938
AndrieGnd......Do you understand how a tank circuit works? Draw a tank with the inductor on the left and a cap on the right.

When the positive reactance of the coil, matches the negative reactance of the cap........ maximum current will be do-si-doed between them.

Now split the coil and cap with a long pair of wires.

The coil is now the source, and the cap is now the load. If the source now has positive reactance, we want the load to have the same, but opposite negative reactance, so that we can get maximum current.

Does this make any sense to you?

crutschow

Joined Mar 14, 2008
25,384
Think of it this way.
The maximum power to the load occurs when the power lost in the source is a minimum.
If you have control over the source impedance (you can vary it) then the minimum power lost in the source is obviously for a source impedance of zero.
So you thus want to make the source impedance as low as possible for a fixed load impedance.

Conversely, if the source impedance is fixed, and the load impedance can vary, then the maximum load power occurs when the load is the complex conjugate of the source impedance, where the power dissipated in the load equals the power dissipated in the source.

See the difference between the two cases?

WBahn

Joined Mar 31, 2012
26,141
Think of it this way.
The maximum power to the load occurs when the power lost in the source is a minimum.
HUGE holes in this line of reasoning!

If you have control over the source impedance (you can vary it) then the minimum power lost in the source is obviously for a source impedance of zero.
Similarly, by this approach, the power lost in the source is zero when the source impedance is infinite.

Conversely, if the source impedance is fixed, and the load impedance can vary, then the maximum load power occurs when the load is the complex conjugate of the source impedance, where the power dissipated in the load equals the power dissipated in the source.
But how does this have anything to do with minimizing the power lost in the source???

If you want to minimize the power lost in the source, simply make the load impedance go to infinity, in which case you once gain drive the power lost in the source to zero.

As you vary the load impedance, the power lost in the source is a minimum when the load impedance is infinite (zero current) and a maximum when the load impedance is has zero real component and the reactance is the opposite that of the source (maximum current). Neither of these extremes relates to maximum power delivered to the load.[/QUOTE]

Last edited:

BR-549

Joined Sep 22, 2013
4,938
Think of source impedance as a vertical tilted line. Think of the load impedance as a vertical tilted line. The height is the resistance. The tilt is the reactance. If the source tilt is to the left, then we want the tilt of the load impedance, to tilt the same amount to the right......to match the left tilt..........taking all the tilt away and leaving a truly vertical line.....of only resistance.

Maximum power transfer requires a chiral match of phase.

We called it tuning.

Edit: A signal has a twist. To catch all of it, we need the proper length, anti-twist box......or some of it will bounce back out.

If the twist of the source and load do not match, we can take another component that has a variable twist, and match to two up, using the variable twist of the transmission line. The transmission line contains both twists.

We can vary the transmission line twist, with it's length.

But that is plan B. We want the load twist to match the source twist if at all possible.

Last edited:

crutschow

Joined Mar 14, 2008
25,384
Similarly, by this approach, the power lost in the source is zero when the source impedance is infinite.
Okay.
I should have said that if the source is delivering power to the load, and you can adjust the source impedance, the minimum source impedance dissipates the minimum power in the source and delivers the maximum power to the load.

WBahn

Joined Mar 31, 2012
26,141
Okay.
I should have said that if the source is delivering power to the load, and you can adjust the source impedance, the minimum source impedance dissipates the minimum power in the source and delivers the maximum power to the load.
That's a kluge patch that sidesteps the issue and only when you can adjust the source impedance. It doesn't help the overall claim that "The maximum power to the load occurs when the power lost in the source is a minimum." If you have a fixed source impedance, then choosing the load impedance to be its complex conjugate does NOT minimize the power lost in the source. Minimizing power lost in the source is irrelevant to maximizing power delivered to the load -- that it just happens to turn out that way for max power delivered to the load when you can change the source impedance is little more than a coincidence.

AndrieGnd

Joined Jun 25, 2019
52
Much appreciated guys, all is understood.

best thank to the enriched answers of @WBahn /@nsaspook

AndrieGnd

Joined Jun 25, 2019
52

nsaspook

Joined Aug 27, 2009
7,586
https://archive.org/details/in.ernet.dli.2015.177615/page/n57

My copy is a first edition of IMO the best book for a practical (general electromagnetism without the use of higher mathematics) understanding of the subject. While the technology of 1945 is outdated, the basis of Electromagnetic Engineering theory in these out of copyright
Section II on Antennas is especially good.

https://archive.org/details/in.ernet.dli.2015.177615/page/n85

A more typical book on the subject from the same era.
https://archive.org/details/in.ernet.dli.2015.177429/page/n2

Last edited:

crutschow

Joined Mar 14, 2008
25,384

AndrieGnd

Joined Jun 25, 2019
52
https://archive.org/details/in.ernet.dli.2015.177615/page/n57

My copy is a first edition of IMO the best book for a practical (general electromagnetism without the use of higher mathematics) understanding of the subject. While the technology of 1945 is outdated, the basis of Electromagnetic Engineering theory in these out of copyright
Section II on Antennas is especially good.

https://archive.org/details/in.ernet.dli.2015.177615/page/n85

A more typical book on the subject from the same era.
https://archive.org/details/in.ernet.dli.2015.177429/page/n2
thanks alot, it's really good. I wanted more book with solving problems on transmission line/anntena which I didn't find .. I mean with problems ..those for practicing as student of engineering who's new on anntena/transmissionline subjects

WBahn

Joined Mar 31, 2012
26,141
Well, I'm a kluge patch kind of guy.
We all are, from time to time. And at times a good kluge is the perfect tool for the job.

AndrieGnd

Joined Jun 25, 2019
52

what I understood is, the subject of transmission line is all about E H K, so after reading the subject of antenna, I understand that the direction of E must be directed into the antenna to absorb it and then it's transmission/receiving it. that's how the antenna is working.
So, what I didn't understand how dipole is related to antenna and how it works to develop its functionality? and what about if I can put many dipoles on the antenna (over Z axis) then my antenna can work much better?, How can I calculate the number of Erectile Dysfunction of the antenna?
lets assume it's given dipole like this :I*d(current*distance)

thanks alot!

Last edited:

nsaspook

Joined Aug 27, 2009
7,586

what I understood is, the subject of transmission line is all about E H K, so after reading the subject of antenna, I understand that the direction of E must be directed into the antenna to absorb it and then it's transmission/receiving it. that's how the antenna is working.
So, what I didn't understand how dipole is related to antenna and how it works to develop its functionality? and what about if I can put many dipoles on the antenna (over Z axis) then my antenna can work much better?, How can I calculate the number of Erectile Dysfunction of the antenna?
lets assume it's given dipole like this :I*d(current*distance)

thanks alot!
The last thing we need is Erectile Dysfunction of the antenna. I hope something was lost in translation.

The 'dipole antenna' is one of many physical mechanisms of separation of charge for efficient EM energy storage and transfer by radiation. When properly designed the RF currents (equal but opposite currents and voltages) in the dipole elements result in EM fields that reinforce at a point away from the dipole.

AndrieGnd

Joined Jun 25, 2019
52
Sorry for the last term, I don't know what's called , but I think it's about how many "dots" in the field of light of the antenna
here's the equation I'm talking about: https://ibb.co/KxCjXJ5

but I don't understand it, may please explain it for me or actually what's called that I can search over google(I mean the correct term that's called in antenna aspects) ?!

updating: it's called number of "lobes"

thanks alot

Last edited:

bogosort

Joined Sep 24, 2011
485
Section II on Antennas is especially good.
What strikes me most from the blurb you posted is the excellence of the writing. I've noticed that engineering, math, and physics books from the early and mid-20th century (through the early 70s) tended to have a significantly higher quality of writing than more recent efforts. I get the sense that the authors of old were expected to be experts in their technical field, as well as masters of the craft of written communication. Whereas today, it seems that technical expertise -- and sometimes not even that -- is the essential criterion; any problems with the writing can be "fixed" by a publisher's in-house editors. It's probably a scale effect, but modern textbooks are worse for it.

Anyway, my apologies for the tangent; I get excited when I come across genuinely good technical writing.