Why do patch antennas have leakage if they have standing waves?

[legyptien21]

Hi

Ok I have a contradiction in my mind:

Patch antenna is called a leaky wave resonant cavity because of the magnetic slots which radiates. We all agree on the fact that they are standing waves with clearly identified max and min as a characteristic of a specific mode inside this cavity.

1) My question is if we have standing waves, in my mind we would have a max reflection (=1) on the magnetic walls so how comes we have leakage if we have full reflection on the wall ??

2) If we have NOT full reflection on the wall so it means there is no standing wave in the cavity right ? the max and mins are moving ?

Thanks

 

[davenn]

Patch antenna is called a leaky wave resonant cavity because of the magnetic slots which radiates. We all agree on the fact that they are standing waves with clearly identified max and min as a characteristic of a specific mode inside this cavity.

That's not what I am familiar as a patch antenna

what you described is a slotted waveguide

these are patch antennas ...

so what type of antenna are you really talking about ?

Dave

 

[legyptien21]

Thanks for your answer. I'm definitely talking about the 2 last pics, the patch antenna ! I try to understand why your thing that I'm describing a slotted waveguide. Maybe because I wrote magnetic slot ? I was talking about the fringing field which can be "remplaced" by 2 magnetic current. The patch is equivalent to 2 magnetic slots...

when I talk about reflection on walls, I talk about the 4 magnetic walls which are delimiting the patch cavity...

 

[Jeff Rosenbury]

What is a magnetic wall?

 

[legyptien21]

What is a magnetic wall?

https://books.google.ca/books?id=_e...esc=y#v=onepage&q=patch magnetic wall&f=false

You see the boundary condition implied by a PEC (pefect electric conductor) ? A PMC (magnetic conductor) is the one which implies the opposite condition. For example, if you have an interface of air and a VERY VERY high dielectric constant matter, this matter will be as good PMC as its epsilon is high...

 

[Jeff Rosenbury]

It's my understanding that a patch antenna works by having the electric field fringe between the patch and the ground plane. The magnetic field is caused by currents moving down the edge of the patch and the resulting image current moving in the ground plane. The "end" of the antenna where the standing wave typically forms depends on where the feed point is and the shape of the patch.

 

[legyptien21]

look what I don't understand is that an incident wave is brought by the transmission line then a reflection occurs inside the cavity (between the metallic patch and the ground plane) at the end of the cavity (limit of the metallic patch). This reflection isn't a full reflection for me since there is a leakage at the end. so it's not a standing wave inside the cavity ? I'm even confused on the phenomena of a partially reflected wave at a load which interfere with itself. It shouldn't be a standing wave if there is NOT a reflection coefficient of 1...to me...

let me know what you think

thanks

 

[Baluncore]

It shouldn't be a standing wave if there is NOT a reflection coefficient of 1...to me...

Any reflected wave will generate standing waves with the incident wave. The position of those nodes and nulls will be determined by the nature of the reflector.

Once a wave is resonant in a structure, with a Q of say 100, radiation of energy through a slot or fringing field need only be 1% of the circulating energy per cycle for the full power available to be radiated.

 

[Jeff Rosenbury]

As a rough rule of thumb, elements less than 1/10^th of a wavelength can be lumped together. Since the fringe is less than that, it can be considered a sudden shift to 377Ω; i.e. an open. This will cause a reflection coefficient (∫˜) ~= 1. (Of course nothing is perfect, and this presumption less than most.) As Baluncore pointed out, we don't need ∫˜ to be 1 to get standing waves.

Remember, EM waves add linearly (at least in most dielectrics). So a ∫˜ of 1/10^th will give a standing wave of 1/10^th the amplitude (compared with ∫˜= 1). The rest of the wave goes on its merry way, but there's now a new wave with 1/10^th the energy just standing there...

 

[legyptien21]

The position of those nodes and nulls will be determined by the nature of the reflector.

You anticipated my question. Suppose we are in a high permittivity dielectric cavity which is in contact with air. You said a standing wave appear whatever the reflection coefficient at the interface, fine but it means that the position of the node and nulls will not "move" along the cavity ? Look I'm going to tell you what disturb me: the amplitude of the standing wave is :

Vi*(1+alpha) with alpha the coefficient of reflection and Vi the incident wave amplitude. If it's a full reflection, it's the simple case for me, alpha = 1 and the amplitude of the association of the 2 waves is 2 *Vi. Suppose we have no reflection, it should be a progressive wave with alpha = 0 , the position of the max or min is moving at C (speed of light). At any infinitesimal reflection we will have a standing wave ??! How comes we have such a discontinuity in speed ??! Another question is that what is the min value of a standing wave in a NON full reflection coefficient ?

thanks

Ps: Sorry lots of questions but it has to be extremely clear...

 

[legyptien21]

The rest of the wave goes on its merry way, but there's now a new wave with 1/10th the energy just standing there...

Interesting ! This means to me that the whole wave obtained after reflection is an addition of the standing wave that you described and a progressive wave. If I had the ability to see the wave (the whole one) with my eyes, the node and the nulls will note be standing, they will be moving at the speed of C right ? Because this speed is introduce by the progressive wave... You see where I want to go right ? I want to talk about the discontinuity...

 

[Baluncore]

1) My question is if we have standing waves, in my mind we would have a max reflection (=1) on the magnetic walls so how comes we have leakage if we have full reflection on the wall ??

The leakage of signal is not through the open or conductive reflector but from the part of the resonant cavity exposed through a slot or aperture in the cavity wall.
A resonant dipole has full reflection at both ends and maintains a standing wave. Yet it still transmits a 2.15 dBi signal broadside.

 

[legyptien21]

The leakage of signal is not through the open or conductive reflector but from the part of the resonant cavity exposed through a slot or aperture in the cavity wall.
A resonant dipole has full reflection at both ends and maintains a standing wave. Yet it still transmits a 2.15 dBi signal broadside.

That's fine, I'm following you. I thought we have a standing wave only when there is a full reflection. I agree with you we have a standing wave with any reflection and the amplitude of this standing wave is as small as the reflection is. This is solved ok.

Now what about the whole wave please ? the whole one is NOT a standing wave right ? Their should be a mathematical way to calculate the speed of the full wave. I'm sure it goes at C because of it's progressive part... I'm sure I missed something because of the speed discontinuity...

 

[legyptien21]

Ok I have an answer for this apparent discontinuity, I will give my opinion later if someone is interested. Actually the partially reflected case if the same as a progressive wave modulated (with addition not multiplication like in an amplitude modulation) by a standing wave. The amplitude of the standing wave and the one of the progressive wave depends on the reflection coefficient. I think we agree on that...

Now I have only one question. what the value of the minimum of the whole wave ?

 

[Baluncore]

Now I have only one question. what the value of the minimum of the whole wave ?

If only the world was so simple. What "whole wave" in what "environment" ?

 

[legyptien21]

A resonant dipole has full reflection at both ends and maintains a standing wave. Yet it still transmits a 2.15 dBi signal broadside.

Yes but this radiation is not the result of a leakage because since there is a full reflection there couldn't be a leakage, you agree ? Is this radiation is the result of leakage for you ?

I will talk about whole wave later...

 

[Jeff Rosenbury]

A standing wave is not stationary in the sense of propagation. If it were a single wave like a soliton, it would move right along. The standing effect is typically (but not exclusively) caused when two waves moving in opposite directions interfere with each other. Since an incident wave train and its reflected wave wave train (with ∫˜=1) are just such a pair, they form a standing wave. But both wave trains are propagating at full speed.

At ∫˜<1, there will be a small standing wave equal to the reflected wave plus as much of the incident wave as needed to match that. This will be swamped by the incident wave for ∫˜<<1, but will still exist.

Other types of standing waves exist, but aren't really what we are talking about.

What is a "whole wave"? Waves add linearly, so a standing wave will typically be twice the amplitude of the incident wave. But with clever (or perhaps not so clever) design a waveguide resonator could bounce the wave back and forth six ways from Sunday until the voltage breaks down the dielectric and let's the magic smoke out.

 

[Jeff Rosenbury]

Since PECs don't exist, nothing has a ∫˜of 1. But it has a nominal value of 1 (Claimed anyway. It sounds reasonable, but it's not my understanding of what goes on.). Since it is a resonator, the voltage keeps building until the small leakage power (out of the antenna) matches the incoming power. At least that's my understanding of the claim. (I'd buy it but haven't done the math myself.)

 

[legyptien21]

A standing wave is not stationary in the sense of propagation. If it were a single wave like a soliton, it would move right along. The standing effect is typically (but not exclusively) caused when two waves moving in opposite directions interfere with each other. Since an incident wave train and its reflected wave wave train (with ∫˜=1) are just such a pair, they form a standing wave. But both wave trains are propagating at full speed.

By your last sentence you demonstrate that both waves are propagating and we all agree on that. However how can you say that the addition of these 2 waves which are giving standing wave will not propagate ? your link say the opposite of that no ?

 

[Baluncore]

Now I have only one question. what the value of the minimum of the whole wave ?

I will talk about whole wave later...

No. You talked about it before. Your term “whole wave” has no obvious meaning.

If you will not clarify your statements and you will not answer questions then your misuse of the terminology will continue and you will only waste the time of respondents. The more you write, the more nonsensical your thinking on this subject appears to be. That needs to change.

 

[legyptien21]

At ∫˜<1, there will be a small standing wave equal to the reflected wave plus as much of the incident wave as needed to match that. This will be swamped by the incident wave for ∫˜<<1, but will still exist.

No. You talked about it before. Your term “whole wave” has no obvious meaning.

If you will not clarify your statements and you will not answer questions then your misuse of the terminology will continue and you will only waste the time of respondents. The more you write, the more nonsensical your thinking on this subject appears to be. That needs to change.

Ok Whole wave means the addition of the stationnary wave and the propagating one (which happen when there is partial reflection)
Look it's not that I don't want to clarify it's that I try to solve one question after the other one. If you can look at my message 16 and if I can understand your point of view on it, after that we can talk about the whole wave which is a not clear term I agree...

 

[Jeff Rosenbury]

By your last sentence you demonstrate that both waves are propagating and we all agree on that. However how can you say that the addition of these 2 waves which are giving standing wave will not propagate ? your link say the opposite of that no ?

Because they are propagating in two different directions.

The addition is done linearly. It is done point by point in a 3+time space. So each point sees two time varying waves and adds them. In some times and places they add. In some times and places they subtract. In addition there are a few points where they always cancel.

For ∫˜=1 they are the same amplitude, so that place forms a zero point. 1/4^th wavelength later (away from the reflective surface) they double which causes a rise and fall of twice the amplitude of the incident wave.

 

[legyptien21]

By your last sentence you demonstrate that both waves are propagating and we all agree on that. However how can you say that the addition of these 2 waves which are giving standing wave will not propagate ? your link say the opposite of that no ?

ok now it's my mistake, "will propagate" because you stated that the stationary will propagate : your sentence was "A standing wave is not stationary in the sense of propagation. I"

 

[legyptien21]

ok one last question, after that I won t bother...

If we have a transmission line missmatched at one of its end, we will have a partially reflected wave. How is the distribution of current along the transmission line ? My main question is the maximum and minimum of current will move along this line or not ?

I have an opinion but I don`t want to influence you so don`t read the following unless you know the answer.

To me since there is a partially reflected wave, the max and min should move. We do have a standing wave but we have to add to it a progressive wave which is bringing the movement to the distribution.

Thanks for your time...

 

[Jeff Rosenbury]

This is not a competition. I was trying to help you understand my thinking. Perhaps I'm way off base and you are right. That's fine with me.

In my experience reality doesn't really care what I think.

 

[Baluncore]

There are two quite independent waves propagating on the TL. One is in the forward direction from the source, the other is the reflected component traveling back towards the source. The sum of those two propagating waves will vary along the line and will form a standing wave pattern. That standing wave can be seen by measuring the total voltage across, or current flowing in the line, which will show nodes or nulls in fixed positions along the line.

The propagating waves cannot see each other and do not influence each other, they are traveling waves, propagating in opposite directions on the same line.

 

[legyptien21]

This is not a competition.

! I never said or thought it s a competition. I do try to understand you. That s why I wanted to know (and asked) why did you say "A standing wave is not stationary in the sense of propagation.". I m not saying you are wrong, I just wanted to understand what do you mean by that.

sorry if I offended you...

 

[legyptien21]

The sum of those two propagating waves will vary along the line and will form a standing wave pattern. That standing wave can be seen by measuring the total voltage across, or current flowing in the line, which will show nodes or nulls in fixed positions along the line.

excellent ! We are touching here something which drives me crazy for a long time. We were saying in all what we said until now that in the general case of interference between the incident and reflected wave, we will have a standing wave PLUS a propagating wave. If we measure the total voltage as you say, it will give the standing PLUS (addition mathematically) a propagating wave.

I`m stuck with that for a long time, I have to understand that. To me the nodes or nulls won t be fixe in the general case (partially reflection).

 

[Baluncore]

in the general case of interference between the incident and reflected wave, we will have a standing wave PLUS a propagating wave.

No. There is an incident wave and a reflected wave, both of which are propagating, but in different directions. The sum of those is a fixed standing wave pattern. There is no "PLUS a propagating wave" as you put it.

 

[legyptien21]

Vi*sin (wt - kx ) + Vr*sin (wt + kx ) = Vr*(sin (wt - kx) + sin (wt + kx)) + C*sin (wt + kx) with Vi = Vr + C

Vr*(sin (wt - kx) + sin (wt + kx)) represent a standing wave if we use the Simpson formula...

Do we agree ? if not why ?

 

[Baluncore]

Do we agree ? if not why ?

No.
Where do the equations come from ?
What do the symbols mean ?

 

[legyptien21]

No.
Where do the equations come from ?
What do the symbols mean ?

the equations come fro my mind. Vi and Vr are the amplitude of the incident and reflected wave. K: wave number. w=2*pi*f with f the frequency. C is the amplitude of a wave which is part of the incident wave since we decide Vi = Vr + C. I hope it s ok now.

 

[Baluncore]

C is the amplitude of a wave which is part of the incident wave since we decide Vi = Vr + C.

So you are saying that the part of the incident wave that is not reflected, but which passes through the impedance mismatch, is reflected as C.
That is nonsensical.
If Vi = Vr + C, then C is not reflected and so is no longer propagating on the line. It is lost from the line.

 

[legyptien21]

So you are saying that the part of the incident wave that is not reflected,

I never said such a thing nowhere, sorry. I did a simple derivation, and I don t think I did a mistake mathematically. Then I interpretated the results as a superposition of standing wave and propagating wave. You may not agree with this physical interpretation but at least we should agree on the mathematical derivation... Do we ?

thanks

 

[Baluncore]

No.

Then I interpretated the results as a superposition of standing wave and propagating wave.

You cannot have a superposition of a standing wave and a propagating wave.

 

[legyptien21]

do we agree on the mathematical derivation ?

 

[Baluncore]

do we agree on the mathematical derivation ?

No.

 

[legyptien21]

Is it possible to have soe details about the reason of this no...?

why mathematically it s wrong ?

 

[Baluncore]

For a lossless line with a characteristic impedance that is real, terminated in a resistive load.
Avoiding common scale factors.
The incident wave at the load will be Ei = Sin(t).
At a point a time x before the load, Ei = Sin(t+x).
The reflected wave will have an amplitude, A, between –1 and +1, determined by Zo and R.
The reflected wave at the load will be Er = A*Sin(t).
At a point back up the line, a time x after reflection from the load, Er = A*Sin(t–x).
Then the sum of the incident and reflected waves is Es = Ei + Er = Sin(t+x) + A*Sin(t–x)
For values of x = wave period * n / 4 ; there will be maxima and minima in Es.
Es = Sin(t+x) + A*Sin(t–x) represents the standing wave.

Vr*(sin (wt - kx) + sin (wt + kx)) represent a standing wave if we use the Simpson formula...

That should be Es = Vi * Sin(wt + kx) + Vr * Sin(wt - kx)

 

[sophiecentaur]

If we have NOT full reflection on the wall so it means there is no standing wave in the cavity right ? the max and mins are moving ?

If you ever had a 'complete' reflection at the ends of a cavity, the amplitude of the standing wave would build up until it was infinite. A cavity, just like a resonant wire (as in a tuned dipole) will have a resonant frequency but, because of its finite Q factor, it will: 1. have a finite standing energy and 2. a finite bandwidth.
There will be power entering the cavity at one end and power leaving the cavity at the slots, resulting in a standing wave (when the frequency and dimensions are appropriate) but the (stationary) nodes of the standing wave will not be perfect because of the net power flowing through them.

 

[legyptien21]

a finite bandwidth.

You mean a bandwidth different than 0 ? because if we had a full reflection as you said, we would have had a infinite quality factor (with bandwidth = 0) if we suppose a lossless cavity right ?
We agree on these two points ?

There will be power entering the cavity at one end and power leaving the cavity at the slots, resulting in a standing wave (when the frequency and dimensions are appropriate) but the (stationary) nodes of the standing wave will not be perfect because of the net power flowing through them.

Sophie please can you tell me if you agree with my mathematical derivation at message 30 ? If so I would like to know your opinion about the speed of the sum of the standing wave and propagation wave ?

Thanks

 

[davenn]

you have already been told that your workings in post # are incorrect

Baluncore corrected them in post # 39

 

[legyptien21]

you have already been told that your workings in post # are incorrect

Baluncore corrected them in post # 39

And ?

1) I can be wrong, he can be wrong, we are all human.
Most importantly,
2) the justification of Baluncore doesn`t make sense to me because his equation have no sense. Where is the wave number, where is the angular speed... Can you guess the wavelength of his equations... ?

If the equations are right then we take the most general case to do a derivation not a case where we add time in sec with X in meters...

 

[davenn]

when are you going to stop your own misunderstandings and listen to people who know what they are talking about ??

to me because his equation have no sense.

then you need to get back to the textbooks and start learning the real stuff and not what you make up out of your head

I trust what Baluncore says because I know he has had a lot of history working in RF electronics

 

[Baluncore]

If the equations are right then we take the most general case to do a derivation not a case where we add time in sec with X in meters...

If you go back and look you will see that I clearly defined x as a time relative to incidence at the load. That eliminates the velocity factor from the equation.

At a point a time x before the load, ...
... At a point back up the line, a time x after reflection from the load, ...

Can you guess the wavelength of his equations... ?

The period T is sufficient. Wave number and angular speed are the same for all.

 

[legyptien21]

If you go back and look you will see that I clearly defined x as a time relative to incidence at the load. That eliminates the velocity factor from the equation.

if you start to switch all letter and their meaning, noboday will follow easily. Anyway, I m open to talk about that :

Ei = Sin(t) this is your incident wave I believe ? in every incident wave there is X which represent the distance. so where is the distance in your equation, where is the propagation. there is no point to write it that way and to eliminate the velocity...

If you want to write your derivation with letters and their meaning as your asked me then I will follow you otherwise no one will be able to...

It s late for me now I will answer tomorrow

 

[Baluncore]

Ei = Sin(t) this is your incident wave I believe ?

I clearly defined the incident wave at the load when I wrote ...

The incident wave at the load will be Ei = Sin(t).

if you start to switch all letter and their meaning, noboday will follow easily.

I clearly defined x as a time. You chose to ignore it.

in every incident wave there is X which represent the distance. so where is the distance in your equation, where is the propagation.

The incident wave will be a sine wave at the load, Ei = Sin(t). Earlier on the line it will have a time shift of x, giving Ei = Sin(t+x).
Ei does not exist after it has reached the load as it is a forward traveling wave.
The distance in my equation is measured by time along the transmission line from the load.
The time x, is an analogue of distance, just like "Light Years" in astronomy.
I keep t and x separate so as to show the time shift of the incident and reflected waves at any travel time x from the load.
The time shift of Ei and Er is 2 * x. That explains the n * T / 4 standing wave pattern, where n is an integer and T is the period of the wave.
The sign of the reflection amplitude parameter, A, is also important because it may invert the reflected wave.

 

[Drakkith]

Thread locked, pending moderation.

 

[berkeman]

if you start to switch all letter and their meaning, noboday will follow easily. Anyway, I m open to talk about that :

Ei = Sin(t) this is your incident wave I believe ? in every incident wave there is X which represent the distance. so where is the distance in your equation, where is the propagation. there is no point to write it that way and to eliminate the velocity...

If you wanna write your derivation with letters and their meaning as your asked me then I will follow you otherwise no one will be able to...

It s late for me now I will answer tomorrow

Thread cleaned up some and reopened for now. @legyptien21 -- What exactly are you asking about in this thread? You started asking about antennas, and then moved more into asking about transmission lines with resonant cavities on the end. What exactly do you want to ask about? What is the physical application? It is better to deal with real physical systems when discussing antenna systems, versus abstract questions. Especially when there is a bit of language translation issue.

BTW, it would be best if you would use "want to" instead of "wanna" -- the word want to has very negative connotations in scientific discussions. Thanks.

 

[legyptien21]

As you may know, patch antenna, dipole antenna, transmission line, resonance, quality factors, all that are related. And when you start a conversation and ask about antenna, you notice that we don t agree with some more fundamental stuff. If we are not using the same mathematical langage and we do not agree on a very simple matheatical derivation then not need to go further.

I m sure you have good background in physics and you will notice that Sophie has an answer who is not the same at all than Balunchore (position of nulls/nodes are moving around a position because of the flow of energy). It s now very clear, many thanks to Sophiecentaur.

I m done with this post.