Wireless routers vs. microwave ovens

[Vanadium 50]

Let me point out that the first use of the photon concept (but not the word) was an equation that was not relevant to the problem at hand. Why the devil do people want to reinforce this misunderstanding by dragging in photons?

 

[vanhees71]

The classical particle model almost always leads to qualitatively (!) wrong results. Why should one teach it? For me the most difficult thing in my study of physics concerning concepts was to unlearn the wrong pictures about photons provided by popular-science textbooks. The same is true for the qualitatively (!) wrong picture of the atom the Bohr-Sommerfeld model provides as if the atom were a minature planetary system with point electrons running around point atomic nuclei.

I think you can teach a qualitative photon picture that is at least not as mistaken as the "bullet picture" in the following way. As an example take a polarization filter and start with the model of light provided by classical electrodynamics. You have to explain that electromagnetic fields (including light) are transverse waves (it's sufficient to discuss the plane-wave solutions) and that the polarization filter is a material that absorbs all field components in one polarization direction and let's all field components in the perpendicular direction through. Then you can explain what happens to a general em. wave, which formally leads to a projection operator.

Then you tell the students that the classical picture is not entirely right but that quantum theory tells us that matter can not absorb em. fields of any energy but only in integers of $E=\hbar \omega$. Since you cannot detect any electromagnetic field if it is not absorbed by the detector (that's of course an oversimplification ;-)) this implies that there's a state of the electromagnetic field which corresponds to a plane em. wave with frequency $\omega$ of minimal possible energy $\hbar \omega$, and there cannot be an electromagnetic-field state with a lower energy. This is what can be done on a qualitative level to make photons plausible.

It's of course not fully accurate and now you have to also explain the much less intuitive concept of probabilities. This is also not too difficult at this level: if you have a polarization filter and electromagnetic waves linearly polarized at an angle $\varphi$ relative to the orientation of the filter. The intensity $I$ behind the filter is given by $I/I_0=\cos^2 \varphi$.

If you now use this setup with a single-photon source (note that it's now plausible that photons are wave-like entities with a polarization as transverse electromagnetic waves naturally have; there's no problem to explain these wave-like properties of photons as in the erratic bullet model!) you have the following phenomenon. For a single photon $I/I_0=\cos^2 \varphi$ cannot be true anymore! What happens for a true single-photon state is that this photon is either completely absorbed or it goes completely through. All that this model can then predict is the probability for such a photon coming through being $\cos^2 \varphi$.

You can drive this qualitative model quite far, providing a simple example of a two-dimensional quantum system for polarization states of photons and develop the complete concept of quantum theory (2D Hilbert space description, observables, probabilities and Born's rule, and all that).

 

[sophiecentaur]

I think the simplified "classical" particle model and the wave model give both good explanations when we dealing with phenomena like this where we try to study the power emitted by an antenna or a tube.

Hmm. How does the little bullet model (and it really is no more than that) deal with how an antenna interacts with space or, indeed, how a 'tube' interacts with a circuit and, then with an antenna? I have read a fair few books on EM and circuits but I've never found one which tried to explain things using photons. There must be a good reason for that. Can you cite any reasonable source that uses the photon model?

Why the devil do people want to reinforce this misunderstanding by dragging in photons?

I can't think of one - except that waves are 'just too hard'. Strangely, the cleverest brains around shy away from using photons when discussing EM theory - that rather implies it must be the photon model that's actually 'just too hard'. Now, which side of the fence should we choose?

 

[vanhees71]

But why are waves considered "just too hard"? You have plenty clearly comprehensible around you (like water waves on a pond). You can do experiments with a slinky which is fun etc. etc. I think it's not difficult at all to introduce waves and even tell about the wave equation in the final high-school years.

For a very good book about the history of the photon concept, see

K. Hentschel, Photons - the history and mental models of light quanta, Springer (2018)

 

[etotheipi]

But why are waves considered "just too hard"? You have plenty clearly comprehensible around you (like water waves on a pond). You can do experiments with a slinky which is fun etc. etc. I think it's not difficult at all to introduce waves and even tell about the wave equation in the final high-school years.

A very common high-school problem is to estimate the thrust on a solar sail, and it's usually solved at that level by using the intensity on the sail to determine the rate of photon collisions (with each photon being of a known frequency, or from a known distribution of frequencies) to find the rate of change of momentum.

That's arguably easier to introduce than working out the radiation pressure using the Poynting vector (which requires a bit more E&M background), since by that point the idea of momentum is quite familiar to students. It is made worse by the fact that nowadays, in the British A Level at least, basically no electromagnetism is covered. Every exam question can be answered by copying down the formula booklet, which itself only goes as far as Faraday's law of induction.

Maybe the British system has it backwards, they should instead do more E&M and leave photons to a proper QM or QFT course at university? I think I agree yes

 

[sophiecentaur]

But why are waves considered "just too hard"?

It must be because of the maths that's necessary to describe pretty well any wave phenomenon. And my "too hard" was only referring to the sort of thinking that's based on the 'concrete' level. And the majority of people seldom venture into the 'Formal' realm of thinking. People stick to facts and figures and waves need more than that.
It's tempting to be elitist about these things and that would be rude but it's easy to over estimate what a nodding head actually signifies. It doesn't necessarily truly mean "I understand fully".

 

[NTL2009]

Back to the OP. While the huge difference in power ( ~ 1000:1) is one explanation (and all that's needed really, it fully explains it), it seems to me there is an additional reason. The MW oven constrains the power inside the oven, while the radio antenna of the router spreads the power omnidirectionally. You can use your router from ~ 30 meters away if there are no walls in between - do the math on the power density of that versus the inside on a MW oven. Let's see - my MW is ~ .35 x .25 x .5 M, so ~ .044 cubic meters. 30 x 30 x 30 = 27,000, over 600,000 times the volume (OK, that radiated power isn't evenly distributed through that space, but good enough to make the point).

Combine those two effects, and it should be obvious your router won't melt a Barbie sized marshmallow given a century to do it.

 

[vanhees71]

It must be because of the maths that's necessary to describe pretty well any wave phenomenon. And my "too hard" was only referring to the sort of thinking that's based on the 'concrete' level. And the majority of people seldom venture into the 'Formal' realm of thinking. People stick to facts and figures and waves need more than that.
It's tempting to be elitist about these things and that would be rude but it's easy to over estimate what a nodding head actually signifies. It doesn't necessarily truly mean "I understand fully".

There is nothing "elitist" in the demand to teach high-school students (I mean a final high-school degree that provides the prerequisites to study at a university like the German Abitur) the fundamental subjects in the STEM area right. It has been possible 30 years ago (when I myself got my Abitur). So why shouldn't it be possible anymore today? We have so many more "electronic tools" to make concepts in physics which need necessarily more advanced maths accessible to high-school students than then.

For years and years they debate about "digitalization at schools". All that has been achieved in Germany by now is that after years of political debate there's the posibility that the federal state give 5 G€ to the states to provide the schools with adequate hardware. The result so far is that the states shy away from writing the necessary proposals to make use of this money.

Even worse is the fact that nobody has developed teaching concepts that really serves the in my opinion indispensable need for a basic understanding how to program a computer. Also this was no problem 30 years ago. There the whole "home-computer" hype just started. Most of us had a Commodore 64. I taught myself to program in Basic from the accompanying manual. At school we had a small pool of Apple 2e's and the "nerds" among the teachers (which were of course the best STEM teachers we had anyway) full of enthusiasm taught us programming as a side subject. They used Pascal as a programming language, because that was thought to be the best one from a didactical point of view, but I think that's not so important: You learn how to program simple things, we did numerical root finding, numerical integrals, numerical solving of ODEs, learned about "chaos" (non-linear dynamics) etc. etc. Today we have much better developed tools, which are available for free (e.g., Python for programming, geogebra for exploring math) etc.

Instead of using all these opportunities what happened in Germany is that they lowered the standards dramatically, particularly in math. Recently I bought a new addition of the textbook we used to learn towards our final high school exam in physics (Metzler Physik). I still have the old version from 30 years ago. The new version is so much worse than the old one that I was simply shocked. E.g., in the old version electromagnetism was introduced in a nice conventional way starting with Coulomb's law, carefully explaining experiments leading to the description of forces acting between charged bodies towards the field concept. Today they start with Faraday's Law of induction (a topic which is often difficult still at the university level) and never got to explain anything in a logical order using what was learned before about mechanics. In the new version of the book Coulomb's law of electrostatics never occurs, but in quantum theory they still teach Bohr's model, but in a way that's even worse than the version you get when you have Coulomb's law at hand. In the old book there was also a chapter about Schrödinger wave mechanics and it even treated the ground-state wave function of the hydrogen atom that was comprehensible at the time when we were in high school. In the new version all this is gone.

 

[PeterDonis]

he is probably right that a photon is not a massless classical point particle

Not just "probably" right, he is right.

I don't know enough quantum field theory myself in order to be able to tell what exactly a photon is

Then please do not make claims that you cannot back up with your own knowledge.

I think we can use the "classical" photon model

There is no such thing as a classical photon model. The concept of "photon" is inherently quantum mechanical.

 

[PeterDonis]

the simplified "classical" particle model

There is no such thing.

 

[PeterDonis]

The classical particle model

There isn't one for photons.

 

[PeterDonis]

it's usually solved at that level by using the intensity on the sail to determine the rate of photon collisions (with each photon being of a known frequency, or from a known distribution of frequencies) to find the rate of change of momentum

This is basically treating the radiation as a photon gas with a given pressure, using the equation of state $p = \rho / 3$ (pressure is 1/3 of energy density). This model works all right in a limited domain (for example, it is also used to describe radiation dominated universes in cosmology), but it can't be applied to cases like those being discussed in this thread.

 

[sophiecentaur]

There is nothing "elitist" in the demand to teach high-school students (I mean a final high-school degree that provides the prerequisites to study at a university like the German Abitur) the fundamental subjects in the STEM area right.

That's a bit of an oxymoron. The population you describe is not 'average'. Education at a lower age / level doesn't assume what you are assuming. I don't remember coming across the Poynting Vector till University and the principle of the 'light sail' and photon momentum does make intuitive sense at a much lower level. But I would say that, pretty soon after that, EM is the way to go.
But, as is usual with PF, the rules of engagement in this thread are so vague that we can be arguing all night from correct but different positions.

 

[PeterDonis]

Everyone, please bear in mind that the thread topic is EM radiation in wireless routers and microwave ovens, not education in general. If participants want to discuss education in general, please start a separate thread in the appropriate forum.

 

[sophiecentaur]

Everyone, please bear in mind that the thread topic is EM radiation in wireless routers and microwave ovens, not education in general. If participants want to discuss education in general, please start a separate thread in the appropriate forum.

I think the drift can be put down to frustration at the lack of education. There's no more to be said, really - in fact the first half dozen posts said all that was needed.

 

[kevinisfrom]

If you are interested in how a microwave works classically then you can look into dielectric heating. I think this paper gives a good overview, they state that the microwave power absorbed by a dielectric per unit volume goes as $$P/V = \omega \epsilon_0 \epsilon_2 E_{eff}^2$$(N.B. that the $\epsilon_2$ they use here is the imaginary part of the complex permittivity, $\epsilon = \epsilon_1 + \epsilon_2 i$, I think Wikipedia uses a different notation)

You can see that the power absorbed varies with the amplitude of the electric field (as well as the absorption properties of the material - you can check up some values for water). Then it is maybe less mysterious why you are not cooked by your router

Looks like the power absorbed per unit volume is proportional to the frequency and amplitude.

Does this suggest the % attenuation for a single frequency is constant for all amplitudes?

That is, say you have 2.5GHz with amplitude 'alpha' and another with amplitude beta=1000*alpha

For both cases, the % absorbed/attenuated (that is, Pabsorbed/Pgenerated) is the same (just the Pabsorbed for the dielectric absorbs is 1000x greater since Pgenerated is 1000x greater)

Is this the right way of looking at it?

 

[kevinisfrom]

ohhh
don't you realize the difference in power levels ?

microwave oven ~ 600 to 1000W
router ~ 10 - 25mW (milliWatt) a tiny fraction of 1W

Absorption appears greatest for H20 at 22GHz. Any ideas why microwaves were not designed at the absorption peak? Wouldn't this provide more efficient transfer of energy?

 

[berkeman]

Absorption appears greatest for H20 at 22GHz. Any ideas why microwaves were not designed at the absorption peak? Wouldn't this provide more efficient transfer of energy?

There may have been pre-existing allocated communication bands at 22GHz by the time that microwave ovens were starting to be designed? Just a guess, but a check of the FCC website does show some mobile comm bands at 22GHz. Not sure how long they've existed there...

https://transition.fcc.gov/oet/spectrum/table/fcctable.pdf

 

[sophiecentaur]

Absorption appears greatest for H20 at 22GHz. Any ideas why microwaves were not designed at the absorption peak? Wouldn't this provide more efficient transfer of energy?

The available power from affordable sources limited the frequency to around 2GHz at the time that uWave ovens were first introduced. I think that probably applies even now. A source of useful power at 22GHz is still probably too expensive for a domestic application which doesn't actually need that high a frequency.
Then there's the old pen pushers at work. They allocated the present frequency and there's been no pressing reason to change it even if someone invented a cheap source of high power 22GHz sources.
Edit: @berkeman you got there just before me - I concur.

 

[berkeman]

Edit: @berkeman you got there just before me - I concur.

I dunno, I like your reply better than mine. I didn't even think about the source for a 22GHz oven...

 

[kevinisfrom]

ohhh
don't you realize the difference in power levels ?

microwave oven ~ 600 to 1000W
router ~ 10 - 25mW (milliWatt) a tiny fraction of 1W

Another thought, is it possible, hypothetically, to use thousands of routers and create an array that had a lot of constructive interferences at 0th order to reach the power level of a microwave?

 

[sophiecentaur]

Another thought, is it possible, hypothetically, to use thousands of routers and create an array that had a lot of constructive interferences at 0th order to reach the power level of a microwave?

No need to have them synchronised. Just use the normal spread of tuning and the signals would add power wise. Could be a big electricity bill. The magnetron is a lot more efficient than a router, I'd bet, and the combining network (??) would be a nightmare. You couldn't 'beam' the signals because you'd need very directive antennae and the beams wouldn't all fit into the space of a microwave oven cavity.

You can use arrays of 8 or 16 RF power transistors to combine their powers at UHF but afaik, the losses in the combiner networks (arrays of nominally 3dB directional couplers) become significant and require phase locking of the outputs and consistency in the couplers. (I'm talking about what people here may call Old Fashioned systems but I bet the situation won't be much better.

 

[kevinisfrom]

No need to have them synchronised. Just use the normal spread of tuning and the signals would add power wise. Could be a big electricity bill. The magnetron is a lot more efficient than a router, I'd bet, and the combining network (??) would be a nightmare. You couldn't 'beam' the signals because you'd need very directive antennae and the beams wouldn't all fit into the space of a microwave oven cavity.

You can use arrays of 8 or 16 RF power transistors to combine their powers at UHF but afaik, the losses in the combiner networks (arrays of nominally 3dB directional couplers) become significant and require phase locking of the outputs and consistency in the couplers. (I'm talking about what people here may call Old Fashioned systems but I bet the situation won't be much better.

Don't radars use a bunch of low power solid state RF sources to create an RF beam of higher power? I was thinking the same for a router-based microwave

 

[sophiecentaur]

Don't radars use a bunch of low power solid state RF sources to create an RF beam of higher power? I was thinking the same for a router-based microwave

No doubt but the process of adding more and more sources becomes diminishing returns for each layer of combiners - as I mentioned above. Initially, pairs are combined and then each pair of pairs is combined and then pairs of pairs of pairs. etc. You need 2,4,8,16 amps for it to work.
I suspect the limit will still bent more than 16X. Router sources would require many more layers AND they would need to be frequency locked (not possible) for nominally lossless combiners to work at all. Your multi - amplifier Radar sources are all driven from the same source so the phases are right for combining according to the above description.
The devil is always in the Engineering detail.
There will be waveguide equivalents but I don't know if a single multi-port combiner is in fact feasible. One problem is that 2GHz waveguide is massive and it would fill up your kitchen!

 

[kevinisfrom]

No doubt but the process of adding more and more sources becomes diminishing returns for each layer of combiners - as I mentioned above. Initially, pairs are combined and then each pair of pairs is combined and then pairs of pairs of pairs. etc. You need 2,4,8,16 amps for it to work.
I suspect the limit will still bent more than 16X. Router sources would require many more layers AND they would need to be frequency locked (not possible) for nominally lossless combiners to work at all. Your multi - amplifier Radar sources are all driven from the same source so the phases are right for combining according to the above description.
The devil is always in the Engineering detail.
There will be waveguide equivalents but I don't know if a single multi-port combiner is in fact feasible. One problem is that 2GHz waveguide is massive and it would fill up your kitchen!

I wasn't sure what combiners were. It sounds like they are used to sync the phase? Which makes me wonder, do you need to also sync the polarization?

 

[sophiecentaur]

Combining two amplifier outputs in a way that means the amps are still matched and don’t “fight each other” requires that their output signals are the same amplitude and phase. You can then use a coupler (various methods) which has four ports. Two input ports and two output ports. One of the two outputs produces A+B and the other produces A-B. If A =B exactly then you get 2A from one and 0 from the other. You terminate the difference port with a matched load and that absorbs any imbalance without feeding back into the amplifiers. Hah. That was 30 yrs ago I last did that.
You can’t just connect amps in parallel and they need isolation like I described. Any other way of combining signals involves losing signal and you may as well use just one amp.
So forget trying to combine more than just a few.

 

[kevinisfrom]

Combining two amplifier outputs in a way that means the amps are still matched and don’t “fight each other” requires that their output signals are the same amplitude and phase. You can then use a coupler (various methods) which has four ports. Two input ports and two output ports. One of the two outputs produces A+B and the other produces A-B. If A =B exactly then you get 2A from one and 0 from the other. You terminate the difference port with a matched load and that absorbs any imbalance without feeding back into the amplifiers. Hah. That was 30 yrs ago I last did that.
You can’t just connect amps in parallel and they need isolation like I described. Any other way of combining signals involves losing signal and you may as well use just one amp.
So forget trying to combine more than just a few.

I think I get it. So you're saying that the loss from the A-B coupler output is wasted energy, and so linking a bunch of routers together and ensuring they all have the same phase, you may be left with a final phased-matched output that has much less power than if you'd just use a single unmatched router by itself?

 

[berkeman]

Another thought, is it possible, hypothetically, to use thousands of routers and create an array that had a lot of constructive interferences at 0th order to reach the power level of a microwave?

do you need to also sync the polarization?

Of course the polarizations need to be aligned. Fortunately, aligning the antennas in one polarization is a lot simpler than shifting the phase of the multiple Tx waveforms...

I think I get it. So you're saying that the loss from the A-B coupler output is wasted energy, and so linking a bunch of routers together and ensuring they all have the same phase, you may be left with a final phased-matched output that has much less power than if you'd just use a single unmatched router by itself?

The problem with your proposal is much worse. Do you know how antenna array beam forming and beam steering works? You use destructive interference at the beam angles where you want little/no power, and constructive interference where you want the most power. But there is no magic going on here -- you still are transmitting full power out of all of the antennas in the array, and losing all of the power at the angles where you are using destructive interference to cancel the Tx waveform.

You do get some addition of the power in the main lobe(s), but you still are wasting all of the power at the angles where you are generating destructive interference. It's not like the power at those angles somehow magically gets transferred to the angles where you have constructive interference.

Antenna arrays are not about generating more power. They are about sacrificing power in order to generate a Tx power pattern that is more focused.

https://en.wikipedia.org/wiki/Antenna_array

 

[davenn]

Don't radars use a bunch of low power solid state RF sources to create an RF beam of higher power?

NO, they use a high power device like a magnetron etc as a microwave oven does

 

[kevinisfrom]

NO, they use a high power device like a magnetron etc as a microwave oven does

Even for phased arrays? I thought there were lower power RF sources for each antenna in the array? Like the giant phased arrays you see on battleships.