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Antenna Theory

antenna-theory.com

128 pointsbsilvereagle52 comments

Once upon a time, when I was very young, I travelled to a faraway island with an antenna in my bag that I had put together myself. Everything I knew about antennas I had learned in a single evening from an elderly retired naval engineer, a no nonsense expert in his field, shaped by lifetime in the military, we sat in his den - a clean office with medals and oil paintings of grey steel warships hung square and level. His serious visage beamed with love and delight when his partner - whose projected persona was the polar opposite of his own reserve - a flamboyantly camp man in trailing colorful silks who brought us cups of tea and exquisite little cakes, and would look at the the notes I was taking an theatrically shudder, swooning with the the back of hand to his forehead that ‘he never would never understand all that stuff’

I wasn’t entirely sure I did either - the retired engineer was able to explain things in the lingo of his trade, but couldnt confirm my attempts to connect the terms he was using to my first year university physics concepts.

But a month later I was sending an email from the jungle via length of unspooled cable

I love this story !!! Dawww. Also naval engineers IME have been some of the best no-B.S. teachers for engineering stuff.

Thanks quinnjh

Antenna theory is a pet peeve of mine. The problem is that it is universally taught with the "Path Loss Equation" and that equation leads to a very poor understanding of how antennas work.

Almost every technically trained person understands that electromagnetic radiation energy dissipates according to the inverse square law in the far field. But the Path Loss Equation jumps through hoops to shoe horn in a frequency term that clearly, if you think about it, has no reason to be there. The distance term is necessary of course but the frequency term scientifically illiterate.

This all comes down to the fact that at some point someone decided they would deem the gain transmitting and receiving antennas as "equal and reciprocal" if they are physically the same. In order to make this delusion work out mathematically a phantom frequency term has to forced into the equation to make the maths work out.

For those who care (not many I expect) the way things really work is that the gain of the transmitter can be function of frequency (geometry and all that) but the receiver has no gain, the energy it traps depends only on its area.

Ok I'm stepping of my soap box, thanks for listening.

> but the receiver has no gain, the energy it traps depends only on its area.

Is that true though? Isn’t this one of those “wave / particle duality” things? Like if you treat the photons as particles the “area” thing makes sense but as a wave, does it?

Nah this is cool.

Where’s a good place to learn more?

It is misleading, but it's there because otherwise you would have to assume the receiving antenna size would change along with the distance.

People practically calculating loss are usually doing so with a specific (or a few specific) antennas in mind. It's not often they would be calculating based on an antenna large enough to not take it into account.

Quite interesting. As someone else mentioned, could you recommend any materials where one can learn more about this?

The ARRL Handbook is a good place to dig into the basics. You can go in several directions from there, but that'll get you started.

"but the receiver has no gain, the energy it traps depends only on its area"

Really no directionality, no resonance? Just make bigger area antenna out of whatever and it collects more energy regardless of geometry?

Please go on this is new information to me.

An antenna is just a passive impedance-matching device, nothing more or less. It matches 377 ohms to whatever the feedline impedance is. Making the antenna's effective area larger is the only way to capture more arriving energy from the transmitter.

At the same time, as its size grows, the area of the antenna that's not exposed to the transmitted wavefront increases even more rapidly than the area that is, making it a losing proposition to keep increasing the size alone. Instead, we use directive and/or reflective elements whose geometry allows a smaller antenna element to receive more energy from one direction at the expense of others.

Just like a lens, in other words. A larger lens or mirror captures more light than a smaller one (focal length considerations aside), but that's not all there is to making a good camera or telescope. The right combination of smaller optical elements can do almost as well as a single huge lens, while being much more practical to work with.

One key point is that in neither case is any amplification or "gain" present. It's just a matter of which approach captures more of the limited number of photons available. Another is that the size of the lenses or antenna elements has to be expressed in terms of wavelength, not absolute spatial dimensions, if you want to compare them directly.

That's ultimately what the path loss equation describes, albeit awkwardly. Path loss increases at shorter wavelengths simply because the exposed areas of the antennas get smaller while the wavefront doesn't.

We can sometimes compensate for that by making the antennas bigger in terms of the number of wavelengths. Mathematically, the path losses involved in the Deep Space Network would be much lower if they could use LF/HF frequencies instead of microwaves, for instance... but to take advantage of that, the antenna sizes would have to increase to ridiculous dimensions, on the order of miles. Microwaves end up being a much better fit in practice. Even if lower frequencies were usable, the resulting increase in atmospheric noise (and decrease in available bandwidth) would swamp any advantages.

> At the same time, as its size grows, the area of the antenna that's not exposed to the transmitted wavefront increases even more rapidly than the area that is, making it a losing proposition to keep increasing the size alone.

And this is based on frequency correct? So frequency is direct component.

>One key point is that in neither case is any amplification or "gain" present. It's just a matter of which approach captures more of the limited number of photons available.

Gain: the factor by which power or voltage is increased in an amplifier or other electronic device, usually expressed as a logarithm.

Gain does not require amplification, the transmission gain of antenna is not based on it, nether is reception. In both transmission and reception it is based on how efficient the antenna is and it's directionality. Both are directly tied to frequency and geometry together, you cannot ignore frequency as the GP said.

This paper seems to be a great resource and helped reaffirm my understanding of frequency being a key component in antenna design and it not being "shoehorned" in. Gain and effective area are proportional to each other and therefore the term gain is used for receiving antennas because it matches it transmission characteristics, hence reciprocity:

"Many antenna properties are the same for both transmitting and receiving. It is often easier to calculate the gain of a transmitting antenna than the collecting area of a receiving antenna, and it is often easier to measure the receiving power pattern of a large radio telescope than to measure its transmitting power pattern. Thus this receiving/transmitting “reciprocity” greatly simplifies antenna calculations and measurements. Reciprocity can be understood via Maxwell’s equations or by thermodynamic arguments.

Burke and Graham-Smith [20] state the electromagnetic case for reciprocity clearly: “An antenna can be treated either as a receiving device, gathering the incoming radiation field and conducting electrical signals to the output terminals, or as a transmitting system, launching electromagnetic waves outward. These two cases are equivalent because of time reversibility: the solutions of Maxwell’s equations are valid when time is reversed.”

https://www.cv.nrao.edu/~sransom/web/Ch3.html

And this is based on frequency correct? So frequency is direct component.

Right, frequency and wavelength are inverses of each other. You can turn one into the other by dividing the velocity by either, f=c/m or m=c/f. Of course c isn't really c, but depends on the transmission media.

Gain does not require amplification, the transmission gain of antenna is not based on it, nether is reception.

By default, power gain is what an RF engineer refers to when s/he talks about "gain." And that does require amplification. You can increase voltage or current through impedance transformation, but never both at once.

By default, power gain is what an RF engineer refers to when s/he talks about "gain."

Really they never use that term with antennas without amplifiers? Seems like its all over the literature, again back to previous material:

3.1.3 The Power Gain of a Transmitting Antenna

The power gain G(θ,ϕ) of a transmitting antenna is defined as the power transmitted per unit solid angle in direction (θ,ϕ) relative to an isotropic antenna, which has the same gain in all directions. Frequently, the value of G is expressed logarithmically in units of decibels (dB):

(3.31) For any lossless antenna, energy conservation requires that the gain averaged over all directions be ⟨G⟩=1

(3.32) Consequently, all lossless antennas obey

∫sphereGdΩ=4π.

(3.33) Different lossless antennas may radiate with different directional patterns, but they do not alter the total amount of power radiated. Consequently, the gain of a lossless antenna depends only on the angular distribution of radiation from that antenna. In general, an antenna having peak gain G0 must beam most of its power into a solid angle ΔΩ such that ΔΩ≈4π/G0 This motivates the definition of the beam solid angle ΩA

ΩA≡4πG0.

(3.34) Thus the higher the gain, the smaller the beam solid angle.

Directional antenna direct more power to the receiver they do not add more power through amplification. You could also say they waste less power toward no receiver. Reciprocally it works for the receiving antenna as well and is again referred to as gain everywhere I have seen.

Key phrase: "relative to an isotropic antenna." They can call it power gain all they want, but it's still not power gain. The literature is full of imprecise language, and it sounds like that's an example.

If an antenna exhibited power gain, you could build a perpetual motion machine with a pair of them. It's not power gain. Instead, it's just less power loss.

Please point me to precise language that describes antenna gain without using the word gain rather than making a vague declaration. You seem to be trying to pigeon hole the word gain to mean only electronics gain [1] while the word gain has various related meanings [2] and in the RF world antenna gain is precisely defined and does not involve amplification [3].

[1] https://en.wikipedia.org/wiki/Gain_(electronics)

[2] https://www.merriam-webster.com/dictionary/gain

[3] https://en.wikipedia.org/wiki/Antenna_gain

Antenna gain relative to an isotropic radiator is a thing. Absolute power gain from a passive antenna is not. There is no such term as electronics gain.

I really don't know how to explain this any more clearly; we're probably talking past each other. In engineering, we don't use the M-W dictionary. Things have to be spelled out more precisely, such as (in this case) exactly what the reference is for a given gain figure.

When you see the term 'dB' used in technical writing, it's only a unitless ratio, not a power level, unless explicitly associated with a reference power level. In typical RF discussions, you'll frequently hear 'dBm' or 'dBw' used to describe absolute power levels relative to one milliwatt or one watt, for instance. But the antenna people are more likely to use 'dB' by itself to refer to the gain of one antenna over another, or perhaps 'dBi' to refer to gain over a theoretical isotropic antenna. The latter quantity normally does exceed zero, but only by focusing the existing RF power, not by generating or amplifying it.

A related term is ERP, or effective radiated power. Imagine connecting a 1-watt transmitter to the 70-meter dish at a Deep Space Network tracking station. The ERP will be over ten million watts, but it won't even cook your lunch. It's effective power, expressed relative to what you could deliver to a target antenna with an isotropic radiator. Not actual physical power, in the sense of work divided by time.

"One key point is that in neither case is any amplification or "gain" present."

"Antenna gain relative to an isotropic radiator is a thing."

Which is it? Gain clearly does not mean amplification always as I pointed to multiple references and you provided absolutely none.

"There is no such term as electronics gain."

Again: https://en.wikipedia.org/wiki/Gain_(electronics)

In electronics, gain is a measure of the ability of a two-port circuit (often an amplifier) to increase the power or amplitude of a signal from the input to the output port

What game are you playing here, are you really just redefining the english language to win an internet argument?

At the transmitter there are two kinds of gain. The first is simply crack up the power and more signal energy will be received at the receiver. The other "gain" is where the physical shape of the transmitting antenna directs more of the energy it receives in one direction (usually straight ahead) rather than a different directions. The amount of gain due to the physical shape will vary with the frequency of radio wave relative to the physical shape the antenna.

Think of a flashlight. The beam is brighter in the middle and falls off towards the sides. That's "gain" compared to a flashlight that beams light in all directions equally, like a sphere.

So while the transmitter can "shape the beam" to create gain, the receiver cannot (though the path lose equation implies that it does). The receiver can physically just trap the amount of watts per square metre that it receives and this amount depends only on its size and not on the frequency of the incoming radiation.

So the transmitter and receiver antennas are very different in their physics of how the operate but the Path Loss Equations fudges things to make it look like they are the same ie that the gain of either is equally dependent on the frequency/wave length when in fact that's false and the two antennas are asymmetric in how they respond the carrier frequency.

So radio telescopes don't shape the incoming radiation? You can't just have a big flat antenna with a lot of area, they use dish reflectors and wave guides to shape the incoming radiation down to the actual antenna that has a size determined by guess what, FREQUENCY.

"Figure 3.3: Most high-frequency feeds are quarter-wave ground-plane verticals inside waveguide horns. The only true antenna in this figure is the λ/4 ground-plane vertical, which converts electromagnetic waves in the waveguide to currents in the coaxial cable extending down from the waveguide.

According to the strict definition of an antenna as a device for converting between electromagnetic waves in space and currents in conductors, the only antennas in most radio telescopes are half-wave dipoles and their relatives, quarter-wave ground-plane verticals. The large parabolic reflector of a radio telescope serves only to focus plane waves onto the feed antenna. (The term “feed” comes from radar antennas used for transmitting; the “feed” antenna feeds transmitter power to the main reflector. Receiving antennas used in radio astronomy work the other way around, and the “feed” actually collects radiation from the reflector.)

https://www.cv.nrao.edu/~sransom/web/Ch3.html

What ever it is you think might be happening at the receiver, if it violates conservation of energy it's unlikely to be correct.

Conservation of energy directly leads to the role of frequency in antenna reception and reciprocity:

Figure 3.5: A cavity in thermodynamic equilibrium at temperature T containing a resistor R is coupled to an antenna, also at temperature T, through a filter blocking electromagnetic radiation but passing currents having frequencies in the range ν to ν+dν.

Imagine an antenna inside a cavity in full thermodynamic equilibrium at temperature T connected through a transmission line to a matched resistor (whose resistance equals the radiation resistance of the antenna) in a second cavity at the same temperature (Figure 3.5). A filter between the cavities passes only currents in a narrow range of frequencies between ν and ν+dν. Because this entire system is in thermodynamic equilibrium, no net power can flow through the wires connecting the antenna and the resistor. Otherwise, one cavity would heat up and the other would cool down, in violation of the second law of thermodynamics.

The article casually equates gain to change in "power or amplitude of a signal." While not wrong per se, this is one of the drawbacks of using lay references in specific fields. Power and amplitude mean the same thing to 99% of people, but they are not the same thing at all. Amplitude is measured in volts, while power is measured in watts. Voltage doesn't do work, convey information, or obey conservation laws; power does.

As a result, when engineers refer to gain in voltage alone, they will (or should) go out of their way to use the term "voltage gain." Otherwise it's a power ratio, in which the denominator is typically a given number of watts or the power present at the feedpoint of a hypothetical isotropic antenna.

Antenna people rarely care about voltage gain outside the context of impedance matching or regulatory matters. Voltage is useful when discussing field strength in volts per meter, but at the end of the day, the antenna engineer's job is to deliver power, not voltage. (Also, to avoid embarrassing Steve Jobs.)

You casually provide nothing contradictory to what I have stated and have multiple times dismissed power gain in antennas, electronic amplifiers have electronic gain, antennas have gain not dependent on electronic amplification, gain is the correct word. With antennas it is power gain not voltage gain, but gain non the less, thank you for confirming GAIN is the correct term in the most ridiculous concession possible...WTF.

Sounds good, best of luck in your studies.

I assume you're referring to the Friis transmission formula? It only references frequency because that's usually more convenient than wavelength. I hardly think it's fair to call that scientifically illiterate. Also converting from wavelength to frequency is trivial, not jumping through hoops.

To be clear, given two identical isotropic antennas (zero gain) in the far field, there absolutely needs to be a frequency^2 term (or 1/wavelength^2) in the "path loss". This is the reason AM radio has so much greater range than FM, for instance.

Transmit power, and gain of either or both antennas simply adds (dB) to that path loss. Note that receiving antennas absolutely can have gain. While it does tend to be proportional to area, the "receiving area" concept is actually a somewhat imprecise simplification (consider, what's the area of a Hertzian dipole? or compare the areas of a Yagi and simple dipole).

> the receiver has no gain

That implies that everyone from Yagi onwards has been wasting their time designing better antennae?

Antennas are weird beasts. Their behavior and performance can be predicted and measured in very technical ways but, at the end of the day, throwing a random length of wire over a tree branch, cut to 1/2 or 1/4 of the operating frequency wavelength can be all one needs to communicate with another station, even a very lower transmit power. This applies primarily to HF and VHF. Frequencies reaching up into the microwave range is where antenna design starts becoming a dark art, practiced by wizards and neuromancers.

I've used old school HF portable radios when I was a ranger and in a valley with no line of sight to our VHF repeaters in the park.

The fun part was finding a clearing big enough to string the antenna out. Usually involved ascending to the bushline or descending onto the river flats.

Being able to listen to Scottish life guard boats from the other side of the world, at dusk as the ionosphere layers changed, was cool. Zimbabwean cricket broadcasts could be listened to up until about 9:30am in the morning.

Vector Network Analyzers have come down in price to the $100 range, which is amazing in and of itself, so the home experimenter, likely a Ham radio operator, has a lot more capability to precisely measure things that were pure guesswork in the past.

Of course, the anechoic chamber is a nice thing to have. I once got to see the Anechoic chamber at Northrup Grumman near Chicago during a open house... a theater size room they used for various measurements. I'll never forget it.

This is a nice collection of information. The other place to get this type of data in the past was the Amateur Radio Handbook from the ARRL.

You can always make impedance measurements with a slotted line, 6-port reflectometer, or vector voltmeter if you don't have access to a VNA. My undergrad microwave professor had us learn on the slotted line before letting us touch the VNA.

Any good materials/references for this?

I've got some steady-state 60GHz stuff I'd love to try (non-radar), but the equipment is prohibitively expensive.

Being able to analyze things with much less expensive, even if more labor intensive, tech would be welcome.

With a free space wavelength of 5 mm, any mechanical probing is going to involve mechanical stages and micrometers. Yikes!

There is a rapid cycle of development occurring with these low end VNAs. Cheap spectrum analyzers are beginning to appear as well.

Also, here's a good place for design theory and construction practice of consumer-grade TV and FM radio antennae:

https://www.digitalhome.ca/forums/antenna-research-developme...

Antennas are super fun, they still feel like magic to me every time I see one. In college I took a microwaves theory course where we had to design antennas for some problem sets, and we gave them to some dude in a basement lab who then fabbed them in like an hour for us to test. Kind of mind boggling that with a few tools and handiwork you could produce real electronics with reasonable characteristics!

A $500 mill will let you mill out one or two sided circuit boards without anything particularly dangerous used.

The future is wild: $500 and some free software let’s you build electronics at home.

When I worked with radio engineers, and they told me it's impossible to fully model a Yagi antenna, I was dubious.

But sure enough, developing a new Yagi really depends on trial and error at the end of the day.

R.W.P. King studied wire dipoles for years and supposedly produced over 100 PhD students doing the same. The details are really really hard to get right and absolutely require empirical work. There are two core problems. One is that while Maxwell’s equations do model practically all EM phenomena, and therefore should make everything amenable to simulation, it requires detailed knowledge of material properties everywhere. Dealing with pure vacuum (or crisp, clean air over short distances) is therefore totally easy because it is all homogeneous and well-measured. But antennas convert electrical activity to traveling waves in space, so they are necessarily made up of different matter than the thing you want to transmit or receive into. Now you need to know the material properties of the antenna structure in a way that is incredibly hard to know. So we just approximate it as a series of uniform copper cylinders and say that one of them is connected perfectly to a cable using an infinitesimally thin gap. Yagi-Uda antennas depend upon complex interactions among the wires to achieve surprising levels of gain, and these details actually matter strongly. But they are practically unmodelable. So we simulate something and work hard to reconcile both the simulation (requires a lot of theoretical knowledge) and the actual antenna.

The other problem is also hard. In Maxwell’s equations, you can book it down to a single equation describing how energy is converted to a traveling wave. That energy conversion involves a Dirac delta function (our shorthand for “itty bitty thing the rest of the system doesn’t otherwise interact with “). The delta function goes to infinity at some point. A real energy source is just some weighted collection of these deltas. In other words, I have a bunch of singularities. At some nominal distance from each singularity, the math is well-behaved. Close-up, however, things fall apart. Numerical precision is exhausted quickly, field strengths go off the rails, phase velocities exceed the speed of light (Hertz has some fun wtf moments at the end of one of his notebooks grappling with this), and other fun effects. Software hates this. So theoreticians come up with ways to model these singularities at a close, but non-zero distance for a bunch of special cases. Software must decide among the cases with hints from the human operator and match up with the desired geometry. It’s super hard to get right in all cases. My advisor and others at OSU spent decades coming up more special cases to enable rapid design of dish antennas, and certain shapes of wire antennas, and even to accelerate stealth F-117 design.

Compared to all of this craziness, even a theoretical person like me will still spend a lot of time in the lab because it is just faster and strictly more accurate.

Antenna design is often characterized as black magic. It really isn’t. We just don’t know literally everything about the world and it sometimes matters for these devices. The mystery is not inward towards the mind, but outward towards the universe at small and large scales.

Wow, thanks for that comment, that was really informative and enjoyable :)

A very interesting site full of downloadable papers on various subjects including antennas. https://www.jpier.org/PIER/pier.php

This one for example may turn useful if one needs to build a WiFi multiband planar internal antenna. https://www.jpier.org/PIERL/pier.php?paper=11073004

...yes, that stuff is black magic/voodoo

(2016), previously: https://news.ycombinator.com/item?id=19708982

Excellent stuff, surprised I’ve never stumbled upon the site before. It’s not just about antennas, it also offers concise yet intuitive explanations of related concepts such as Fourier analysis.

I may be mistaken, but this site is by a former Apple antenna engineer, isn't it? If he's who I seem to recall he is, he must have some incredible Steve Jobs war stories.

"You're holding it wrong"

Exactly. For his sin, exiled from the Garden.

Another great site in this area is microwaves101.com A huge range of topics, and pleasantly snarky anonymous editor.

`Complexity is not a sign of intelligence; simplify.` couldn't agree more...

Site looks infested with ads

With Ublock Origin I see only one, which would be very easy to kill using its element zapper tool.

On mobile i see them all and I normally i don't mind but on this site they show ads as navigation links making it pretty hard to navigate the site. Especially when the images the ads use are designed to make them not look like ads.

Firefox Android with uBO and not even that single ad. A nice text only site with GIFs for formulas and diagrams.

Reply on news.ycombinator.com