# TV antenna dish: depth, f/D, or focal distance

In summary: Thanks, Baluncore. The model is: Dish Network Satellite 500 KIT Pro Twin LNB Antenna 110 119 DP LNBF DishPro plus.
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TL;DR Summary
What is the approximate depth, f/D, or focal distance of a standard TV 20 inch (58.8 cm) parabolic (offset) antenna?
I am covering parabolic antennas with a school student in elementary physics, and I was looking for the specs of the (offset) antenna on her family's roof in order to calculate things like focal distance. She sent me a photo (she is on another continent), I found the brand specs, which lists it as a 20 inch antenna... but I could find nowhere the depth or focal distance, or f/D ratio listed. Not being an engineer, I am probably looking incorrectly.

I am not sure whether it is allowed to list a particular brand here, so out of caution, I won't. But if someone tells me it is allowed and desirable, I will post the precise model.

It would help if we had a link to the particular model.
The focal length is the distance from the focus to the vertex. An offset dish is designed so the shadow of the LNA at the focus, and LNA support do not fall on the dish surface, so the vertex can be hard to find or missing. The approximate vertex is probably the surface of the dish that is closest to the focus support.

Thanks, Baluncore. The model is:
Dish Network Satellite 500 KIT Pro Twin LNB Antenna 110 119 DP LNBF DishPro plus

I tried tracking down the information on their website. Pointless, all they have is consumer information there. However I did find a page with a link for support with live chat:
https://my.dish.com/support/contact

Another possible approach is try to get a side-view photo taken at the same distance with the same camera and zoom setting. Knowing the dish diameter, you may be able to do some photogrammetry and calculate the distance from the dish surface to the receive head. Try a Google search for Photogrammetry Software (there are even some free ones).

Please let us know any results, good or bad, so others may benefit from the knowledge.

Thanks,
Tom

I don't know if this would help but this link suggests a formula for an offset dish
f=D2/16c
where
f is the focal length of the reflector
D is reflector diameter in same units as wavelength
c is depth of the reflector

It looks just like a rule of thumb but it may be near enough for you.

Thanks, Tom G. and sophiecentaur.

Tom G.: the link you gave appears to be broken: I tried it on two different browsers, two different computers, two different days. I tried going to the website directly, same result. Timing out, cannot connect to this site, Error message, etc.

sophiecentaur: Thanks, but it is precisely the value c which is missing.

but it is precisely the value c which is missing.
I would think you could make a fixture to measure this.

Place a rigid straight edge across the dish and measure the depth to the center of the dish keeping the measuring instrument square to the straight edge. The measurements should be of the actual parabola. Do not include the rolled edge of the dish in your measurement. When measuring, be as precise as you can be.

Tom G.: the link you gave appears to be broken: I tried it on two different browsers, two different computers, two different days. I tried going to the website directly, same result. Timing out, cannot connect to this site, Error message, etc.
Hmm... Still works here in the USA. They could be selecting which countries they will accept. Their list of language packages includes English, several European, Hebrew, some Asian and Asian-Pacific Islands, and a few African.

It would be worth trying to get access from a computer using a different ISP.
Also if you are using an Educational account, those could be blocked.

Here is their contact info as listed by
https://www.networksolutions.com/whois/results.jsp?domain=dish.com
Registrant Name: Dish Network LLC
Registrant Organization: Dish Network LLC
Registrant Street: 9601 S MERIDIAN BLVD
Registrant City: ENGLEWOOD
Registrant State/Province: CO
Registrant Postal Code: 80112-5905
Registrant Country: US
Registrant Phone: +1.3037231000

Cheers,
Tom

Summary:: What is the approximate depth, f/D, or focal distance of a standard TV 20 inch (58.8 cm) parabolic (offset) antenna?

I am covering parabolic antennas with a school student in elementary physics, and I was looking for the specs of the (offset) antenna on her family's roof in order to calculate things like focal distance. She sent me a photo (she is on another continent), I found the brand specs, which lists it as a 20 inch antenna... but I could find nowhere the depth or focal distance, or f/D ratio listed. Not being an engineer, I am probably looking incorrectly.

I am not sure whether it is allowed to list a particular brand here, so out of caution, I won't. But if someone tells me it is allowed and desirable, I will post the precise model.
For an offset paraboloid, in concept, the reflector is cut from an off axis portion of a very large reflector, so the simple formula relating dish depth and focal length will not work.

sophiecentaur: Thanks, but it is precisely the value c which is missing.
If the student can't get to measure the depth of the dish then you would have to use a 'typical value' for f/D. But do you really need this information? The length of the feed support is a good indicator of the actual focal length f of the parabola. To estimate that remotely then take a photo from the side and, if the dish is a typical 20" (60cm) diameter then simple geometry and scaling can tell you the spacing of the feed from the centre of the parabola. Most offset dishes for domestic TV have the centre of the parabola on the edge of the reflector, just below the feed.

A similar exercise can give you a good approximation for finding f/D if you feel you really need it. What is the context of the OP? It's a school exercise so it will not be too technically demanding.

Thanks very much, sophiecentaur, tech99, TomG and dlgoff. Some comments:

tech99 said:
For an offset paraboloid, in concept, the reflector is cut from an off axis portion of a very large reflector, so the simple formula relating dish depth and focal length will not work.
I have found that out, so, if I understand correctly, the "20 inch" is not uniform, but I need the width and the height (by which I presume is meant the maximum and minimum diameters of the border?) , so that a widespread formula would be Focal length=(width^3) /(16*depth*height) (Taken from http://docshare01.docshare.tips/files/23977/239773115.pdf) , although there seems to be several other formulas proposed on other sites.

dlgoff said:
I would think you could make a fixture to measure this.
Unfortunately, I do not have direct access to the dish -- it would be about ten thousand kilometers of flight -- and I am not about to ask an eleven-year old pupil to go out on her roof to measure it.

Tom.G said:
Hmm... Still works here in the USA. They could be selecting which countries they will accept. Their list of language packages includes English, several European, Hebrew, some Asian and Asian-Pacific Islands, and a few African.

It would be worth trying to get access from a computer using a different ISP.
Also if you are using an Educational account, those could be blocked.
I tried from a different ISP without success, and so that is not the problem. I am not sure what the language package has to do with it -- but the language of the country I am writing from is included in that list. I am not using an Educational account. The idea of trying it from the US induced me to turn on my VPN for the first time in a long time, only to find out that there seems to be a glitch in it -- so I wrote "support", but that may be a while to get it straightened out, so I will just try to find an acquaintance in the US to try it.
sophiecentaur said:
If the student can't get to measure the depth of the dish then you would have to use a 'typical value' for f/D.
That would be fine, but I don't know what a typical value is. In https://www.tutorialspoint.com/antenna_theory/antenna_theory_parabolic_reflector.htm they say it varies between 0.25 and 0.5, but then a calculation in https://www.qsl.net/n1bwt/chap5.pdf the author uses a ratio of 0.69
sophiecentaur said:
What is the context of the OP? It's a school exercise so it will not be too technically demanding.
That is correct, I don't need answers to be down to the micrometer. Most of the calculations will actually be done by me before I present it, in simplified form, to the student.
sophiecentaur said:
The length of the feed support is a good indicator of the actual focal length f of the parabola. To estimate that remotely then take a photo from the side and, if the dish is a typical 20" (60cm) diameter then simple geometry and scaling can tell you the spacing of the feed from the centre of the parabola. Most offset dishes for domestic TV have the centre of the parabola on the edge of the reflector, just below the feed.
Excellent suggestion: that is probably my best bet, as the student has shared quite a good photo of it from as close as she dared get to it. I will probably do that ( as it is her photo and I have not asked for her permission to use it publicly, I guess I don't have the right to post it here). I shall give that a try in the absence of the direct specs.

Excellent suggestion: that is probably my best bet, as the student has shared quite a good photo of it from as close as she dared get to it.
I still think you should do what I suggested in post #2. Measure or estimate the distance between the focus and the point on the dish surface closest to the focus support. That will be close enough for an educational exercise.

Baluncore said:
Measure or estimate the distance between the focus and the point on the dish surface closest to the focus support.

Just to see if I understand this, I refer to a generic picture (this is not the antenna concerned, but a photo with no brand names on it, so as not to trespass any legal boundaries with which I am not familiar): are you saying that the focal distance is the length of the bottom bar in this picture?

are you saying that the focal distance is the length of the bottom bar in this picture?
Approximately yes, but it will depend on how you mount the LNA at the focus.

Find the point on the dish where a normal to the dish surface passes closest to the focus.
That is the vertex. It will be close to where the bottom bar is attached to the dish surface.
Measure the distance from the vertex to the focus.

I ask again what is the context of the enquiry. Why would someone need the f/D ratio unless it was for some relatively advanced comms communication. If it's just to study the action of a parabolic reflector then is the Gain value required? There's a lot of chat about that sort of thing but, as you've already found, manufacturers and suppliers don't want you to 'worry your pretty little head' about that sort of thing if you're 'just' a potential customer. Too many details would enable you to have a valid opinion about their stuff. Like HiFi manufacturers, they thrive on customer ignorance.
If you leave aside the offset issue and looked at what's written about conventional reflectors - e.g. many radio telescopes and microwave link terminals - you might find the sort of general knowledge that your guy may actually be needing.

Baluncore said:
I still think you should do what I suggested in post #2. Measure or estimate the distance between the focus and the point on the dish surface closest to the focus support. That will be close enough for an educational exercise.
If I understand it, this would be exactly correct if the dish were an offset cut from a hemispherical collector. As long as the dish is not too deep this is probably adequate. The spherical reflector is a whole lot easier to understand so that may be a pedagogical plus.

But what does the student actually want to know and why? Are we actually addressing the right question here?

Perhaps the student needs help with formulating a meaningful question. I remember being asked some crazy questions when I was teaching.

I am not about to ask an eleven-year old pupil to go out on her roof to measure it.
I would say it depends on the eleven-year old.

So what are the terms of the study that this 11 year old is doing. Why is f/D relevant?

It looks like the mounting ring for the LNA points directly at the important point in the dish, no?

berkeman said:
It looks like the mounting ring for the LNA points directly at the important point in the dish, no?
That depends on why a point is "important". In an offset dish, the LNA certainly does not point at the vertex.

The focal element points at the centre of the aperture, which is the area of surface that is present. Think transmitter; The antenna element at the focus illuminates the dish surface. Best efficiency per dish area is when the surface is evenly illuminated by the centre of the primary lobe from the focus.

Offset dishes are not usually round, they are elliptical, but not quite as much as the 45° diagonal mirror at a 90° bend in an optical system.

Obviously, the rolled edge of the dish increases the rigidity of the surface so it remains an accurate paraboloid. But less obviously, it introduces a gradual phase error at the edge of the aperture that has been carefully designed to reduce the side-lobes by blurring the sharp step edge of the aperture at the wavelength of operation.

Thanks, Baluncore, sophiecentaur, hutchphd, dlgoff, and berkeman. Some comments:
Tom.G said:
However I did find a page with a link for support with live chat:
https://my.dish.com/support/contact

sophiecentaur said:
There's a lot of chat about that sort of thing but, as you've already found, manufacturers and suppliers don't want you to 'worry your pretty little head' about that sort of thing if you're 'just' a potential customer. Too many details would enable you to have a valid opinion about their stuff. Like HiFi manufacturers, they thrive on customer ignorance.
Indeed, I had a friend in the US contact the company involved and ask for the depth, focal distance, and/or f/D ratio, and when, in response to the chat request for a 16-digit number on the bill, my friend explained that it was for an example for a science class, nothing more, the company refused to give any information. (The company has just dissuaded my friend from ever buying anything from it.)

sophiecentaur said:
I ask again what is the context of the enquiry.

sophiecentaur said:
But what does the student actually want to know and why?

sophiecentaur said:
Perhaps the student needs help with formulating a meaningful question.
The student herself has not posed a question: it is I who hoped to find some meaningful questions based on a real-life example. In general I try to know more about a subject than I am going to ask the student to know, so that my simplification is not too simple (e.g., billions of books on quantum theory get boiled down to "physics of the tiny"...) and that I will be ready to answer any questions the student may have, even if I need to simplify them. The student is only 11 years old, and is not (yet?) into electrical engineering, so much of the interesting and elsewhere useful information presented here, for which I am very grateful, is not going to end up in the final questions that I will pose the student (or other students), but is nonetheless worthwhile for me.

Finally, having put my cursor incorrectly, one quote got embedded in another, and I don't see how to delete the quote-references:

Finally, having put my cursor incorrectly, one quote got embedded in another, and I don't see how to delete the quote-references:
Click on the [ ] in the reply box toolbar to toggle BB code. Then edit and move the text.

The student is only 11 years old, and is not (yet?) into electrical engineering,
In which case I would say that the level of demand that your question to the student would be far too high and would introduce something very far down that particular line of enquiry. At that age, the idea of ray tracing to show how a parabolic dish basically works (laws of reflection to produce a point image from parallel rays) and an idea of why size matters would be, imo, more than enough. The amount of energy intercepted by a dish of that area could be introduced but the numbers involved are so big and so small that there will be a lot of zeros floating around. This is why we use dB in this context but would an 11 year old cope with dB (a lot of adults are totally flummoxed by them)?

Baluncore said:
Click on the [ ] in the reply box toolbar to toggle BB code. Then edit and move the text.
Thanks. Also thanks that you have removed them from the visible post. (Interestingly enough, they reappear when I press "edit".)
sophiecentaur said:
introduce something very far down that particular line of enquiry. At that age, the idea of ray tracing to show how a parabolic dish basically works (laws of reflection to produce a point image from parallel rays) and an idea of why size matters would be, imo, more than enough.
Indeed, I am starting quantitatively on finding the focal distance of a simple parabola, and then only qualitatively discussing the idea of cross-sections of a dish that will give two different parabolas, and why this will alter the focus, and why, roughly, one even wants an offset antenna. (As I work out the information that, for example, Baluncore wrote in #21, may or may not figure into the qualitative explanation, but the information will at least increase my understanding.) Most of the quantitative information I was seeking were for me to work out the details to see if any of them would be worthwhile to present, either in qualitative or quantitative form.
sophiecentaur said:
This is why we use dB in this context but would an 11 year old cope with dB (a lot of adults are totally flummoxed by them)?
The exact mathematical relationships are indeed too advanced for an eleven year old; in schools decibels are first introduced with a brief explanation of a decibel being used as "a measure of intensity, for example, of sound" (because that is where they will first encounter it) as an example of a logarithmic scale, and only a few years later, is the definition connected to power quantities; the kind of depth you are referring to is usually left for the university.

Tom.G
sophiecentaur said:
So what are the terms of the study that this 11 year old is doing. Why is f/D relevant?
Suppose we started with a simple case, where the paraboloid was not offset but was a rotated parabola; then from the D Diameter (20 inches) and the f/D, one has the focal length, and the student could write the equation of the generating parabola.

but the information will at least increase my understanding.
I think that says it all. You are interested in finding stuff for yourself and I fear you are missing what an 11 year old will want or could cope with. Is it really of any consequence that the design criteria of a small aperture dish needs an offset feed because the feed would shade the reflector. Alongside that design aspect you would need to point out why a modern Low Noise Converter is necessary to enable such a small dish to work and why that is stationed at the feed point to allow a lower I.F signal to be taken to the receiver on cheap downlead. Etc. etc. etc.

Suppose we started with a simple case, where the paraboloid was not offset but was a rotated parabola; then from the D Diameter (20 inches) and the f/D, one has the focal length, and the student could write the equation of the generating parabola.
Which country do you live in where 11 year olds know enough co-ordinate geometry to understand about generating 3D curves? The only really important part of the geometry is the Area that intercepts the signal and they can possible do the area of a circle. That tells you roughly and relatively how much Energy is received. Compare it with a large radio telescope, for instance.

Here are a few links you may find useful:

Design Method for Offset Parabolic Reflector:

Offset Fed Parabolic Dish Antennas: (probably more useful)
https://www.qsl.net/n1bwt/chap5.pdf

(above found with:
One design subtley mentioned is that the reflector should appear circular when seen through the borehole. Sorta makes sense but not obvious at first glance!

Also try searching for: offset parabolic reflector

Hope it helps!
Tom

Thanks, Tom and sophiecentaur
Tom.G said:
(probably more useful)

Tom: You are right, the second link is more useful with some very nice simple diagrams that can be used to give the general idea of an offset antenna to a school pupil without going into the mathematics (which is as much as I will cover with this pupil). I will look through the first one to increase my own understanding as a plus, but would not let a school pupil within eyesight of that one -- don't want to scare them away! Yes, I have searched myself for further resources, but the explanations on this Forum have been additionally helpful, and I thank everyone for the help. I think I now have plenty of information, way beyond what I will present to the pupil but it has improved my own understanding enough so that, hopefully, I don't say anything stupid when presenting the simplified version. (Indeed, I would have if I had based my explanation purely on what I knew before I posed my question here.)
sophiecentaur said:
You are interested in finding stuff for yourself
I am afraid that I must have expressed myself badly. My original goal in posting my questions was to fashion some simple problems and explanations based on an antenna connected with the pupil's life (although it may sound silly to an adult, a school child will be more interested if we are talking about HER antenna rather than some generic antenna. Update: I got the f/D (0.49) from a German firm for one of their antennas; at least in this case the Germans appear less paranoid than the Americans.) Upon reading the replies, I realized that my understanding of the antennas was deficient and would have led me to making incorrect statements, even at the most basic level. I now have enough, as I wrote in the above comment, and, as the Americans say, "the rest is gravy". That is, I am glad that a side effect of this query has improved my knowledge not only for the explanation for this child, but also beyond that.

sophiecentaur said:
Which country do you live in where 11 year olds know enough co-ordinate geometry to understand about generating 3D curves?
Actually, the situation involves three countries: I live in one country, the 11-year old lives in another (the sessions are digital), and the 11-year old (almost 12) is being homeschooled by immigrant parents who largely use the standards of their home country. (I am familiar with all three education systems.) Anyway, this international muddle aside, in none of these countries do 11-year olds know anything about generating curves in coordinate geometry -- the only coordinate geometry I will use is a two-dimensional parabola (which is even a little early for most 11-year olds, but this one is doing fine), and the idea of generating a three-dimensional curve is not beyond anyone who has seen (or better felt) a clay pot being made on a potter's wheel. (Also, in the other diretion, the idea of something having different cross-sections is also easy to grasp for anyone who has cut vegetables, fruit, bread...) Again, most of what I have learned here will help me to avoid saying something incorrect when presenting even the basic ideas (for example, the question, after a child has learned about a 2-D parabola's focal point is why the parabolic dish's focal point isn't in the center, and why it appears oval -- I don't want to just wave my hands and give no reply; that is as frustrating for students as an explanation that is above them. But a teacher who doesn't have more background information that she is presenting to the students is likely to veer in one or the other misleading directions. (Or, to use a bit of a silly analogy: an answer should be a vector, not a scalar.)

Last edited:
Tom.G
I am afraid that I must have expressed myself badly.
And my reply was far too heavy - sorry.
I strongly approve of linking Science education with life and, personally, I reckon I have always given better value to students when I am fully across what I am telling them about. There is plenty of juice in your particular lemon of choice and I think you can deliver 'a useful package' as long as you steer her into areas where she is likely to ask questions that are in your level of expertise. So, why not just consider the Area that intercepts the microwaves? How would you deal with "Why is f/D important?"? The f number of camera lenses would be an approach but there's no way she'd be aware of that being an issue on her smart phone. Otoh, the actual Area would make sense to anybody. Offset feeding and shading are no more than asides at this level. A lamp and a mirror would show how offsetting a plane reflector works and that's something she may well have come across before. Looking directly behind you in a mirror is not possible; you have to offset it to get your head out of the way.

In many countries, the size of domestic dishes is limited by planning authorities (makes sense to an 11 year old). The power of a satellite transmitter is limited by the size and cost of the satellite and solar panels. (plenty of example specs for TV satellites).
The satellite has a very wide antenna, to focus all its power into the 'footprint'. That power is spread over the whole of the service area so individuals get much less. 20cm diameter 'just works' most of the time. Work out the area of their country in m2, compared with a 20cm dish area, to give the share that each TV gets.

The geometry of a parabolic reflector is great material and there are several ways she could draw a 2D parabola. This link contains a download with a method involving string and a set square / any rectangle. The cleverness of having equal distances on all paths to the focus could (should) be exciting.

Heavy rain will sometimes block reception (she may be aware of that or she can take a look if there is a rainstorm). Those are all issues that an 11 year old can grasp.

sophiecentaur said:
why not just consider
Thank you, sophiecentaur. Your post contains some excellent suggestions which I will definitely follow up on.
sophiecentaur said:

Thank you, sophiecentaur. Your post contains some excellent suggestions which I will definitely follow up on.

Sorry - senior moment. This was the link (one of many). There are a lot of different methods but the link near the bottom is a document that's obviously aimed at minimal algebra.

It's a development from the ellipse drawing method which uses a length of string between two pins. If you have about three times the length of string (iirc) as the distance between the pins and keep the string taught with a pencil, the pencil will trace out an ellipse. A parabola is the extreme version of an ellipse, with its other focus out at infinity.

Do some searching and you'll find other, harder methods.

Super! The link looks like it contains lots of useful stuff, thanks.

The two-pin-and-a-string method is of course classic for an ellipse; wandering around the Internet a while back I was amused to find that carpenters (or at least the traditional type, not the ones that mass-produce and design by computer) make their oval tables which very closely approximate an ellipse by conjoining four circular arcs. It's a method that is a little too tricky for most school children, but I tried it (making the curve, not making an actual table), and it works beautifully. However, for the students I collect easier methods.

A great method for conic sections is to get a few Styrofoam/Styropor (closed-cell extruded polystyrene foam, if one needs to avoid brand names) cones, and a big knife, color the cones, and then start hacking! Students like it...the bigger the knife and the faster the slices, the more attention one gets.

Thanks again!

Tom.G and sophiecentaur
conjoining four circular arcs
The sandpaper interpolator does a great job. There are worse errors using a jigsaw (for me, at least).

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