View Full Version : Help re: method of moments (Antenna solutions)
I am sure everyone is familiar with the Yagi-Uda directional beam antenna: The reflector is a tad longer than a half-wavelength, and the director(s) is/are a tad shorter, but how do you get the correct dimensions to, say, null the rearward signal and get a great f/b ratio?
Now, before anyone suggests I simply use some antenna program (Yagi for windows, NEC, etc.) or follow "tried and true" formula, let me point out that, should I want to optimize the antenna for some parameter (f/b ratio, gain, impedance, etc.), it is more-or-less required that I actually understand how to work out the problem by hand.
If someone could simply work out a three element Yagi antenna, using the Method of Moments (use only 3 or 4 moment separations, for simplicity), then I would probably be able to understand what is what.
For example, using a program I found on the web, using only four (4) "segments" in the 1/2 wavelength (a Java applet in this case), a Yagi with reflector=0.51 L, driven element=0.475 L, and the sole director=0.46 L, had the following characteristics:
Input impedance = 16.05 - j14.53 Ohms
Gain = 7.89 dBi (which is 5.76 dBd, I think)
f/b ratio = 18.31 dB (wow! good)
Note: The driven element is a little bit shorter than 0.5 wavelength because electricity traverses more slowly in metal than in free space. That is why the 492/f is used for free space and the 468/f is used for most metals.
So, how did the computer arrive at this answer using only 4 "moments?"
PS: I've looked everywhere (library, web, etc.) for the paper Yagi and Uda wrote on this subject or similar, but to no avail? Additionally, one person suggested Maxwell's equations, but I can not seem to apply them to obtain the voltages or amperages.
Thx in advance. 73 de N2GY
KL7AJ
05-03-2006, 07:37 AM
Greetings!
Well, I admire your wanting to work out Yagis by hand. Part of the reason MoM was invented is precisely because such methods are so tedious. But...there are some principles that are pretty simple. FIRST...you can NEVER get a perfect rearward null with a Yagi...because to do so would require that a parasitic reflector absorb and re-radiate ALL the power...a physically impossible situation. ON the other hand, a phased array (ZL special, or W8jk) IS capable, in theory at least, of infinite front to back ratio.
The best way to approach the yagi problem without re-inventing the wheel is graphically, using the tried and true lengh vs spacing charts that have been in the Antenna Book for ages. In my trusty old 1991 Antenna Book on pages 11-4 to 11-5, there are a series of such charts for optimum gain and optimum f/b ratio, based on spacing and relative length. Fig 9 is the most useful, I believe.
You can also derive these charts empirically....we did that with a 450 MHZ antenna in high school...I remember that class well. LOts of cutting and trimming..but very educational.
Good luck!
eric
Thank you for the reply, Eric.
That's right: The reflector would have to be right next to the driven element to get 100% excitation, take 90 degrees to absorb the signal and another 90 to re-radiate it (180 degrees out of phase), however, I am baffled by two or three points, specifically:
1) When trying to calculate how much one element excites another, how is that calculated, when you know the length of the elements and the distance between them?
2) The reflector is longer and has inductive reactance, which introduces a phase delay in the current, ...but HOW MUCH?? (When you know the length of the reflector, you should be able to calculate the phase change, but how?)
3) Since the reflector is longer than a half-wavelength, it is not resonant; That affects the excitation, because it won't be exited as much by the driven element. So, how much less is the excitation, knowing the additional length of this non-resonant parasitic element?
PS: I do know how to add vectors and understand the concept of superposition, that is, adding the separate answers, but I can't bring it all together to make an answer, like the nice computer program did.
And, it only used four (4) moments, which is really only two (2) on top, and double the answer because of the fact that the geometry of the bottom half is identical. Only two moment, and no one has been able to help me -including myself! (Am I not tormented by Maxwell's Demon (http://www.auburn.edu/~smith01/notes/maxdem.htm)?)
A few more comments below:
Quote[/b] (kl7aj @ May 03 2006,00:37)]Greetings!
# #Well, I admire your wanting to work out Yagis by hand. #Part of the reason MoM was invented is precisely because such methods are so tedious. #But...there are some principles that are pretty simple. #FIRST...you can NEVER get a perfect rearward null with a Yagi...because to do so would require that a parasitic reflector absorb and re-radiate ALL the power...a physically impossible situation. #ON the other hand, a phased array (ZL special, or W8jk) IS capable, in theory at least, of infinite front to back ratio.
Yes, I am familiar with phased arrays. Those you mentioned are unique in that they have only one point of connection, which means that if the antenna's getting power, than ALL of the antenna is getting power (unlike the problem mentioned below), but the use of 300 Ohm line complicates things impedance-wise. (Sort of makes the J-Pole much more attractive, since it can tune for impedance by sliding the feed point up or down.)
However, two problems generally arise when using most of your phased arrays:
1) When the elements are real close, say up to a half wavelength, they also exhibit parasitic qualities, and the elements themselves disrupt the "theoretical" pattern, except in cases where the spacing is exactly a multiple of 1/2 wavelength. (You can avoid this problem by adding 1 or 2 full wavelengths to the spacing in some cases, but this drives up the size of the array.)
2) The other major problem is the fact you are using multiple feed points, and, like a series-fed light string for a Christmas tree, if even one light bulb goes out, the whole string goes out. ~~~ If even one feed point has a bad connection or, say, gets rusty/corroded, the whole array becomes as dysfunctional as a drunk Vulcan!
Quote[/b] (kl7aj @ May 03 2006,00:37)]
# #The best way to approach the yagi problem without re-inventing the wheel is graphically, using the tried and true length vs spacing charts that have been in the Antenna Book for ages. #In my trusty old 1991 Antenna Book on pages 11-4 to 11-5, there are a series of such charts for optimum gain and optimum f/b ratio, based on spacing and relative length. #Fig 9 is the most useful, I believe. #
Yes, this, in theory, would help me, but I still would not understand the concept, and this would make for dangerous practice. When one practices electronic magic without a full understanding, one may cast a spell and turn himself into a toad. Ribbit. Ribbit. Er, what was that, I was saying. Hop .. hop ... hop. http://www.qrz.com/iB_html/non-cgi/emoticons/cool.gif
Quote[/b] (kl7aj @ May 03 2006,00:37)]
# # #You can also derive these charts empirically....we did that with a 450 MHZ antenna in high school...I remember that class well. #LOts of cutting and trimming..but very educational. #
# Good luck!
eric
See page 397 to 407 of Antennas by Kraus, 2nd edition, to see a Method of Moments problem worked out in great detail (hand calculator level.)
KL7AJ
05-03-2006, 04:38 PM
Quote[/b] (n2gy @ May 03 2006,02:12)]Thank you for the reply, Eric.
That's right: The reflector would have to be right next to the driven element to get 100% excitation, take 90 degrees to absorb the signal and another 90 to re-radiate it (180 degrees out of phase), however, I am baffled by two or three points, specifically:
1) When trying to calculate how much one element excites another, how is that calculated, when you know the length of the elements and the distance between them?
2) The reflector is longer and has inductive reactance, which introduces a phase delay in the current, ...but HOW MUCH?? (When you know the length of the reflector, you should be able to calculate the phase change, but how?)
3) Since the reflector is longer than a half-wavelength, it is not resonant; That affects the excitation, because it won't be exited as much by the driven element. So, how much less is the excitation, knowing the additional length of this non-resonant parasitic element?
PS: I do know how to add vectors and understand the concept of superposition, that is, adding the separate answers, but I can't bring it all together to make an answer, like the nice computer program did.
And, it only used four (4) moments, which is really only two (2) on top, and double the answer because of the fact that the geometry of the bottom half is identical. Only two moment, and no one has been able to help me -including myself! (Am I not tormented by Maxwell's Demon (http://www.auburn.edu/~smith01/notes/maxdem.htm)?)
Calculation of MOM requires certain assumptions. It also doesn't tell you the mutual impedance between elements by itself. This has to be derived from field theory. And, if you look at any NEC documentation, a measly 4 segments wont always give you a very good answer...it is a VERY bare minimum.
Once you KNOW the currents, MOM gives you very simple far field answers, but NEC and other modeling programs do a lot of preprocessing before you hand it over to the MOM module. MOM is NOT synonymous with NEC...it's just one part of NEC.
eric
KL7AJ
05-03-2006, 04:54 PM
http://www.cebik.com/yagi/eq-yag-1.html
Here is w4RNL's method of equation-based Yagi design. I'd look at RNL's site carefully, it's loaded with good material.
eric
Quote[/b] (kl7aj @ May 03 2006,09:54)]http://www.cebik.com/yagi/eq-yag-1.html
Here is w4RNL's method of equation-based Yagi design. #I'd look at RNL's site carefully, it's loaded with good material.
eric
I just got finished looking at your link, Eric, but I don't know where I can take a look at the Kraus book mentioned by Zachary (W1VT) above. Maybe a local community college or university will have a copy. (These books are expensive, so I just can't go out an buy them, since I don't know if I will be able to understand it at this time.)
All the same, thank you all for your feedback.
In conclusion, if someone could simply work out the problem above, starting with the input data (description of the Yagi) and showing how the results are obtained (e.g., the gain, impedance, etc.), then that would do me.