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Fat dipole for FM
I want to build a fat dipole antenna for FM listening for my
brother-in-law, who refuses to get an antenna rotator. He is located with antenna's all around him but not on top of him. I would of course orient it vertically and use 75 ohm coax from where it is mounted to his tuner. Does the ARRL Antenna Handbook have directions on building one of these? I would be using 8 inches as the diameter. Is the math to figure out the length gonna get me - I've been out of college for 30 years and have only done business math since.... Thanks, Brad |
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On Mon, 31 Jan 2005 02:35:51 -0500, Buck wrote:
I don't know why you want FAT. It will give you lower gain. Hi Buck, No such thing. 73's Richard Clark, KB7QHC |
On Mon, 31 Jan 2005 00:24:03 -0800, Richard Clark
wrote: On Mon, 31 Jan 2005 02:35:51 -0500, Buck wrote: I don't know why you want FAT. It will give you lower gain. Hi Buck, No such thing. 73's Richard Clark, KB7QHC No such thing as 'fat' or 'gain'? -- 73 for now Buck N4PGW |
Buck wrote:
I don't know why you want FAT. It will give you lower gain. . . That's interesting. How much lower? Why? Roy Lewallen, W7EL |
From URL:
http://www.astronantennas.com/polarization.html In the early days of FM radio in the 88-108 MHz spectrum, the radio stations broadcasted horizontal polarization. However, in the 1960's, FM radios became popular in automobiles which used vertical polarized receiving whip antennas. As a result, the FCC modified Part 73 of the rules and regulations to allow FM stations to broadcast RHC or elliptical polarization to improve reception to vertical receiving antennas as long as the horizontal component was dominant. -- Caveat Lector Someone correct me, but don't FM stations transmit both vertical and horizontal? I hope this helps. -- 73 for now Buck N4PGW |
On Mon, 31 Jan 2005 02:21:24 -0800, Roy Lewallen
wrote: It will give you lower gain. . . What were you thinking? My apologies to the OP and others..... I don't know why I said 'lower gain'. (make a note to myself, don't answer usenet when I should be asleep.) The fatter dipole will offer a broader bandwidth and a reduced length. However for the FM broadcast band reception, bandwidth isn't a problem. Thanks Roy and Richard. My apologies to you Brad. -- 73 for now Buck N4PGW |
On Mon, 31 Jan 2005 06:28:37 -0800, "Caveat Lector"
wrote: From URL: http://www.astronantennas.com/polarization.html In the early days of FM radio in the 88-108 MHz spectrum, the radio stations broadcasted horizontal polarization. However, in the 1960's, FM radios became popular in automobiles which used vertical polarized receiving whip antennas. As a result, the FCC modified Part 73 of the rules and regulations to allow FM stations to broadcast RHC or elliptical polarization to improve reception to vertical receiving antennas as long as the horizontal component was dominant. Thanks Caveat Lector. (Caveat emptor means buyer beware, what does caveat lector mean?) -- 73 for now Buck N4PGW |
Reader Beware -- hi hi
I have had some awful experiences on the NG's using my real identity and Amateur Radio call sign -- so thought Caveat Lector was appropriate for the NG's 73 -- Caveat Lector "Buck" wrote in message ... On Mon, 31 Jan 2005 06:28:37 -0800, "Caveat Lector" wrote: From URL: http://www.astronantennas.com/polarization.html In the early days of FM radio in the 88-108 MHz spectrum, the radio stations broadcasted horizontal polarization. However, in the 1960's, FM radios became popular in automobiles which used vertical polarized receiving whip antennas. As a result, the FCC modified Part 73 of the rules and regulations to allow FM stations to broadcast RHC or elliptical polarization to improve reception to vertical receiving antennas as long as the horizontal component was dominant. (Caveat emptor means buyer beware, what does caveat lector mean?) -- 73 for now Buck N4PGW |
Roy, W7EL wrote:
"That`s interesting.(I don`t know why you want fat. It will give you lower gain.) How much lower? Why?" It`s a fact. Fat antennas have more bandwidth, and that is inversely proportional to Q. Teducing antenna Q, by fattening the antenna, reduces the antenna potential by about the same factor. Best regards, Richard Harrison, KB5WZI |
Brad wrote:
"I want to build a fat dipole for FM listening for my brother-in-law, who refuses to get a rotor." A twin-lead dipole may be fat enough. These are sold at Radio Shack and other outlets for just a few dollars and can be used to determine if such an approach is satisfactory. You can still build an "improved antenna" if the bought antenna works on site. Best regards, Richard Harrison, KB5WZI |
Fat antennas have more bandwidth, and that is inversely
proportional to Q. Teducing antenna Q, by fattening the antenna, reduces the antenna potential by about the same factor. Best regards, Richard Harrison, KB5WZI =========================== Richard, If you got this off Terman and Kraus then Terman and Kraus are a couple of the oldest of old wives. --- Reg |
On Mon, 31 Jan 2005 16:55:03 +0000 (UTC), "Reg Edwards"
wrote: If you got this off Terman and Kraus then Terman and Kraus are a couple of the oldest of old wives. Reggie, This has got to be the height of your boredom to force your nemesis into the thread to then complain about them. Sounds unmistakably like the envy of a hausfrau. 73's Richard Clark, KB7QHC |
On Mon, 31 Jan 2005 10:54:43 -0500, Buck wrote:
(Caveat emptor means buyer beware, what does caveat lector mean?) Hi Buck, You got the Caveat part down, but I'm not sure if ***** is being coy, or has taken the wrong translation. His intent may be (if read literally) that "reader beware." However, this is not the same as the meaning of lector, where the meaning would offer "beware reader." It is a subtle distinction at best leading to the same caution, but Lector is one who reads (imparts information) to others (instead of being a silent reader, such as anyone "reading" this post). 73's Richard Clark, KB7QHC |
Reg, G4FGQ wrote:
"Richard, If you got this off Terman and Kraus then Terman and Kraus are a couple of the oldest of old wives." I can`t blame them because I wrote without consulting them first. Terman does in fact say about what I said. I haven`t checked with Kraus yet. In his 1955 edition on page 921 Terman writes: "The second possible way to achieve broad-band characteristics consists in starting with a resonant antenna (as opposed to a rhombic for example), but so proportioning this antenna as to minimize resonance effects. Thus a resonant antenna employing a thin wire is equivalent to a moderately high Q system and so has a relatively narrow frequency band. However, if the diameter of the antenna is made large, the effective Q is very substantially reduced with resulting increase in bandwidth." Best regards, Richard Haarrison, KB5WZI |
Ah I have been misled by my latin teacher
so must now clarify I guess -- Caveat Lector - Reader Beware "Richard Clark" wrote in message ... On Mon, 31 Jan 2005 10:54:43 -0500, Buck wrote: (Caveat emptor means buyer beware, what does caveat lector mean?) Hi Buck, You got the Caveat part down, but I'm not sure if ***** is being coy, or has taken the wrong translation. His intent may be (if read literally) that "reader beware." However, this is not the same as the meaning of lector, where the meaning would offer "beware reader." It is a subtle distinction at best leading to the same caution, but Lector is one who reads (imparts information) to others (instead of being a silent reader, such as anyone "reading" this post). 73's Richard Clark, KB7QHC |
I also wrote:
"Fat antennas have more bandwidth, and that is inversely proportional to Q. Reducing antenna Q, by fattening the antenna, reduces the antenna potential by almost the same factor." Here is support from Ed Laport`s "Radio Antenna Engineering page 37": "It is seen that bandwidth is inversely proportional to antenna (or total circuit) Q. To decrease Q, the same design considerations are required as for the reduction of antenna potential." Best regards, Richard Harrison, KB5WZI |
On Mon, 31 Jan 2005 13:45:59 -0800, "Caveat Lector"
wrote: Ah I have been misled by my latin teacher so must now clarify I guess Hi OM, It could easily be my own mistake through attribution of the English derivation from Latin. Luckily no one ('arry palms) is demanding the root form of the ancient greek assembled phontetically as a cross check. 73's Richard Clark, KB7QHC |
FB Richard -- now back to antennas -- I really enjoy the posts here -- very
informative. -- Caveat Lector (Reader Beware) "Richard Clark" wrote in message ... On Mon, 31 Jan 2005 13:45:59 -0800, "Caveat Lector" wrote: Ah I have been misled by my latin teacher so must now clarify I guess Hi OM, It could easily be my own mistake through attribution of the English derivation from Latin. Luckily no one ('arry palms) is demanding the root form of the ancient greek assembled phontetically as a cross check. 73's Richard Clark, KB7QHC |
As a competent and experienced engineer, it should then be simple for
you to answer the following: What is the gain difference, in dB, between a dipole resonant at 97.5 MHz (the geometric center of the FM band) which is 1 mm diameter and one which is 1 cm diameter? Feel free to assume that the conductor is perfect, or use copper if you prefer. Also feel free to calculate the antenna Q and "antenna potential", although the question here is about gain. Roy Lewallen, W7EL Richard Harrison wrote: Roy, W7EL wrote: "That`s interesting.(I don`t know why you want fat. It will give you lower gain.) How much lower? Why?" It`s a fact. Fat antennas have more bandwidth, and that is inversely proportional to Q. Teducing antenna Q, by fattening the antenna, reduces the antenna potential by about the same factor. Best regards, Richard Harrison, KB5WZI |
On Mon, 31 Jan 2005 15:14:49 -0800, Roy Lewallen
wrote: As a competent and experienced engineer, it should then be simple for you to answer the following: What is the gain difference, in dB, between a dipole resonant at 97.5 MHz (the geometric center of the FM band) which is 1 mm diameter and one which is 1 cm diameter? Feel free to assume that the conductor is perfect, or use copper if you prefer. Also feel free to calculate the antenna Q and "antenna potential", although the question here is about gain. Roy Lewallen, W7EL Richard Harrison wrote: Roy, W7EL wrote: "That`s interesting.(I don`t know why you want fat. It will give you lower gain.) How much lower? Why?" It`s a fact. Fat antennas have more bandwidth, and that is inversely proportional to Q. Teducing antenna Q, by fattening the antenna, reduces the antenna potential by about the same factor. Best regards, Richard Harrison, KB5WZI Hi Roy, What an unusual demand to throw in the face of someone who agrees with you: no difference in gain. Richard's quote is merely your ironic question to Buck's quote (already discounted by Buck). However, for Brad's interest (and conforming to his original design, not of 1cM but more like 170mm diamter) the Q for the fatter dipole is indeed much less (in fact it covers the entire FM band into a 50 Ohm load between 2:1 VSWR points) where the thin dipole (1mm) is something less than 6MHz. Bandwidth (and inferentially Q) differential 4:1 which would translate the input V to the tips to something less (at the same proportion) than that experienced with the thin dipole (which for a recieve antenna is a strange characteristic to focus upon). 73's Richard Clark, KB7QHC |
Richard Clark wrote:
On Mon, 31 Jan 2005 15:14:49 -0800, Roy Lewallen wrote: As a competent and experienced engineer, it should then be simple for you to answer the following: What is the gain difference, in dB, between a dipole resonant at 97.5 MHz (the geometric center of the FM band) which is 1 mm diameter and one which is 1 cm diameter? Feel free to assume that the conductor is perfect, or use copper if you prefer. Also feel free to calculate the antenna Q and "antenna potential", although the question here is about gain. Roy Lewallen, W7EL Richard Harrison wrote: Roy, W7EL wrote: "That`s interesting.(I don`t know why you want fat. It will give you lower gain.) How much lower? Why?" It`s a fact. Fat antennas have more bandwidth, and that is inversely proportional to Q. Teducing antenna Q, by fattening the antenna, reduces the antenna potential by about the same factor. Best regards, Richard Harrison, KB5WZI Hi Roy, What an unusual demand to throw in the face of someone who agrees with you: no difference in gain. Richard's quote is merely your ironic question to Buck's quote (already discounted by Buck). However, for Brad's interest (and conforming to his original design, not of 1cM but more like 170mm diamter) the Q for the fatter dipole is indeed much less (in fact it covers the entire FM band into a 50 Ohm load between 2:1 VSWR points) where the thin dipole (1mm) is something less than 6MHz. Bandwidth (and inferentially Q) differential 4:1 which would translate the input V to the tips to something less (at the same proportion) than that experienced with the thin dipole (which for a recieve antenna is a strange characteristic to focus upon). 73's Richard Clark, KB7QHC If you were agreeing with me, Richard (Harrison), I apologize. It wasn't apparent to me with my poor language skills. Thanks to Richard (Clark) for effectively applying his superior parsing skills to the problem. There are only two ways to change the free space gain of an antenna -- change the efficiency, or change the pattern. Those are all the choices you've got. A fat antenna is certainly no less efficient than a skinny one -- in fact, it'll be more efficient. But the difference in this case would be so small as to be unmeasurable. There would be some very slight change in pattern between a fat antenna and a slim one, but again the change would be negligibly small. Considering only free space performance to remove the additional variable of ground reflection, and assuming that an antenna is essentially 100% efficient, it's impossible to design an antenna that has gain in its best direction which is any less than 2.15 dB below that of a half wave dipole. The lowest possible gain of any efficent antenna is the isotropic, at 0 dBi. Roy Lewallen, W7EL |
Roy, W7EL wrote:
"There are only two ways to change the free space gain of an antenna---change the efficiency , or change the pattern." I agree. Terman defines "directive gain" and "power gain" which involve the pattern and efficiency of an antenna. The isotropic antenna is by definition omnidirectional. All others are more directional and thus have gain in their best direction. The power ratio of a 1/2-wave resonant conductor radiates in its best direction 1.64 times the power per unit area from an isotropic antenna. This is a simple power ratio, not dB. This is from Terman`s Table 23-1 in his 1955 edition. My original posting in this thread was based on the fact that antenna voltage distribution depends on constructon and frequency. Voltage amplitudes at all points on the sntenna increase when the rms voltage at any point rises.. Radiation and reception from an antenna are a function of antenna voltage. This is unrelated to directive gain. A higher antenna Q results in higher voltage. The dipole we discussed was resonant. We`ve seen the textbook curves for resonant circuits which pften show impedance versus frequency, and we have tuned lumped and distributed versions. A high Q series resonant circuit has little resistance to limit current at resonance. A high Q parallel resonant circuit has little conductance to limit voltage. My posting said: "Reducing antenna Q by fattening the antenna, reduces the antenna potential by about the same factor." A higher Q antenna results in more voltage, more radiation, and more reception. It also has less bandwidth. I usually read Roy`s postings because they are interesting and I often learn something from them. They are greatly appreciated by me and many others have said they appreciate them too. Some aren`t even EZNEC users, so there is still room for growth. On the issue of antenna Q, I recall a Yagi design article which advised against large diameter parasitic elements as they would have insufficient Q and not perform properly. That seemed strange to me at the time but maybe there was something to it. Best regards, Richard Harrison, KB5WZI |
"Richard Harrison" wrote
My original posting in this thread was based on the fact that antenna voltage distribution depends on constructon and frequency. Voltage amplitudes at all points on the sntenna increase when the rms voltage at any point rises.. Radiation and reception from an antenna are a function of antenna voltage. This is unrelated to directive gain. __________________ TV and FM broadcast transmit antenna designs include many using 1/2-wave, resonant dipoles with "fat" radiators -- however they all have published gains based on the standard gain of a dipole (1.64X that of an isotropic radiator). There is no difference in gains between slender and fat radiator designs in the broadcast industry. Examples on request. RF |
Richard Harrison wrote:
. . . A higher Q antenna results in more voltage, more radiation, and more reception. It also has less bandwidth. . . . There's a problem here. Let's say we begin with a smallish loop antenna, one small enough so it has essentially equal current around the perimeter. We'll make it using a perfect conductor. Put 100 watts into it; since it has no loss, 100 watts will be radiated, distributed in a dipole-like pattern. Now reduce the size of the loop. The Q will increase. You've said that because of the increase in Q, it will have more radiation. My question is, does that greater radiation result from a more directional pattern, or from more power being radiated? If the former, why would the smaller loop have a sharper pattern than the larger one (considering the assumption made about the initial loop size)? If the latter, we've really stumbled onto something here -- more than 100 watts out with 100 watts in. Perpetual motion, here we come! Roy Lewallen, W7EL |
Richard Fry wrote:
. . .There is no difference in gains between slender and fat radiator designs in the broadcast industry. Rest assured, there's no difference in any other industry either. Roy Lewallen, W7EL |
Why does everybody insist on OVER-COMPLICATING this simple problem?
The Q of a resonant 1/2-wave dipole is given by - Q = Omega * L / 2 / R Where L is the end-to-end wire inductance and R is the radiation resistance of about 71 ohms. Just the same 'formula', in fact, as any other tuned circuit or transmission line. Resonant rise in voltage and current, and bandwidth, etc., all follow. It's so simple it doesn't occur to Terman and other 'beings' to mention it. ---- Reg |
"Reg Edwards" wrote
Just the same 'formula', in fact, as any other tuned circuit or transmission line. Resonant rise in voltage and current, and bandwidth, etc., all follow. ______________ The impedance bandwidth of a fat dipole can be so large that an acceptable input match is possible at frequencies where the dipole is no longer very near a resonant 1/2 wavelength. In those cases and at a constant input power, there is a redistribution of the current in the radiators, resulting in a relatively modest change in the peak gain of the radiation pattern. It is true that the Q of a fat radiator is less than a thin one, but that in itself does not produce a change in gain. A gain change results from a change in the radiation pattern of the antenna -- which is related only to the length of the dipole elements with respect to the operating frequency; independent of Q. For example, a "short" dipole (fat or thin) has a gain of 1.50X and a 3dB beamwidth of ~90°. A standard 1/2-wave dipole (fat or thin) has a gain of 1.64X and a 3dB beamwidth of ~78° [Kraus, 3rd Ed, Table 6-2]. Another example is that of the vertical radiators used in MW AM broadcasting. There is no term for Q in the equations for their radiation patterns. For a given set of installation conditions, a thin tower produces the same elevation pattern/peak gain at the carrier frequency as a fat one. RF |
Reg, G4FGQ wrote:
"Its so simple it doesn`t occur to Terman and other "beings" to mention it." Well, Ed Laport had experience with many high-powered transmitters, so it occurred to him to mention antenna Q in "Radio Antenna Engineering". Ed assumes power in a dipole is all radiated and none is used to heat the dipole. Radiation resistance of his horizontal dipole is a function of its height above ground. To calculate the Q of the antenna, he first calculates a factor "m" which is the ratio of the attenuated voltage 180-degrees from the generator on an infinite line to the generated voltage: m = Zo-radiation resistance / Z0+radiation resistance Then: Q = 1+m / 1-m Radiation resistance = 276 log l/rho where l is the total length of the dipole, and rho is the radius of the conductor in the same units. Laport is interested in antenna Q to make sure the antenna won`t plume at maximum voltage. Ed picks a wire size and computes maximum voltage at the antenna tips to make sure that under assumed conditions the voltage is below the corona firing potential. The calculation is on page 241 of "Radio Antenna Engineering". A trial wire size has a radius of 0.102 inch. m ccomputes as 0.84 Q computes as 11.4 Balanced dipole feedpoint volts are picked as 690 rms from the unmodulated applied power. Volts at the ends of the dipole a QV/2=3950 volts as rounded. Corona is initiated on peaks and a further safety factor is added to avoid pluming, but that`s the way a wire size might be checked. Best regards, Richard Harrison, KB5WZI |
On Wed, 2 Feb 2005 08:57:29 -0600, "Richard Fry"
wrote: "Reg Edwards" wrote Just the same 'formula', in fact, as any other tuned circuit or transmission line. Resonant rise in voltage and current, and bandwidth, etc., all follow. ______________ The impedance bandwidth of a fat dipole can be so large that an acceptable input match is possible at frequencies where the dipole is no longer very near a resonant 1/2 wavelength. In those cases and at a constant input power, there is a redistribution of the current in the radiators, resulting in a relatively modest change in the peak gain of the radiation pattern. It is true that the Q of a fat radiator is less than a thin one, but that in itself does not produce a change in gain. A gain change results from a change in the radiation pattern of the antenna -- which is related only to the length of the dipole elements with respect to the operating frequency; independent of Q. For example, a "short" dipole (fat or thin) has a gain of 1.50X and a 3dB beamwidth of ~90°. A standard 1/2-wave dipole (fat or thin) has a gain of 1.64X and a 3dB beamwidth of ~78° [Kraus, 3rd Ed, Table 6-2]. Another example is that of the vertical radiators used in MW AM broadcasting. There is no term for Q in the equations for their radiation patterns. For a given set of installation conditions, a thin tower produces the same elevation pattern/peak gain at the carrier frequency as a fat one. RF How FAT would an FM broadcast dipole have to be to lose one db gain? approximately -- 73 for now Buck N4PGW |
"Buck" wrote
How FAT would an FM broadcast dipole have to be to lose one db gain? approximately ______________________ Dipoles consisting of radiators of any practical diameter all will have the same gain if they have the same electrical length at the operating frequency. "Q" has nothing to do with it. RF |
Buck wrote:
How FAT would an FM broadcast dipole have to be to lose one db gain? approximately A perfect application for the free EZNEC demo program, from http://eznec.com. Roy Lewallen, W7EL |
Thanks for the overload of info guys. I may have resolved his issue by
purchasing a Marantz ST-17 tuner, which has provision for two antennas. The ST-2 that he has is fine for all stations he listens to except one. I'll have him get the Radio Shack Yagi abd some good coax and aim it for best reception on that station. However, I need to make a good omnidirectional antenna to go in my attic. I did not get an answer on if the ARRL handbook has the directions for makinng the fat dipole. I live outside of Atlanta, GA (hilly) and cannot have an outside antenna, and have very little room horizonally in attic - a directional is out, but do have an area for a tal vertical antenna. What would be your recommendations? What suggestions |
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On Wed, 02 Feb 2005 14:44:07 -0800, Roy Lewallen
wrote: Buck wrote: How FAT would an FM broadcast dipole have to be to lose one db gain? approximately A perfect application for the free EZNEC demo program, from http://eznec.com. Roy Lewallen, W7EL I was kinda thinking that the antenna would become a capacitor if the elements get too fat. -- 73 for now Buck N4PGW |
On Wed, 02 Feb 2005 20:26:39 -0500, Buck wrote:
I was kinda thinking that the antenna would become a capacitor if the elements get too fat. Hi Buck, And the inductance goes down (think about the product and proportionalities of the two. 73's Richard Clark, KB7QHC |
Richard Clark wrote:
On Wed, 02 Feb 2005 20:26:39 -0500, Buck wrote: I was kinda thinking that the antenna would become a capacitor if the elements get too fat. Hi Buck, And the inductance goes down (think about the product and proportionalities of the two. 73's Richard Clark, KB7QHC Then, the next step is to think about why having less inductance and more capacitance should reduce the gain. Does it cause the pattern to change? Does it reduce the efficiency? Those are the only ways to change the gain. Roy Lewallen, W7EL |
Brad wrote:
"What would be your recommendations?" Brad also wrote: "---but do have an area for a tall vertical antenna." There are often obstructions in an otherwise line-of-sight path. Antenna gain is usually not enough to overcome an obstructed path. Antenna height can overcome the obstruction. Flagpoles are usually acceptable where antennas are banned. In Terman`s 1955 edition of "Electronis and Radio Engineering" on page 902 are found "Flagpole Antennas". These are balanced vertical dipoles, transformed to a coax feed through the bottom of the dipole. If the flagpole is tall enough, you receive FM broadcasts. Q = f/BW means your dipoe needs a Q of less than 4.8 to span 88 MHz to 108 MHz. The antenna would center upon 97.5 MHz, the geometric mean or center of the band. Such a bandwidth is likely impractical. You can settle for less or center the response on the part of the band you would most use. Multiply the lowest frequency of high interest by the highest frequency of high interest and take the square root of the product to find the frequency the dipole should be cut for. The fatter the dipole is, the lower its Q will be, and the more even its frequency response will be. You can probably do quite well with uneven response in your antenna is high enough. Best regards, Richard Harrison, KB5WZI |
I dont know where YOU got your antenna info from....but just because a
dipole has wide b/w (low Q) does not lower its gain unless the diameter of the dipole causes the resonant length to be much shorter than 1/2 wavelength...but in practical terms, that wont happen (unless he makes the dipole out of 4 ft pipe for instance! ;) A wide b/w (fat) dipole made for 80m (a cage dipole) does not have any less signal strength than a single wire dipole (2.15 dbi).....sorry. Chris WB5ITT PG-9-5322 FCC Commercial Telecom/Broadcast engineer for 30 years "Richard Harrison" wrote in message ... Roy, W7EL wrote: "That`s interesting.(I don`t know why you want fat. It will give you lower gain.) How much lower? Why?" It`s a fact. Fat antennas have more bandwidth, and that is inversely proportional to Q. Teducing antenna Q, by fattening the antenna, reduces the antenna potential by about the same factor. Best regards, Richard Harrison, KB5WZ |
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