This is really for a TV antenna, but the same principles would apply to FM or whatever.
In the past I've always started from twinlead folded dipoles, the kind that used to be boxed with every FM receiver in the 1970's, with 300 ohm connection.
It seemed obvious that if you want a higher frequency than these are made for (the twinlead folded dipoles for FM are generally tuned to the middle of the FM band) you simply cut it as needed, Pretty much according to the wavelength of the broadcast frequency (more on that assumption later).
But some time ago, some guy who knew a lot more than me about radio, questioned as to why I was starting from a twinlead folded dipole, which I could in perhaps even less space use the genuine article: a halfwave dipole, made from simple wire instead of twinlead.
Well, I had simply started from what I knew worked. I wasn't sure if a "regular dipole" needed to be that same length, or perhaps twice as much.
So now I was informed, that except for some esoteric factors (the velocity) I could just use a wire instead of twinlead, and it would be about the same length (not double etc). AND, there'd be another big advantage. Unlike the twinlead dipole, which is matched to 300 ohms, a half wave dipole is nearly a perfect match for standard 75 ohm coax, which is now the more common connection for tv's and tuners, and actual coax cable doesn't have to be run in a straight line free of obstructions.
There is one tiny difference in the performance of an antenna made with wire and that of twinlead. Because the twinlead is thicker, primarily, being two wires instead of just one, it has a wider bandwidth. So this is what you'd want if you want to cover the FM band, say, the purpose for which these "indoor antennas" were included with tuners and receivers. But if you only want some specific frequency, and you can tune for it precisely, you can get better tuning with the narrower bandwidth wire. But really, for reception at least, a wire can cover quite a bit of bandwidth as well.
Anyway, here's a guy who discusses making a TV tuner out of twinlead, sort of how I used to do it. The overall length of the antenna is a half wave, making each side a quarter wave. That part is easy enough if you know a few simple things. The wavelength of 300 Mhz being 1 meter is a good place to start. If you ultimately prefer to use inches, to 3 digits you can conveniently use 39.4 inches. The actual antenna that works best for reception is in either case a "half wave dipole antenna", with each side being a quarter wavelength. That works well intuitively because each end is at the opposite displacement at any time, aka 180 degrees apart. (Full wave dipoles are fundamentally more resonant, but difficult to match to lead-in cables and generally not used.)
The trick is knowing the frequency of the channel of interest. The link above gives some formulae for doing so for TV channels. You can also just ask your search engine. However, this assumes you know the "actual broadcast channel" which for TV stations may not be the number used anymore. Once again the "real channel" or the plain old "real frequency" of any actual channel can be fairly easily looked up. For my channel of interest, the real Channel 9, the frequence in the middle of the channel is 189 mhz. That was their original VHF broadcast channel in the analog era and they stuck with it.
So then the wavelength of 189 Mhz is
300 million meters/sec / 189 million cycles/sec
300/189 = 1.587 meters = 62.5 inches
1/2 wavelength is 31.25 inches
1/4 wavelength is 15.6 inches
OK, so then I could just cut the sides of my dipole to that length. What I'm actually doing in my fashion is buying a ready made "dipole" for FM, made with insulated single wire instead of twinlead. The pre-attached lead in is very fine twisted pair (for low-cost-to-the-manufacturer and semi-invisible appearance, otherwise coax would have been better for performance, but all the prebuilt ones for the FM band I could find were exactly like this--none used actual coax) terminated with a push-on F connector. This is very convenient and not balun is required as I've needed to use for my twinlead antennas for decades. Eliminating the balun saves space, cost, installation difficulty, and a potential reliability issue as the ends of the balun can work loose and if not sufficiently or constantly retightened can cause drop outs. Reaching back behind the TV to tighten the connections of the balun is a chore I've long gotten tired of. And the balun itself has loss, so eliminating the need for it might actually improve performance, depending on how well the lead-in is matched (with real coax, it would be better than twinlead overall).
I'm cutting this "ready made FM band antenna" to the required length for Channel 9, in such a way as to re-attach the terminations (with nail holes) at the correct length. As I learned before, the wires must be spliced and soldered well and nicely insulated. Unsoldered bare copper twisted stranded wires generate noise at RF frequencies in RF antennas.
NOW, the complicating factor is that the correct length is not as I just described, it is adjusted by a Velocity factor. The link above gives the velocity factor for a twinlead dipole working in non-differential mode as 0.95. That is higher than the normal propagation velocity cited for twinlead because that normally assumed differential model, as the author explains. But other than simply saying that it's higher than differential, he does not derive the 0.95 or give further sources (I think it can be derived, from Maxwell equations, if you know every minute detail of the construction and materials in the twinlead, and other factors such as mounting height, ground density, air humidity, etc, etc, and how they are all used in the equations, which is no simple task).
I decided to take the advice of another old ham. Start your dipole longer than needed and cut it bit by bit until you hit the target resonance. He said never, ever, did he cut a dipole correctly just from calculations.
So I took that advice, and I now have a SARK-1 antenna analyzer I needed to justify getting. I started longer than half wavelength total and ultimately cut it to about 12.25 inches as it crept to 189 mhz notch. As installed on the wall, 7 feet high, with larger nails (and not stainless) than I would have liked (because, smallest thing I could find on hand) it still measures a VSWR notch at 184 mHz, which is remarkably close to target, within about 3%, probably far closer than I've ever gotten by calculation. The reverse calculated "velocity factor" is .79.
The resulting antenna works extremely well and not only do I get channel 9, I get the other VHF channel 12 and I get nearly every UHF channel as good as I get them in the Kitchen, which has two antennas I spent a month colocating for best performance. Notably on the twinlead dipole in the kitchen I could not get all the UHF channels as well, but that might be as much a factor of location.
This from very cheap-to-make antenna which actually uses just the two wires in zip form as the "cable" from the dipole, and thence to an F connector. Using a real RG6 might be a bit better, but far uglier.
In the past I've always started from twinlead folded dipoles, the kind that used to be boxed with every FM receiver in the 1970's, with 300 ohm connection.
It seemed obvious that if you want a higher frequency than these are made for (the twinlead folded dipoles for FM are generally tuned to the middle of the FM band) you simply cut it as needed, Pretty much according to the wavelength of the broadcast frequency (more on that assumption later).
But some time ago, some guy who knew a lot more than me about radio, questioned as to why I was starting from a twinlead folded dipole, which I could in perhaps even less space use the genuine article: a halfwave dipole, made from simple wire instead of twinlead.
Well, I had simply started from what I knew worked. I wasn't sure if a "regular dipole" needed to be that same length, or perhaps twice as much.
So now I was informed, that except for some esoteric factors (the velocity) I could just use a wire instead of twinlead, and it would be about the same length (not double etc). AND, there'd be another big advantage. Unlike the twinlead dipole, which is matched to 300 ohms, a half wave dipole is nearly a perfect match for standard 75 ohm coax, which is now the more common connection for tv's and tuners, and actual coax cable doesn't have to be run in a straight line free of obstructions.
There is one tiny difference in the performance of an antenna made with wire and that of twinlead. Because the twinlead is thicker, primarily, being two wires instead of just one, it has a wider bandwidth. So this is what you'd want if you want to cover the FM band, say, the purpose for which these "indoor antennas" were included with tuners and receivers. But if you only want some specific frequency, and you can tune for it precisely, you can get better tuning with the narrower bandwidth wire. But really, for reception at least, a wire can cover quite a bit of bandwidth as well.
Anyway, here's a guy who discusses making a TV tuner out of twinlead, sort of how I used to do it. The overall length of the antenna is a half wave, making each side a quarter wave. That part is easy enough if you know a few simple things. The wavelength of 300 Mhz being 1 meter is a good place to start. If you ultimately prefer to use inches, to 3 digits you can conveniently use 39.4 inches. The actual antenna that works best for reception is in either case a "half wave dipole antenna", with each side being a quarter wavelength. That works well intuitively because each end is at the opposite displacement at any time, aka 180 degrees apart. (Full wave dipoles are fundamentally more resonant, but difficult to match to lead-in cables and generally not used.)
The trick is knowing the frequency of the channel of interest. The link above gives some formulae for doing so for TV channels. You can also just ask your search engine. However, this assumes you know the "actual broadcast channel" which for TV stations may not be the number used anymore. Once again the "real channel" or the plain old "real frequency" of any actual channel can be fairly easily looked up. For my channel of interest, the real Channel 9, the frequence in the middle of the channel is 189 mhz. That was their original VHF broadcast channel in the analog era and they stuck with it.
So then the wavelength of 189 Mhz is
300 million meters/sec / 189 million cycles/sec
300/189 = 1.587 meters = 62.5 inches
1/2 wavelength is 31.25 inches
1/4 wavelength is 15.6 inches
OK, so then I could just cut the sides of my dipole to that length. What I'm actually doing in my fashion is buying a ready made "dipole" for FM, made with insulated single wire instead of twinlead. The pre-attached lead in is very fine twisted pair (for low-cost-to-the-manufacturer and semi-invisible appearance, otherwise coax would have been better for performance, but all the prebuilt ones for the FM band I could find were exactly like this--none used actual coax) terminated with a push-on F connector. This is very convenient and not balun is required as I've needed to use for my twinlead antennas for decades. Eliminating the balun saves space, cost, installation difficulty, and a potential reliability issue as the ends of the balun can work loose and if not sufficiently or constantly retightened can cause drop outs. Reaching back behind the TV to tighten the connections of the balun is a chore I've long gotten tired of. And the balun itself has loss, so eliminating the need for it might actually improve performance, depending on how well the lead-in is matched (with real coax, it would be better than twinlead overall).
I'm cutting this "ready made FM band antenna" to the required length for Channel 9, in such a way as to re-attach the terminations (with nail holes) at the correct length. As I learned before, the wires must be spliced and soldered well and nicely insulated. Unsoldered bare copper twisted stranded wires generate noise at RF frequencies in RF antennas.
NOW, the complicating factor is that the correct length is not as I just described, it is adjusted by a Velocity factor. The link above gives the velocity factor for a twinlead dipole working in non-differential mode as 0.95. That is higher than the normal propagation velocity cited for twinlead because that normally assumed differential model, as the author explains. But other than simply saying that it's higher than differential, he does not derive the 0.95 or give further sources (I think it can be derived, from Maxwell equations, if you know every minute detail of the construction and materials in the twinlead, and other factors such as mounting height, ground density, air humidity, etc, etc, and how they are all used in the equations, which is no simple task).
I decided to take the advice of another old ham. Start your dipole longer than needed and cut it bit by bit until you hit the target resonance. He said never, ever, did he cut a dipole correctly just from calculations.
So I took that advice, and I now have a SARK-1 antenna analyzer I needed to justify getting. I started longer than half wavelength total and ultimately cut it to about 12.25 inches as it crept to 189 mhz notch. As installed on the wall, 7 feet high, with larger nails (and not stainless) than I would have liked (because, smallest thing I could find on hand) it still measures a VSWR notch at 184 mHz, which is remarkably close to target, within about 3%, probably far closer than I've ever gotten by calculation. The reverse calculated "velocity factor" is .79.
The resulting antenna works extremely well and not only do I get channel 9, I get the other VHF channel 12 and I get nearly every UHF channel as good as I get them in the Kitchen, which has two antennas I spent a month colocating for best performance. Notably on the twinlead dipole in the kitchen I could not get all the UHF channels as well, but that might be as much a factor of location.
This from very cheap-to-make antenna which actually uses just the two wires in zip form as the "cable" from the dipole, and thence to an F connector. Using a real RG6 might be a bit better, but far uglier.
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