I'd like to know if there is a general rule of thumb for determining the antenna impedance Z(w) and therefore the matching inductance L3.
Also, I'd like to know what is the meaning behind the choice of the "12 inches of AWG 28" (cause 12inches do not seem to me like any fraction of the wavelength lambda).
It is a fraction of the wavelength, a very small one. (1/36) Many remote control toys use 27Mhz and a similar short antenna. I would think the designer picked the L and C for the 12 in antenna.
A vertical 12 inch piece of #28AWG wire, over ground, at 27MHz, will look something like 0.3 ohms radiation resistance, in series with about 2.5pF. Required series inductance will be 13.92uH.
Radiotron Designer's Handbook, Chapter 22, Section iii gives:
-jZo cot(2*pi*L/lambda) for the reactive component, where:
Zo=138 log(lambda/d) - 104 ohms, where d = wire diameter.
I do it on a spreadsheet I adapted from an HP41 calculator library program.
Just a convenient piece of wire? No other reason I can see. #28 wire won't self-support very well, anyway.
A quick and dirty simulation using the above antenna model shows resonance at about 28.37MHz, with your published component values. Probably not much radiation from the "antenna" at 27MHz.
--
"Design is the reverse of analysis"
(R.D. Middlebrook)
With a properly-designed PA stage, which the quoted example isn't...
Out of a hat, according to my calculations, and simulation. Preferred value components, without any adjustment are a dead giveaway. Resonance is over a meg away. 2N2222 isn't a very good choice, either.
--
"Design is the reverse of analysis"
(R.D. Middlebrook)
"License free" transmitters often have quite strong limitations, not just power input, but antenna length too. 12inches seems short for 27MHz, but that may be a factor. I'm not even sure if the laws deal with input power anymore, or just radiated power. The latter is harder to measure for the hobbyist, so things may be kept very simple to avoid too strong a signal.
I can't emember what the antenna length is for the 160 to 190KHz band, but it's extremely short for the frequency.
Some designs use the inductor series circuit as a loading coil for the antenna. calculations don't always hold up in real life. No idea if this applies here, just sayin'.
Yes, but I can't remember if loading coils are allowed by the rules for unlicensed operation or not. I seem to recall something about "well we'll just use a giant loading coil" but then "no, that's not allowed".
Back many years ago when I first got my FCC First Class License I think the rule came under part 95, unlicensed transmitters. Then 11 meters was taken from the hams and CB was born. The unlicensed band was limited to
100mW and a 5 foot antenna. I don't recall any restrictions on loading coils but that was back when the Pope was an Alter Boy.
I've been reading about the loading coil, but I just can't figure out the p urpose? I thought that the inductor was there to match the antenna load. Ha s the "loading coil" this purpose? I mean, is it just another name for impe dance matching? Or does it serve different purposes?
It is interesting, but I'm looking for a (possibly simple) mathematical formulation that
- applies to a generic dipole of arbitrary length (not lambda /2 or lambda/4, and in general way smaller than the wavelength), - does not take in integrals nor starts from Maxwell's equations - possibly takes in all conventional approximations/simplifications for far field, isotropic, linear, homogeneous, non-dispersive medium, - binds the antenna complex impedance to the length and lambda
The closest to this was Fred's answer but the source is not exactly an "handbook".
I'm now starting from scratch to understand the current and voltages distribution across the dipole to understand how the ratio between them is defined and therefore the impedance.
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.