Hi,
You seem to have come to the correct conclusions, but perhaps for the wrong reasons.
dB are a relative measurement, e.g. 0dB means that two signals have the same power (maybe transmitted or received). It's a logarithmic scale so +3dB means that a signal is double the compared value and +6dB is four times the reference. The suffix indicates the reference, i.e. the "m" means a 1 mW reference, the "i" an "isotropic" antenna (which radiates equally in all directions and hardly existis in practice).
An antenna is a passive component so it cannot "amplify" signals except by being directional, i.e. transmitting/receieving in one direction at the expense of other direction(s). A "monopole" antenna (e.g. a 16 cm piece of wire in the case of 433 MHz) transmits/receives most power at right angles to its length (and theoretically nothing in a direction along its length) and thus has a maximum "gain" of +3dBi (relative to that theoretical isotropic antenna).
In a very simplistic fashion, antenna design is all about resonance at the required frequency. Basically, electrons (i.e. a current) rush up the antenna (wire) at nearly the speed of light and at the end find there is nowhere to go! So they rush back again to meet the next "wave" in phase. So you might think that the optimum length would be half a wavelength, but in practice the end of the antenna looks like a "mirror" (to the electrons) so they are turned "upside down" (180 degrees phase shift). Therefore the optimum length is a quarter wavelength. There are various tricks (see later) to "slow down" the electrons but they cannot travel faster than the speed of light so an antenna even only slightly longer than a quarter wavelength works very badly.
The other requirement is to correctly match the impedance at the "feed" end so that the "new" and the "returning" electrons assist each other (to increase the current in the antenna wire and radiate more power). A tuned monopole is between 50 and 75 ohms so any connecting cable used (and the output of the transmitter) must be similar. However, just as the electrons can bounce back and forth along the antenna they can do the same in the feed cable (except their effective speed is typically nearer 2/3 the speed of light). This can cause an unmatched feed cable to change the apparent end impedances, so to avoid "unexpected" effects (unless you know exactly what you're doing), it's best to make the feed cable an exact integer number of wavelengths long.
Now for the "tricks": A quarter wave monopole can be made shorter by putting a "loading coil" (inductor) at its feed end, which has the effect of correcting its impedance. Also, a "rod" (i.e. larger diameter than a wire) antenna has a wider bandwidth, so the length is not so critical. I guess the "helical wire" antenna you describe basically uses these principles. Finally, a monopole should ideally be used above an "earth plane", but alternatively a second (inverted) monopole can be used to create a "dipole" antenna, as is often used for radio and TV broadcasting.
Cheers, Alan.
You seem to have come to the correct conclusions, but perhaps for the wrong reasons.

(27-03-2016, 22:57)Palmyweather Wrote: ...only 40mm in length with an apparent 13dbm of gain.
dB are a relative measurement, e.g. 0dB means that two signals have the same power (maybe transmitted or received). It's a logarithmic scale so +3dB means that a signal is double the compared value and +6dB is four times the reference. The suffix indicates the reference, i.e. the "m" means a 1 mW reference, the "i" an "isotropic" antenna (which radiates equally in all directions and hardly existis in practice).
An antenna is a passive component so it cannot "amplify" signals except by being directional, i.e. transmitting/receieving in one direction at the expense of other direction(s). A "monopole" antenna (e.g. a 16 cm piece of wire in the case of 433 MHz) transmits/receives most power at right angles to its length (and theoretically nothing in a direction along its length) and thus has a maximum "gain" of +3dBi (relative to that theoretical isotropic antenna).
In a very simplistic fashion, antenna design is all about resonance at the required frequency. Basically, electrons (i.e. a current) rush up the antenna (wire) at nearly the speed of light and at the end find there is nowhere to go! So they rush back again to meet the next "wave" in phase. So you might think that the optimum length would be half a wavelength, but in practice the end of the antenna looks like a "mirror" (to the electrons) so they are turned "upside down" (180 degrees phase shift). Therefore the optimum length is a quarter wavelength. There are various tricks (see later) to "slow down" the electrons but they cannot travel faster than the speed of light so an antenna even only slightly longer than a quarter wavelength works very badly.
The other requirement is to correctly match the impedance at the "feed" end so that the "new" and the "returning" electrons assist each other (to increase the current in the antenna wire and radiate more power). A tuned monopole is between 50 and 75 ohms so any connecting cable used (and the output of the transmitter) must be similar. However, just as the electrons can bounce back and forth along the antenna they can do the same in the feed cable (except their effective speed is typically nearer 2/3 the speed of light). This can cause an unmatched feed cable to change the apparent end impedances, so to avoid "unexpected" effects (unless you know exactly what you're doing), it's best to make the feed cable an exact integer number of wavelengths long.
Now for the "tricks": A quarter wave monopole can be made shorter by putting a "loading coil" (inductor) at its feed end, which has the effect of correcting its impedance. Also, a "rod" (i.e. larger diameter than a wire) antenna has a wider bandwidth, so the length is not so critical. I guess the "helical wire" antenna you describe basically uses these principles. Finally, a monopole should ideally be used above an "earth plane", but alternatively a second (inverted) monopole can be used to create a "dipole" antenna, as is often used for radio and TV broadcasting.
Cheers, Alan.