How critical is the length of the antenna wire fitted to the receiver on the boat?
Neilthebus, since you asked about the length of the
receiver antenna, let's try to answer your question in easy terms...
First of all, there
is a formula to calculating the required length, but it's relatively simple and requiring just a basic level of math knowledge.
Let's assume that your receiver is crystalled for, say, 40.200 MHz. In order to ascertain the antenna length, you simply divide 300 (three-hundred) by the operating frequency. In this case, we're assuming the operating frequency to be 40.2 MHz. So dividing 300 by 40.2 will yield the length of the antenna... in metres. i.e: 7.462 metres. This is the
electrical length that your receiver antenna needs to be in order to resonate nicely with your 40.2 MHz frequency (otherwise known as a
full-length antenna.). But an antenna at nearly seven-and-a-half metres is waaaaaay too long for practical R/C purposes. So radio designers overcome this by simply calculating their antenna lengths to a
division or
multiple of the calculated full-wavelength. In other words, if you divide your 7.426 by 2, you effectively end up with a
half-length antenna. This again is too long to be practical. So half that figure again... the answer is a
quarter-length antenna. And again, this too is an impractical length.
All R/C radio equipment have their antenna lengths calculated and pruned to 1/8 (one-eighth) length. Ergo, your one-eighth-length antenna, resonating at 40.2 MHz, will be 0.933 metres long (or 933 millimetres). You simply divide 300 by your crystal frequency, then divide that answer by 8.
Metric to Imperial?... That's easy too. Just divide 933 by 25.4. This is the same length, only now in inches.
So how come most all brand-name R/C transmitters/receivers use a bog-standard antenna length?... Or why is the antenna length at the transmitter the same for different crystal frequencies? The answer is one of compatibility. i.e: 'twould be hellish for R/C manufacturers to supply a dedicated antenna for each and every crystal frequency. So they exploit the fact that a slightly de-tuned antenna will still work, because the output power from the Tx is relatively small, and the unwanted feedback currents from the mis-matched antenna will cause no harm to the Tx output transistor. The amount of power reaching a mis-matched antenna is still large enough to work over the specified distance as long as that mis-match is not tooooo far off. (Try to avoid powering your Tx with its antenna collapsed.).
Now you're probably wondering.... "
But if the above formula is true, it implies that a half-length antenna would effectively have twice the sensitivity, therefore twice the range, over a quarter-length... and FOUR times more than a one-eighth length.".
Good point. But your receiver has a tuned input. This means it will only allow the frequencies of interest to pass (i.e: signals from your Tx), while blocking out those that aren't (i.e: signals from other R/C transmitters, etc.). And although it does a good job, a longer antenna would probably swamp the tuned input. When that happens, you'll likely experience unwanted servo jitter (among other odd behavior).
Experiments on a 35, 40 and 72MHz systems has shown that the range has increased by some 8 - 10% once both ant's. had been pruned to their resonant frequency. So to answer your question - in the case of low-power R/C transmissions - the length is not toooo critical as long as both the Rx and TX lengths are within, say, 10 to 15% of the electrical length of your transmitting frequency. The closer you get them to match, the sweeter it will be. In a nutshell, if you add that thin wire to the outside of your tug, just make sure that the total length is the same as what you started with.
Hope this is of help.
Best regards and happy modelling.
