[Lowfer] Re: Amplifiers for 136k

[James Moritz]

Dear Bill, Lowfers,

At 04:01 23/08/2002 -0400, you wrote:
>Do you know of anyone who has actually measured and cataloged the amplitudes
>of the harmonics for a square-wave driven LF loop, particularly using
>step-down transformer coupling? This is something I could do fairly easily
>with my setup.

No-one I know of over here - but it would be interesting to find out. To 
try to get an idea, one con make a very rough sort of analysis:

Suppose you have a loop resonated by series capacitance, with a resistance 
at resonance of a few ohms, being directly driven by a square wave. To 
deliver 100W at LF, a square wave of some 10s of volts amplitude is 
required. The RMS amplitudes of the harmonics of an ideal square wave are 
V*2sqrt(2)/pi*n, where n is an odd harmonic number, and V is the amplitude 
of the square wave. Harmonics in the HF range (from about the 21st to the 
200+ for 137k) will have RMS amplitudes of between 10s and several 100s of 
millivolts

At various HF frequencies, the loop will resonate (eg. when it is roughly a 
number of full wavelengths in perimeter - the LF tuning capacitor will have 
little effect). At these frequencies it will have some dBs of gain over 
isotropic, and a feed point resistance of perhaps 10s of ohms. Tens or 
hundreds of millivolts of harmonics applied at these frequencies will 
radiate powers of the order of microwatts to milliwatts EIRP - so perhaps 
similar to a Hifer beacon, but transmitting on many frequencies simultaneously.

However, the output of a switching PA is not an ideal square wave; on the 
one hand the rise and fall times are not instantaneous, which will reduce 
the harmonic content. On the other hand, there is usually a certain amount 
of ringing and switching spikes on the edges, which tend to increase the 
harmonic content at certain frequencies. So if you look at the output on a 
spectrum analyser, instead of a uniformly decaying comb spectrum, what you 
will see are broad peaks and nulls in the harmonic output, which vary 
according to circuit parasitics such as wiring inductance, transistor 
capacitance, etc. If the peaks of harmonic emission do not coincide with 
the resonances of the loop, the whole thing will be quite innocuous as a 
source of QRM. On the other hand, if they do coincide, the complete 
assembly might emit 10s or 100s of milliwatts of harmonics.

The whole scheme is remarkably similar to that with SMPSU's etc. Some are 
perfectly harmless and generate no interference at the frequencies you are 
interested in. On the other hand, when they generate lots of noise at 
frequencies efficiently radiated by the cables, we all know what the 
results can be like! A switch mode lowfer TX driving an antenna without 
filtering could be very similar, except with better frequency stability, 
and no 50/60Hz modulation!

At MF, the loop antenna probably won't be an efficient radiator (unless it 
is hundreds of metres in perimiter), but the harmonics will be higher in 
amplitude - so it might really mess things up for local medium wave listeners!

Cheers, Jim Moritz
73 de M0BMU