On 24 May 2007 14:46:38 -0700, K7ITM wrote:

[all my good stuff snipped]


I haven't thought terribly deeply about this, but it occurs to me
you're caught between a rock and a hard place any time you are stuck
with a tube whose output capacitance represents a low reactance at the
operating frequency, and which wants to see a high load impedance.
However you resonate that capacitance, you end up with a high Q. It
is convenient that the Q of coils goes up as the frequency increases,
and for practical tubes at VHF/UHF, you can use transmission lines
that are physically large enough to have very high Qu.

In fact, it's not just the tube capacitance that gives you grief--it's
the ratio of the reactance and the desired load resistance. And for a
pure pi network, it's also the ratio between the resistance you're
matching: if you want to present a 5000 ohm load to a tube and
transform that to 50 ohms, the Q of the pi will be at least 10, at
which point the network has degenerated into a simple L with no output
capacitance. If you need to get from 10k ohms to 10 ohms, then the
loaded Q is 31.6 minimum.

But if you add just one more inductor forming a cascade of two L
networks each performing a 31.6:1 impedance transformation (for the
10k to 10 ohm example), the Ql of each will be about 5.6. The
capacitance at the plate end becomes much smaller, though, so this
method is only practical at lower frequencies. The comparison between
the "minimum Q" pi degenerated into a single L network and the cascade
of two L networks is interesting: the -3dB bandwidth of the single L
is about 6%, versus 26% for the cascade of two; but the harmonic
attenuation is better for the cascade: at the second harmonic, it's
42dB versus 33.5, and at the third, 59dB versus 42dB. Loss with Q=100
coils is also better for the cascade, about .48dB versus .72, although
if you use the same volume for the single coil case as you do for the
two coil network, the loss is pretty similar since the larger coil has
higher Qu. You can carry this even further and cascade more L
sections to get a flatter wide passband, better harmonic suppression,
and reasonably low loss.


Yep.

A number of years ago in this group our departed friend, Reg, made a
comment more or less saying that the fewer (non-ideal) reactances were
in the matching network, the lower the losses were.

I offered an example that proved this wrong. I'm extremely strapped
for time but I think the thread has something to do with L-networks if
anyone cares to search for it.

Wes