On May 23, 1:08 pm, Wes Stewart wrote:
On 23 May 2007 09:37:00 -0500, wrote:

Ralph Hanna, W8QUR, in a brief article "Pi Networks" on page 108 of
the December, 1965, issue of 73 MAGAZINE, after discussing power-
supply filters and high- and low-pass TV filters, wrote:

(Paraphrasing) "The most popular of all pi networks is the output
circuit of a transmitter ... with which the output of almost any
transmitter can be matched to almost any antenna ... another
advantage is the reduction of harmonics....

(Actual quote) "The big disadvantage of this system is the low
efficiency. It is not possible to run more than 50% efficiency
and it tends to be more like 30%. Other methods of feeding the
antenna will result in efficiencies of as high as 65% to 70%."

Is that "low efficiency" of 30-50% really true?

As others have stated, No.

Clearly at that time the author was talking about a vacuum tube
transmitter where the pi-network was used to transform the load
impedance (usually 50 ohm) up to the load that the tube(s) want to
see.

The usual implementation was the low-pass form of shunt C(s), series
L, although this isn't the only option. The network can be thought of
as two L-networks back-to-back with a "virtual" impedance common to
the midpoint. The usual design sets a overall network Q (the sum of
the two L-network Q's) at something between 10 and 12 for harmonic
suppression reasons.

The loss in the network is usually considered to be only in the
inductor, (although this isn't totally correct) because inductors
generally have lower unload Qs than the air or vacuum variable
capacitors that are typically used.

The network efficiency using this assumption is then:

eff = 1 - (Ql/Qu)

So for example if the inductor Q = 200 (a reasonable value) and the
network Q is set to 12 then the efficiency is 94%, a long way from
what the author claims.

At higher frequencies with tubes with high output capacitance it may
be necessary to design for a higher loaded Q than we would like. In
this case, the efficiency will reduce as is often the case with
amplifiers on 10-meters for example.

All of this stuff in any ARRL Handbook and can be worked out by the
reader.


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.

Cheers,
Tom