Steve Thompson wrote:
>
>
>Ian White GM3SEK wrote:
>
>> An Lnetwork only has two variables, so the working Q is automatically
>> determined for you. With a resistive load, this is automatically the
>> lowest that can be achieved  so that is an advantage. The only case
>> where an Lnetwork won't give the lowest possible Q is with certain
>> highly reactive loads... in which case, you need to switch to a totally
>> different configuration of Lnetwork.
>I disagree. I haven't time to try and remember how to do the maths, but
>looking at a Smith chart, I think a three element network can give a
>lower loaded Q if there is any reactance in either impedance. The
>difference might be minimal when the reactance is low, but I think it's
>there.
>
You're right, I generalized too far. However, I think
>>
>> This last point is the major DISadvantage of Lnetworks: lack of
>> flexibility. There are a total of 8 different configurations, and they
>> all have a limited matching range. Between them, they can match any
>> impedance (except a 1:1 match requires theoretically zero or infinite
>> component values) but it's a matter of finding which one out of the 8,
>> and most practical Lnetwork tuners can switch between a maximum of 2
>> configurations. However, I'd conjecture that for any pair of
>> impedances, there will always exist at least one Lnetwork configuration
>> that can match them at the lowest possible working Q.
>
>I think not, except for the particular comparison of L against three
>element matching between two pure resistances.
Let's think of two totally generalized impedances, (R1 in series with
jX1) and (R2 in series with X2). In this context X1 and X2 can have
either sign.
Now add series elements X1 and X2 to cancel both reactances out. We
now have resistive impedances R1 and R2, which can be matched with the
minimumQ solution using two elements in one of the Lnetwork
configurations.
We have now added a total of four elements, but one of either X1 or X2
can always be absorbed into the series arm of the Lnetwork. So that
brings us back to needing three elements to match any arbitrary pair of
impedances with the minimum possible Q.
In ATU applications, one impedance is always nonreactive (namely 50
+j0). In that case, the load reactance can always be absorbed into the
series arm of an Lnetwork, so we're back to two elements again. That
line of argument seems to be general enough to prove  at least in
principle  that any reactive load can be matched to any resistive load
at the minimum possible Q, using only two elements.
What we don't know is which one of the Lnetwork configurations might be
required, or whether it's at all practical. I'm not aware of any
reallife Lnetwork tuner that can manage more than two different
configurations (out of the possible 8) so it cannot "always" have the
lowest possible losses of any configuration.
One thing we can be sure of: this area is too tricky for either sweeping
generalizations or sweeping condemnations.
The best way to investigate reallife power handling in an L or
Tnetwork ATU is to analyse a range of cases using something like the
AAT software that comes with the ARRL Antenna Handbook. That will
calculate and map out the range of load impedances that can be matched
(1) at all, (2) without arcing the capacitors and (3) without melting
the inductor.

73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek
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