[Amps] *** SPAM *** Re: Antenna traps

[Ian White GM3SEK]

Steve Thompson wrote:
>
>
>Ian White GM3SEK wrote:
>
>> An L-network 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 L-network 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 L-network.
>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 L-networks: 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 L-network 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 L-network 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 
minimum-Q solution using two elements in one of the L-network 
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 L-network. 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 non-reactive (namely 50 
+j0). In that case, the load reactance can always be absorbed into the 
series arm of an L-network, 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 L-network configurations might be 
required, or whether it's at all practical. I'm not aware of any 
real-life L-network 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 real-life power handling in an L- or 
T-network 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