[Amps] Matching

[Ian White GM3SEK]

Steve Thompson wrote:
>
>
>Peter Chadwick wrote:
>> Steve said:
>>
 >>As an example, take an impedance of 100 + j50 ohms, which
 >>you want to match to 50R resistive.
 >>
 >>I can see two L match solutions, which have a loaded Q of
 >>about 1.2. A T match can do it with a loaded Q of about 1.04.
 >>I can't see any L match that betters this. Can someone correct
 >>me if I'm wrong?

>>  >Can someone correct me if I'm wrong?<
>>
>> No - 'cos you're not wrong!
>After more peering at Smith charts (considering matching some impedance
>to a resistance), I think there's some impedances where you can't get
>lower Q than an L match, and others where you can. There's nowhere that
>an L match gives lower Q than 3 element matching circuits.
>
>It all depends if you are inside or outside the constant R and Y circles
>for the resistance you're aiming for.

And also whether the series output C of the T-network is helping or not. 
In the particular case of 100+j50, the series C tunes out the reactance 
and leaves 100+j0 to be matched. None of the L-networks can do this, so 
they are forced to match the equivalent *parallel* impedance instead, 
which is always higher (in this case 125 // j250). Hence the increase in 
loaded Q.

If the impedance had been 100 -j50, then you'd need series L at the 
output to cancel the reactance and leave 100 ohms resistive. The series 
output C of a  typical C-L-C T-network would then become a disadvantage, 
increasing the equivalent resistance that has to be matched, and thus 
increasing the working Q.

Part of the confusion in this debate has been between an optimum 
configuration of L or T network, and the more limited capabilities of 
real-life ATUs which have a fixed configuration. I've certainly been 
guilty of mixing the two in the same posting.

But beyond that, we're using working Q as a proxy for more practical 
power handling limitations: heat dissipation in variable inductors or 
arcing in variable capacitors. That adds a whole other level of 
complexity, leaving us with only one valid generalization: no ATU 
configuration can be "best" in all possible cases.




-- 
73 from Ian GM3SEK