On Mon, Oct 26, 2020 at 02:30 PM, alan victor wrote:
There is a fundamental idea that is easy to grasp but it has big implications
in achieving lossless
impedance matching. Although we can achieve matching between networks with
resistors only,
they waste power. Ideal energy storage elements, like L and C do not and of
course this whole
bit about matching is either about maximizing the power delivered from one
network to another or
providing a source or a load resistance of a particular value to optimize
voltage or current gain for
that network.
So how is this done?! THE BASIC RULE USED IS SIMPLE!
Z=1/Y.
Yep that's it. Given a series circuit, I can transform it to an equivalent
parallel
circuit which has the IDENTICAL voltage, current and frequency response. Wow.
That's
pretty nifty. So if I have a series 50 ohm resistor and I need to terminate a
filter into 150
ohms, I could add a series 100 ohm resistor, wasting power, or I could add a
PIECE of
REACTANCE in series with that 50 ohm resistor and accomplish the same goal.
That is
produce a R value of an EQUIVALENT PARALLEL network OF 150 OHMS from
that single 50 ohm unit.
I tentatively answer this message, though I've read the following ones, both to follow the order of the messages and to possibly get some prompt that I could use to better understand the rest.
Reading that to achieve the goal of maximum power transfer from a source to a load just resistors could be used was definitely illuminating. Of course, power waste in resistors would be an outstanding undesirable aspect. But considering this chance I may finally understand what the designer of the circuits 5 and 6 in the scrap I attach again - I still wonder what L1 is for in circuit 5, but I can wait to figure out this. Would you confirm the designer was interested just in letting the NanoVNA see an about 50 ohm load and in letting the filter components see a source with an about 300 ohm output impedance?
This would address precisely my previous question: why just resistors there? At the same time, I still wonder why the output impedance of the filters is not considered at all. I'm sure a LT10.7MA5 has not a 50 ohm output impedance and I can safely bet a XT6.5MB has not a 50 ohm impedance.
As for the relation between Z and Y, I'm embarassed to confess it still does not mean any much to me. In other words, I'm terribly embarassed to admit I still don't what's the importance of using Y instead of Z, since Y is banally the reciprocal of Z. The only answer I could find so far is pretty miserable: we use Y instead of 1 / Z when we want to want to write something in the form of a product, rather than in the form of a division.
Later on, after reading something you wrote about that relation in one or more of the following messages, I suspected Z could be the output impedance of the source and Y could be the input admittance of the load. But, again, why are we mentioning an input admittance rather than an input impedance? I just didn't feel like asking this, I tried to find an answer elsewhere before, but with no luck.
Thanks!
A.
