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Hi Dana,

thanks for your clarification request.
Sorry that I thought it was obvious, I was a bit too short, I think.

The following should take care, hopefully:

On



You can find a circuit diagram, that (disregarding the + and – DC signs) we will use here.

Zs and ZL each are a series of a resistance and a reactance, in the resonance example, XS and XL
are reactances of of equal magnitude but opposite sign – as typical in a resonant serial LC circuit.



Let’s understand ZS as impedance of the source, (in my earlier example it is Z2 = R2 + j X2)
and ZL as impedance of the Load, (in my earlier example it is Z1 = R1 + j X1) .

As was written in the simple resonance example, let be:

Generator (or Thévenin equivalent) impedance: Z2 = R2 + jX2 = 50 +j100 Ohm,
Load impedance: Z1 = R1 + jX1 = 100 –j100 Ohm.

meaning:

R1 = 50 Ohm
X1 = +100 Ohm ( represents omega * L)
R2 = 100 Ohm
X2 = -100 Ohm ( represents 1 / (omega * C)

we can use the (ATIS published) left part “false assumption” formula, neglecting also the magnitude signs, that are falsely arbitrary, too,
as the reflection factor in general has a complex value, of course – just look at any Smith diagram):

as found here:





from this we get: RC = (50 + j100 – (100 – j100)) / (50 + j100 – (100 – j100)) = -50 / (-50 + j 200).

Using EXCEL (because of it’s ability to easily do complex math), this yields:

RC = 0.3333 –j 1.3333

or, if we don’t ignore the magnitude, as ATIS uses it:

RC = | 0.3333 –j 1.3333 | = 1.374

already here we see, that RC (or gamma, as it is sometimes called, too) in a passive lumped element circuit is > 1 ! That is wrong already.

Nevertheless carrying on with it, we get:

SWR = 1 + |RC| / ( 1 - | RC |) = 1 + 1.374 / (1 – 1.374) = -6.342 which, of course, is negative, the fact that the otherwise excellent
article of Trevor S. Bird had quoted, not noticing that it yields a negative result, which he wanted to prove is not correct – just as you had said, too,
as in a passive lumped element circuit RL must be positive.

I don’t know if you can use complex EXCEL, but I hope so.
Feel free to use – besides the simple resonance example – also any other complex values by entering these in the yellow EXCEL fields.

Just in case not - I also add a picture of the EXCEL. In some other work sheet programs, you may be able to make use of that, too.



73, Hans
DJ7BA








-----Ursprüngliche Nachricht-----
Von: [email protected] <[email protected]> Im Auftrag von Dana Whitlow
Gesendet: Dienstag, 2. Juni 2020 01:49
An: [email protected]
Betreff: Re: [nanovna-users] Presentation on the NanoVNA for the Raleigh Amateur Radio Society



Hans, I don't understand your "obvious example" circuit.

Could you please describe it in detail, perhaps expressed as a spice netlist in the body of your reply, for simplicity?



Thanks,



Dana







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