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Sorry, a typo lapsus had entered, a "-" instead of a "+":

evaluating the false formula, Instead of below

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

please read:

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

The result at the right was not influenced by the typo lapsus, however.

Sorry. I hope there were no other ones. (Let me know, if so.)

Further, instead of the so far headline "Presentation on the NanoVNA for the raileigh Radio Society"
where the above was just one point of so many, I think, we should better call the headline now
"False Return Loss calculations".

73, Hans,
DJ7BA

-----Ursprüngliche Nachricht-----
Von: [email protected] <[email protected]> Im Auftrag von DJ7BA
Gesendet: Dienstag, 2. Juni 2020 16:14
An: [email protected]
Betreff: Re: [nanovna-users] Presentation on the NanoVNA for the Raleigh Amateur Radio Society

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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