On 10/12/21 11:20 AM, Andrew Kurtz via groups.io wrote:
Yes, R cannot be < 0, but my interpretation is simply that the -2 is error in some small number like, say 1 or 2 ohms.
exactly. Let's say the gamma measurement is +/- 5%.? If you convert gamma = 1.05 (angle = 0) you get -2050 ohms and Mag S11 = 0.4238 dB
If you convert gamma=0.95, you get 1950 ohms and mag S11 = -.4455 dB
Here's some examples (excel attached if you want to fool with it yourself).? For any coil with a reasonably high Q (>100), your DC resistance might be pretty low, especially if the reactance is something like 100 ohms.? In such a case, gamma is VERY close to 1, so small uncertainty in the measurement will result in negative resistance
Z = Z0*(1+gamma)/(1-gamma)
Z0 50
gamma mag gamma ang complex
Z
Zreal Zimag
0.5 0 0.5
150
150.0 0.0
0.5 90 3.06287113727155E-17+0.5i 30+40i
30.0 40.0
0.95 0 0.95
1950
1950.0 0.0
0.99 0 0.99
9950
9950.0 0.0
1 0 1
#NUM!
#NUM! #NUM!
1.01 0 1.01
-10050
-10050.0 0.0
1.05 0 1.05
-2050
-2050.0 0.0
0.95 90 5.81945516081595E-17+0.95i 2.56241787122207+49.9342969776609i 2.6 49.9
0.99 90 6.06448485179767E-17+0.99i 0.50249987374375+49.9974748750063i 0.5 50.0
1 90 6.1257422745431E-17+i
50i
0.0 50.0
1.01 90 6.18699969728853E-17+1.01i -0.49750012375625+49.9975248750062i -0.5 50.0
1.05 90 6.43202938827026E-17+1.05i -2.43757431629014+49.9405469678954i -2.4 49.9
gamma = (Z-Z0)/(Z+Z0)
R X Z Q gamma
gamma mag gamma angle
0 500 500i #DIV/0! 0.98019801980198+0.198019801980198i 1.000 11.42
1 500 1+500i 500 0.97981005617555+0.197940625729906i 1.000 11.42
2 500 2+500i 250 0.979422565531214+0.197859946815246i 0.999 11.42
-1 500 -1+500i -500 0.980586447755754+0.198097471880064i 1.000 11.42
-2 500 -2+500i -250 0.980975331346312+0.198173631809246i 1.001 11.42
0 100 100i #DIV/0! 0.6+0.8i
1.000 53.13
1 100 1+100i 100 0.595270216649472+0.793587810491231i 0.992 53.13
2 100 2+100i 50 0.590680100755667+0.787153652392947i 0.984 53.12
-1 100 -1+100i -100 0.604870574953633+0.80638658172728i 1.008 53.13
-2 100 -2+100i -50 0.609882964889467+0.812743823146944i 1.016 53.12
I will admit that many of you experts talk about how you attach your DUT very carefully, solder it, sometimes have to throw it away when done testing, and all this sounds bizarre to a non-EE who is simply playing with crystal radio. My nanoVNA attaches to my DUT via 2 alligator clips which are on little connectors (BNC maybe?) which screw into the VNA. I recognize that I am accepting error, even though I do my calibration at the same alligator clips, but except for R, I am convinced that the error I am accepting is negligible when my interest is 0.5 to 25 MHz, picking up AM signals. (I welcome any insights if you think I am wrong.)
Andy
On Oct 12, 2021, at 10:05 AM, Jim Lux <jim@...> wrote:
On 10/12/21 6:05 AM, DougVL wrote:
On Mon, Oct 11, 2021 at 09:21 AM, Andrew Kurtz wrote:
R is quite low and may vary between -2 and 5 ohms.
That "-2" suggests to me that you're not actually reading 'Resistance' there. Resistance should be positive, but Reactance can be in negative ohms.
Depending on how the conversion from reflection or transmission coefficient (gamma) to R+jX is done, a coefficient with magnitude >1 will result in negative R.
If you're measuring low impedances (so |gamma| is close to 1) then noise or roundoff errors in a measurement can wind up with gamma>1
