What is the difference between the curves in "Real/Imaginary" vs "R+jX (Ω)" Charts - in NanoVNA Saver and NanoVNA 2_2 ?

What do they represent, as they usually have resonance on different frequencies?

Simen Tobiassen

Imaginary = ±jX (just presented in different forms)

Capacitive reactance carries the negative sign (bottom half of the Smith
Chart).

Inductance reactance carries the positive sign (top half of the Smith
Chart).

Also remember, resonance is defined as zero imaginary or zero ±jX values -
purely resistive. It is the radiation (pure) resistance that radiates
energy from an antenna structure.

Also: Resistance is frequency independent.
Reactance is frequency dependent.

Resistance can dissipate power but cannot effect phase.
Reactance cannot dissipate power but does effect phase.

We'll not address parasitics of the real world implementations of the above
statements.

Dave - WØLEV

--
*Dave - WØLEV*
*Just Let Darwin Work*

On Tue, Oct 27, 2020 at 03:03 PM, Simen Tobiassen wrote:

What is the difference between the curves in "Real/Imaginary" vs "R+jX (Ω)"
Charts - in NanoVNA Saver and NanoVNA 2_2 ?

The first displays the complex scattering parameter (S11 or S21), the second display the complex impedance calculated from S11.

Regards
Christian

REAL and IMAG parameters are quite different from RESISTANCE and REACTANCE parameters. REAL and IMAG apply to reflection coefficient Γ, in its complex form (a+j.b). That's why values are always in the [-1,1] interval, without any associated unit. When REAL=-1 and IMAG=0, it is the Short circuit situation. When REAL=1 and IMAG=0, it is the Open circuit situation. When REAL=0 and IMAG=0, it is the normal Loaded (50 ohms) situation.

LINEAR is the Γ modulus form of combined REAL and IMAG values, and finally POLAR is the geometric representation of REAL, IMAG and PHASE values. When POLAR is displayed by the NanoVNA, and even if data values are exactly displayed as for Smith Chart, results must not be read in the same way. Have a try by displaying two CH0 traces, POLAR and SMITH.

SWR and LOGMAG (Return Loss) are derivated from Γ modulus (LINEAR). For educational purposes I have created an ods file (see below), showing and calculating NanoVNA parameters. You can play with it by entering values in the blue fields, and also checking what are the arithmetic relations behind the different results. Here Group Delay is not relevant as calculations are done for a discrete (CW) frequency.

A last word about the use of REAL and IMAG parameters. The following case (see attachment) is an opened coaxial cable (length 2 meters), creating a quarter wave stub (at red marker). An opened coaxial cable remains a good use case for education and increase of knowledge. On the NanoVNAsaver snapshot we see clearly that displayed values between RESISTANCE/REACTANCE and REAL/IMAG do not allow an immediate comparison. For example at red marker, R+jX or Smith Chart highlight a value of 0+j0 ohms (short circuit situation), and checking this with REAL/IMAG chart you get -1 (REAL) and 0 (IMAG) which is the same thing. Be careful with REAL and IMAG curves which follow sinus and cosinus rules, it reflects simply a monotonous variation of PHASE.

REAL is also interesting if you want to measure a coaxial cable length, thanks to advanced TDR function.

73 from Jean-Roger / F6EGK

Thank you for answering, David. This is also what I know and related to, with both the Impedance and Admittance having a Real and an Imaginary part.

But Jean-Roger have got to the core here; The "Real/Imaginary" Chart shows neither Impedance nor Admittance. The Reflection Coefficient Γ in its complex form is also a complex number; with a Real and an Imaginary part (a+jb). These are the ones being displayed in the "Real/Imaginary" Chart :)

Regards,
Simen

Thank you Christian, for answering!

Complex Scattering (including the impedance from S11) refers to all the S-parameters being calculated from readings of scattered current and voltage waves, being complex numbers; magnitudes and angles.

In the context of S-parameters, scattering refers to the way in which the traveling currents and voltages in a transmission line are affected when they meet a discontinuity caused by the insertion of a network into the transmission line. This is equivalent to the wave meeting an impedance differing from the line's characteristic impedance.

https://en.wikipedia.org/wiki/Scattering_parameters

Regards,
Simen

Thank you, Jean-Roger, for taking the time for an extensive answer! I had to lay down flat on my bed with this one ;)

This response got long. I tried to get it all in there, not necessarily expecting you to answer them all ;)



RESISTANCE IN YOUR COAXIAL CABLE STUB

Your antenna has R = 0 Ω.
The R+jX (Ω) chart allows for positive and negative R values.

1) What is the significance of R = 0 Ω in your “antenna”; Is there an “RR-resonance” (one +R Ω
and one –R Ω meeting and cancelling at = 0 Ω) – in the same way the LC meet in resonance at ±jX = 0 Ω?

This would be like the Negative Resistance Oscillator type amplifier in the old reflex Klystron microwave emitters, used for radar. And in the Gunn Diode.



+R and –R SPIKES

The attached Touchstone file “Coil L3 - 11-32 Mhz –66154.1 Ohm Negative Spike.s1p” shows a negative resistance in the R+jX (Ω) Chart: R = –66154.1 Ω.
On the same frequency the |Z| Chart shows a 67785 Ω spike.

The attached Touchstone file “L3 Coil in series - How do I move –R up.s1p” shows a negative R in the R+jX (Ω) Chart: R = –18141.3 Ω.

2) How is this Resistance being created, incl these Resistive spikes, while the resistance in the wire is close to 0 Ω?

I have tried to correct these negative resistances using resistors, and only got them up to about –800 Ω.

3) Any ide on how to move -R’s up into 0 Ω?



SERIAL C (F) AND SERIAL L (H)

The Serial C (F) is explained to be a measurement of a capacitor in series with a resistor, and the Serial L (H) an inductor in series with a Resistor. Regardless of this, I do not find instructions on how to actually connect the NanoVNA to a coil to get the values right in the Serial C (F) and Serial L (H) Charts.

I either connect one end of my coil to the S11 center terminal, or I connected in Parallel to the S11 port.

On the Serial C (F) Chart I typically get curves with large, abrupt “Spikes” at frequencies where the Reflection Coefficient is in resonance and the Phase Angle is 0°, falling steep.

The Serial L (H) Chart usually shows a curve almost identical to the SRF curve on the R+jX (Ω) Chart, on the same frequency.

I then thought I could use the C value at the Marker on the Serial C (F) Chart and the H value for the same Marker in the Serial L (H) Chart, to calculate the +jX and –jX values on that frequency. I expected to get two different reactance values, but NanoVNA Saver always give me the same but opposite reactance values.
I expected the same reactance values only when the R+jX (Ω) Chart shows ±jX = 0 Ω = LC resonance.

4) How do I connect to get the Serial C (F) and Serial L (H) Chart values right?

5) Is the NanoVNA not able to measure/show the true L and C values
and their actual, separate +jX and –jX values?

6) At an ordinary LC resonance point the XL and XC are cancelling, resulting in 0 Ω.
At a coil’s or a capacitor’s SRF point though, is there actually no L and C as the NanoVNA suggest?


¼ WAVE + PHASE ANGLE 0° + SRF – AT ONE FREQUENCY?

Your coaxial cable stub has

Red Marker: 27,0275 MHz
Phase Angle Chart: 0° (where it actually crosses)
Real/Imaginary Chart: REAL = -0.95, IMAG = 0 (short circuit situation)
R+jX (Ω) Chart: 0+j0 Ω (short circuit situation)

Green Marker: 54,0050 MHz
R+jX (Ω) Chart: Approximately SRF


Will there be some kind of better resonance if we get all the following to resonate at the same frequency?

A Reflection Coefficient Resonance --> Length related
Open or Closed = Standing waves

B Phase Angle 0°, with Steep change --> Length related
- as in your ¼ wave cable stub

C Self-Resonant Frequency --> Length related
David KNIGHT, PhD in Microwave Spectroscopy, concludes that
the SRF is mostly related to length, in his “self-res.pdf”
http://g3ynh.info/zdocs/magnetics/appendix/self-res.html


The attached Touchstone file “L3 Coil in series - How do I move –R up.s1p” shows at 13.36 MHz:

a) Real/Imaginary Chart: REAL = 1, IMAG = 0 (open circuit situation)
b) Phase Angle Chart: 0°
c) Serial C (F) Chart: At “SRF” point C and L is zero
d) Serial L (H) Chart: At “SRF” point C and L is zero
e) R+jX (Ω) Chart: R = –18141.3 Ω, +jX = 967 Ω

7) What would be the significance of a) – e) being on the same frequency,
incl - R+jX (Ω) Chart: R = 0 Ω, ±jX = 0 Ω?

RESISTANCE IN YOUR COAXIAL CABLE STUB

Your antenna has R = 0 Ω.
The R+jX (Ω) chart allows for positive and negative R values.

1) What is the significance of R = 0 Ω in your “antenna”; Is there an “RR-resonance” (one +R Ω
and one –R Ω meeting and cancelling at = 0 Ω) – in the same way the LC meet in resonance at ±jX = 0 Ω?

This would be like the Negative Resistance Oscillator type amplifier in the old reflex Klystron microwave emitters, used for radar. And in the Gunn Diode.

Be careful Simen with the "saver" R+jX chart, there is never negative values for R. The R scale (red) is on the vertical left side of the chart, and for this example with a range from 0 to 2000 ohms. Negative to positive values apply only to X (reactance) and are shown on the right scale (cyan) of the chart.

I suggest you to have a look to stub circuits behavior. I have put below a capture of data provided by W4RNL at http://www.antentop.org/w4rnl.001/loadtl4.html which is a good summary.

Red marker in "saver" capture is the short circuit situation equivalent to a RLC series circuit with R=0 and LCw = 1/Cw (cancellation of reactive part) at 27.075 MHz.
Green marker in "saver" capture is the highest impedance situation equivalent to a RLC parallel circuit with high R (theorical infinite value) and LCw = 1/Cw (cancellation of reactive part) at 54.050 MHz

You can also check that L and C have not the same values for these two situations. Green marker behavior is equivalent to add a lambda/4 stub to the first one. The first provides the short circuit situation (red marker) which is the load value for the second lambda/4 stub. Finally you get the high impedance situation at the end of this second stub (green marker).

I hope it is enough clear as english is not my native language ! Please note that I don't succeed in downloading your s1p files from this message (file format probably unknown from the website).

Jean-Roger