Dave Casler sets out in his Youtube video to answer why two wire transmission line has so little loss . With more than 10,000 views, 705 likes, it is popular, it must be correct… or is it?

He sets a bunch of limits to his analysis, excluding frequency and using lossless impedance transformation so that the system loss is entirely transmission line conductor loss.

He specified 300Ω characteristic impedance using 1.3mm copper and calculates the loop resistance, the only loss element he considers, to be 0.8Ω.

Above is Dave’s calculation. Using his figures, calculated \(Loss=\frac{P_{in}}{P_{out}}=\frac{100}{100-0.27}=1.0027\) or 0.012dB.

Above is my calculation of the DC resistance at 0.395Ω per side, so I quite agree with his 0.8Ω loop resistance… BUT it is the DC resistance, and the RF resistance will be significantly higher (skin effect and proximity effect).

Casler’s is a DC explanation.

Self taught mathematician Oliver Heaviside showed us how to calculate the loss in such a line.

Let’s calculate the loss for that scenario more correctly.

Casler’s 1.3mm 300ohm two wire line
Parameters
Conductivity	5.800e+7 S/m
Rel permeability	1.000
Diameter	0.001300 m
Spacing	0.015000 m
Velocity factor	0.800
Loss tangent	0.000e+0
Frequency	14.000 MHz
Twist rate	0 t/m
Length	30.480 m
Zload	300.00+j0.00 Ω
Yload	0.003333+j0.000000 S
Results
Zo	301.80-j0.66 Ω
Velocity Factor	0.8000
Twist factor	1.0000
Rel permittivity	1.562
R, L, G, C	4.864062e-1, 1.261083e-6, 0.000000e+0, 1.384556e-11
Length	640.523 °, 11.179 ᶜ, 1.779231 λ, 30.480000 m, 1.271e+5 ps
Line Loss (matched)	0.213 dB
Line Loss	0.213 dB
Efficiency	95.21 %
Zin	3.031e+2-j1.940e+0 Ω
Yin	3.299e-3+j2.112e-5 S
VSWR(50)in, RL(50)in, MML(50)in	6.06, 2.892 dB 3.132 dB
Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end)	2.183e-3-j2.105e-3, 0.003∠-43.9°, 50.364 dB, 1.01, 0.000 dB
Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end)	-2.990e-3+j1.096e-3, 0.003∠159.9°, 49.938 dB, 1.01, 0.000 dB
V2/V1	1.973e-1+j9.504e-1, 9.707e-1∠78.3°
I2/I1	2.055e-1+j9.590e-1, 9.808e-1∠77.9°
I2/V1	6.576e-4+j3.168e-3, 3.236e-3∠78.3°
V2/I1	6.164e+1+j2.877e+2, 2.942e+2∠77.9°
S11, S21 (50)	9.347e-1-j6.326e-2, 2.295e-2+j3.253e-1
Y11, Y21	8.345e-5+j6.986e-4, -1.011e-5-j3.385e-3
NEC NT	NT t s t s 8.345e-5 6.986e-4 -1.011e-5 -3.385e-3 8.345e-5 6.986e-4 ‘ 30.480 m, 14.000 MHz
k1, k2	1.871e-6, 0.000e+0
C1, C2	5.916e-2, 0.000e+0
MHzft1, MHzft2	5.702e-2, 0.000e+0
MLL dB/m: cond, diel	0.006999, 0.000000
MLL dB/m @1MHz: cond, diel	0.001871, 0.000000
γ	8.058e-4+j3.676e-1

 

Above is the complete output from RF Two Wire Transmission Line Loss Calculator.

One of the results shows the values of distributed R, L, G and C per meter, and R is 0.486Ω/m or 14.81 for the 30.48m length, nearly 20 times Dave Casler’s 0.8Ω.

Unsurprisingly, the matched line loss is larger, calculated at 0.213dB, much higher than Dave Casler’s 0.12dB.

Now for a bunch of reasons, the scenario is unrealistic, but mainly:

• the conductor diameter is rather small, smaller than many 300Ω commercial lines and impractical for a DIY line; and
• two wire line is most commonly used with high standing wave ratio and the often ignored loss under the specific mismatch scenario is more relevant.

Conclusion

It is common that the loss in two wire line system underestimates the line loss under mismatch and impedance transformation that may be required as part of an antenna system.

Casler’s DC explanation appeals to lots of viewers, probably hams, and might indicate their competence in matters AC, much less RF.

… Read widely, question everything!

 

This article reports and analyses a user experiment measuring current in a problem antenna system two wire transmission line.

A common objective with two wire RF transmission lines is current balance, which means at any point along the transmission line, the current in one wire is exactly equal in magnitude and opposite in phase of that in the other wire.

Note that common mode current on feed lines is almost always a standing wave, and differential mode current on two wire feed lines is often a standing wave. Measurements at a single point might not give a complete picture, especially if taken near a minimum for either component.

MFJ-854

The correspondent had measured feed line currents using a MFJ-854.

Above is the MFJ-854. It is a calibrated clamp RF ammeter. The manual does not describe or even mention its application for measuring common mode current.

So, my correspondent had measured the current in each wire of a two wire transmission line, recording 1.50 and 1.51A. He formed the view that since the currents were almost equal, the line was well balanced.

I have not used one of these, I rely on my correspondents guided measurements. (I have used the instrument described at Measuring common mode current extensively.)

MFJ-835

This is the instrument that MFJ sell for showing transmission line balance. One often sees recommendations by owners on social media, it is quite popular.

 

If the needles cross within the vertical BalancedBarTM the balance is within 10%. If not, you know which line is unbalanced and by how much.

Note the quote uses current like it is a DC current, not an AC current with magnitude and phase.

So, in the scenario mentioned earlier, the needles would deflect to 50% and 50.3% on the 3A scale, the needles would cross right in the middle of the BalancedBarTM, excellent.

… or is it?

One more measurement with the MFJ-854

I asked the chap to not only measure the (magnitude) of the current in each wire, but to pinch the wires together and close the clamp around both and measure the current. The remeasured currents were of 1.50 and 1.51A in each of the two wires, the current in both wires bundled together was 1.2A.

What does this mean?

With a bit of high school maths using the Law of Cosines, we can resolve the three measured currents into common mode and differential mode components.

Above is the result, the current in each wire comprises a differential component of 1.38A and a common mode component of 0.6A. The common mode components in each wire are additive, so the total common mode current on the feed line is 1.2A.

Above is a phasor diagram of I1, I2 and I12, and the components Ic and Id.

Note in this diagram that whilst the magnitude of i1 and i2 are similar, they are not 180° out of phase and that gives rise to the relatively large sum I12 (the total common mode component of I1 and I2).

This is a severe imbalance, sufficient to indicate a significant problem and to prompt a physical and electrical check of the antenna and feed line conductors and insulators.

Repairs were made and the measured result was quite good.

Above are the measurements and calcs.

Above is the phasor diagram… a bit harder to read as there is very little common mode current.

By contrast with the previous case I1 and I2 are almost 180° out of phase and the sum of them, I12 has very small magnitude.

Conclusions

The MFJ-854 can be used effectively for measuring current balance.

Understanding the relative common mode and differential components hinted there was something very wrong in the antenna system.

Forget the MFJ-835 for proving balance. If the needles do not cross in the BalancedBarTM it indicates unbalanced amplitudes. If they do cross in the BalancedBarTM it indicates approximately balanced amplitude, but does not prove the phase relationship is approximately opposite and as shown in this example, is a quite erroneous result.

This article walks through a simple verification of nominal 50Ω coax cable with connectors against manufacturer specifications using a NanoVNA.

The instrument used here is a NanoVNA-H4 v4.3 and NanoVNA-D firmware NanoVNA.H4.v1.2.33.

The DUT is a 10m length of budget RG58-A/U coax with crimped Kings BNC connectors, budget but reasonable quality. It was purchased around 1990 in the hey day of Thin Ethernet, and at a cost of around 10% of  Belden 8259, it was good value.

The notable thing is it has less braid coverage than 8259 which measures around 95%.

The cable has BNC(M) connectors, and BNC(F)-UHF(M) + UHF(F)-SMA(M) are used at both ends to simulate the impedance transformation typical of a cable with UHF(M) connectors.

Step 1: calibrate and verify the VNA

Note that |s11|<-40dB, or ReturnLoss>40dB. You really want at least 30dB ReturnLoss for this test to be as simple as described here.

The Smith chart plot of s11 is a very small spiral in the centre of the chart… approaching a dot.

Step 2: measure

The measurement fixture removed a ~150mm patch cable used during through calibration, so 750ps e-delay is configured on Port 2 to replace it. (one could just leave that cable in the test path and no e-delay compensation is needed).

Note that recent NanoVNA-D allows specification of e-delay separately for each port, don’t do as I have done if you use other firmware, leave the through calibration cable in place.

Above is a screenshot of the measurement from 1-31MHz.

Step 3: analysis

|s11|

Before rushing to the |s21| curve, let’s look at s11.

The Smith plot shows a small fuzzy spiral right in close to the chart centre, that is good.

The |s11| curve shows a periodic wave shape, lower than about -25dB. Recalling that ReturnLoss=‑|s11|, we can say ReturnLoss is greater than about 25dB. That is ok given the use of UHF connectors.

That wavy shape is mainly due to small reflections at the discontinuity due to the UHF connectors. They typically look like about 30mm of VF=0.67 transmission line of Zo=30Ω, so they create a small reflection. At some frequencies, the reflection from the far end discontinuity arrives in opposite phase with the near end reflection and they almost cancel, at other frequencies they almost fully reinforce, and in between they are well, in between… and you get the response shown in the screenshot. The longer the DUT, the closer the minima and maxima, and if the DUT is less than 180° electrical length, you will not see a fully developed pattern.

If you see a Smith chart spiral that is large and / or not centred on the chart centre, the cause could be that Zo of the DUT is not all that close to 50Ω, a low grade cable, possibly with migration of centre conductor or bunching of loose weave braid.

If your |s11| plot shows higher values, investigate them before considering the |s21| measurement. Check connectors are clean and properly mated / tightened.

|s21|

Now if that is all good, we can proceed to |s21|.

We can calculate InsertionLoss=‑|s21|, see Measurement of various loss quantities with a VNA.

It is interesting to decompose InsertionLoss into its components, because we may be more interested in the (Transmission) Loss component, the one responsible for conversion of RF energy to heat.

InsertionLoss for commercial coax cables is often specified as frequency dependent Matched Line Loss (MLL) or Attenuation (measured with a matched termination).

If InsertionLoss and MismatchLoss are expressed in dB, we can calculate \(Loss_{dB}=InsertionLoss_{dB}-MismatchLoss_{dB}\)

Above is a chart showing MismatchLoss vs ReturnLoss.  If ReturnLoss>20dB, MismatchLoss<0.05dB and can often be considered insignificant, ie ignored.

For example, the marker, ReturnLoss=26.05dB, so MismatchLoss is very small and can be ignored in this example and we can take that Loss≅InsertionLoss=‑|s21|.

We can calculate the MismatchLoss given |s11|:

As stated, at 0.011dB, it is much less than InsertionLoss so can be ignored.

So do we give this budget cable and connectors a pass?

At 15MHz, we can take MatchedLineLoss to be 6.8dB/100m which is a little higher than Belden 8259 datasheet’s 6.2dB/100m. That is not sufficient reason to FAIL the cable, we will give it a PASS.

Problem analysis

Let’s discuss a problem scenario to encourage some thinking.

Above is a through measurement after calibration.

What is wrong, shouldn’t |s11| be much smaller, shouldn’t the Smith chart plot be a dot in the centre?

Yes, they should.

If the calibration process was done completely and correctly, then this indicates that Zin of Port 2 is significantly different to the LOAD used for calibration. Note that they could BOTH be wrong. An approach to resolving this is to validate the LOAD, and when that is proven sufficiently accurate, remeasure Port 2 using a short through cable and check |s11|. If it is bad then perhaps a GOOD 10dB attenuator on Port 2 might improve things.

Now let’s ignore that problem and proceed to try the cable measurement (with that setup).

Above is a through measurement of an unknown 10m coax cable with 50Ω through connectors… no UHF connector issues here.

As before, look at |s11| first. The cyclic wavy nature hints that there is problem with one or more of LOAD, Port 2 Zin and DUT Zo. They should all be the same.

Note also the spiral Smith chart trace, if it is not centred on the centre of the chart, it hints that DUT Zo, LOAD and Port 2 Zin are significantly different.

So, to resolve this, one path is to validate the LOAD, and when that is proven sufficiently accurate, remeasure Port 2 using a short through cable and check |s11|. If it is bad then perhaps a GOOD 10dB attenuator on Port 2 might improve things. If these are both good, then the measurement suggests the DUT cable Zo is wrong.

The |s21| measurement is suspect until you resolve these issues.

Conclusions

Analysis of the |s11| measurement is important, good |s11| results are a prerequisite to analysing |s21|.

Comparison with manufacturers data gives a basis for PASS/FAIL.

This article documents the Port 1 waveform of my NanoVNA-h4 v4.3 which uses a MS5351M (Chinese competitor to the Si5351A) clock generator.

There are many variants of the NanoVNA ‘v1’, and most use a Si5351A or more recently a loose clone, and they will probably have similar output.

Above is the Port 1 waveform with 50+j0Ω load (power setting 0). By eye, it is about 3.3 divisions in the middle of each ‘pulse’. At 50mv/div, that is 165mVpp, 0.136W, -8.7dBm. The fundamental component (which is what is used for measurement below ~300MHz) is 3dB less, -11.7dBm.

Importantly, is is not a sine wave, it is a complex wave shape that is rich in harmonics. See square wave for more discussion.

Above is the Port 1 waveform with no load. By eye, it is about 6.6 divisions in the middle of each ‘pulse’. At 50mv/div, that is 330mVpp.

The voltage measurements are low precision, but suggest that if it behaves as a Thevenin source, since loaded voltage is half unloaded voltage, assuming that then Zsource=Zload=50+j0Ω.

How can you make good measurements with a square wave?

The instrument is mostly used to measure devices with frequency variable response, so how does that work (well)?

The NanoVNA-H is essentially a superheterodyne receiver that mixes the wave (send and received) with a local oscillator (LO) to obtain an intermediate frequency in the low kHz range, and digital filtering implements a bandpass response to reject the image response and reduce noise. So, whilst the transmitted wave is not a pure sine wave, indeed is rich in harmonics, the receiver is narrowband and selects the fundamental or harmonic of interest. The fundamental is used below about 300MHz, then the third harmonic is selected by the choice of the LO frequency above that, and still higher the fifth harmonic is selected.

Of course the power in the harmonics falls with increasing n which reduces the dynamic range of the instrument in harmonic modes. Though the NanoVNA adjusts power for the harmonic bands, one can observed a reduction in dynamic range.

How did you get those waveforms when it sweeps?

There is a stimulus mode labelled CW which causes output to be on a single frequency. In the sense that CW means continuous wave, and unmodulated sine wave, this is not CW but simply a single frequency approximately square wave. If you dial up 600MHz, the output is the fundamental 200MHz approximately square wave.

That is of little consequence if you use the NanoVNA’s receiver as a selective receiver, but if you use a broadband detector or power meter (which responds to the fundamental plus harmonic content), you may get quite misleading results.

The NanoVNA is not a good substitute for a traditional sweep generator that produced levelled sine waves of calibrated amplitude and had a source impedance close to 50+j0Ω

This article is a remeasure of NanoVNA-H4 – a ferrite cored test inductor impedance measurement – s11 reflection vs s21 series vs s21 pi using a VNWA-3E of both a good and sub-optimal test fixture estimating common mode choke impedance by three different measurement techniques:

• s11 shunt (or reflection);
• s21 series through
• s21 series pi;

Citing numerous HP (and successor) references, hams tend to favor the more complicated s21 series techniques even though the instruments they are using may be subject to uncorrected Port 1 and Port 2 mismatch errors. “If it is more complicated, it just has to be better!”

s21 series pi is popularly know as the “y21 method” (The Y21 Method of Measuring Common-Mode Impedance), but series pi better describes the assumed DUT topology.

What is an inductor?

Above is the test inductor, enamelled wire on an acrylic tube, an air cored solenoid.

We speak naively of this sort of component as an inductor, perhaps thinking it is a frequency independent inductance with perhaps some small series resistance. Let me make the distinction, Inductance is a property, Inductor is a practical thing (that includes Inductance… that might be a function of some variables).

Above is an s11 reflection measurement of the impedance of the air cored solenoid.

Above, focusing below about 5MHz, R is very low and X is approximately proportional to frequency, and the calculated equivalent series L is approximately independent of frequency… so the naive model discussed earlier might be adequate. Measured inductance at 1kHz is 20µH, at 5MHz apparent series inductance is still close to 20µH, but then starts rising, more quickly as the first resonance is approached (see previous plot).

We can calculate a value of shunt C that will resonate the inductor at this first resonance, in this case it is 1.02pF (often referred to as Cse). The parallel combination of 20µH and 1.02pF will have an impedance that is a good approximation of what was measured up to perhaps 1.2 times the frequency of the first resonance, BUT NOT ABOVE THAT. Such an equivalent circuit is useful, be be mindful of the acceptable frequency range.

The existence of higher order resonances shows that this is not simply an inductance. Calculated Cse will not explain the impedance curve much above the first resonance, it will NOT explain higher order resonances.

Understand the nature of the DUT

The DUT is a small test inductor, 6t on a Fair-rite 2843000202 binocular core (BN43-202).

We speak naively of this sort of component as an inductor, perhaps thinking it is a frequency independent inductance with perhaps some small series resistance.

You might look up the Al parameter for the core and calculate its inductance to be \(L=A_l n^2=2200*36=79,200 \text{ nH}\) and calculate its impedance @ 10MHz \(Z=\jmath 2 \pi f L=\jmath 2 \pi \text{ 1e7} \text{ 79.2e-6}=\jmath 4976\).

In fact it measures 3206+j1904, so the notion of a fixed inductance with small series resistance is not an adequate model for this component at HF. It exibits a first resonance at about 16.3MhHz.

In fact the DUT is a resonator, plotted here around its first resonance.

Using a ferrite core that is both lossy and frequency dependent permeability might make higher order resonances harder to observe, they are not simply harmonically related and they may be severely damped.

The test fixture

The test uses a small test inductor, 6t on a Fair-rite 2843000202 binocular core (BN43-202) and a small test board, everything designed to minimise parasitics. This inductor has quite similar common mode impedance to a HF good antenna common mode chokes.

Above is the SDR-KITS VNWA testboard.

The nanoVNA-H4 v4.3 was calibrated using the test board and its associated OSL components. The calibration / correction corrects Port 1 and Port 2 mismatch error. The test board is used without any additional attenuators, it is directly connected to the nanoVNA-H using 300mm RG400 fly leads.

Above, the test inductor mounted in the s11 shunt measurement position.

Above is the sub-optimal test setup, the DUT is connected by the green and white wires, each 100mm long.

Measurements and interpretation

Optimal

Above are the results of the three impedance measurement techniques.

Note that s21 series through and s21 series pi show no significant difference.

There is a difference between the s11 shunt method and the s21 series methods, the self resonant frequency is slightly different.

Sub-optimal

It is often held that the series pi or Y21 method corrects a sub-optimal fixture, but if you look closely, the series through and series pi curves have no significant difference between them, and they are only a little different to the plots from the optimal fixture… probably insignificant difference.

Does that mean series through undoes untidy fixtures in general? I doubt it.

Why the difference?

There are differences between the measurement methods, well between s11 shunt and s21 series through though in this case no significant difference from s21 series through to s21 series pi; and differences between the test jigs.

Note the test jig affected one measurement method differently to the other.

The results are sensitive to small changes in fixture layout, temperature, component tolerances etc

Sensitivity to parasitic fixture capacitance

Above is a chart of the measured s11 shunt impedance and two calculated values with 0.2pF of shunt capacitance subtracted and added. Note the effect on maximum R, and the self resonant frequency (SRF) (where X passes through zero).

From this information, we can calculate that the inductor at resonance is represented by some inductance with some series resistance, and Cse=1.5pF. So it is very easy for untidy fixtures, long connections etc to disturb the thing being measured.

BTW, for this DUT that is high impedance around resonance, 6mm of 200Ω transmission line (connecting wires?) has an equivalent Cse if about 0.2pF.

A rule to consider

A good measurement technician challenges his measurements, the fixtures, the instrument etc.

A guide I often give people is this:

if you reduce the length of connections and measure a significant difference, then:

• they were too long; and
• they may still be too long.

Iterate until you cannot measure a significant difference.

A challenge to your knowledge

Q: what is the formula for the resonant frequency of a parallel resonant circuit?

What you answer simply \(f=\frac1{2 \pi \sqrt{L C}}\) ?

Practical inductors also have an equivalent series R, and that is not included above… so it is a formula for ideal components, not for the real world.

A: that is the correct formula for a series resonant circuit, no matter how much series R is involved, and it is a good approximation for parallel resonant circuits with high Q, but has significant error for slow Q values (eg single digit.)

Why do I mention this?

Well, ferrite cored inductors may well have Q in the single digit domain, particularly broadband common mode chokes in the region of their SRF.

The common resistive Return Loss Bridge discussed the role, characteristics and behavior of an ideal Return Loss Bridge.

Let’s look at the Return Loss Bridge embedded in the NanoVNA-h4 v4.3.

Above is an extract from the schematic for a NanoVNA-h4 v4.3. It includes the source, Return Loss Bridge circuit and detectors. Other NanoVNA versions may have similar implementations, but small differences can have large impact on behavior.

Let’s create a calibrated LTSPICE model of the Return Loss Bridge, source and detector input.

Above is a DC LTSPICE model.

The model assumes that the clock output pin of the si5351A is well approximated by a Thevenin or Norton equivalent circuit, and the output impedance is taken from the datasheet Rev. 1.1 9/18. The datasheet hints that the output impedance is drive level dependent.

Model calcs / measurement

NanoVNA firmware calculates raw S11 as approximately (Va-Vb)/Vs. So let’s tabulate some results from the model for various Zu.

Above are three tables, all are from the model.

Analysis

Note that the the calculated voltage (Va-Vb)/Vs for sc should be -oc, it is not nearly, demonstrating significant departure from symmetry, from ideal. That said, the calculated voltage (Va-Vb)/Vs s11 for the 50Ω load case is quite good.

These values from the model reconcile well with saved sweeps of raw s11 for sc and oc terminations, s11m.

Equivalent source impedance Rth calculated from the model is very close to 50Ω. A load pull test on Port 1 came in very close to 50+j0Ω.

The right hand table compares:

• the model voltage (Va-Vb)/Vs (which is used by the firmware to calculate raw s11 with (Va-Vb);
• the reference voltage Vs; and
• the model bridge unbalance voltage.

Note that:

• Vs, the reference voltage is load dependent.
• (Va-Vb) for oc is very nearly -(Va-Vb) for sc, so this is only a small departure from ideal.
• (Va-Vb) for the 50Ω load is very small, corresponding to raw ReturnLoss=60dB, substantially better than the Vs adjusted case above.
• (Va-Vb)/Vs for oc is quite different to -(Va-Vb)/Vs for sc,  a large departure from ideal. So, raw s11 is calculated based on a load dependent reference voltage Vs… building significant error into the raw measurements.

Realist that this is a DC model, but will be a good predictor of AC behavior at say 1MHz, things change as frequency increases and there are step changes where each of the harmonic modes are engaged.

The common resistive Return Loss Bridge set out:

Essential requirements of a good resistive RLB:

1. The source has a Thevenin equivalent source impedance of almost exactly Zref;

2. three of the bridge resistors are almost exactly Zref; and

3. the detector is a two terminal load almost perfectly isolated from ‘ground’ and has an impedance of almost exactly Zref.

The NanoVNA-h4 v4.3 fails two of them:

• the Thevenin equivalent source impedance seen by the bridge itself is not close to Zref (~25Ω); and
• the detector impedance is a long way from Zref and is not isolated, the grounding of R20 and R21 in the original schematic provides a current path to ground which disturbs the bridge. It is hard to understand why this point is grounded as the bridge output voltage is not balanced, nor is one side grounded, so the load needs to be isolated from ground.

Notwithstanding those problems, it appears the source impedance looking into Port 1 in the simulation happens to be close to 50+j0Ω, and a load pull test supports that, but measurement experience is that there is significant Port 1 mismatch error that needs correction.

These all contribute to less than ideal response report in the model results and saved raw s11 measurement.

The response to this criticism might well be a nonchalant “never mind, VNA error correction will paper over all problems.”

Perhaps… though tests on s21 correction indicate that it does not properly deal with error:  An experiment with NanoVNA and series through impedance measurement… more.

That article has inspired review of s21 correction, and Enhanced Response Correction has been added to NanoVNA-D v1.2.32  by Dislord, and it has significantly improved s21 measurement accuracy.

NanoVNA-App has been changed to improve the accuracy of s21 measurement.

The change is to implement Enhanced Response Correction.

NanoVNA-App-Setup-v1.1.209-OD18.exe

 

An experiment with NanoVNA and series through impedance measurement… more concluded with:

The NanoVNA-H4 v4.3 NanoVNA-D v1.2.30 using 5 term calibration does not appear to give good accuracy on series through measurement of impedance.

Further investigation identifies several possible contributions, the main one being the s21 correction algorithm and implementation.

Dislord confirmed that the s21 correction algorithm did not include Enhanced Response correction, and has released v1.2.32 which includes the feature (which has to be enabled on the calibrate menu).

Note the E in the cal status column at left.

The nanoVNA-H4 v4.3 with Dislord v1.2.32 was calibrated using a SDR-kits test board and its associated OSL components. The test board is used without any additional attenuators, it is directly connected to the nanoVNA-H4 using 300mm RG400 fly leads.

Test inductor

The test inductor gives a small DUT that has similar characteristics to a HF common mode choke.

Above, the test inductor mounted in the s11 shunt measurement position, but the tests below are in the s21 series through connection.

Above is a plot of |Z| from 1 to to 30MHz without Enhanced Response correction.

Above is a plot of |Z| from 1 to to 30MHz with Enhanced Response correction, and the without case shown in cyan for comparison. In this case the non ERC trace is inflated about 10%.

Above, it is interesting to compare three methods of impedance measurement. The series-π method is often known as the K6JCA Y21 method.

200Ω

A s21 series through measurement of the 200Ω SM 1% resistor was also conducted and results were very close to the measured value of the resistor.

Conclusions

The NanoVNA-H4 v4.3 using 5 term calibration does not appear to give good accuracy on series through measurement of impedance unless Enhanced Response correction is enabled (Dislord NanoVNA-D v1.2.32 and later).

 

Let’s get on the same page by calling up an accepted industry definition of Return Loss. (IEEE 1988) defines Return Loss as:

(1) (data transmission) (A) At a discontinuity in a transmission system the difference between the power incident upon the discontinuity. (B) The ratio in decibels of the power incident upon the discontinuity to the power reflected from the discontinuity. Note: This ratio is also the square of the reciprocal to the magnitude of the reflection coefficient. (C) More broadly, the return loss is a measure of the dissimilarity between two impedances, being equal to the number of decibels that corresponds to the scalar value of the reciprocal of the reflection coefficient, and hence being expressed by the following formula:

20*log₁₀|(Z₁+Z₂)/(Z₁-Z₂)| decibel

where Z₁ and Z₂ = the two impedances.

(2) (or gain) (waveguide). The ratio of incident to reflected power at a reference plane of a network.

A mathematically equivalent expression is that \(ReturnLoss=\frac{P_{incident}}{P_{reflected}}=\frac{P_{fwd}}{P_{rev}}\).

ReturnLoss is fundamentally a power ratio that can be expressed in dB. This article uses ReturnLoss as simply a power ratio.

Return Loss Bridge (RLB)

A Return Loss Bridge (RLB) is a common implementation of a Directional Coupler, a device that can in a given transmission lines context (meaning wrt some given characteristic impedance Zref), be used to measure forward wave to reverse wave components and calculate their ratio, ie the ReturnLoss.

Let’s look at the common resistive RLB in detail.

Above is an LTSPICE model of an ideal RLB and source with Zref=50+j0Ω. Note:

• ALL the resistors (except for the unknown Zu) are equal to Zref;
• I1 and R3 model an ideal source with Zs=Zref; and
• R13 is the ‘floating’ measurement detector, again it presents a load of Zref.

Let’s explore some interesting properties of this ideal RLB.

Above are measurements of V(a)-V(b) for short circuit (sc) Zu and open circuit (oc) Zu.

Note that the magnitude of V(a)-V(b) is exactly the same for the sc case as for the oc case, but the polarity is opposite.

Also reported above is:

• the voltage Voc across Zu for oc; and
• the current Isc through Zu for sc.

From these we can calculate a Thevenin equivalent looking into the Zu terminals, it is Vth=25V and Rth=50Ω.

Rth is a very important property, for an ideal RLB, it presents a Thevenin source impedance equal to the design impedance Zref. If this does not match the measurement context, then error is introduced.

A measurement procedure

To use an RLB to measure ReturnLoss of some Zu, a matched generator is connected to the bridge, a matched detector connected to the bridge. The detector is then read with an oc or sc on the Zu port and the magnitude V1 written down (it should be the same for either oc or sc). The unknown is then connected and detector magnitude written Vu down. \(ReturnLoss=(\frac{V_1}{V_u})^2\). The magnitude of the complex reflection coefficient \(\rho=\frac{V_u}{V_1}\).

If you measure the detector voltages as complex quantities, Vo=oc voltage, the complex reflection coefficient \(\Gamma=\frac{V_u}{V_o}\).

LTSPICE model results

 

Above is a table of results for three different Zu. Gamma (or s11) is calculated by dividing the detector voltage V(a)-V(b) by that measured for Zu=oc (Gamma=1).

Note that because everything is resistive in the model and it is DC excitation, all values above are purely real… but it works with AC and complex values though you will need a phase reference.

Key properties of the ideal RLB

1. The unknown port has a Thevenin equivalent source impedance of Zref;
2. ReturnLoss and Gamma are measured wrt Zref;
3. \(ReturnLoss=(\frac{|V_o|}{|V_u|})^2=(\frac{|V_s|}{|V_u|})^2\)
4. \(\Gamma=\frac{V_u}{V_o}=\frac{V_u}{-V_s}\); and
5. \(\rho=|\Gamma|=\frac{|V_u|}{|V_o|}=\frac{|V_u|}{|V_s|}\).

Essential requirements of a good resistive RLB

1. The source has a Thevenin equivalent source impedance of almost exactly Zref;
2. three of the bridge resistors are almost exactly Zref; and
3. the detector is a two terminal load almost perfectly isolated from ‘ground’ and has an impedance of almost exactly Zref.

A RLB is not just a null indicator

Most ham RLB designs lack some of the essential requirements to permit it being used to measure ReturnLoss, though they may correctly null on the reference load.

Above is a table of ‘measurements’ from the ideal model in yellow, and calculated values. All of these columns are accurate only when the RLB meets the stated essential requirements.

Links / References

• Bird, Trevor. April 2009a. Definition and Misuse of Return Loss. IEEE Antennas & Propagation Magazine, vol.51, iss.2, pp.166-167, April 2009.
• ———. April 2009b. Definition and Misuse of Return Loss. http://ieeeaps.org/aps_trans/docs/ReturnLossAPMag_09.pdf. (accessed 06/09/11).
• IEEE. 1988. IEEE standard dictionary of electrical and electronic terms, IEEE Press, 4th Edition, 1988.

An experiment with NanoVNA and series through impedance measurement concluded with:

The NanoVNA-H4 v4.3 and Dislord firmware v1.2.30 using 5 term calibration does not appear to give good accuracy on series through measurement of impedance.

The method

The focus is on the corrected s21 measurement as that is what drives the conversion to series through impedance.

The test fixture was designed to be very close to ideal at 1MHz, the test Zx is a 1% SM 200Ω resistor, taken as being 200+j0Ω.

The method of error correction based on a one path calibration does not correct all errors. In particular it does not correct load mismatch error, but an ‘enhanced response’ calibration of s21 (done properly) should correct source mismatch errors. Of course there remain other errors that cannot be corrected but in a good implementation and effective application, they should be relatively insignificant.

Above is an extract of the published schematic of the NanoVNA-H4 v4.3, the circuitry around Port 1 and Port 2 jacks is of particular interest.

Some notable observations:

1. raw (ie uncorrected) s21 measurement reported by the combination of hardware and firmware tested has a gross error, phase of s21 at low frequencies is approximately 180° where it should be approximately 0°;
2. cursory circuit analysis of the Return Loss Bridge (RLB) associated with Port 1 would suggest that the ‘detector’ impedance (the circuitry connected between both sides of the RLB to measure the imbalance or ReturnLoss) would appear to be substantially higher than 50+j0Ω which compromises the bridge; and
3. cursory circuit analysis of Port 2 circuity suggests that the designer did attempt to obtain a Port 2 load impedance close to 50+j0Ω, measurement indicates quite good ReturnLoss.

A superficial response to observation #1 is “never mind, correction will fix it”, but it does question the rigor of the firmware design and testing.

Same thing for observation #2, no need to design hardware to have an equivalent source impedance of 50+j0Ω when correction fixes it. But in this case, the corrected s21 reported does not fix it, the firmware is probably defective (or lacks Enhanced Response correction).

Observation 3 is very important as it is uncorrected in the simple one path calibration. This area has been redesigned with successive hardware versions, and is fairly good in this version. ReturnLoss could be improved with an external precision attenuator… at cost of dynamic range. Note, “precision attenuator”.

Let’s run a series of tests, same fixture and parts used for all tests.

Using the NanoVNA measurement with internal correction

From the dataset used in the previous article, internally corrected measurement of the series through 200Ω DUT yielded s21=0.305207264 -0.000040260.

This is the scenario discussed at An experiment with NanoVNA and series through impedance measurement which concluded:

The NanoVNA-H4 v4.3 and Dislord firmware v1.2.30 using 5 term calibration does not appear to give good accuracy on series through measurement of impedance.

Using the NanoVNA for raw measurement with external correction

A set of raw measurement were made for SOLT calibration and saved to .sxp files. A raw s21 measurement of the series through 200Ω DUT.

In both the calibration and measurement files with relevant s21 data, the s21 value needed inversion (see observation #1 above).

Scikit-RF was used to correct the raw measurement and obtain s21=(0.33152261949111933-0.0045085939553834485j).

Now this is significantly different, it is actually quite close to expectation (based on DC measurement of the DUT and s11 reflection measurement).

Using the VNWA-3E measurement with internal correction

The same test was conducted using a one path calibration of the VNWA-3E.

Above is a screenshot of the sweep 1-30MHz. Note how flat the lines are, the fixture and DUT do not seem to have significant imperfections.

Above is calculation of Zx using the measured internally corrected s21. It appears very close to expectation (based on DC measurement of the DUT and s11 reflection measurement).

Conclusions

The NanoVNA-H4 v4.3 NanoVNA-D v1.2.30 using 5 term calibration does not appear to give good accuracy on series through measurement of impedance.

Further investigation identifies several possible contributions, the main one being the s21 correction algorithm and implementation.

s21 series through impedance measurement

HP and their successors describe this technique in many publications, the following is from 5988-0728EN.pdf.

Note in the second formula the use of 2Zo and 100 synonymously. The formula depends on the Port 1 source being a Thevenin source with source impedance Zo and the Port 2 input impedance Zo (which they take to be 50+50Ω).

Derivation of the expression for the unknown impedance in an s21 series through measurement shows that the critical value is actually Zsource+Zload or Zs+Zl. If Zs+Zl ≠ 100 then that formula is not correct, the measurements will have error.

The experiment

This article reports an experiment to determine whether assuming Zs+Zl = 100 is sound.

A NanoVNA-H4 v4.3 was used with a SDR-kits test jig pictured above. The setup was SOLIT calibrated from 1 to 101MHz, the reference plane is in the middle of the test jig. The picture shows a 200Ω 1% SM resistor in the series through path for measurement using the s21 series through method (as described above).

Find Zx assuming Zs+Zl=100Ω

Above is a plot of R and X components of Zx calculated using the formula set out above.

Above is a screenshot from the NanoVNA displaying the R and X components of Zx using the formula set out above.

Note the lack of reconciliation at the marker of s11 and the calculated Zx. If Zin of Port 2 (Zl) was 50+j0Ω, we would expect s11 reflection measurement of Z to be 20+200=250+j0Ω… but it reads 243.3-j37.08Ω implying Zx=193.3-j37.08Ω and Zx from s21 reads 212.3-j25.64Ω.

Why is it so?

Find Zs+Zl assuming Zx=200Ω

Since we know Zx, let’s turn it around and find Zs+Zl implied by Zx=200+j0Ω.

Above is calculation of Zs+Zl from the measurement.

The error in Zs+Zl is a large contribution to the failure of the calculation of Zx assuming Zs+Zl=100Ω.

How about KISS, an s11 reflection measurement of the nominal 200Ω resistor used above?

Above, s11 reflection of the 200Ω 1% SM resistor.

Above, s11 reflection presented as equivalent impedance components.

Is the series pi (so-called Y21) method the answer?

See NanoVNA-H4 – a ferrite cored test inductor impedance measurement – s11 reflection vs s21 series vs s21 pi for explanation / discussion of this method which I prefer to call the s21 pi method.

Above is a comparison of:

• s11 shunt (s11 reflection);
• s21 series through; and
• s21 π.

Both s21 based method are very poor.

Conclusions

The NanoVNA-H4 v4.3 and Dislord firmware v1.2.30 using 5 term calibration does not appear to give good accuracy on series through measurement of impedance.

References

• Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
• Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.

For more, see An experiment with NanoVNA and series through impedance measurement… more .

NE6F’s common mode current tester – Part 1 ended with the following:

Common mode current adjacent to a small choke

Consider a straight section of coaxial feedline not close to other materials, and with a small common mode choke inserted in the feedline. A “small” choke means one that is a very tiny fraction of a wavelength, say λ/100, from connector to connector.

Q1: Ask yourself that if say 1A of common mode current flows into one connector, what is the common mode current at the other connector?

Q2:What is your answer if you were told the balun was specified to have a CMRR of 20dB?

The answer to Q2 is relatively easy, CMRR is not a meaningful statistic for a common mode choke deployed in a typical antenna system, it would not change the answer to Q1.

The answer to Q1 needs a longer explanation… let’s do it!

Common mode current distribution is almost always a standing wave.

Above is a plot of current distribution of an example dipole antenna system with coax feed. The dipole is slightly off centre fed to drive a significant common mode current on the vertical coax feed  which is grounded at the lower end.

Note the standing wave on the vertical section, it has maxima and minima (if it is long enough), and these are unrelated to possible standing waves inside the coax, ie in differential mode.

Note that if we took spot measurements of the magnitude of common mode current |Icm| at points A, B and C we would get different results.

Broadly, Icm changes relatively slowly over a small electrical distance (say λ/100), except near deep minima if they exist.

Above is the same model with a common mode choke inserted near ground. Note that it has changed the magnitude and distribution of Icm, and more importantly, note that |Icm| at both ends of the choke are very similar, and in fact slightly lower on the antenna side of the choke.

If you make spot measurements either side of an electrically short (say length<λ/100), you will not usually find a large difference… except in the region of a current minimum.

The common notion that |Icm| is much lower on the tx / ground side of the choke is deeply flawed, and even worse is to think that CMRR can be used to calculate the reduction.

NE6F’s video of measurement of his balun’s effectiveness.

N6EF demonstrates measurement with his dual probe meter asserting that “this choke is doing a pretty good job,” but is the measurement a valid basis for that assertion?

Above is a capture from the video with my added notations of four currents, I1-4.

Having set his instrument to read 100% of scale on the Port A probe, he switches to display the Port B probe.

Above. a stunning drop, it is reading perhaps <1% of scale on Port B. Some might infer that proves CMRR>40dB.

Let’s look at that test setup again.

Above is a capture from the video with my added notations of four currents, I1-4.

NE6F demonstrates that I4 is less than 1% of I1 (though the meter response may not be linear at low readings).

Now look at the conductive bulkhead and the bulkhead adapter which connects the coax shield to the bulkhead. At this point a circuit node with three conductors is formed and currents annotated:

• I1: shield from the antenna side;
• I2: bulkhead conductor; and
• I3: shield to the choke.

The measurement made ignores the presence of current path I2, and so all conclusions are invalid.

With the information given earlier, you might well think that it is likely that I3 is approximately the same as I4 (measured at <1% of I1), and that I2 is probably almost the same as I1, ie that this shunts, diverts common mode current on the antenna feed line to ground. That might be an effective measure in preventing ingress to the equipment cluster, but it does not reduce Icm on the main feedline or the undesirable effects of that.

Of course that is just supposition… but it should drive measurement of |I3| to better infer |I2|.

Homework

Make or buy an effective common mode current meter, and make some measurements adjacent to a common mode choke to test your understanding of what it does or does not do.

A test of NanoVNA s21 series through impedance measurement.

This technique is very popular, its users believing it gives superior accuracy, especially on higher impedance DUT.

Above is the test setup, a nominally 100Ω resistor is connected from Port 1 inner contact to:

• Port 2 shield for s11 reflection measurements; and
• Port 2 inner contact for s21 through measurements.

Note: my NanoVNA-H4 has been modified by addition of a short direct wire between the ground side of Port 1 and Port 2 jacks inside the case (see above).

I have intentionally used an ‘ordinary’ metal film resistor with wire leads to demonstrate with a readily available component… but you could buy some similar value 0.1% tolerance SM resistors (50pcs of 100Ω 0.1% 1210 resistors for less than $10 on Aliexpress) and solder some pigtails to them and depend on their marked value.

The instrument was SOLIT calibrated with the reference plane at the Port 1 connector. A 200mm coax jumper was used for the through calibration, it has a delay of 1.5ns and loss of 0.05dB @ 1MHz which needs to be adjusted out.

s11 reflection measurement of impedance using the NanoVNA

Above is a screenshot of s11 reflection measurement @ 1MHz gives 98.91+j0.510Ω. This reconciles well with measurement of the resistor @ DC using a high accuracy ohmmeter, 98.7Ω.

s21 through impedance using the NanoVNA

HP and their successors describe this technique in many publications, the following is from 5988-0728EN.pdf.

Note in the second formula the use of 2Zo and 100 synonymously. The formula depends on the Port 1 source being a Thevenin source with source impedance Zo and the Port 2 input impedance Zo (which they take to be 50+50Ω).

Derivation of the expression for the unknown impedance in an s21 series through measurement shows that the critical value is actually Zsource+Zload. If Zsource+Zload ≠ 100 then the formula is not correct, the measurements will have error.

Above is a screenshot of the native s21 series through measurement of DUT R and X, @1MHz Z=112+j2.06Ω.

This is significantly different to an s11 measurement of the DUT (R is 13% high), and significantly different to high accuracy DC measurement of the DUT.

What is wrong?

s21 improved impedance measurement

Let’s exercise the first calculation phase of Calculate Z from series s21 – enhanced to find Zs+Zl.

Above is a screenshot of the s21 path with the resistor in series. It is adjusted for the missing coax jumper’s delay, but 0.05dB more loss needs to be added to |s21|.

The partial calculation result using the previously measured resistor for the calibration part is that Zs+Zl=87.28-j1.099Ω, definitely not even close to 100Ω. This is 13% low and contributes most of the 13% error discussed above.

Conclusions

NanoVNA’s inbuilt s21 series through facility for measuring Z depends on an assumption that Zs+Zl=100Ω. Verify it on a known DUT before trusting it blindly.

Do and learn

Repeat the first test and second tests on your own NanoVNA, did the results reconcile?

This is essentially verification that the instrument gives correct results on a known quantity. If it does not, you cannot depend on it, and you should be reluctant to recommend the measurement technique… well unless you are an armchair expert.

References

• Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
• Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.

This article describes some operational changes to two calculators on this site:

• Calculate Z from series s21 – enhanced
• Calculate Z from shunt s21 – enhanced

Calculate Z from series s21 – enhanced

The previous versions of the calculator required input of the impedance of Port 2 (Zl), and it calculated and reported the Thevenin equivalent source impedance of Port 1 (Zs) from the Zc measurement.

The important data is actually Zs+Zl and this can be directly calculated from Zc, so the calculation has been simplified and entry of Zl is no longer needed. See Derivation of the expression for the unknown impedance in an s21 series through measurement.

The results for Zu are unchanged.

Calculate Z from shunt s21 – enhanced

The previous versions of the calculator required input of the impedance of Port 2 (Zl), and it calculated and reported the Thevenin equivalent source impedance of Port 1 (Zs) from the Zc measurement.

The important data is actually 1/Zs+1/Zl and this can be directly calculated from Zc, so the calculation has been simplified and entry of Zl is no longer needed.

The results for Zu are unchanged.

References

• Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
• Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.

A correspondent asked my thoughts on a Youtube video featuring…

NE6F’s common mode current tester

Above is the schematic of NE6F’s common mode current tester.

The concept is that current probes A and B are placed either side of a current mode choke, and by calibrating and switching between them, a relative reading of current on one side compared to the other may be found.

Note that the two transformers are intended to be current transformers, they have a ratio of 1:10 turns so the \(Is=\frac{I_p}{n^2}=\frac{I_p}{100}\) … provided there is a low impedance load (called a burden) connected to the secondary.

If the burden was say 100Ω, then the current transformer inserts an impedance of approximately 100/10^2=1Ω in the primary circuit. If a current sensing element does not have a very low impedance, it is likely to disturb the thing being measured.

A general rule about current transformers is that if there is no burden on a current transformer:

• excessive / dangerous voltage may be developed by the secondary winding;
• a high impedance may be inserted in series with the primary line.

So, this is a current transformer with a burden of megohms, a deeply flawed design, but that problem is easily fixed by connecting a resistance of say 100Ω across each secondary winding.

Common mode current adjacent to a small choke

Consider a straight section of coaxial feedline not close to other materials, and with a small common mode choke inserted in the feedline. A “small” choke means one that is a very tiny fraction of a wavelength, say λ/100, from connector to connector.

Ask yourself that if say 1A of common mode current flows into one connector, what is the common mode current at the other connector?

What is your answer if you were told the balun was specified to have a CMRR of 20dB?

Take your time… a follow up will be posted in a day or three.

This article presents a simple way to make measurements of a prototype Guanella 1:1 current balun, measurements that can guide refinement of a design.

The usual purpose of these transmitting Guanella 1:1 current baluns is to reduce common mode feed line current. Not surprisingly, the best measure of a device’s effectiveness is direct measurement of common mode current (it is not all that difficult), but surprisingly, it is rarely measured.

Above is the prototype transformer being a Fair-rite 5943003801 (FT240-43) wound with 11t of solid core twisted pair stripped from a CAT5 solid core LAN cable and wound in Reisert cross over style. Note that Amidon #43 (National Magnetics Groups H material) is significantly different to Fair-rite #43.

There is no need to wind a prototype using expensive materials, the measurements made with the above prototype are very useful in guiding development without wasting expensive materials. Further, the measured results are very close to the behavior of the ‘raw’ balun.

s21, s11 measurement of through transmission

 

Above is the configuration for the through test, the clothes pegs are used to clamp one conductor to the outside of the SMA jacks, the inner wire is poked into the inner pin, the VNA is sitting on a cardboard box, the whole thing is on a wooden table. An alternative to the clothes pegs are small zip ties.

Above is a screenshot from the NanoVNA of the through measurement. The relevant traces are s11 Logmag, S11 Smith, and S21 Logmag.

Above is an expanded graph of |s21|. At first glance, you might be horrified by the value of -1.8dB @ 30MHz. Many would assert that this shows a loss of 1.8dB… but more correctly it is InsertionLoss of 1.8dB and conversion of RF energy to heat is likely to be less.

See Measurement of various loss quantities with a VNA for discussion of Loss terms.

Above is a graph disaggregating InsertionLoss into (Transmission) Loss and MismatchLoss. Thicker conductors will have less Loss, and would be used in practical baluns.

Above is a graph showing InsertionVSWR wrt 50Ω and ReturnLoss wrt 50Ω.

The significant mismatch is due to the fact that the balun introduces about 800mm of transmission line with Zo around 100Ω.

If you want low InsertionVSWR wrt some reference Zo, then the transmission line (the twisted pair or coax) needs to be that same Zo.

Is the InsertionVSWR and associated impedance transformation a problem? Well if you are using an ATU, it should not matter, and imperfection is dealt with by the ATU.

s11 reflection measurement of Zcm

Above, the DUT was reconfigured for Zcm measurement by twisting the white wire around the green wire at each end to bond them, leaving a short straight section of the green wire for connection. One end is inserted into Port 1 jack inner, the other was clamped to the male threads of Port 2, ie grounded.

Note: my NanoVNA-H4 has been modified by addition of a short direct wire between the ground side of Port 1 and Port 2 jacks inside the case (see above).

(If wound with coax, Zcm measurements are made between shield ends, ignore the inner conductor.)

Above is a screenshot of the Zcm measurement, |Zcm| peaks at about 14.6MHz.

Above is a plot of |Zcm| taken from the .s1p file saved during measurement. |Zcm| > 2000Ω from 3MHz to more than 40 MHz.

Above is a plot of the R and X components of Zcm taken from the .s1p file saved during measurement.

Above is a plot of the ReturnLoss taken from the .s1p file saved during measurement.

Above is a plot of the InsertionVSWR taken from the .s1p file saved during measurement.

Conclusions

Good / valid measurements of a prototype Guanella 1:1 balun can easily be made with a NanoVNA using low cost materials in capable hands.

Keep in mind that you are measuring a sample of one or a small number and that ferrite has a wide tolerance specification, and is temperature sensitive.

Experimenting with measurement setups and prototypes is the beginning of understanding of these things, more so that soaking up the utterings of armchair experts.

Go build and measure some prototypes, try different cores, different turns, different winding layouts, twisted / untwisted / coax etc.

Downloads

Proto-G11-FT240-43-11t.7z

A frequently asked question is how to measure transmission line velocity factor. The wide adoption of the NanoVNA has spurred these questions.

So, it is good that ownership of a NanoVNA stimulates thinking and search for applications of the instrument.

I note that when these questions are asked online, early responses include recommendation of using the VNA to perform a TDR transform to measure the electrical length of the cable and calculate the velocity factor as \(vf=\frac{\text{PhysicalLength}}{\text{ElectricalLength}}\). The resolution of the NanoVNA swept from 1 to 1500MHz with 401 steps is around 60mm, so you can only measure to about 0.25% resolution if you have a test cable 20m long. So this method might not be very practical in a lot of situations for that reason alone. More later…

It is practical to measure the quarter wave resonance of a shorter section of test cable to better than 0.1% resolution.

A significant problem measuring short cables is the contribution of the test fixture, the reference plane is usually not at the very beginning of the uniform cable, if you know where that is anyway (it may be inside a connector).

Let’s look at an example, a measurement of some ordinary nominally 300Ω TV windowed ribbon line.

Above is the test fixture, the VNA and 1:1 transformer board have been OSL calibrated to a point very close to the pins of the grey terminal block. The transformer module is described at Conversion of NOELEC style balun board to 1:1.

A section of line that measured 0.303m from the grey terminal block to the end of the line was measured observing phase of s11, and the frequency where phase switched from -180° to 180° noted as 209.000MHz, see above. We can calculate the electrical length as c0/fo/4=0.3586m and vf=0.845.

That went well, let’s try a longer section.

A section of line that measured 1.750m from the grey terminal block to the end of the line was measured observing phase of s11, and the frequency where phase switched from -180° to 180° noted as 37.115MHz, see above. We can calculate the electrical length as c0/fo/4=2.019m and vf=0.867.

Why do they disagree?

The problem is that the length measurements made are not from the reference plane, it is somewhere towards the VNA, and in fact both sections are physically a little longer.

We can use Velocity factor solver.

Above is the solution, the distance measurement zero point (the outer edge of the grey terminal block) is in fact 36.18ps (9.45mm) from the reference plane.

The final solution is good to 0.1% of velocity factor (pu).

What about the nanoVNA ‘measure cable’ facility?

From this and the measured length of 1.750m we can calculate VF=1.75/2.073=0.844. The 3% error is attributable to the error in length measurement datum and reference plane. The error will be worse for a short cable section, less for a long cable section.

What about the nanoVNA TDR (FDR) facility?

Above is a sweep 1-1500MHz with 401 steps and VF set to 100%. Range resolution is about 78mm in free space, more like 68mm for this cable for maximum cable length of 31m in free space, more like 27m for this cable.

So, we measure the first impulse peak at 2.109m. From this and the measured length of 1.750m we can calculate VF=1.75/2.109=0.829. The 5% error is attributable to range resolution and the error in length measurement datum and reference plane. The error will be worse for a short cable section, less for a long cable section.

Parting thoughts

Some parting thoughts:

• popular alternatives are not as accurate as often believed;
• velocity factor is not independent of frequency, though it is approximately so for most good RF cables above about 10MHz;
• most applications are not as phase critical as believed;
• many if not most measurements I see described online give questionable results;
• solid dielectric coax cables are usually very close to datasheet, and results otherwise are questionable;
• foam dielectric coax cables do have significant variation (due to variation in gas content) and warrant accurate measurement for phase critical applications; and
• two wire lines pose a challenge with used with an ‘unbalanced’ instrument, and workarounds proposed are often troublesome.

Power standing wave null… more left readers with “homework” to create the Pfwd and Prev traces.

Remember that Pfwd and Prev are interpretations in the context of some Zref of V and I at a point, and that \(P=P_{fwd}-P_{rev}=V_{fwd}I_{fwd}-V_{rev}I_{rev}\) is valid ONLY if Zref is purely real.

So let’s plot Pfwd and Prev wrt:

• Nominal Ro (ie the real part of the nominal Zo of the RG58A/U at 10MHz);
• 50Ω; and
• 75Ω to demonstrate the effect of different contexts, ie Zref.

Above IndFwd50 and IndFwdRo are almost coincident (at 10MHz Nominal Ro is very close to 50Ω), as are IndRev50 and IndRevRo. IndFwd75 and IndRev75 are separated from the others. In all cases, the IndFwdxx-IndRevxx is equal to p.

Note that if Zref is close to the line Zo, the shape of Pfwd and Pref are essentially a logarithmic decay in the direction of wave travel with a small superimposed cyclic variation.

If Zref is quite different to line Zo, the exponential element still exists but with a much larger cyclic variation along the line.

Above is a model of load VSWR=10, and p, Pfwd and Prev wrt 50Ω, and there is still the exponential element and only a relatively small cycle variation.

So, from those we learn that if you were to insert a 50Ω directional wattmeter at various points along a nominal 50Ω line, even with high VSWR, there will be only a small cyclic variation with displacement  and the exponential decay will be more significant.

The cyan trace is the voltage along the line, and you may observe that the ratio of max to min near to load is almost 10, VSWR at the load is 10, but measuring the first peak brings a little line loss to bear. The solid magenta curve is 50 times the current (so that it is viewable under the right hand axis scaling).

So, under mismatch there may be a wide variation in voltage and current along the line, but that will not be so apparent on a directional wattmeter which responds to both current and voltage and is sensitive to their phase relationship.

A point for pondering

Noting that in this example there is a small standing wave (VSWR=2), and that whilst Matched Line Loss (MLL per meter is uniform along the line, loss under standing waves is not uniform along the line. So the popular graphs that give you (uniform) line loss under standing waves based on VSWR and MLL are unsound, they are an approximation based on usually unstated assumptions.

Downloads

The download below contains the original SimNEC model, and a revised one with the above calcs and traces added.

SWDisplacement.7z

Power standing wave null? discussed the “Power Standing Wave” concept unfolding on social media.

Already a correspondent has asked if the graphs given in Power standing wave null? can be replicated in SimNEC.

They can. The original Mathcad graphs were wrt displacement from the source along the line to the load, and the sign of displacement is -ve (consistent with the Telegraphers Equation). So, that requires a bit of manipulation in SimNEC, and because SimNEC does not allow us to sample a TL element at an arbitrary displacement, the following model uses two TL elements of overall length 30m, and by adjusting the length of each we can move the observation point (T1 input).

The calculations of lengths and power are visible in the popups.

In a passive system, real power (ie watts) must decrease monotonically from source to load. Online postings showing otherwise attest to the knowledge of AC fundamentals of the modeller / poster.

Why (T1.V*Conj(T1.I)).R ?

This relies on basic principles of Alternating Current. The power at a point excited by a sine wave is \(P=V I^*\) (meaning V times conjugate of I) where V and I are RMS values, it is a complex quantity comprising the real power (watts) and reactive power (VAr). We are interested in the real power, so we multiply V times conjugate of I at T1 input, and take the real component of it for real power.

Homework

Interested readers can construct the other plots.

Downloads

SWDisplacement.7z