NanoVNA examination of stacked ferrite cores of different mixes studied an example stacked core scenario, presenting measurements of a stack of BN43-202 and BN73-202, 5t wound through both.

 

The article stated:

They are somewhat similar (but only somewhat) to two series chokes with the same number of turns, so you might expect overlap of the responses.

Above is the measurement of the stacked configuration.

This article compares the stack with measurement of two series chokes of the same number of turns.

Above is the measurement of the series configuration.

They appear quite similar up to perhaps 5MHz or so, lets compare R, X on the same graph.

The magenta and cyan traces are R and X for the stacked configuration.

Below self resonance peaks, they are very similar which hints that the stacked cores are approximately the sum of responses of each of the cores at lowish frequencies, but as resonance comes into play, they differ.

It is clear that the stacked cores do not behave as equivalent chokes in parallel, that proposition is very wooly thinking.

This is measurement of a specific scenario, and the results cannot simply be extended to other scenarios. I have not (yet) been able to create a simple model of the stacked cores above self resonance, I would suggest that for reliability, any proposed configurations be measured. Whilst in this case, the series configuration appears to have a better impedance characteristic, that might not apply to other geometries and mixes.

Build, measure, learn.

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.

A recent series of articles discussed the question of how accurate does a calibration LOAD need to be.

Following on from that I requested a change to allow the actual resistance of LOAD to be used

These tests are not conducted in a temperature stable laboratory, so allow some latitude in results.

The NanoVNA-H running NanoVNA-D firmware v1.2.35 was SOL calibrated, but the calibration kit had a LOAD that measured 51.273Ω at DC using a high accuracy ohmmeter.

Above is an |s11| sweep after calibration. Measurement is limited by the instrument noise floor, about -80dB @ 1MHz. This says nothing about the load as it is based on a flawed calibration, but it shows us the noise floor. For reasonable accuracy, we might say here that we can measure |s11| down to about -70dB… subject to an accurate calibration LOAD.

Now that LOAD sets the instrument’s calibration reference impedance to 51.273Ω and if I was to measure a true 50Ω DUT, we would expect |s11|=-38dB.

I do not have a termination that is exactly 50Ω, so let’s measure another termination that measured 49.805 at DC using a high accuracy ohmmeter. We would expect the VNA based on the calibration above to show|s11|=-36.8dB.

Above is a screenshot of exactly that measurement, calibrated with 51.273Ω and measuring 49.805Ω, expect |s11|=-36.8dB and we get -36.6dB. That reconciles well.

Now lets specify the “Standard LOAD R”.

Above is a screenshot of the data entry.

Now with the correction applied, let’s measure the termination that measured 49.805 at DC using a high accuracy ohmmeter. We would expect the VNA to now show|s11|=-54.2dB.

Above is a screenshot of exactly that measurement, calibrated with 51.273Ω, “Standard LOAD R” correction applied for that value, and measuring 49.805Ω, expect |s11|=-54.2dB and we get -53.1dB. That reconciles well.

So what is the effective directivity with the “Standard LOAD R” correction?

If the measurement of the LOAD was without error, then the limit for low jitter measurement would be around 10dB above the noise floor measured earlier, so say |s11|=-70dB, which corresponds to ReturnLoss=70dB.

You could use that ReturnLoss as coupler Directivty in Calculate uncertainty of ReturnLoss and VSWR given coupler directivity to calculate uncertainty of a given measurement.

Above is a sample calculation.

But, measurement of LOAD has uncertainty.

Let’s say you measure LOAD with 1% uncertainty, and you measure 49.0Ω , but it could be as low as 48.5Ω (ie -1%), we can calculate the implied inherent ReturnLoss of the 48.5Ω using Calculate VSWR and Return Loss from Zload (or Yload or S11) and Zo) .

The LOAD could be specified as 48.5Ω with ReturnLoss=45dB.

So, entering “Standard LOAD R” is better than using the default 50Ω, but due to the uncertainty of measurement of that LOAD, the instrument Directivity is around 45dB. So, you can see that the accuracy of measurement of LOAD flows into the effective instrument Directivity which feeds calculation of s11 measurement uncertainty.

The instrument I used to measure the terminations has uncertainty of 0.035Ω on a 50Ω reading, which corresponds to a ReturnLoss of 69dB.

By contrast for example, a Fluke 106 has specified uncertainty of 1.1% at 50Ω which implies ReturnLoss 45dB… you are probably better just accepting 50Ω unless you know the LOAD is really bad.

SDR-kits sells relatively inexpensive calibration kits where they supply the measured DC resistance of LOAD.

A chap asked the assembled experts online:

Has anybody tried stacking say a type 43 on top of a 61 on top of a 31 for a wider bandwidth? Would the losses be any greater than using one toroid for each band?

There were some very firm assertions that this will not work well (without evidential support of course). Beware of firm assertions!

Quickly the case was compared to parallel chokes… and there is no parallel (pardon the pun), they are not the same.

They are somewhat similar (but only somewhat) to two series chokes with the same number of turns, so you might expect overlap of the responses. Two series chokes carry the same current and with the same number of turns apply the same magnetomotive force (mmf) to both magnetic cores.

But rather than hypothesise, even if from experience… lets measure.

Above is the DUT. It is a stack of BN43-202 and BN73-202, 5t wound through both. This is not two chokes in series, it is just like stacking a FT240-43 and FT240-73 in concept.

Above is the measured choke impedance from 1-41MHz.

It has an impedance profile that is the sum of the contribution of both cores, it is not a low impedance result. |Z|>2kΩ from 1-34MHz.

I will leave it to readers to measure 5t on each core type and compare them.

But fact does not often get in the way of energetic discussions on social media. Do we know what fact (or truth) is anymore?

I will do some thinking here…

One of the concerns was this will increase heat loss and reduce the power handling of the combination.

My analysis is that loss in ferrite is related to the flux, which is related to the current. Deployed in an antenna system, the combination has higher impedance which will often lead to lower current, reducing flux and heating.

I would argue that appropriate combinations of core mixes is capable of a broader band higher impedance profile, and improved power handling.

Build, measure, learn.

Read widely, question everything.

… NanoVNA examination of stacked ferrite cores of different mixes – more detail

 

This article discusses measurement of a coaxial filter. These are often referred to as “cavity filters”, but strictly speaking, a resonant cavity is different, these are a low loss transmission line section without input and output coupling.

The DUT is a single coaxial resonator configured as a band pass filter with adjustable separate coupling loops. The inside of this nearly quarter wave tube is a coaxial rod grounded at the right had end and almost reaching the left hand end with coupling loops attached to the coax connectors. The rod length is adjustable to tune it, everything is silver plated brass. The adjustable coupling loops allow some adjustment of bandwidth, but narrow bandwidth brings higher loss.

The filter is currently set for its tightest coupling, widest bandwidth, lowest loss.

It was last used for experiments to show that some ham grade receivers commonly used lack sufficient front end selectivity to deliver in the real world, the ‘shielded room’ performance stated in the specifications.

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

It was SOLIT calibrated at the ends of 300mm RG400 patch leads on both ports. It was attached to the DUT with SMA(F)-N(M) adapters.

Let’s assess the NanoVNA s21 noise floor

Above is a plot of the noise in the s21 path, the noise floor is approximately -80dB, so measurements cannot be made with confidence down to about -70dB.

Whilst that noise floor probably permits measuring single stage rejection, especially with notches in duplexer filters, it is probably not sufficient to measure a cascade of two filter sections, much less three (which is a common configuration).

Now the measurement of s11 and s21

Above is a wide sweep from 130-160MHz (note the changed |s21| scale from the previous screenshot.

Above is a narrower sweep  over the ~3dB bandwidth. 3dB bandwidth is about 800kHz. ReturnLoss>20dB bandwidth (VSWR<1.2) is less than 100kHz (ReturnLoss=-|s11|.)

What if it had a notch filter as well?

We might expect that a notch would be 30dB to more than 50dB down. That is far enough above the |s21| noise floor to measure, but the notch of a cascade of filter sections will probably dip into the noise.

It might seem sufficient to measure the depth of notch in one stage of a filter, but thorough measurement requires assessment of the notch overall to demonstrate that they all line up on the correct frequency.

So, the often asked question…

Is this NanoVNA suitable for alignment and measuring performance of a typical repeater duplexer?

IMHO, no, it lacks sufficient dynamic range to measure the notch depths typically required.

I have corresponded with many people trying to make valid measurements of a Guanella 1:1 balun, also known as a common mode choke.

In common mode, the device looks like a ferrite cored inductor. That might sound simple, but it is anything but, and it can be a challenge to measure.

There are lots of measures quoted, most of them IMHO are bogus or incomplete, usually specious… which accounts for their popularity.

This article focusses on making a valid measurement of the R and X components of the choke’s common mode impedance by the simplest means that is likely to give direct results.

Let’s start by proving the measurement instrument

I have taken an ordinary 1% metal film resistor and measured it with an accurate ohmmeter to be 221.4Ω. That is good, it reconciles with its markings. Now this is not a pure resistance at RF, it has some self inductance so we must expect to see that when measured with the VNA.

The wires are trimmed short. The bare end can be safely inserted into the centre pin of a SMA(F) jack.

One wire is poked into the Port 1 centre pin and the plastic clothes peg secures the other wire to the outside male threads of the SMA jack. Alternatively you could use a zip tie to secure the other wire to the outside male threads of the SMA jack.

Above, the test configuration.

Above, a screenshot. Focusing on the marker at 1MHz so that self inductance effects are small, we measure Z=222.1+j0.303. That reconciles well.

Now let’s move on to an unknown inductor

To simulate a small common mode choke, I have wound a Fair-rite 2843000202 (BN43-202) binocular core with 6t of single conductor stripped from an 4pr LAN cable. Note the specific core part, non-genuine parts may have different responses. The wires are trimmed short and 8mm of insulation stripped.

The bare end can be safely inserted into the centre pin of a SMA(F) jack.

Above is the test setup. One wire is poked into the Port 1 centre pin and the plastic clothes peg secures the other wire to the outside male threads of the SMA jack. Alternatively you could use a zip tie to secure the other wire to the outside male threads of the SMA jack.

The key thing is very short connections, they are less than 0.6° over the frequency range measured.

Here is a screenshot. The inductor is self resonant around 18.7MHz. The R and X curves are very similar to what you would get for a practical Guanella 1:1 balun though commonly the resonance would be somewhat lower, below 10MHz often. Narrower peaks will be observed with lower loss ferrite, eg #61 mix.

For the enquiring mind

If you have your own technique, fixture, test jig, cables etc try measuring a resistor like this and a choke like this (preferably exactly like this) by the method I have shown and your own technique and compare them.

Read widely, question everything.

NanoVNA – how accurate does the LOAD need to be – part 2? answered the question in the context of an instrument that assumes the LOAD is exactly 50+j0Ω.

As mentioned in the article, there are more sophisticated models of the imperfection of nominal SHORT, OPEN and LOAD calibration parts (or ‘standards’), but the NanoVNA-H4 does not currently implement any of them.

A simple improvement is to accurately measure the DC resistance of the LOAD part, and use that resistance to calculate the expected LOAD response, and to use that in calculating the error terms that will be used in correction of raw measurements.

Precision Loads are expensive

LOADs with specified high ReturnLoss is an expensive option. Try to find a LOAD with ReturnLoss>40dB (VSWR<1.02)  for less than the price of the entire NanoVNA.

Roll your own

Another option is to buy some 0.1% 100Ω SMD resistors (50 for $7 on Aliexpress) and make a LOAD device that is suitable for calibration, but it is challenging to make such a lot that is good above say 100MHz.

Select for DC resistance

An option I have used is to buy a few inexpensive 6GHz Chinese terminations (~$6 ea) and measure their DC resistance, selecting the best as ‘good’ terminations. The best of a bunch of three I purchased had Rcd=49.085 which equates to RL50=54dB.

If the NanoVNA-H4 supported calibration based on DC resistance of the LOAD…

Some suppliers offer inexpensive calibration kits with measured DC resistance, eg SDR-KITS.

Some users may have a 4W ohmmeter that is capable of high accuracy measurement of loads, preferably to 0.1% uncertainty or better.

If the DC resistance was used during calibration / correction, then the instrument Directivity at frequencies below about 100MHz would be limited mainly by the instrument noise floor.

I have suggested such a facility to Dislord for NanoVNA-D so that its accuracy as a stand alone VNA can be improved.

See Dislord’s NanoVNA-D firmware v 1.2.35 includes a facility to apply a correction based on the DC resistance of the LOAD for implementation details.

 

This article continues on from NanoVNA – how accurate does the LOAD need to be – part 1?

Measures such as ReturnLoss, Gamma, s11, ro |s11|, VSWR are all wrt some reference impedance, often, but not necessarily 50+j0Ω.

The process of SOL calibration of a VNA, and its subsequent correction of DUT measurements, means that raw measurements are corrected with error terms that are derived from the calibration measurements and a set of responses expected of the calibration parts.

Those responses may be ideal responses; a simple short circuit (sc), a simple open circuit (oc) and an ideal load of some nominal value (say 50+j0Ω).

More sophisticated calibration may use a more accurate model for each of the SOL components, but NanoVNA uses simple ideal models for the SOL parts, including that L is 50+j0Ω.

So, if you use for example a 55Ω resistor for LOAD, then the correction factors are calculated to correct the raw measurement for a 55+j0Ω DUT to have \(s_{11}= \frac1{\infty}+\jmath 0\) (though noise will result is a lesser value, perhaps around 1e-40), and it its further computation assumes that s11 is wrt 50Ω, so it will render that DUT impedance as 50+j0Ω, ReturnLoss in dB as a very large number (perhaps 80dB).

If you did connect a DUT that was exactly 50+j0Ω, it will ‘correct’ the raw measurement to s11=-0.04762+j0, and it will render that DUT impedance as 45.45+j0Ω, ReturnLoss in dB as 26.4dB.

Saying it renders ReturnLoss as 26.4dB for an ideal 50+j0Ω DUT is equivalent to saying it has a Directivity (wrt 50Ω) of 26.4dB.

We can return to Calculate uncertainty of ReturnLoss and VSWR given coupler directivity and calculate the uncertainty of that system when it indicates for an unknown DUT, a ReturnLoss of say 21dB (equivalent to VSWR=1.2).

So for DUT with displayed ReturnLoss=21dB, actual ReturnLoss wrt 50Ω could be anywhere from 17.3dB to 27.7dB… quite a range!

So, to obtain a reasonably low uncertainty range, the Directivity of the instrument (the ReturnLoss of the LOAD calibration part) needs to be perhaps 10dB better than the DUT… use the calculator to try different instrument Directivity values and DUT measured ReturnLoss to find a combination with acceptable uncertainty.

So if you did want to measure ReturnLoss with uncertainty of less than 3dB, you might find the following works.

So, minimum coupler directivity is 32dB, you will need a LOAD calibration part that has ReturnLoss>32dB, equivalent to VSWR<1.05. That is a pretty practical component, and will not be outrageously expensive.

An exercise for the reader: what LOAD part ReturnLoss is needed to measure ReturnLoss of 30dB (VSWR=1.065) with less than 3dB uncertainty.

So, whilst you might see |s11| displays on your NanoVNA showing -30dB, they have very wide uncertainty unless the L calibration part is one of high accuracy.

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

I purchased on of these batteries on Big-W online for a mid-high price ($77), expensive enough compared to genuine to expect it would have near to rated capacity.

Above is a pic of the battery advertised. The delivered battery was labelled 7Ah.

They say a picture is worth a thousand words:

So, there it is, after three charge discharge cycles to develop full capacity, two measured discharge cycles. It measures <2Ah, <30% of rated capacity.

Full refund claimed, promptly processed by Big-W Online – return label within a few hours.

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 .

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.