This article reports nanoVNA measurement of a two wire line where no common mode countermeasures were taken.
Above is a Smith chart of the complex reflection coefficient Γ (s11) looking into a length of nominally 142Ω transmission line of similar type to that in the reference article, the chart is normalised to Zref=142+j0Ω. Note the locus is a spiral, clockwise with increasing frequency, and centred on the chart prime centre Zref. More correctly it is centred on transmission line Zo, and the keen observer might note that the spirals are offset very slightly downwards, actual Zo is not exactly 142Ω, but 142-jXΩ where X is small and frequency dependent, a property of practical lines with loss.
Above is a Smith chart of the same data, but normalised to Zref=50+j0Ω, ie the prime centre is 50+j0Ω. The spirals are offset, but again they are centred on Zo. It might not look centred on Zo, but note that the spiral inwards is not symmetric on this scale, and if the line was long enough, the spirals converge on Zo.
So what does this spiral with Zref=50+j0Ω translate to in a cartesian plot of |s11| vs f?
Whilst the value of |s11| wrt actual Zo, when mapped under Zref=50+j0Ω (as in the VNA reports), it has a cyclic variation with f.
Now that we know the phenomena to expect of a normal practical (lossy) transmission line, we can review a measurement data set.
The DUT is the same test line documented at Measure transmission line Zo – nanoVNA – PVC speaker twin. It is 1m in length and that article documented nominal Zo≈142Ω and VF≈0.667.
The DUT is directly connected to the nanoVNA Port 1 jack (CH0 in nano speak), no measures have been taken to reduce potential for common mode excitation of the system, and the nanoVNA is connected to the desk computer by a USB cable… all a bit non-descript because the only detail that is important is no common mode counter measures used.
Above is a Smith chart of a scan from 1-100MHz. The form is broadly a clockwise spiral from low to high f, but notable deviations at the high and low f end. Beware, it might look like 80% of the locus is a spiral, but it represents more like just 30% of the frequency range.
Let’s look at |s11| for a better perspective.
Above is a plot of |s11| vs f. Recall that we might expect some smooth cyclic variation in |s11| with f, and that accounts for the dip at Marker 1, but the shenanigans around 30MHz are an anomaly cause by common mode excitation. Likewise the range 66-100MHz is affected.
This dataset is seriously compromised by common mode excitation of the DUT, the data is worthless and no reliable conclusions can be drawn about the pure differential mode characteristics of the DUT.
Measure transmission line Zo – nanoVNA – PVC speaker twin reported measurements and analysis of the same line section, and it described the common mode countermeasures.
Common mode current gives rise to unquantified radiation loss and affects the input impedance of the line section.
If countermeasures are apparently needed and are not described, the experimenter may be naive and none were used, and the data is questionable, possibly worthless… certainly suspect until the common mode issue can be clarified.
]]>Well, as the article showed, it is not quite the no-brainer but with care, it can give good results. This article documents such a measurement of a 0.314mm cable.
The nanoVNA was carefully SOLT calibrated from 1 to 201MHz. Care includes that connectors are torqued to specification torque… no room here for hand tight, whether or not with some kind of handwheel adapter or surgical rubber tube etc.
Above is the Smith chart view over the frequency range from a little under λ/8 to a little over λ/8. It is as expected, a quite circular arc with no anomalies. Since the DUT is coax, and the connector is tightened to specification torque, we would expected nothing less. The situation may be different with two wire lines if great care is not taken to minimise common mode excitation. The sotware does not show Marker 2 properly, it should be between ‘c’ and ‘i’ of the word Capacitive.
Above is the R,X scan, Marker 2 is at the λ/4 resonance (X≈0) and Marker 1 is exactly half of that frequency, so λ/8 electrical length at which point |X|=|Zo|.
From the λ/8 measurement, we can calculate VF=0.314/(1.767384/4)=0.710 which reconciles with the datasheet.
]]>The transformer of interest is the one to the left, and if you follow the tracks, the multiturn winding is connected between ground and a track that routes across to the through line. The transformer primary appears in shunt with the through line.
The transformer appears to comprise a 24t primary on a 2646665802 #46 toroid. Note that #46 is a MgZn ferrite, where other designs tend to use either powdered iron or NiZn ferrite.
For the purpose of this article, flux leakage is ignored as it will have very little effect on the calculated ReturnLoss due to this component alone.
Above is the calculated ReturnLoss due to the magnetising admittance of the voltage transformer that is in shunt with the through line based on the published permeability characteristics and assuming 3.5pF of equivalent shunt capacitance to model self resonance. ReturnLoss is presented here as InsertionVSWR is very very small, VSWR=1.02 equates to ReturnLoss=40dB.
ReturnLoss at the lowest specified frequency, 1.8MHz, is 47dB.
Now this is not the only source of mismatch that would drive low ReturnLoss, but in most ham designs, this single component is responsible for ReturnLoss less than 20dB at their specified lower frequency limits.
There is little point having an instrument that indicates VSWR down to say 1.1 when it invisibly causes VSWR=1.3 looking into it (eg
Grebenkember’s original Tandem match).
Measurement of VK4MQ’s wattmeter using one of these couplers showed ReturnLoss (-|s11|) jack to jack at 1.8MHz to be 46dB, and it remains above 30dB to 30MHz, 25dB at 50MHz.
I purchased one of the couplers for use with a DIY digital display, and although I have had it longer, it isn’t yet realised!
A common failing of almost all hammy Sammy designs is appalling InsertionVSWR at the lower end of the specified frequency range. This coupler is specified for 1.8-54MHz, and differently to most, has meaningful published characteristics.
In this implementation, 60mm lengths of solder soaked braid coax similar to Succoform 141 were used between the PCB and box N connectors. The expected matched line loss of both of these is about 0.01dB @ 50MHz.
The measurements here were made by VK4MQ using an Agilent E5061A ENA, data analysis by myself.
Above are the raw s parameter measurements plotted. It is a full 2 port measurement, and it can be observed that the device is not perfectly symmetric, quite adequate, and quite good compared to other ham designs that I have measured.
ReturnLoss is -|s11|, it is simply stunning, a huge departure from most ham designs. Some that I have measured were less than 20dB at their specified lower frequency limit.
An interesting perspective is to disaggregate InsertionLoss (-|s21|) into Mismatch Loss and (Transmission) Loss.
As we expect from the |s11| plot, MismatchLoss is very low, InsertionLoss is dominated by Loss. Loss tells us how much of the actual input power is converted to heat.
Above is a plot of the expected dissipation due to Loss. Most of it is likely to be in the ferrite cores, roughly equally with a 50Ω load.
Difficulties were encountered in adapting Kiciak’s design to the unmodified coupler. Kiciak didn’t deal with intercept and gain calibration entirely in the coupler or the display electronics, it is spread between them.
The VK3AMP coupler would have been much easier to use if it incorporated pots for intercept and gain calibration in each channel. This will not be an issue in my digital meter project as each channel (fwd, rev) will have slope and intercept calibration in the firmware.
Custom meter scales were designed to suit two available taut band meters.
Above, the forward power meter scaled in dBm (Bruce’s preference). The sharp mind will recognise 56dBm is 400W.
Above, the return loss meter scaled in dB.
Above is the interior of VK4MQ’s build.
Above is the inside of the front panel. The electronics is built dead bug style on the PCB that is visible, the two meter movements are in the lower part.
Above is the front panel with the rescaled meters recovered from some e-waste. The meter does not overhang the edge, it is a perspective issue with the pic.
This article shows the use of the Smith chart to look for departures from pure transmission line behavior in that test, or any other that depends on measuring purely Zin of a length of line in purely differential mode with short circuit or open circuit termination.
Above is a Smith chart plot of what we should see looking into a line of similar characteristic swept from 1 to 20MHz. There is no magic there, this is basic transmission lines and Smith chart.
Above is the Smith chart plot of a scan of the NEC model with the USB cable included. A significant anomaly can be seen and the measurement frequency is in the seriously disturbed area, little wonder the test gave wrong results. The whole curve is wrong, and will give erroneous results.
Any significant common mode current gives rise to power lost to radiation, and the measured impedance is not that of the transmission line alone. The Smith chart might not have strong hints as in the above, but it is a first place to look for departure from expected pure transmission line behavior.
You would not see this huge hint of an invalid experimental setup if you focus on the narrow band of frequencies where the electrical length is λ/8.
Above is the NEC Smith chart plot with the USB cable removed, quite as expected.
]]>Apparent gross failures are often wrongly attributed to factors like manufacturing tolerances, polluted line surface, other esoteric factors etc that might imply a knowledgeable author… but that is social media, an unreliable source of information.
Let’s explore an estimate using measurements with a nanoVNA using the popular eighth wavelength (λ/8) method.
The λ/8 method relies upon the property of a lossless line terminated in an open circuit that differential impedance \(Z_d=\jmath X=- \jmath \left| Z_0 \right| cot \left(\pi/4\right)=- \jmath\left| Z_0 \right|\). So, if you measure the reactance looking into the λ/8 (\(\frac{\piᶜ}{4} \:or\: 45°\)), you can estimate Zo as equal to the magnitude of the reactance.
A similar expression can be written for the case of a short circuit termination and it leads to the same result that you can estimate Zo as equal to the magnitude of the reactance (an exercise for the reader).
The fact that the two cases lead to the same result can be used to verify that the line length is in fact λ/8 (they will not be equal if the length is a little different to λ/8)… though writeups rarely mention this, or perform the test.
So, the method depends critically on:
Most online articles do not include details of the measurement setup, perhaps thinking that it not all that relevant. Of course, one of the greatest failings in experiments is to ignore some factor that is in fact relevant.
The nanoVNA is such a limited device without a computer attached, lets model a scenario that might well be used by the naive.
Above is a graphic of the scenario. It comprises a vertical section of the modelled transmission line from height 2 to 7m, so it is 5m in length and comprises 1mm diameter copper conductors spaced 20mm, dielectric is a vacuum. Impedance is measured in the horizontal segment bonding both sides of the transmission line.
We might expect the quarter wave resonance of this part of the scenario alone would be approximately 15MHz, but the NEC model gives a slightly lower frequency of 14.97MHz and therefore λ/8 is 7.485MHz.
Also included is a connection from one side of the transmission line to real ground to represent the ground connection of the nanoVNA via its USB cable to a computer used to capture the measurement results.
Above is the impedance plot from the model, it looks well behaved and we might suggest that we would expect that the nanoVNA would measure Zin=Rin+jXin=92.5-j195Ω or |Z|=215Ω.
If you not into the ‘j value’ stuff, you might then say that Zo=215Ω. If you were a little more savvy, you might say that Zo=|X|=195Ω. Not a whole lot of difference… but the difference should be concerning. In fact, the relatively large value of R in Z should sound a warning that the naive might overlook.
Let’s look at a simple model of the transmission line using TWLLC.
Parameters | |
Conductivity | 5.800e+7 S/m |
Rel permeability | 1.000 |
Diameter | 0.001000 m |
Spacing | 0.020000 m |
Velocity factor | 1.000 |
Loss tangent | 0.000e+0 |
Frequency | 7.485 MHz |
Twist rate | 0 t/m |
Length | 0.125 wl |
Zload | 1.000e+100+j0.000e+0 Ω |
Yload | 0.000000+j0.000000 S |
Results | |
Zo | 444.04-j1.48 Ω |
Velocity Factor | 1.0000 |
Length | 45.000 °, 0.125000 λ, 5.006554 m, 1.670e+4 ps |
Line Loss (matched) | 2.28e-2 dB |
Line Loss | >100 dB |
Efficiency | ~0 % |
Zin | 8.486e-1-j4.418e+2 Ω |
Above is an extract of the output.
Key calculated results are:
Note that:
By comparison with the TLLC prediction, a key point of reconciliation failure is that in the measurement Rin is relatively quite large and quite inconsistent with even a low loss line, and so the premise for applying the λ/8 method vanishes.
Let’s model a better DUT,
Above is a graphic of the scenario. It comprises a vertical section of the modelled transmission line from height 2 to 7m, so it is 5m in length and comprises 1mm diameter copper conductors spaced 20mm, dielectric is a vacuum. Impedance is measured in the horizontal segment bonding both sides of the transmission line.
We might expect the quarter wave resonance of this part of the scenario alone would be approximately 15MHz, but the NEC model gives a slightly lower frequency of 14.97MHz and therefore λ/8 is 7.485MHz.
There is no connection to ground, the instrument and the transmission line section are relatively isolated from ground.
Above is the impedance plot from the model, it looks well behaved and we might suggest that we would expect that the nanoVNA would measure Zin=Zoc=Rin+jXin=0.879-j458Ω.
As a simple check, Rin is relatively small, and we might accept that Zo=|Xin|=458Ω… but this value is sensitive to the electrical length.
Running the same model with a short circuit termination, Zsc=3.98234+j463.85Ω.
We can calculate Zo=Ro+jXo from Zoc and Zsc.
As you see, Ro lies between the |Xoc| and |Xsc|.
This calculation if of higher accuracy than basing Zo on |Xoc| or |Xsc| alone of an assumed λ/8 section.
A simpler approximation for low loss line is \(Z_o\approx \sqrt{-X_{oc} X_{sc}}=460.8\) which reduces sensitivity to actual length.
Calculated Zo based on the second NEC model does not reconcile exactly with the TWLLC calculation as they use different methods of modelling, but the results are reasonably close.
What’s the problem was asked. The problem is that the λ/8 method depends on a valid differential mode impedance measurement, and that did not happen in the first example, the common mode current path prevented pure differential mode excitation of the DUT.
This article compares the results for the FT240-43 example at 3.5MHz with calculation using tools on this web site.
Above is a very simple approximation of an ideal 1:1 transformer where the effects of flux leakage and conductor loss are ignored. A 1:n transformer can be modelled the same way, as if flux leakage and conductor loss are ignored, the now ideally transformed secondary load becomes 50Ω.
First step is to find the complex permeability of the core material.
Next, calculate the RF impedance and admittance at 3.5MHz of a 4t winding.
The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).
We can calculate core magnetising loss as \(Loss_m=10 log \left(1 + \frac{Gm }{0.02}\right)=10 log \left(1 + \frac{0.00168}{0.02}\right)=0.35 \; dB\).
We can calculate InsertionVSWR using Ym+0.02 S as the load admittance.
Above, InsertsionVSWR is 1.21.
Measured | Predicted | |
Loss (dB) | 0.32 | 0.35 |
InsertionVSWR | 1.15 | 1.21 |
Given the tolerance of ferrite cores, the reconciliation is very good.
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It means that the line geometry imposes a natural constraint on a wave travelling in the line that V/I=50… but remember that TEM waves are free to travel in (only) two directions. This natural ratio of V/I is called the characteristic impedance Zo.
Let’s say that at some point on a 50Ω line (it could be start, finish, or anywhere in between), V=100V and I=1A, therefore Z=V/I=100/1=100Ω. This situation could be created at the end of a transmission line by simply attaching a 100Ω load.
Zo is a complex value (having real and imaginary parts), but for simplicity we will assume that Zo is a purely real value, Zo=50+j0Ω. It makes the maths easier, it becomes arithmetic you can do in your head, and in fact practical transmission lines at 100MHz have Zo that is very very close to a purely real number.
So how can V/I at a point on a Zo=50Ω line be 100/1=100Ω?
So the voltage at the point of interest point is 100V and I=1A, Z=100Ω. (For simplicity, I am assuming I in phase with V, so the actual power is easily calculated P=V*I=100*1=100W. P is the energy flow past the point averaged over a full RF cycle.
This 100W is the power that the transmitter ‘makes’.
Because of the Zo constraint that a travelling wave MUST have V/I=50, then this 100V/1A can only be due to the sum of two waves travelling in opposite directions, there MUST be a forward wave and a non-zero reflected wave such that their sums deliver the observed voltage and current.
A Bird 43 50Ω wattmeter ‘explains’ V and I at a point as being due to two waves travelling in opposite directions (taking into account their relative phase). The Bird wattmeter is calibrated for a purely real Zo, 50Ω in this example.
Now because there is 100W flowing, then the difference between the indicated forward wave Pf and reflected wave Pr MUST be 100W, ie \(P=P_f-P_r=100\). This does not tell us the value of Pf or Pr.
To find Pr and Pf, we need to calculate the complex reflection coefficient: \(\Gamma=\frac{Z-Z_0}{Z+Z_0}=\frac{100-50}{100+50}=0.33\).
Now \(V=V_f(1+\Gamma)\), which we can rearrange to \(V_f=\frac{V}{(1+\Gamma)}=\frac{100}{1+0.33}=75\) and therefore \(V_r=V-V_f=100-75=25\).
So, we know Vf and Vr, we can calculate \(P_f=\frac{{V_f}^2}{Z_0}=\frac{{75}^2}{50}=112.5\) and \(P_r=\frac{{V_r}^2}{Z_0}=\frac{{25}^2}{50}=12.5\) and \(P=P_f-P_r=100\).
Similarly we can say \(I=I_f(1-\Gamma)\) (-ve due to the wave travelling in the opposite direction), which we can rearrange to \(I_f=\frac{I}{(1-\Gamma)}=\frac{1}{1-0.33}=1.5\) and therefore \(I_r=I-I_f=1-1.5=-0.5\).
Forward power can be greater than the transmitter ‘makes’, you must deduct the reflected power to find the ‘net’ power, and that ‘net’ power cannot be greater than the actual transmitter output power under those load conditions (though it may be greater than the transmitter’s notional ‘rated’ power).
The transmission line supports TEM waves travelling in two possible directions, and you must consider both waves to calculate the power at a point on the line. Forward power is a notional quantity associated with one of two possible travelling waves.
The law of conservation of energy is not violated by any of the discussion above.
]]>The discussion of an example worked up the loss components at 3.5MHz of the example configuration, a 4t winding on a FT240-43.
This article demonstrates that a graph of the loss components from the saved .s2p is possible.
Let’s review some meanings of terms (in the 50Ω matched VNA context):
It is assumed that Zin of VNA Port 2 is 50+j0Ω, and that therefore P2r=0. Error in Zin of VNA Port 2 flows into the results. A 10dB attenuator is fitted to Port 2 prior to calibration to improve accuracy of Zin.
With the quantities expressed in dB, we can derive that \(Loss=-|s21|-MismatchLoss\).
The graph gives a wider perspective of the contribution of Mismatch Loss and (Transmission) Loss to Insertion Loss.
Loss is core and copper loss, mostly core loss in this case.
Try 2, 3, 4, 5 turns on a FT240-43, what does that say about all the articles on the ‘net using 2t primaries?
Try FT240-61, how many turns are sufficient, how does the Loss compare? Before you jump to the conclusion that #61 is superior, you need to measure the broad band performance which may be impacted adversely by the length of the windings… a story for another article.
]]>Above is a very simple approximation of an ideal 1:1 transformer where the effects of flux leakage and conductor loss are ignored. A 1:n transformer can be modelled the same way, as if flux leakage and conductor loss are ignored, the now ideally transformed secondary load becomes 50Ω.
This simple equivalent circuit does contain the elements that are most important to low frequency performance, the inductor and resistor represent the magnetising impedance as a parallel equivalent circuit of the magnetising inductance and core loss.
Let’s simulate that circuit.
Above is a simulation of the |s11| and |s21| we would expect to measure for our simplified transformer.
The design object is:
In this case, at the low frequency end, |s11| increases, and |s21|decreases, both due to the combined effects of the winding inductance and core loss.
Now ferrite cores yield a frequency dependent inductance and core loss. There are many articles on this website explaining how to design with ferrite cores using the published core characteristics, but this article is about using a nanoVNA to validate such a design, or even to find a combination by cut and try.
Most failed published ham designs failed to provide sufficient magnetising impedance to deliver adequate low frequency performance.
Let’s measure a couple of examples by winding the primary winding alone, and measuring it in shunt with a through connection from Port 1 to Port 2 (nanoVNA CH0 and CH1). As always, the fixture is very important.
Let’s try a FT240-43 core with a 2t winding connected in shunt with a through connection from VNA Port 1 to Port 2.
Above is a plot of |S21|, and recall that InsertionLoss=-|s21|.
Without capturing the effects of a secondary winding and flux leakage, the primary winding is not at all suitable for a low InsertionVSWR broadband transformer, it has low magnetising impedance, a result of the combination of ferrite characteristic and the number of turns.
Let’s try a FT240-43 core with a 4t winding connected in shunt with a through connection from VNA Port 1 to Port 2.
Above is a plot of |S21|, a huge improvement on the 2t case.
Above is a plot of |s11| which tells us there is some mismatch at the lowest frequencies, but mismatch is unlikely to make a large contribution to the InsertionLoss in this case.
Above is a plot of InsertionVSWR, another presentation of the |s11| measurement.
We can calculate the Loss from the s11 and s21 measurements recorded in the saved .s2p file at 3.5MHz.
As suggested, the main contribution to InsertionLoss is Loss (conversion of RF energy to heat) in the core material and winding, mainly the core material in this case.
Increasing turns increases magnetising impedance and reduces losses, but more turns means longer conductors which compromises high frequency performance, so for a broadband transformer, you need sufficient turns for low frequency response, but no more.
Stacking cores increases magnetising impedance, reduces losses and increases surface are, but longer turns means longer conductors which compromises high frequency performance, so for a broadband transformer, you need sufficient turns for low frequency response, but no more.
Based on measurement results, you may choose different turns and / or different core material.
This measurement does not capture all the important influences on transformer performance, but it does provide a very useful first step for selection / screening / validation test to select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer.
If a DUT does not pass muster, it is going to be worse when built with a secondary winding and load.
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