The example for explanation is a common and inexpensive 5943003801 (FT240-43) ferrite core.

It helps to understand what we expect to measure.

See A method for estimating the impedance of a ferrite cored toroidal inductor at RF for an explanation.

Note that the model used is not suitable for cores of material and dimensions such that they exhibit dimensional resonance at the frequencies of interest.

Be aware that the tolerances of ferrite cores are quite wide, and characteristics are temperature sensitive, so we must not expect precision results.

Above is a plot of the uncalibrated model of the expected inductor characteristic, it shows the type of response that is to be measured. The inductor is 11t wound on a Fair-rite 5943003801 (FT240-43) core in Reisert cross over style using 0.5mm insulated copper wire.

Above is the expected impedance of the same model, but looking through 100mm of lossless 200Ω line to demonstrate that connecting wires will substantially alter the measured impedance.

Make a measurement, then reduce the connecting wires to half length, if you see a significant change in the measurement then:

- the original connections were too long; and
- the reduced connection MAY still be too long.

The prototype inductor (DUT) was wound and connected to a calibrated nanoVNA with very short connecting wires. Measurement used s11 reflection technique.

Above, one terminal is tied to the SMA threads with a zip tie, and the other wire poked into the female centre pin with a little sideways tension to ensure good contact.

Above is a smoothed capture using nanoVNA-App. Note that the self resonant frequency (SRF) in this jig is 13MHz. We will use that to calibrate the predictive model in Simsmith.

This is the latest version of nanoVNA-App (v1.1.208), and it throws memory protection exceptions.

The measurements are an average of 16 sweeps (done within nanoVNA-App), there is a little measurement noise, but the results are quite usable.

The next step is to calibrate the predictive model based on measurement. The simplest calibration is to adjust the equivalent shunt capacitance to reconcile the predicted SRF with measured. In this case, the adjusted Cse is 1.48pF.

Above is a plot of the calibrated model (solid lines) and measured (circles) using a nanoVNA.

It reconciles reasonably well given the tolerances of ferrite cores.

Above is the same calibrated model with the activation of a trace to show expected core loss at 40mA inductor (common mode) current. The core is unlikely to withstand more than about 40mA continuous current in the 14MHz band, a little more in the adjacent ones, depending on enclosure and ambient conditions etc.

The model can be adjusted to explore other configurations.

The 2631803802 (FT240-31) has the same geometry as the 5943003801 (FT240-43) above but a different material, so the same aol factor is used in the Simsmith model but a different material file is called up. Additionally the number of turns is changed to 13.

Above is a plot of the uncalibrated model of the expected inductor characteristic, it shows the type of response that is to be measured. The inductor is 13t wound on a Fair-rite 2631803802 (FT240-31) core in Reisert cross over style using 0.5mm insulated copper wire.

The next step would be to measure a real inductor, and adjust the model Cse calibrate the SRF.

… an exercise for the reader.

- file: ferrite material complex permeability CSV file;
- aol: core geometry ΣA/l (Magnetic core coefficients converter);
- n: number of turns;
- cores: number of cores in stack;
- cse: equivalent shunt capacitance to account for SRF.

This article has described how to measure the choke as a component with very short leads. Packaging a choke into an enclosure introduces connecting wires etc, and measuring the packaged choke may present a greater challenge, but understanding the basic component choke is an important step in the design process.

Likewise for coming up with a realistic power rating given materials used, the environment, and intended use (duty cycle etc).

At the end, we have measurement of a single prototype, and a calibrated / validated predictive model. The latter is the better design tool, it is the objective of the process. The predictive model is a better estimator of chokes built on commercial supply of cores, you would not base a production design on a single prototype alone.

Sample Simsmith model for download: CMCSSModel.7z . (Compressed with 7zip.)

]]>This article models the transformer on a nominal load, being \(Z_l=n^ 2 50 \;Ω\). Keep in mind that common applications of a 50Ω:200Ω transformer are not to 200Ω transformer loads, often antennas where the feed point impedance might vary quite widely, and performance of the transformer is quite sensitive to load impedance. The transformer is discussed here in a 50Ω:200Ω context.

Above is the prototype transformer using a 2843009902 (BN43-7051) binocular #43 ferrite core, the output terminals are shorted here, and total leakage inductance measured from one twisted connection to the other.

The prototype transformer is a 3:6 turns autotransformer with the two windings twisted bifilar.

Above is the equivalent circuit used to model the transformer. The transformer is replaced with an ideal 1:n transformer, and all secondary side values are referred to the primary side.

- Secondary side leakage inductance Lls is divided by n^2 to obtain the value primary referred leakage inductance in the circuit diagram.
- Cse is an equivalent shunt capacitance to partially model self resonance effects.
- Bm is the magnetising susceptance (calculated from other parameters).
- Gm is the magnetising conductance (calculated from other parameters).
- Llp is the primary side leakage inductance.
- Ccomp is a compensation capacitance.

A Simsmith model was built to implement the transformer model above.

- Complex core permeability is captured from a permeability data file.
- np is the number of turns on the primary.
- ratio is the turns ratio.
- cores is the number of cores in a stack.
- cse is Cse per the circuit diagram.
- Ll is the value of Llp and Lls’ (which are assumed equal).

Having measured the short circuit input inductance to be 43nH, it is distributed equally over Llp and Lls’ so Ll is entered as 22nH.

Above is a screenshot of the Simsmith model. Block D1 is used for data entry to supply some values direct and calculated to the following blocks.

Tfmr is the model of the transformer as shown in the diagram earlier.

Above is a plot of the measured total leakage inductance over 1-30MHz.

Above is a plot of calculated 1-k where k is the flux coupling factor. Again the measured leakage inductance and winding inductances show that k is not independent of frequency, and 1-k (which determines leakage inductance in a coupled inductor model) varies over more than 2:1 range in this example. The graph demonstrates that models that are based on an assumption that k and 1-k are independent of frequency are flawed.

Above is the modelled VSWR response of the compensated transformer on a nominal load. It is very good from 3.5-30MHz.

Above, drilling down on more detail, the \(Loss=10 log \frac{PowerIn}{PowerOut}\) curve is very good. Maximum loss is at about 4MHz, and at 0.06dB loss @ 7.0MHz means that 98.6% of the transformer input power power reaches the transformer output terminals, the deficit being lost mostly in heating the ferrite core.

So, in contrast to the FT240-43 2t:14t transformer:

- ΣA/l is nearly nine times that of the FT240 core, so fewer turns are required for similar core loss;
- shorter winding length helps to reduce flux leakage;
- lower leakage flux improves VSWR bandwidth;
- smaller cores can dissipate less heat;
- reducing core loss reduces the need to dissipate as much heat; and
- compensation capacitor assumes Q of silver mica, the appropriate choice for a transmitting application;

The transformer in free air can probably dissipate around 2W continuous, an at 4MHz where transformer loss is 1.35%, continuous power rating would be 148W (200Ω load, free air). Of course an enclosure is likely to reduce power rating.

Note that leakage inductance is sensitive to the diameter of conductors and the spacing relative to other conductors, so changing the wire conductor diameter and insulation diameter, and wire to wire spacing all roll into changes in leakage inductance. For broadband performance, the goal is least leakage inductance.

Try changing model parameters in the sample model (link below), change mix type, measure the leakage inductance for some different winding configurations and use it.

If you have heard online experts advising the #43 mix is not suitable for this type of application, and that you should use something else… try something else in the model… if you can find a binocular of this size in a more suitable material.

The model input value aol is the core geometry ΣA/l (m) and can be calculated from dimensions using Calculate ferrite cored inductor – rectangular cross section. Some datasheets give ΣA/l or ΣA/l in various units which can be inverted / scaled as necessary. Calculate ferrite cored inductor (from Al) can calculate ΣA/l (m) from Al.

The model does not give a definitive design, but it does help to explore the effects of magnetising admittance and leakage inductance on VSWR bandwidth, loss etc.

Sample Simsmith model for download: EFHW-2843009902-43-2020-3-6k.7z . (Compressed with 7zip.)

]]>This article models the transformer on a nominal load, being \(Z_l=n^ 2 50 \;Ω\). Real EFHW antennas operated at their fundamental resonance and harmonics are not that simple, so keep in mind that this level of design is but a pre-cursor to building a prototype and measurement and tuning with a real antenna.

Above is the prototype transformer measured using a nanoVNA, the measurement is of the inductance at the primary terminals with the secondary short circuited.

The prototype transformer follows the very popular design of a 2:14 turns transformer with the 2t primary twisted over the lowest 2t of the secondary, and the winding distributed in the Reisert style cross over configuration.

The winding layout used in the prototype is that recommended at 10/(15)/20/40 Mini End fed antenna kit, 100 Watt 1:49 impedance transformer .

Above is a plot of the equivalent series primary inductance of the prototype transformer with short circuit secondary calculated from s11 measured with a nanoVNA from 1-31MHz. Note that the inductance is fairly independent of frequency, rising a little at the high frequency end probably due to effects of distributed capacitance and self resonance. This suggests that leakage flux is for the most part not immersed in the ferrite core, and it provides hints as to how to minimise it.

Note that since the inductance of the primary and secondary are frequency dependent (by virtue of the ferrite characteristic), and that leakage inductance is relatively independent of frequency (see above), that the flux coupling coefficient k is frequency dependent, and making it constant is not a very good model at these frequencies.

It might appear that k is fairly independent of freq, but 1-k is not, and it is 1-k that is used to evaluate leakage inductance in the k based approach, so it delivers a poor estimate of leakage inductance when the magnetising inductance is frequency dependent (as it is likely to be with ferrite).

It can be seen above that 1-k varies over a 2:1 range in this model, which would drive a 2:1 variation in leakage inductance… when leakage inductance is almost constant (see the earlier chart).

Above is the equivalent circuit used to model the transformer. The transformer is replaced with an ideal 1:n transformer, and all secondary side values are referred to the primary side.

- Secondary side leakage inductance Lls is divided by n^2 to obtain the value primary referred leakage inductance in the circuit diagram.
- Cse is an equivalent shunt capacitance to partially model self resonance effects.
- Bm is the magnetising susceptance (calculated from other parameters).
- Gm is the magnetising conductance (calculated from other parameters).
- Llp is the primary side leakage inductance.
- Ccomp is a compensation capacitance.

A Simsmith model was built to implement the transformer model above.

- Complex core permeability is captured from a permeability data file.
- np is the number of turns on the primary.
- ratio is the turns ratio.
- cores is the number of cores in a stack.
- cse is Cse per the circuit diagram.
- Ll is the value of Llp and Lls’ (which are assumed equal).

Having measured the short circuit input inductance to be 360nH, it is distributed equally over Llp and Lls’ so Ll is entered as 180nH.

Above is a screenshot of the Simsmith model. Block D1 is used for data entry to supply some values direct and calculated to the following blocks.

Tfmr is the model of the transformer as shown in the diagram earlier.

Above is the modelled VSWR response of the compensated transformer on a nominal load. It is not brilliant, but might be acceptable to many users.

Above, drilling down on more detail, the \(Loss=10 log \frac{PowerIn}{PowerOut}\) curve is troubling. 1dB loss @ 7.0MHz means that only 74% of the transformer input power power reaches the transformer output terminals, the deficit being lost mostly in heating the ferrite core. Of course you transmitter might not develop its rated power into the load that it sees, there could be a further reduction in power output.

So despite its popularity, this is an appalling design. It has high loss due to insufficient turns, and high leakage inductance due to winding layout and high turns. Acceptable designs are a compromise between bandwidth and loss for a give core, and small is beautiful from the transmission parameters, but not for power handling.

Try changing model parameters in the sample model (link below), change mix type, measure the leakage inductance for some different winding configurations and use it.

The model input value aol is the core geometry ΣA/l (m) and can be calculated from dimensions using Calculate ferrite cored inductor – rectangular cross section. Some datasheets give ΣA/l or ΣA/l in various units which can be inverted / scaled as necessary. Calculate ferrite cored inductor (from Al) can calculate ΣA/l (m) from Al.

The model does not give a definitive design, but it does help to explore the effects of magnetising admittance and leakage inductance on VSWR bandwidth, loss etc.

Sample Simsmith model for download: EFHW-5943003801-43-2020-2-14xk.7z . (Compressed with 7zip.)

]]>This article models the transformer on a nominal load, being \(Z_l=n^ 2 50 \;Ω\). Real EFHW antennas operated at their fundamental resonance and harmonics are not that simple, so keep in mind that this level of design is but a pre-cursor to building a prototype and measurement and tuning with a real antenna.

The prototype transformer follows the very popular design of a 2:16 turns transformer with the 2t primary twisted over the lowest 2t of the secondary, and the winding distributed in the Reisert style cross over configuration.

Above is a plot of the equivalent series impedance of the prototype transformer with short circuit secondary calculated from s11 measured with a nanoVNA from 1-31MHz. Note that it is almost entirely reactive, and the reactance is almost proportional to frequency suggesting close to a constant inductance.

Above is a plot of the equivalent series primary inductance of the prototype transformer with short circuit secondary calculated from s11 measured with a nanoVNA from 1-31MHz. Note that the inductance is fairly independent of frequency, rising a little at the high frequency end probably due to effects of distributed capacitance and self resonance. This suggests that leakage flux is for the most part not immersed in the ferrite core, and it provides hints as to how to minimise it.

Note that since the inductance of the primary and secondary are frequency dependent (by virtue of the ferrite characteristic), and that leakage inductance is relatively independent of frequency (see above), that the flux coupling coefficient k is frequency dependent, and making it constant is not a very good model at these frequencies.

Above is the prototype transformer measured using a LCR meter, the measurement 335nH @ 100kHz is of the inductance at the primary terminals with the secondary short circuited.

Above is the equivalent circuit used to model the transformer. The transformer is replaced with an ideal 1:n transformer, and all secondary side values are referred to the primary side, eg \(L_{ls}^\prime=\frac{L_{ls}}{n^2}\).

- Secondary side leakage inductance Lls is divided by n^2 to obtain the value primary referred leakage inductance in the circuit diagram.
- Cse is an equivalent shunt capacitance to partially model self resonance effects.
- Bm is the magnetising susceptance (calculated from other parameters).
- Gm is the magnetising conductance (calculated from other parameters).
- Llp is the primary side leakage inductance.
- Ccomp is a compensation capacitance.

A Simsmith model was built to implement the transformer model above.

- Complex core permeability is captured from a permeability data file.
- np is the number of turns on the primary.
- ratio is the turns ratio.
- cores is the number of cores in a stack.
- cse is Cse per the circuit diagram.
- Ll is the value of Llp and Lls’ (which are assumed equal).

Having measured the short circuit input inductance to be 350nH, it is distributed equally over Llp and Lls’ so Ll is entered as 175nH.

Above is a screenshot of the Simsmith model. Block D1 is used for data entry to supply some values direct and calculated to the following blocks.

Tfmr is the model of the transformer as shown in the diagram earlier.

Above is the modelled VSWR response of the compensated transformer on a nominal load. It is not brilliant, but might be acceptable to many users.

Above, drilling down on more detail, the \(Loss=10 log \frac{PowerIn}{PowerOut}\) curve is troubling. 1dB loss @ 3.5MHz means that only 74% of the transformer input power power reaches the transformer output terminals, the deficit being lost mostly in heating the ferrite core. Of course you transmitter might not develop its rated power into the load that it sees, there could be a further reduction in power output.

So despite its popularity, this is an appalling design. It has high loss due to insufficient turns, and high leakage inductance due to winding layout and high turns. Acceptable designs are a compromise between bandwidth and loss for a give core, and small is beautiful from the transmission parameters, but not for power handling.

Try changing model parameters in the sample model (link below), change mix type, measure the leakage inductance for some different winding configurations and use it.

The model input value aol is the core geometry ΣA/l (m) and can be calculated from dimensions using Calculate ferrite cored inductor – rectangular cross section. Some datasheets give ΣA/l or ΣA/l in various units which can be inverted / scaled as necessary. Calculate ferrite cored inductor (from Al) can calculate ΣA/l (m) from Al.

The model does not give a definitive design, but it does help to explore the effects of magnetising admittance and leakage inductance on VSWR bandwidth, loss etc.

Sample Simsmith model for download: EFHW-5943003801-43-2020-2-16x.7z . (Compressed with 7zip.)

]]>I am about to measure a 1/4 wave of 450 ohm windowed twinlead for the 2m band using my NanoVNA. My question is, since I will be making an unbalanced to balanced connection, should I use a common mode choke, balun or add ferrites to the coax side to make the connection, or does it really matter at 2m frequencies? The coax lead from my VNA to the twinlead will be about 6″ to 12″ long. I will probably terminate the coax in two short wires to connect to the twinlead.

It is a common enough question and includes some related issues that are worthy of discussion.

I must say I found the collective advice of the assembled online experts wanting, let’s explore the subject.

Let’s deal with the measurement fixture first, failure to get that right produces confusing and incorrect results.

Calibration of a VNA establishes a correction regime based on a certain place known as the reference plane. The beauty of the VNA is that you can make this reference plane wherever you like (within reason) by choosing the point at which you connect the calibration parts during the process.

If you want to measure a length of transmission line (DUT), then making the reference plane the connection point of the DUT makes for simpler interpretation of the measurement data.

It is ok to use a short piece of coax, but the calibration should be done at the place where the DUT will be connected, that becomes the reference plane.

Connection of a symmetric DUT to the asymmetric VNA may have problems.

If you connect a line such as that mentioned directly to the coax port of a VNA or similar antenna analyser, you drive the line (DUT) with both common mode and differential drive, and your instrument makes measurement of the combined effect. If you want to measure only differential effects (which would usually be the case, and is the case in this example), then you must ensure that common mode drive is insignificant at the frequencies of interest.

Above is an example of a fixture and the calibration parts suited to measuring small components. I see the twisted transmission line has untwisted one turn with handling, it does not affect the results significantly, but to be thorough, the measurements below were redone with that line twisted uniformly. I might mention that the turned pin sockets I use are not particularly robust, the female part requires replacement from time to time.

Can you see the kinks in the green Smith chart spiral where markers M1 and M2 are located? That should not happen, it is not an attribute of the differential mode of the transmission line, but an aberration caused by common mode drive. The departure is easier to see on the plot of |s11dB| in yellow.

The departure is easier to see on the above plot of |s11|. The problem is that common mode drive is significant, and altering the load seen by the VNA port, most notably around 25MHz and its third harmonic.

The common mode loading also shows up as kinks in the impedance plot, so for instance if you were trying to find the frequency where X=0, you might get an inaccurate result.

The article Antenna analyser – what if the device under test does not have a coax plug on it? discusses some possible solutions to connection, and it is feasible to use a short coax extension to the reference plane (ie OSL calibrated at the end of the extension), but this does not address the common mode drive problem.

Above is a better fixture and the calibration parts, all of which connected to pin sockets under the end of the PCB. Again, the untwisted end of the line was corrected for all measurements below.

This fixture is described in detail at A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly.

I have tried a number of different fixtures for two wire line sections for the range 1-100MHz, and this one (which is a voltage balun) is the best that I have tried.

You might think that this is clearly an application for a current balun, but keep in mind that good voltage baluns deliver good current balance on symmetric loads… and this load is symmetric.

So, what to we measure?

This time, the plot of |s11| looks more like expected, no local glitches.

Above is a plot of R,X (and the hammy |Z|… why do they insist on adding that) looking into the line. As the line section is open circuit, the first resonance (X=0) by interpolation is about 41MHz, accuracy could be improved by narrowing the scan to the neighborhood of 41MHz.

The velocity factor can be calculated as \( \frac{length}{FreeSpaceWavelength/4}=\frac{1370}{1828}=0.76\). Again, that could be improved by narrowing the sweep. That is probably good enough for most purposes, but if you want to reduce errors due to the end terminations, see Velocity factor solver.

We can approximate Zo as \(Zo=|X_{\lambda / 8}|=33 \; \Omega\). (You might have heard that it is not possible to make a twisted pair line of such low Zo, more ham myth!)

You cannot do these things accurately if the measurements are disturbed by common mode loading.

- Common mode drive disturbs the thing being measured.
- You might have experience of having made some measurements that appeared correct, and that is quite possible, but if you want to make reliable measurements, deal with the common mode drive problem.

Above is a plot of:

- red x: raw MLL based on the measurements
- blue: a curve fit to the model \(MLL = k_1\sqrt f+k_2f\);
- green: a curve fit to the model \(MLL = k_1\sqrt f\) based on measurements from 5-10MHz; and
- a curve fit to the AC6LA (Johnson) model (coefficients created with ZPLOTS).

Looking at the higher frequencies first, the green curve does not track measurements, and the higher slope of ‘measured’ MLL suggests there is significant contribution from dielectric loss that is not captured by the \(MLL = k_1\sqrt f\) model. The other two models are quite good at the mid to higher frequencies.

At the lower frequencies, there are few data points and measurements on the nanoVNA were noisy, so the scatter of few points makes estimation challenging. To the eye, I fancy that the brown curve is probably an overestimate of the MLL. It is a more complicated model, it is harder to compute, yet it seems likely that it is an overestimate. It is difficult to choose between the green and blue curves at low frequencies given the data and noise.

Overall, only the blue curve seems a good estimator at low, mid and high frequencies. That is not to say that would be the case for other line types.

I might comment that the study has some underlying weaknesses:

- it used a low grade VNA, and measurement noise is an issue;
- the frequency sweep was limited by the basic nanoVNA mode to 101 points, and worse, linearly spaced (which causes undue emphasis on the higher frequency points at the expense of capturing the low frequency effects well).

At least one nanoVNA client application can do log sweeps of larger set of points, but on my inspection at the time, it had other defects that cause me to set it aside.

I downloaded DisLord’s nanoVNA firmware v1.0.69 and installed it for the measurements in this article. I used the nanoVNA-App v1.1.207 as the PC Client. I was already aware of issues in nanoVNA-App, so I tried a quite old nanoVNA_mod v3 and experienced the same issues with DisLord firmware. I gathered information to report the problems, but DisLord’s github repo does not that that version, I was told only reliable versions go on github… enough said?

So, I have reverted to ttrftech firmware v0.8.0, no frills, but it seems correct and reliable.

]]>So, let’s measure a sample of 14×0.14, 0.22mm^2, 0.5mm dia PVC insulated small speaker twin.

Above is the nanoVNA setup for measurement. Note that common mode current on the transmission line is likely to impact the measured Zin significantly at some frequencies, the transformer balun (A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly) is to minimise the risk of that. Nevertheless, it is wise to critically review the measured |s11| for signs of ‘antenna effect’ due to common mode current.

Above is a plot of the measured |s11| for SC and OC line sections.

Observe that there are no anomalous kinks or the like, but the OC section measurements become a little noise at the lower end.

Above is a plot of the calculated MLL (red dots) based on the s11 measurements, and a curve fit to the model \(MLL = k_1\sqrt f+k_2f \text{ dB/m}\).

Allowing for the scatter at the lower frequencies as we are measuring 1m of line with an inexpensive hobby grade VNA, \(MLL=\text{3.26e-5} \sqrt{f}+\text{1.39e-9}f \text{ dB/m}\) is a pretty good estimator.

]]>Take a look at the antenna with a VNA and sweep with the Phase function.

Let’s do that!

There are lots of competing firmwares for the nanoVNA, and having tried many and found them wanting, I use the latest firmware from ttrftech, the ‘originator’ of the nanoVNA. So, my comments are in the context of that firmware.

Let’s look at display of the magic phase quantity with a very good load on the nanoVNA, you might think of this load as the ultimate goal of an antenna system.

Above is a screenshot of my nanoVNA where I have selected the ONLY display format labelled phase, and it can be seen that the yellow trace appears to be quite random.

Above is a screenshot of nanoVNA Saver which seems the preferred PC client of the masses, again the same good load is attached. The upper left plot is the ONLY phase plot derived from s11, again it is quite random. Also show are plots of impedance (which is very good), VSWR (which is very good), and Return Loss (which is very good). Return Loss might look noisy, and it is, but it is always greater than 65dB… excellent! The only plot that has NO VALUE in this case is the phase plot!

In fact, when the magnitude of s11 becomes very small, the phase of s11 becomes dominated my measurement noise and it worthless. Yes, the closer you approach the Nirvana of VSWR=1 (ReturnLoss very high, |s11| very low), the less value in the phase of s11.

Let’s look at a sweep of a real antenna, a 5/8λ 144MHz vertical on my car, looking into 4m of RG58 feedline.

On this chart, the easiest curve to interpret for most hams is the VSWR curve (magenta). The markers show its minimum (1.09) and the VSWR=1.5 bandwidth (145.05-150.05MHz)… this is a good antenna from that point of view… but it could be improved by lengthening a little to move the frequency for minimum VSWR down to 147MHz (… but there is no adjustment left).

So, look at the Return Loss blue curve. Return Loss is related to VSWR and you could make exactly the same conclusions. We should accept Return Loss > 15dB.

Look at the s11 phase curve in red. It does not cross the zero phase line (the middle of the chart, in this sweep, it is 44° at minimum VSWR even though it is sometimes less at higher VSWR. Can you make any rational conclusion from the phase curve, and does the fact it is not zero condemn the antenna system?

Look at the R and X curves, green and black. Can you draw any conclusions from them directly? Can you see where the phase of R+jX would be zero? Hint: it is where X is zero… but hey, that doesn’t happen with this antenna system.

After all that information overload, the VSWR curve is the key performance indicator, and I could have used an ordinary VSWR meter to come to the same conclusions pretty much.

Yet another example where the focus on s11 phase is so misguided.

]]>Reflection Bridge and Return Loss Bridge are somewhat synonymous, in practice to measure Return Loss one is interested in the magnitude of the response, and to measure the complex reflection coefficient or s11, both magnitude and phase are of interest.

Above is Oristopo’s graph.

We can create a model of a Return Loss Bridge or Reflection Bridge in Simsmith and plot its response for swept Zu.

Above is the Simsmith model with plot for R swept from 1-2500Ω and X=0Ω (for simplicity). When plotted on a log frequency scale, the |s11| response is symmetric, and the markers at 50/10 and 50*10 both produce |s11|=-1.73dB.

Note that this simulated bridge complies with ALL the requirements for correct response:

- source impedance is 50+j0Ω by virtue of the G element definition;
- the three known elements of the bridge are specified as 50(+j0)Ω;
- the bridge detector load impedance is 50+j0Ω by virtue of the definition of element L.

For convenience, the source power is defined as 16W so that it produces 1W or 0dBW at the detector when Zu=0 (or ∞).

The calculated |s11| (or -ReturnLoss) can be calculated easily to verify these two cases using a calculator, or good online calculator. For example using Calculate VSWR and Return Loss from Zload (or Yload or S11) and Zo.

From a point of digitising the s11 response, the challenge is as great for 5Ω as it is for 500Ω. Very low and very high impedances are sensitive to different aspects of the fixture, so it is easy to make a fixture that compromises high or low impedances.

When |s11| becomes relatively large (ie approaching 1, or 0dB) as it does for measurement of very high and very low impedances, the ADC resolution becomes an issue, internal noise of the instrument becomes significant, and accurate phase measurement is more difficult, and as a result, measurement accuracy is compromised.

Several recent articles have used measurements of transmission line sections with SC and OC terminations.

Above is an example where at HF, |s11| >-0.05dB, which is the magnitude of |s11| with a load of 17370+j0Ω, or 0.1439Ω. Sure, there is some noise, but the measurements are usable for the purpose at hand.

One wonders if some online experts have condemned high impedance measurements as grossly inaccurate based on their own experience, perhaps with flawed fixtures, maybe they are just quoting another online expert they have read.

Generalised assertions by online experts that VNAs cannot accurately measure impedance above a few hundred ohms are not borne out by careful measurement experience of known DUTs in appropriate fixtures… or they have unreal expectations about the accuracy required for common analyses.

]]>Oristopo gives a diagram and explanation.

Above is his diagram. He gives an expression that he states applies when R1=R3=R4=Rm: im = sqrt(Vf*(Rm – R2)/(12*Rm + 4*R2)).

This is deeply flawed, if R2>Rm the expression results in the square root of a -ve number… which might be acceptable in a complex number scenario, but this is a DC circuit.

Nevertheless, let us calculate the current with R2=0 and R2=5 while R1=R3=R4=Rm=50.

- R2=0: Im=0.28867513459481287;
- R2=5: Im=0.26940795304016235.

We can calculate \(ReturnLoss=20 log10 \frac{0.28867513459481287}{0.26940795304016235}=0.6 \;dB\).

Wrong, the ReturnLoss of a 5Ω load on a 50Ω Return Loss Bridge should be 1.7dB.

So, the circuit / expression does not have the response of a Return Loss Bridge.

That is understandable, the schematic is not that of a Return Loss Bridge. If a Return Loss bridge uses R1=R3=R4=Rm, then its source MUST also have a source impedance Rs where Rs=R1=R3=R4=Rm for an accurate Return Loss response.

Analysis based on the schematic above with Zs=0 is not representative of the Return Loss Bridge used in accurate instruments, and conclusions are not soundly based.

The Return Loss Bridge is a deceptively simple thing… it does take careful attention to all details to obtain accurate results.

In the more general sense of a VNA, the reflection bridge must respond proportionally to the complex reflection coefficient.

Oristopo’s graph would imply that the nanoVNA can measure down to zero ohms but not above a few hundred ohms. The simple fact is that a reflection bridge calibrated for 50Ω returns the same magnitude voltage for 2.5+j0Ω load as for 1000+j0Ω, just the phase is opposite… so if measurement noise is a problem for one, it is likely to be much the same for the other.

Generalised assertions by online experts that VNAs cannot accurately measure impedance above a few hundred ohms are not borne out by careful measurement experience of known DUTs in appropriate fixtures… or they have unreal expectations about the accuracy required for common analyses.

]]>