The article uses Rigexpert’s Antscope as the measurement / analysis application, the techniques will work with other good application software.
To demonstrate the technique for matching such an antenna, let’s use NEC4.2 to create 80m feed point impedance data for a 12m high vertical with 8 buried radials (100mm) and centre loading coil resonating the antenna in the 80m band for simulation of measurement data.
An s1p file was exported from 4NEC2 for import into Antscope, to simulate measurement of an example real antenna.
Above is the VSWR curve displayed in Antscope. Note that the actual response is dependent on soil types, antenna length and loading etc, but this is a good example for discussion. It is not real bad, another example might be better or worse.
Above is a plot of the feed point impedance, ie the serial components of feedpoint impedance R and X. The possibility of a shunt match does not jump out, other that seeing that R<50.
Above is a Smith chart presentation, and this is more revealing. We can ‘see’ that the curve crosses the undrawn circle where G=1/50S. It is undrawn probably because the software author did not foresee the utility of G circles etc.
So, at the cursor, the admittance Y=1/49.5+j1/64.5S (the unit of admittance is Siemens), but they write it in a hammy way that Zpar=49.5j64.5 ohms and it is quite flawed, algebraically it is wrong, they perhaps should have written Zpar=49.5j64.5 Ω to mean 49.5Ω in parallel with j64.5Ω. A lot of people cannot handle admittance, and talk in the parallel impedances equivalent.
Talking in hammy parallel impedance, the capacitive element of Zpar can be ‘tuned out’ by an equal but opposite parallel reactance, leaving Zpar=49.5… pretty much right on target.
Above is a presentation of the parallel equivalent impedance components.
An important characteristic of this antenna is that at Rp passes through 50Ω, so it may be a good candidate for a shunt match at the frequency where Rp=50Ω. Rp does not pass through 50Ω, it is not candidate for a shunt match.
It can be seen that around the cursor, Rp is frequency sensitive, and at the cursor, Rp is almost exactly equal to 50Ω, so we just need to ‘tune out’ the parallel reactance with an appropriate inductor (one with X=64.5Ω).
You could then calculate the inductance of the shunt coil, make a coil and measure / adjust to minimum VSWR. In this case, \(L=\frac{X}{2 \pi f}=\frac{64.5}{2 \pi 3.538e6}=\text{2.9e6}\), so we could design an inductor for 2.9µH.
This section shows simulation in Simsmith.
Above is a Simsmith model of the match. The s1p file is imported into the L element. The frequency is dialed to the point where the L element impedance crosses the G=0.02 circle, and the shunt inductor adjusted until the impedance at G is approximately 50+j0Ω.
In this case, a 2.9µH inductor could be prototyped as 10t of 2mm wire on a 38mm diameter form, stretched out to 33mm in length. (Design from Hamwaves RF Inductance Calculator.)
Above, the VSWR=2 bandwidth is about 130kHz.
Now the frequency at which we achieve this match might not be what we would prefer.
To do this, we go back to Step 2 and adjust the antenna (length; loading coil inductance, position; etc) to move the frequency where Rp≈50Ω.
Having done that, we calculate the inductance of the shunt coil, make a coil and measure / adjust to minimum VSWR at the preferred frequency.
The sweeps above were used to show what is happening in a wider context, but they are not essential. You do not need a scanning analyser… but scanning might well provide more confidence that the antenna is behaving as you assume.
You could simply set your analyser to display the parallel equivalent components at the frequency of interest, adjust the system to achieve Rp≈50Ω, note the required parallel opposite reactance, calculate the inductance of the shunt coil, make a coil and measure / adjust to minimum VSWR at the preferred frequency.
]]>The example for explanation is a common and inexpensive 5943003801 (FT24043) 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 Fairrite 5943003801 (FT24043) 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 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. (Take no notice of the display, it is not locally calibrated, correction is performed in the PC client app.)
Above is a smoothed capture using nanoVNAApp. 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 nanoVNAApp (v1.1.208), and it throws memory protection exceptions.
The measurements are an average of 16 sweeps (done within nanoVNAApp), 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 (FT24031) has the same geometry as the 5943003801 (FT24043) 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 Fairrite 2631803802 (FT24031) 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.
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 (BN437051) 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.
A Simsmith model was built to implement the transformer model above.
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 130MHz.
Above is a plot of calculated 1k where k is the flux coupling factor. Again the measured leakage inductance and winding inductances show that k is not independent of frequency, and 1k (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 1k 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 3.530MHz.
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 FT24043 2t:14t transformer:
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: EFHW284300990243202036k.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 precursor 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 131MHz. 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 1k is not, and it is 1k 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 1k 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.
A Simsmith model was built to implement the transformer model above.
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: EFHW5943003801432020214xk.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 precursor 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 131MHz. 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 131MHz. 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 \(L_{ls}^\prime=\frac{L_{ls}}{n^2}\).
A Simsmith model was built to implement the transformer model above.
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: EFHW5943003801432020216x.7z . (Compressed with 7zip.)
]]>To take an example, let’s use one posted online recently:
Stranded Tinned copper center conductor, 0.037″ od Solid, white dielectric (not foamed), 0.113″ od Od of jacket, 0.196″
The dimensions we are interested in are OD of dielectric, 2.97mm (0.113″) and OD of the inner conductor, 0.989mm (0.037″). A solid white dielectric (as opposed to translucent) is likely to be PTFE which has a velocity factor around 0.7 (in most PTFE cables) and we will assume a loss tangent of 1e4 (typical of nonpolar polymers).
Plugging those values into CLLC, we get:
Parameters  
Conductivity  5.800e+7 S/m 
Rel permeability  1.000 
Inner diameter  0.00099 m 
Outer diameter  0.00297 m 
Velocity factor  0.700 
Loss tangent  1.000e4 
Frequency  7.000 MHz 
Length  100.000 m 
Results  
Zo  46.16j0.72 Ω 
Velocity Factor  0.7000 
Rel permittivity  2.041 
Length  1200.831 °, 20.958 ᶜ, 3.335641 λ, 100.000000 m, 4.765e+5 ps 
Line Loss (matched)  2.844 dB 
R, L, G, C  3.012797e1, 2.199246e7, 4.541158e7, 1.032497e10 
S11, S21 (50)  5.317e2+j8.620e3, 3.702e1j6.166e1 
Y11, Y21  8.817e3+j1.143e2, 4.032e3+j2.320e2 
NEC NT  NT t s t s 8.817e3 1.143e2 4.032e3 2.320e2 8.817e3 1.143e2 ‘100.000 m, 7.000 MHz 
k1, k2  1.071e5, 1.300e11 
C1, C2  3.388e1, 1.300e2 
Mhf1, Mhf2  3.266e1, 3.964e4 
dB/m @1MHz: cond, diel  0.010714, 0.000013 
γ  3.274e3+j2.096e1 
Estimated Zo is 46Ω based on the measurements and assumptions. The calculated result is quite sensitive to small error in measurement, the cable’s nominal Zo is probably 50Ω.
Loss will probably be a little higher than estimated, the calculator assumes solid conductors and stranded inner conductor and braided outer conductor increase loss, tinned conductors further increase loss, but silver plated conductors decrease loss.
The cable is likely to be an RG400 type, the reported measurements are quite close.
]]>On testing two wire line loss with an analyser / VNA – part 1
This article series shows a method for estimating matched line loss (MLL) of a section of two wire line based on physical measurements (Duffy 2011).
Above is a short piece of the line to be estimated. It is nominal 300Ω windowed TV ribbon. It has copper conductors, 7/0.25, spaced 7.5mm. The dielectric is assumed to be polyethylene… but later measurements suggest is has slightly higher loss than polyethylene. The test section length is 4.07m.
From physical dimensions 

Parameters  
Conductivity  5.800e+7 S/m 
Rel permeability  1.000 
Diameter  0.000750 m 
Spacing  0.007200 m 
Velocity factor  0.850 
Loss tangent  1.000e4 
Frequency  146.000 MHz 
Twist rate  0 t/m 
Length  1.000 m 
Results  
Zo  301.49j0.36 Ω 
Velocity Factor  0.8500 
Twist factor  1.0000 
Rel permittivity  1.384 
R, L, G, C  2.710030e+0, 1.184609e6, 1.195499e6, 1.303216e11 
Length  206.260 °, 3.600 ᶜ, 0.572945 λ, 1.000000 m, 3.924e+3 ps 
Line Loss (matched)  4.06e2 dB 
S11, S21 (50)  6.650e1+j4.265e1, 3.312e1+j5.045e1 
Y11, Y21  8.574e5j6.647e3, 7.850e5j7.429e3 
NEC NT  NT t s t s 8.574e5 6.647e3 7.850e5 7.429e3 8.574e5 6.647e3 ‘ 1.000 m, 146.000 MHz 
k1, k2  3.231e6, 1.072e11 
C1, C2  1.022e1, 1.072e2 
Mhf1, Mhf2  9.847e2, 3.268e4 
MLL dB/m: cond, diel  0.039037, 0.001565 
MLL dB/m @1MHz: cond, diel  0.003231, 0.000011 
γ  4.675e3+j3.604e+0 
Above is a set of results from TWLLC.
In the above, the estimated velocity factor is 85% based on experience of measuring a range of windowed ladder lines, loss tangent is an estimate in the range of virgin polyethlyene.
A test section of line was measured by two techniques at:
It was noted in the previous article that the dielectric component of MLL was higher than expected for good polyethylene. That may be due to impurities like fillers, plasticisers and pigments… especially the latter if carbon black was used.
Above is a plot of the components of MLL from the measurements used in the second article. At the frequency of interest (146MHz), the dielectric component of MLL is smaller than conductor loss, but one would normally expect virgin polyethylene to be perhaps a tenth of that measured.
With experience, estimating MLL from physical measurement can be quite good, good enough for some purposes, and a check on measurements where they are made.
On testing two wire line loss with an analyser / VNA – part 1
Above is a short piece of the line to be measured. It is nominal 300Ω windowed TV ribbon. It has copper conductors, 7/0.25, spaced 7.5mm. The dielectric is assumed to be polyethylene… but later measurements suggest is has slightly higher loss than polyethylene. The test section length is 4.07m.
The Noelec 1:9 balun (or perhaps Chinese knock off) is available quite cheaply on eBay and provides a good hardware base for a 1:1 version.
Above is a modified device with the original transformer replaced with a Macom ETC11T2TR 1:1 transformer. The replacement is not exactly the same pads, but it is sufficiently compatible to install easily.
See A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly for more detailed info.
Performance of the fixture is crucial to valid measurement.
This method gives a good estimate of transmission line characteristic impedance and propagation constant.
Above is a plot of s11 for the DUT for OC termination. It is really important there are no unexpected bumps in this, for whatever reason.
Above is a plot of s11 for the DUT for SC termination. It is really important there are no unexpected bumps in this, for whatever reason.
Did I mention bumps are a problem? Make sure after OSL calibration that the s11 response is flat for each of OSL… you can’t make good measurements if the cal set are flawed.
So we can calculate \(MLL=\frac{20}{2len} log_{10} \frac{1+\sqrt{\frac{{Z_{sc}}}{Z_{oc}}}}{1\sqrt{\frac{{Z_{sc}}}{Z_{oc}}}} \; dB/m\\\).
Above is a plot of MLL (dB/m) calculated from the measurements saved as s1p files (raw), and fits to two models:
The data is a bit noisy, this is a low end analyser, the nanoVNA. Nevertheless, the curve fit COVs are less than one tenth the coefficient for both coefficients… good enough.
The green curve is a fit to a model often used and often provided in some analysis tools. It can be seen here that although the slope of the blue line is similar to the green line around 10MHz, the green line slope increases with increasing dielectric loss as frequency increases… the green line is a better model.
We could use the loss model coefficients in ATLC to solve a given line section, for example to find Rin of a quarter wave OC line section at 146MHz.
Above, Zin is 8.048e1j3.335e4Ω, Rin=0.8048Ω.
More advanced techniques include log scan, and avoiding frequencies where clock harmonics etc might degrade accuracy. The nanoVNA’s accuracy is limited as witnessed by the noise on the raw plot above, and measures like adjustable bandwith have not improved it in my experience. I did try NanoVNAApp for its averaging, but it still throws memory protection exceptions, so I cannot trust it.
Continued at On testing two wire line loss with an analyser / VNA – part 3.
Above is a short piece of the line to be measured. It is nominal 300Ω windowed TV ribbon. It has copper conductors, 7/0.25, spaced 7.5mm, though as can be seen the spacing is not perfectly uniform. The dielectric is assumed to be polyethylene… but later measurements suggest is has slightly higher loss than polyethylene. The test section length is 4.07m.
The Noelec 1:9 balun (or perhaps Chinese knock off) is available quite cheaply on eBay and provides a good hardware base for a 1:1 version.
Above is a modified device with the original transformer replaced with a Macom ETC11T2TR 1:1 transformer. The replacement is not exactly the same pads, but it is sufficiently compatible to install easily.
See A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly for more detailed info.
The system is OSL calibrated at the fixture load pins.
Performance of the fixture is crucial to valid measurement.
This method gives a good approximation of MLL if Ro and Rin of a resonant section near the desired frequency (146MHz) are known. See (Duffy 2016) for more information.
Above is a chart of Zin to the test section near the frequency of interest with OC termination. At exactly half way between the resonance and antiresonance, \(R_0 \approx X_{in}\), in this case we will take Ro to be 298Ω.
Above is a zoomed in scan of Zin near the resonance, and we will take Rin to be 7.35Ω.
We can calculate MLL from these values.
Above, estimated MLL is 0.053dB/m.
Continued at On testing two wire line loss with an analyser / VNA – part 2.
Above is an archived extract of a spreadsheet that was very popular in the ham community, both with antenna designers and sellers and end users (buyers / constructors). It shows a column entitled G/T which is actually the hammy calculation. The meaning possibly derives from (Bertelsmeier 1987), he used G/Ta.
Ta is commonly interpreted by hams to be Temperature – antenna. It is true that antennas have an intrinsic equivalent noise temperature, it relates to their loss and physical temperature and is typically a very small number. But as Bertelsmeier uses it, it is Temperature – ambient (or external), and that is how it is used in this article.
Let’s calculate the G/Ta statistic for the three scenarios in Do I ‘need’ a masthead preamp to work satellites on 2m? – space noise scenario.
Above is a calculation of the base scenario, G/T=29.74dB/K.
Also shown in this screenshot is G/Ta=23.98dB/K.
Above is a calculation of the masthead amplifier scenario, G/T=25.21dB/K.
Also shown in this screenshot is G/Ta=23.98dB/K.
Above is a calculation of the LNA at the receiver scenario, G/T=25.754dB/K.
Also shown in this screenshot is G/Ta=23.98dB/K.
Scenario  G/T (dB/K)  G/Ta (dB/K) 
Base  29.74  23.98 
With masthead LNA Gain=20dB NF=1dB  25.21  23.98 
With local LNA Gain=20dB NF=1dB  25.75  23.98 
Note that G/Ta is the same for all three configurations, it does not contain the important information that differentiates the performance of the three configurations.
Importantly, you cannot derive G/T from G/Ta without knowing either G or Ta (and some other important stuff), the G/Ta figure by itself cannot be ‘unwound’… so if you select an antenna ranked on a G/Ta value (even if mislabeled), the ranking of ‘real’ G/T may be different depending on many factors specific to your own scenario, ie the one with the better G/Ta might have the poorer G/T.