If we consider a two wire transmission line, we can define currents I1 and I2 flowing in the same direction in each conductor.
These two currents can be decomposed into differential and common mode components:
The diagram shows the relationship of the various example phasors, their sums and phase relationships.
Rearranging these, we can write:
So the component currents Ic and Id fully account for the current at each terminal, I1 and I2.
I1 and I2 can be measured directly by placing a current probe around each of the wires, and I1+I2 (I12 or 2Ic) can be measured directly by placing a current probe around both of the wires.
Measurement of the magnitudes of these three currents I1, I2 and I12 can be resolved into components Id and Ic.
The calculation is not very difficult, it used no more than high school maths.
The measured values I1, I2 and I12 are the magnitudes of three phasors, and for some of the calculator results, we need to find the magnitude of the phase angle between I1 and I2. The Law of Cosines provides the solution, \(\theta_{12}=acos\frac{(I_{12})^2I_{1}^2I_2^2}{2 I_1 I_2}\).
We can then calculate using the Law of Cosines \(2I_d=I_1^2+I_2^22 I_1 I_2 cos \alpha\) and since \(\alpha=\pi\theta_{12}\) we can write \(2I_d=I_1^2+I_2^22 I_1 I_2 cos(\pi\theta_{12})\).
Now to find magnitude of the phase angle between Ic and Id, θ_{dc} using the Law of Cosines \(\theta_{dc}=acos\frac{I_2^2I_c^2 I_d^2}{2 I_c I_d}\).
Using the lengths of the phasors in the figure above, we can calculate the components.
Above, the example to scale.
Above, the calculated results.
A graph is not presented, it will be impractical to read.
I12 varies from 1030mA depending on recent weather, seasonal vegetation changes etc.
Low Ic is achievable with good design, good symmetry, and an effective common mode choke.
]]>But can you trust what you read / see online?
Here an author gives his take on Return Loss.
Errr, no!
Using his terms, \(Return\_Loss=\frac{P_{sent}}{P_{return}}\), a result greater than unity, or we can express it in dB (not db, the B is for Bell, a person’s name, so it must be capitalised in the unit) \(Return\_Loss\_dB=10 log_{10}\frac{P_{sent}}{P_{return}}\) which will yield a positive dB value.
If we use a VNA and it reports the magnitude of S11, we can calculate \(Return\_Loss\_dB=20 log_{10} S11= S11\_dB\).
So it is quite wrong to speak of, or worse to label a plot of S11_dB as Return_Loss.
But “everybody does it, it must be right”! No, but it is true that on social media, popularity is taken to determine fact.
]]>This article details configuration of RTKLIB rtknavi to work on a Win10 workstation using stunnel to connect to a NTRIP server that is only available using TLS.
The version of rtklib used is v2.4.3b33, and stunnel v5.60.
The GPS receiver used here is a Ublox LEA6T.
GPS traffic may be falsely detected by Windows as mouse traffic, and cause havoc
If you are not using a serial mouse (and most of us do not these days) t is advisable to disable serial mouse detection at startup. You can do that with the following command in a administrator authorised Powershell.
SetItemProperty path "HKLM:\SYSTEM\CurrentControlSet\Services\sermouse" name "start" Value 4
Reboot for it to take effect.
Above is a screenshot of the serial port options. Use an appropriate COM port for your configuration.
!UBX CFGRATE 200 1 1 !UBX CFGMSG 2 16 0 1 0 1 0 0 !UBX CFGMSG 2 17 0 1 0 1 0 0 !UBX CFGMSG 240 0 0 1 0 1 # NMEA GGA !UBX CFGMSG 240 1 0 0 0 0 # NMEA GLL !UBX CFGMSG 240 2 0 0 0 0 # NMEA GSA !UBX CFGMSG 240 3 0 0 0 0 # NMEA GSV !UBX CFGMSG 240 4 0 1 0 1 # NMEA RMC !UBX CFGMSG 240 5 0 0 0 0 # NMEA VTG !UBX CFGMSG 240 8 0 0 0 0 # NMEA ZDA
The above commands set the message rate, enable the raw messages needed and disable some of the default NMEA messages.
!UBX CFGRST 0
The above command resets the GPS to avoid the binary messages continuing after shutdown of the RTKLIB connection.
The combination localhost:2102 directs the packets to stunnel running on the workstation, which in turns forwards the packets in an SSL tunnel. Use your userid and password.
Stunnel needs the following section added to its configuration file and activated. This redirects connections to localhost:2102 to ntrip.host:443 in this case, but use the applicable destination host and port
[ntrip] client=yes accept=localhost:2102 connect=ntrip.host:443 verifyChain = yes CAfile = cacerts.pem
Stunell needs to be directed to reload the configuration when updated.
You must start stunnel before attempting to connect with rtklib, otherwise it will fail to connect to localhost:2102. If you see that message, check that you have stunnel configured correctly and running.
This solution works with Geoscience Australia’s TLS NTRIP caster.
The stunnel solution might well work with other NTRIP client apps.
]]>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.)
]]>References without any qualification surely imply a recommendation.
In the same thread, Roger Need compared his measurement of a FT5043 with Calculate ferrite cored inductor (from Al) (one of a set of related calculators), and Ferrite permeability interpolations.
Above, his calculation reconciles well with measurement at 3.6MHz.
Above is the same scenario calculated with VK3CPU’s calculator. An impressive GUI, if you like that sort of thing… and people do. Note the values at 3.6MHz in the cursor callout.
The value L is 7.06µH and it varies with frequency, but what does L mean. The notes state:
Tapping on a data point will display the parameters for a single frequency.
L(μH) : Inductance in microhenries.
Roger’s measured impedance @ 3.6MHz implies an equivalent series inductance (Ls in my calculators) of 3.965µH.
Though several posters to the thread have discussed VK3CPU’s calculator and the merits of it, it seems no one tried to reconcile it with Roger’s or any other measurements.
Wait a minute, v0.8 just released gives different values (including data for old #43 mix).
Now L=4.09µH which reconciles with Roger’s measurement.
]]>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.