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.
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.
Wright gives the schematic of the minimal VSWR detector he simulates in SPICE.
The schematic is sparse, it does not show where the forward and reflected signals are measured.
QEX on SWR dependence on output impedance set out an analysis if his model that showed why his conclusions were invalid. This article derives a simple mathematical expression for the solution of the VSWR detector Wright used.
Lets assume that the values of R1 and R2 are much much less than RL, it makes the maths a little simpler. This is not an impractical assumption, a good VSWR detector, one with very low InsertionVSWR will have R1 and R2 are much much less than RL.
The purpose of the VSWR detector formed by R1, R2, C1, C2, R3 and their indicating circuits (not shown) is to respond to Z, the ratio V/I seen looking to the right into RL (node 4) (Bruene 1959).
Let’s apply a bit of high school maths and basic circuit analysis.
If we assume that the current through the capacitor branch is insignificant (which it should be in a good design), we can write a simple expression \(Z=\frac{V}{I}=\frac{V_L+I R_L}{I}\) where \(I=\frac{V_SV_L}{R_S+R_1+R_2+R_L}\)
Substituting for I: \(Z=\frac{V}{I}=\frac{V_L+\frac{V_SV_L}{R_S+R_1+R_2+R_L} R_L}{\frac{V_SV_L}{R_S+R_1+R_2+R_L}}\) so it can be seen that Z is a function of RS.
Little wonder that Wright proved that indicated VSWR depended on RS in his scenario. One wonders if there is confirmation bias at play here. He actually hinted the problem when he observed that this only occurs when VL is not zero.
So, lets solve the previous expression for VL=0 \(Z=\frac{V}{I}=\frac{0+\frac{V_S0}{R_S+R_1+R_2+R_L} R_L}{\frac{V_S0}{R_S+R_1+R_2+R_L}}=R_L\).
The use of VL does not simulate a mismatched load independent of the source, but using test cases for RL will properly simulate mismatched loads independent of source.
Wright gives the schematic of the minimal VSWR detector he simulates in SPICE.
The schematic is sparse, it does not show where the forward and reflected signals are measured.
So, the crux of his proof depends on this test case:
Wright’s circuit is trivial to solve by hand. Lets assume that the values of R1 and R2 are much much less than RL, it makes the maths a little simpler. This is not an impractical assumption, a good VSWR detector, one with very low InsertionVSWR will have R1 and R2 are much much less than RL.
Lets solve this using Python as a complex number calculator.
I will ignore the very small current flowing in the capacitor branch.
If we calculate the voltage impressed from Vs to Vl, we get 1.5.
We can calculate the current through the series path, I get 0.018015162531799005j0.008215654291790999.
We now know the current in RL and can calculate the voltage looking into RL from the left 1.4007581265899502j0.41078271458954996.
So, at that node, we know V and I, we can calculate Z looking right into RL: 72.976+j10.478.
Here is the Python code:
>>> import cmath >>> rs=17.928+31.434j >>> rl=50 >>> vs=2 >>> vl=0.5 >>> r1=0.5 >>> r2=0.5 >>> zt=rs+r1+r2+rl >>> zt (68.928+31.434j) >>> i=(vsvl)/zt >>> i (0.0180151625317990050.008215654291790999j) >>> v=vl+i*rl >>> v (1.40075812658995020.41078271458954996j) >>> z=v/i >>> z (72.976+10.478j) >>> z0=50 >>> rho=abs((zz0)/(z+z0)) >>> rho 0.20460301944607484 >>> vswr=(1+rho)/(1rho) >>> vswr 1.5144676795317642
Knowing Z looking into RL, we can calculate VSWR(50).
The answer is VSWR=1.51 which reconciles with Wright’s calculation.
The serious flaw in his thinking is that the ratio V/I seen by the VSWR detector is 50Ω, it is in fact 72.976+j10.478Ω.
The presence of VL means that the ratio V/I at the VSWR detector depends on the entire series circuit. This is a contrived circuit that does not represent usual implementations.
The circuit is not a clear representation of a fixed mismatched load, and the conclusion he draws that indicated VSWR depends on source impedance is wrong.
Heaviside gave us the well accepted theory that VSWR is a function of load impedance and characteristic impedance of the line. Source impedance does not enter into the equation.
More at QEX on SWR dependence on output impedance #2 .
Above, the dipole from the ARRL Antenna Book.
Now zip line in the US where 110V AC distribution is used is somewhat thicker than the figure 8 line used in Australia (230V AC distribution). Australian figure 8 twin used to be 23/0.0076″ and the modern metric version is 24/0.2mm.
Rummaging around in the shed, I found an ‘archived’ (ie lost) offcut of 10m length of line manufactured about 50 years ago, NOS. It was quite stiff, it would seem the plasticisers in the PVC insulation had degraded / evaporated to some extent, but the copper was shiny bright. A candidate for measurement, surely!
Measurements were made using a nanoVNA of impedance looking into the 10m section with short circuit and open circuit terminations, and from that the line characteristics calculated.
Above is a plot of:
Nominal Zo=146Ω and VF=0.696.
Above is a plot of the components of MLL. Dielectric loss is a large part of the MLL at HF, considerably higher than good RF cables.
The calculated loss coefficients were used to populate an entry in TLLC (development version initially).
An example scenario of a half wave dipole on 14MHz with 20m of feed line was evaluated.
Above, the calculated results. Two issues stand out:
Increasing the feed line length to 1.5λ (22.4m) would improve VSWR(50) in this application at a small expense of some additional line loss.
Various authors have warned of the poor performance of zip line, speaker twin etc over the years, but still it is common advice to newcomers. The ARRL Antenna Book gives zip line MLL=12.4dB/100m @ 14MHz, the AU line discussed in this article was 12.6dB/100m… quite similar despite smaller conductors and higher Zo.
]]>Base scenario is a low end satellite ground station:
A metric that may be used to express the performance of an entire receive system is the ratio of antenna gain to total equivalent noise temperature, usually expressed in deciBels as dB/K. G/T is widely used in design and specification of satellite communications systems.
G/T=AntennaGain/TotalNoiseTemperature 1/K
Example: if AntennaGain=50 and TotalNoiseTemperature=120K, then \(G/T=\frac{50}{120}=0.416 \text{ } 1/K\) or 3.8 dB/K.
The utility of G/T is that receive S/N changes dB for dB with G/T, in fact you can calculate S/N knowing G/T, wavelength, bandwidth and the field strength of the signal (Duffy 2007).
\(Signal/Noise=S \frac{\lambda^2}{4 \pi} \frac{G}{T} \frac1{k_b B}\) where:
S is power flux density;
λ is wavelength;
k_{b} is Boltzmann’s constant; and
B is receiver equivalent noise bandwidth
Usage in this article is consistent with the industry standard meaning of G/T given at (ITUR. 2000) (as opposed to the meaning used by some Hams who have appropriated the term for their own purpose).
Note this is not the bodgy G/T figure used widely in ham circles.
Ambient noise temperature Ta is an important factor in calculation of G/T. Ta depends on frequency, the environment, the antenna’s ability to reduce off boresight noise, and the onboresight noise. For the purposes of this discussion let’s assume total ambient noise for the given omni satellite scenario at 144MHz is 1500K.
Above is a calculation of the base scenario, G/T=33.41dB/K.
Above is a calculation of the masthead amplifier scenario, G/T=31.99dB/K.
Scenario  G/T (dB/K) 
Base  33.41 
With masthead LNA Gain=20dB NF=1dB  31.99 
The first finding is that adding a masthead LNA with 20dB gain and 1dB NF makes only a small difference to G/T and hence S/N, just 1.4dB in this case.
The foregoing analysis assumed a linear receive system, no intermodulation distortion. Now let’s talk about the real world.
Some LNAs are sold without specifications, those that have meaningful NF and Gain specifications are usually based on laboratory measurements with no interfering signals.
When attached to an antenna, the out of band signals will give rise to noise due to intermodulation distortion, so the NF insitu might be poorer than specification NF. Indeed, the IMD noise can be so great as to deliver worse G/T with the LNA.
One way of reducing IMD noise is to limit the amplitude of interfering signals arriving at the LNA active device, and front end filtering is one possible solution.
Be aware that lots of hammy Sammy LNA designs have very little front end selectivity, relying upon the narrow band response of a high gain antenna. When these are used with low gain tuned antennas, or worse, broadband antennas like Discones, the IMD noise can be huge.
On the other hand, there are LNAs available with a very narrow front end filter… but they cost a lot more.
The benefit / necessity of front end filtering depends on your own IMD scenario.
Base scenario is a low end satellite ground station:
A metric that may be used to express the performance of an entire receive system is the ratio of antenna gain to total equivalent noise temperature, usually expressed in deciBels as dB/K. G/T is widely used in design and specification of satellite communications systems.
G/T=AntennaGain/TotalNoiseTemperature 1/K
Example: if AntennaGain=50 and TotalNoiseTemperature=120K, then \(G/T=\frac{50}{120}=0.416 \text{ } 1/K\) or 3.8 dB/K.
The utility of G/T is that receive S/N changes dB for dB with G/T, in fact you can calculate S/N knowing G/T, wavelength, bandwidth and the field strength of the signal (Duffy 2007).
\(Signal/Noise=S \frac{\lambda^2}{4 \pi} \frac{G}{T} \frac1{k_b B}\) where:
S is power flux density;
λ is wavelength;
k_{b} is Boltzmann’s constant; and
B is receiver equivalent noise bandwidth
Usage in this article is consistent with the industry standard meaning of G/T given at (ITUR. 2000) (as opposed to the meaning used by some Hams who have appropriated the term for their own purpose).
Note this is not the bodgy G/T figure used widely in ham circles.
Ambient noise temperature Ta is an important factor in calculation of G/T. Ta depends on frequency, the environment, the antenna’s ability to reduce off boresight noise, and the onboresight noise. For the purposes of this discussion let’s assume total ambient noise for the given satellite scenario at 144MHz is 250K.
Above is a calculation of the base scenario, G/T=29.74dB/K.
Above is a calculation of the masthead amplifier scenario, G/T=25.21dB/K.
Above is a calculation of the LNA at the receiver scenario, G/T=25.754dB/K.
Scenario  G/T (dB/K) 
Base  29.74 
With masthead LNA Gain=20dB NF=1dB  25.21 
With local LNA Gain=20dB NF=1dB  25.75 
The first finding is that adding a masthead LNA with 20dB gain and 1dB NF makes a small difference to G/T and hence S/N, 4.5dB in this case.
Note that there is only a small degradation in moving the LNA from masthead to local to the transceiver. There are additional reliability / maintenance issues with masthead located amplifiers… particularly if high performance narrow band front end filtering is used. It is much more practical to house a coaxial resonator (‘can’ in repeater parlance) in the shack that at the masthead.
The foregoing analysis assumed a linear receive system, no intermodulation distortion. Now let’s talk about the real world.
Some LNAs are sold without specifications, those that have meaningful NF and Gain specifications are usually based on laboratory measurements with no interfering signals.
When attached to an antenna, the out of band signals will give rise to noise due to intermodulation distortion, so the NF insitu might be poorer than specification NF. Indeed, the IMD noise can be so great as to deliver worse G/T with the LNA.
One way of reducing IMD noise is to limit the amplitude of interfering signals arriving at the LNA active device, and front end filtering is one possible solution.
Be aware that lots of hammy Sammy LNA designs have very little front end selectivity, relying upon the narrow band response of a high gain antenna. When these are used with low gain tuned antennas, or worse, broadband antennas like Discones, the IMD noise can be huge.
On the other hand, there are LNAs available with a very narrow front end filter… but they cost a lot more.
The benefit / necessity of front end filtering depends on your own IMD scenario.
For satellite work, a low gain antenna will tend to have higher Ta by virtue of side lobe contribution, and so the improvement seen above might be diminished a little.
Terrestrial ambient noise is much higher, and the improvement would be considerably less. Likewise for an omni satellite antenna. In both cases, the improvement in G/T might be less than 1dB with the same masthead LNA… download the spreadsheet and explore.
As mentioned Ta is frequency dependent, so the case for 432MHz might be quite different than the above case. In particular, the choice of masthead mounting becomes clearer on higher frequencies.
From MFJ’s web site listing:
Connects directly to the transmitter with PL259 connector. No patch cable used, reduces SWR. Finned aluminum, aircooled heatsink. Handles 100 Watts peak, 15 Watts average. 50 Ohms. Covers DC to 500 MHz with less than 1.15:1 SWR. 1 ⅝” round by 3″ long.
That is pretty stunning for a device with a UHF connector, more on that later.
Bogard wrote a review of the device, making some VSWR measurements using a spectrum analyser with tracking generator and a VSWR accessory (a directional coupler).
The VB1032 VSWR bridge specification directivity is modest at 30dB. That challenges making really low VSWR measurements (as the article does) with low uncertainty.
Above is a calculation of the uncertainty in measurement for indicated VSWR=1.15 using a 30dB directivity coupler, the actual VSWR uncertainty range is 1.08 to 1.23.
Note that the test equipment does not use UHF connectors, so there was some kind of N(M) to UHF(F) adaption used, but no detail.
Above is the reported VSWR response.
In summary, it is pretty good at low frequencies and rises fairly uniformly to just over 1.5 at 500MHz… so on the surface of it, it fails to meet spec in a big way.
UHF connectors do not have a controlled characteristic impedance, and experience is that most UHF connectors are well represented by a transmission line section with Zo in the range 3540Ω.
Realise that there are at least two cascaded UHF connectors in this test setup, and that the effect of a very short series line section of low Zo is to cause InsertionVSWR.
Let’s look at a model in Simsmith to illustrate the effect.
Above, the Simsmith model that models the UHF connectors as a 37mm length of line with Zo=35Ω and VF=0.66. These values were arrived at by calibrating the model to the published measurements.
The model assumes that the load has little reactance at low frequencies, but the resistance is wrong and causes the low frequency VSWR=1.045. This gives two choices.
Calibration included adjusting the load resistance for low frequency VSWR and the transmission line parameters to achieve the shape, slope and 500MHz VSWR.
It is not a perfect fit, but it gives a very plausible possible explanation the measurements.
So, the question is how much of the nonideal behavior is due to the test fixture and how much is in the DUT? It is possible that although the DUT has a UHF connector, that the effect of the connector has been compensated inside the DUT and that at some reference plane, it meets the stated specifications. The very slight wavy nature to the VSWR response might hint some level of internal compensation.
So, (Bogard 2021) is a bit unsatisfying. On the surface it shows noncompliant VSWR, but does not address it leaving one wondering about whether a significant part is due to the test setup (coupler directivity and UHF connectors / adapters).