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 \(I=\frac{V_S-V_L}{R_S+R_1+R_2+R_L}\)
Substituting for I: \(Z=\frac{V}{I}=\frac{V_L+\frac{V_S-V_L}{R_S+R_1+R_2+R_L} R_L}{\frac{V_S-V_L}{R_S+R_1+R_2+R_L}}\) 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 \(Z=\frac{V}{I}=\frac{0+\frac{V_S-0}{R_S+R_1+R_2+R_L} R_L}{\frac{V_S-0}{R_S+R_1+R_2+R_L}}=R_L\).
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 0.018015162531799005-j0.008215654291790999.
We now know the current in RL and can calculate the voltage looking into RL from the left 1.4007581265899502-j0.41078271458954996.
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=(vs-vl)/zt >>> i (0.018015162531799005-0.008215654291790999j) >>> v=vl+i*rl >>> v (1.4007581265899502-0.41078271458954996j) >>> z=v/i >>> z (72.976+10.478j) >>> z0=50 >>> rho=abs((z-z0)/(z+z0)) >>> rho 0.20460301944607484 >>> vswr=(1+rho)/(1-rho) >>> 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.
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 (ITU-R. 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 on-boresight 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 in-situ 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 (ITU-R. 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 on-boresight 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 in-situ 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 PL-259 connector. No patch cable used, reduces SWR. Finned aluminum, air-cooled 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 35-40Ω.
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 non-ideal 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 non-compliant 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).
TLLC and TLDetails are two line loss calculators, and they use quite different predictive models.
Above is the calculation results from TLLC. for the 10m section of Belden 8267 (RG213) with short circuit termination. Note the calculated loss model coefficients k1 and k2 which will be used in a later graph.
Above is the calculation from TLDetails for the same section. Note the calculated loss model coefficients k0, k1 and k2 which will be used in a later graph. The loss model is different and although the coefficients are named similarly, they are only valid in their associated loss model.
Above is a plot of MLL (dB/m) calculated from the measurements used in the previous article and saved as s1p files (raw), and predicted loss using the models and coefficients from TLLC and TLDetails (labelled ac6la).
We should not expect the predicted values to reconcile exactly with measured, the DUT is an old section of cable in good order and subject to manufacturing variation.
That said, I find it difficult to reconcile TLDetails MLL=0.0089dB/m @ 1MHz with the measured value of 0.0055dB/m. The shape of the ac6la curve at low frequencies questions whether it is a good model for the measured coax section.
Above is a plot of MLL (dB/m) calculated from the measurements used in the previous article and saved as s1p files (raw), and fits to two models:
It is clear that the apparent slope of the raw data points is greater than the green curve, so it appears that loss increases at a greater rate than simply square root of f (conductor loss in presence of well developed skin effect).
The blue curve is a better fit and it sizes the extent of the contribution of loss proportional to f (dielectric loss). The coefficient k2 is 3.14e-9 as against the k2=5.28e-10 used in TLLC (see previous graph) and derived from Belden’s published characteristics. The suggestion is that this cable has higher dielectric loss than expected, though it really needs a higher frequency scan to provide convincing evidence of this.
Is it plausible? The cable section is Belden 8267 purchased new in 1970, it is 50 years old. It has never been exposed to the weather, never wet, never abused. It has crimped Kings N plugs that are in good condition. An issue with coax construction of this type is leaching of plasticisers from the PVC jacket to the PE dielectric degrading its performance. Though this is specified as a non-contaminating jacket, it is quite old cable and it is possible that is an explanation of the apparently higher dielectric loss coefficient.
]]>So, does it work in practice?
Let’s measure a 10m length of Belden 8267 (RG-213) fitted with N connectors using a Rigexpert AA-600 and an instrument grade N(F) short circuit.
ReturnLoss @ 3.5MHz is 0.15dB.
ReturnLoss @ 3.5MHz is 0.29dB.
In fact, it turns out that in this case, and in general, that the average of the two is a fairly good approximation, \(MLL^\prime \approx \frac{RL_{OC}+RL_{SC}}{4}=\frac{0.15+0.29}{4}=0.110\) which reconciles with the expected MLL from TLLC.
The measurement graphs above are zoomed in a much as permitted in Antscope… it clearly is pretty disabled for this type of application. Let’s export the data and look at both data sets in VNWA software.
Above is a plot of measured ReturnLoss wrt 50+j0Ω (RL(50)) for open (OC) and short circuit (SC) terminations. The data is a little noisy (jaggy), but quite acceptable for the purpose.
So contrary to the common belief, RL(50) is not the same for OC and SC terminations, and relying upon just one of them to estimate ReturnLoss wrt actual Zo, and then MLL wrt actual Zo, is actual MLL, is prone to error
RLoc (dB) | RLsc (dB) | MLL (dB) | MLL/100m (dB) | |
TLLC | 0.146 | 0.276 | 0.106 | 1.06 |
Measurement | 0.15 | 0.29 | 0.11 | 1.1 |
Measurement of a real cable with the AA-600 provided a calculated MLL which reconciled with TLLC and which reconciles with interpolation from the Belden datasheet.
What does it say for the simple half ReturnLoss measurement technique?
It is a trap for the inexperienced.
Because it works sometimes (and it was pretty good in the example shown in the video mentioned) does not mean that it always works, it does not mean that it is reliable.
Be wary of what you read (or see, eg Youtube), think!
]]>The example gives MLL’ (based on half ReturnLoss) of about two thirds cable MLL.
Why is that?
What does it say for the measurement technique?
Recall that MLL’ calculated as half the RL(50) figure did not reconcile with the MLL calculated from line parameters.
Above is the complete output from TLLC for the same line section with short circuit termination, we are interested in the highlighted quantities. Again, \(MLL^\prime = \frac{RL(50)}{2}\) quantity does not reconcile with MLL, but is considerably higher.
In fact, it turns out that in this case, and in general, that the average of the two is a fairly good approximation, \(MLL^\prime \approx \frac{RL_{OC}+RL_{SC}}{4}\).
Above is the same report with some magenta highlights. Note that Zo is not exactly 50+j0Ω, so ReturnLoss calculated / measured wrt 50+j0Ω (as is usually the case with an antenna analyser) is not that for the actual DUT. The report does contain ReturnLoss wrt the actual Zo, it is the second magenta highlighted quantity, RL at the load end, and it is 0.211dB, half of that reconciles with the MLL of 0.105dB.
It is a trap for the inexperienced, and it appears in places that might surprise, like the Bird 43 user manual.
(Bird 2004) gives the following advice.
Line loss using open circuit calibration: The high directivity of elements can be exploited in line loss measurements, because of the equality of forward and reflected power with the load connector open or short circuited. In this state the forward and reflected waves have equal power, so that φ = 100% and ρ = ∞.
Open circuit testing is preferred to short circuit, because a high quality open circuit is easier to create than a high quality short. To measure insertion loss, use a high quality open circuit to check forward and reverse power equality, then connect an open-circuited, unknown line to the wattmeter. The measured φ is the attenuation for two passes along the line (down and back). The attenuation can then be compared with published data for line type and length (remember to halve Ndb or double the line length to account for the measurement technique).
This also contains the hoary old chestnut that a good o/c termination is hard to achieve, but this author’s experience of measurement with modern VNAs is not consistent with Bird’s assertion.
What does it say for the simple half ReturnLoss measurement technique?
It is a trap for the inexperienced, and it appears in places that might surprise, like the Bird 43 user manual.
Because it works sometimes (and it was pretty good in the example shown in the video mentioned) does not mean that it always works, it does not mean that it is reliable.
Be wary of what you read (or see, eg Youtube), think!