This series of seven articles has:

- explained the meaning and value of G/T as a single metric for receive system performance;
- defined and explained the G and T terms;
- explained the relationship between Teq and Noise Figure;
- explained how to analyse simple cascaded stages and hence more complex networks;
- described how to estimate transceiver Noise Figure and Teq;
- demonstrated application of the analysis techniques to a set of practical configuration options to provided quantitative comparison of the S/N performance of the options; and
- discussed measurement of G/T as a means of validating system performance.

Sufficient information has been given to allow the reader to build a valid system model to calculate G/T, and to measure G/T for validation.

Designing high performance VHF/UHF receive systems – Part 1

Designing high performance VHF/UHF receive systems – Part 2

Designing high performance VHF/UHF receive systems – Part 3

Designing high performance VHF/UHF receive systems – Part 4

Designing high performance VHF/UHF receive systems – Part 5

Designing high performance VHF/UHF receive systems – Part 6

Designing high performance VHF/UHF receive systems – Part 7

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G/T can be measured using celestial noise sources provided the antenna can be pointed to them. The noise source that is most appropriate will depend on expected G/T, frequency, time etc.

(Duffy 2007) described a method of measuring G/T using the Sun as a noise source, and an expression for calculating G/T for wide antennas.

**G/T=10*LOG((10^(Y/10)-1)*2/(SolarFlux*1E-22)/Wavelength^2*4*π*1.3806504E-23)dB/K** where:

Y is the measured noise increase in dB; and

SolarFlux is in SFU

Note that for antennas where the beamwidth is not large compared to the angle subtended by the radio Sun, less Sun noise is captured and the SolarFlux should be divided by a beamwidth correction factor (BWCF=1+0.38*(Ws/Wa)^2 where Ws is the angle subtended by the radio Sun and Wa is the antenna half power beamwidth).

(ITU-R 2000) details a method of measurement of satellite earth station receive systems, and lists reference noise levels from a number of radio stars

One might have thought that amateur radio operators would share observation of noise rise on celestial objects, both for forming a shared view of the noise flux level and establishing some experience on state of the art G/T achievable with some common configurations on each band.

There is a dearth of information of this type published on the Internet by radio hams, the few boasts of Sun noise rise do not give the solar flux level (or a date to allow determination of solar flux). Some calculators historically gave solar flux based on flawed extrapolation from 10cm flux, some users used the 10cm flux for all bands. Basically, any information published is likely to be amateurish.

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net (offline).
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net (offline).
- ———. 2007b. Quiet sun radio flux interpolations. VK1OD.net (offline).
- ———. 2007c. Noise Figure Meter. VK1OD.net (offline).
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000) Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

Designing high performance VHF/UHF receive systems – Part 7

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This part explains how to build a model of the entire receive system to calculate G/T.

Firstly, make an inventory of all of the system elements that you intend to model.

A model needs to be no more detailed than is necessary to provide adequate accuracy for the purpose at hand.

You could build a model with an element for every identifiable loss or gain element, eg every coax connector, every coax adapter. Sure it will work, and it might be more accurate if you have accurate characteristics for all of the elements, but the uncertainty of just a few elements will tend to dominate the overall uncertainty and better to work on getting better accuracy on big-ticket items that including a large number of very small ticket items.

For example, if there is 20m of LMR-400 from the transmitter to the LNA, ignore the loss in coax connectors as it will be very small compared to the LMR-400 section and smaller than the uncertainty of your LMR-400 loss estimate anyway.

Some guidelines:

- do include every element with more than 0.2dB of loss or gain;
- don’t rely on old wives tales about element loss, use reliable data or measure it;
- in the absence of receiver measurement, use the receiver specifications.

Above is a clip from a spreadsheet model that incorporates the formulas that make calculation of G/T a bit tedious.

In this case, the configuration is a very simple one. It comprises a IC-9100 transceiver with LMR-400 feed line to a single Yagi with 14dBi gain. External noise is entered as SkyNoise, and it is taken to be 1200K, a fairly quiet location for terrestrial operations on 144MHz.

The calculated G/T is -19.5dB/K, just 2.7dB shy of the ultimate G/T achievable for the given antenna gain and external noise with a lossless / noiseless receiver system.

Now everybody knows that better feed line makes a difference.

Above is the model changed to include LDF4-50 for most of the run, and some sections of LMR-400 and LMR-400UF around the rotator and to the feed point.

This has improved things, G/T is now -19.2dB/K. 0.3dB better so S/N on weak signals will also be 0.3dB better. But note that although feed line loss was reduced by 0.5dB, S/N has improved by only 0.3dB.

Looking at the contribution to percentage of total noise, the IC-9100 contributes 38.4% so it is an obvious target for improvement. Lets put a LNA with Gain=25dB and NF=0.8dB right next to the IC-9100.

Now that has made a difference, a small difference in absolute terms but a relatively large difference in terms of the 2.4dB shortfall in the previous configuration, we have reduced the shortfall to 0.5dB and improved S/N by 1.9dB. That might seem a small achievement for a 25dB gain, 0.8dB NF LNA… but that is the way it works.

So, in pursuit of further improvement, total feed line noise contribution is 5.5% and a target for improvement.

Lets relocate the LNA between the main rotator loop and antenna tail.

Now we have improved G/T a further 0.2dB.

Although the experts would tell you that a masthead LNA is better than a local LNA, and it is, you might question the disadvantages of masthead location against the improvement of just 0.2dB in G/T or S/N in this scenario.

But. let’s be obsessive. The largest remaining internal noise contribution is the LNA, let’s replace it with a 0.4dB NF and 18dB gain.

Hmmm, that is 0.1dB better G/T although some might view that the new LNA is ‘twice as good’ by specification. The issue now is that the 1.1% contribution of noise on the receiver side of the LNA is now a relatively large part of internal noise, and it can be reduced with more LNA gain… so let’s try a two stage LNA with 0.4dB NF and 33dB gain.

Aha, we are within 0.1dB of ultimate for this antenna and external noise, we have won 0.1dB G/T or S/N improvement.

This might seem outstanding, it is obsessive, and it is probably a bit dumb as several steps back, we should have considered a better antenna.

The models explored above are specific to the scenario modelled, it is unsafe to try to draw generalised conclusions from those results.

The models also assume linear systems, systems where IMD effects are insignificant. If you have significant IMD effects, fixing those would usually be the most productive first step.

The outcomes for EME scenarios will be different to terrestrial scenarios, different from band to band, different for changed feed line configurations, available components etc.

- Duffy, O. 2001. RF Transmission Line Loss Calculator (TLLC). VK1OD.net (offline).
- ———. 2006. Receiver sensitivity metric converter. VK1OD.net (offline).
- ———. 2006b. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net (offline).

Designing high performance VHF/UHF receive systems – Part 6

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We have explained how to calculate Teq from Noise Figure, but most transceiver specifications do not give Teq or Noise Figure directly, in fact they don’t really contain sufficient information to reliably calculate Teq or Noise Figure.

Credible equipment reviews might provide an estimate of Noise Figure or Teq.

The best approach is to directly measure Noise Figure using a known noise generator and the Y Factor Method.

Transceiver specifications usually state receiver sensitivity in the form of some input signal voltage for a given S/N ratio, and that is at some stated receiver bandwidth setting. This might seem at first to provide enough information to calculate Noise Figure, but the problem is that the selectivity specification typically specifies a bandwidth at -6dB response, but they typically do not give the bandwidth of an equivalent rectangular filter that admits the same noise power, the Equivalent Noise Bandwidth (ENB) which is the quantity needed to relate sensitivity specification and Noise Figure.

(Duffy 2009), (Duffy 2009b), (Duffy 2009c) describe a method of measuring and calculating ENB but it is beyond the scope of this discussion. Suffice to say the method is indirect, it uses a sensitivity measurement and for very low noise receivers, calculated NF is very sensitive to small errors in measured sensitivity.

A rough estimate of Noise Figure can be had by assuming ENB=2kHz for a SSB telephony receiver, with an uncertainty of about 1.5dB.

If for example SSB sensitivity was specified as 0.11µV for 10dB S/N, that is equivalent to -126.2dBm for 10dB S/N, and that implies that the total noise power (from source and receiver) is -126.2-10=-136.2dBm. Now if we assume that the ENB=2kHz, the noise power from the generator can be calculated as -174+10*log(2000)=-141dBm. The Noise Figure is given by the increase in total noise over that of the source alone, so NF=-136.2–141.0=4.8dB. Teq can then be calculated as 586K.

(Wilson 2012) gives Noise Figure for the popular IC-9100 transceiver with optional 3kHz roofing filter as 4, 3 and 2dB on 144, 432 and 1296MHz. Unfortunately, the ARRL method is indirect, calculated from a sensitivity measurement and for very low noise receivers, calculated NF is unduly sensitive to small errors in measured sensitivity (Duffy 2014), they report sensitivity (MDS) to precision of 1dB, and in any event the measured configuration is not the basic configuration.

For the purposes of the studies in this series, sensitivity of the IC-9100 will be taken as 0.11µV for 10dB S/N, and ENB=2kHz, giving NF=4.8dB, Teq=586K.

- Allison, B; Tracy, , M; Gruber, M. 2011. Test Procedures Manual Rev L. ARRL Newington.
- Duffy, O. 2006. Receiver sensitivity metric converter. VK1OD.net (offline).
- ———. 2009. Measuring receiver bandwidth. VK1OD.net (offline).
- ———. 2009b. Noise Figure Y factor method calculator. VK1OD.net (offline).
- ———. 2009c. Noise Figure Meter. VK1OD.net (offline).
- ———. 2014. ARRL Test Procedures Manual (Rev L) – Noise Figure calculation. https://owenduffy.net/blog/?p=945 (accessed 23/02/14).
- Wilson, M. 2012 ICOM IC-9100

MF/HF/VHF/UHF Transceiver In QST Apr 2012.

Designing high performance VHF/UHF receive systems – Part 5

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In the last part, the meaning of the equivalent noise temperature of an amplifier was given.

Whilst you will find that working in Teq has advantages for this analysis, amplifier specifications may not give Teq, but may give Noise Figure.

Teq can be calculated from Noise figure.

**Teq=(10^(NF/10)-1)*290 K** where:

NF is Noise Figure in dB

Be rearranging the terms, NF can be calculated from Teq.

**NF=10*log(1+Teq/290)**

Note that since Teq implies a Noise Power Density (W/Hz) of noise, Teq from two sources can simply be added (whereas Noise Figures cannot).

The Noise Figure of an attenuator is simply equal to it attenuation in dB (proof left as an exercise for the reader).

If two amplifiers of known PowerGain (PowerOut/PowerIn) and Teq are cascaded, a simple single stage equivalent can be calculated.

The PowerGain of the cascade is simply the PowerGain of stage 1 multiplied by the PowerGain of stage 2.

**PowerGain=PowerGain1*PowerGain2**

The second stage can be replaced by a noiseless second stage by referring its Teq to the input of the first stage by dividing it by the PowerGain of the first stage.

**Teq=Teq1+Teq2/PowerGain1**

You will see some pretty complicated formulas for multiple stages, but remember that any pair of adjacent stages can be converted to a single equivalent… and taking hamburger size bites lets you eat the elephant.

Remember that the PowerGain of an attenuator or any purely passive network or device (like a transmission line) is less than 1, a 3dB attenuator has a PowerGain of 0.5.

A simple cascade could be a feed line and a receiver.

Lets work a simple example. What is Teq of a feed line with 1dB of loss followed by a receiver with NF=6dB.

First step, convert the receiver NF to Teq2. Teq2=865K

Now calculate the PowerGain of the feed line. PowerGain1=10^(-1/10)=0.794.

Now calculate NF of the feed line as 1dB (equal to its attenuation in dB), and Teq1 as 75.1K.

Calculate Teq as Teq1+Teq2/PowerGain1=75.1+865/0.794=1165K.

More complex networks are analysed by applying these simple rules consistently and reducing the multi stage networks to a single stage equivalent.

- Terman 1955. Electronic and Radio Engineering: McGraw-Hill New York.

Designing high performance VHF/UHF receive systems – Part 4

More installments to come…

]]>For clarity, lets define those terms.

Gain of an antenna is defined (IEEE 1983) as the ratio of the radiation intensity, in a given direction, to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. (Isotropically simply means equally in all directions.)

Gain is often expressed in deciBels as 10*log(gain), and units are dB (or dBi to distinguish it from other references).

If you are a devotee of gain with reference to a half wave dipole in free space (dBd) for whatever reason, add 2.14 to dBd to get gain in dB (dBi). (Thinking in dBd is a handicap, don’t forget to adjust any dBb figures to gain as defined above.)

In addition to external noise, each component of a receiver generates internal noise.

It is convenient to think of a practical amplifier as being noiseless with an input noise source that produces output noise equivalent to that of the practical amplifier.

One of the many methods of expressing that noise source is as a noiseless amplifier with matched input source (Zs=Zin*) where Rs is raised to some temperature to create the same output noise power as the practical amplifier. This temperature is absolute temperature in Kelvins and referred to as the equivalent noise temperature, or Te.

Noise in cascaded amplifiers (and attenuators) can be referred to the input of the previous stage, and hence an equivalent noise temperature can be found for cascaded stages right up to entire systems.

The “total equivalent noise temperature” used for G/T includes not just internal noise, but also the external noise.

It is convenient in some cases to divide external noise into two components, noise received by the antenna ‘on axis’ (skynoise), and noise from sidelobes (spillover or sidelobe noise). In some situations (eg antenna pointed skywards) the background noise field strength might be quite low and antenna gain high, and sidelobe noise may be quite high field strength and low antenna gain, so for example the combined noise might be calculated as 100% of the on-axis noise and 20% of the off-axis noise (that portion calculated from antenna pattern).

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net (offline).
- ———. 2006. Receiver sensitivity metric converter. VK1OD.net (offline).
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net (offline).
- IEEE 1983. IEEE Standard Definitions of Terms for Antennas (IEEE Std 145-1983).
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000) Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

Designing high performance VHF/UHF receive systems – Part 3

More installments to come…

]]>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=50/120=0.416 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).

**S/N=S*λ ^{2}/(4*π)*G/T/(k_{b}*B)** where:

S is power flux density;

λ is wavelength;

k

B is receiver quivalent noise bandwidth

Calculating G/T for configuration alternatives gives a single performance metric that allows comparison of the performance of the configurations. Different levels of performance might be weighed against cost in a cost benefit analysis, eg whether funds applied to antenna improvements will be more cost-effective than applying funds to feed line improvement, whether an LNA with NF=0.8dB and Gain=30dB is more cost-effective than one with NF=0.5dB and Gain=18dB.

Such a quantitative approach cuts through the old wives tales about the relative merit of some approaches, and will quantify the relative performance in the system context. Some options will have different effects depending on other system details, and Rules of Thumb (ROT) that ignore this sensitivity to the rest of the system becomes simply rot.

Inclusion of gain in the metric allows quantitative comparison of configuration changes that include a change in antenna gain.

A key limitation of simple system models is that they assume the system is linear, in particular that there is no significant IMD noise created by system components. Systems with significant IMD are basically unpredictable, and whilst the performance of a particular system can be measured, that does not provide knowledge that is extensible to another system because the environment, and response to the environment are probably different. The bottom line is that components with significant IMD noise don’t belong in a high performance system, fix them or get rid of them.

Note that the popular ham antenna tables published by VE7BQH which show a calculated quantity labelled G/T value for antenna systems appears to ignore receiver equivalent noise (ie it is for a noiseless receiver), and as such, the usage is not consistent with the industry meaning of the term (eg ITU-R. 2000). Don’t confuse this discussion of G/T with those tables.

G/T is calculated with respect to some nominated reference plane. The most common practice is to use the antenna waveguide flange or connector as the reference plane, and to consistently calculate system component contributions relative to that reference plane. In the case of an array of four Yagi antennas, the reference plane would be the connector on the power divider/combiner that provides single connector access to the antenna system.

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net (offline).
- ———. 2006. Receiver sensitivity metric converter. VK1OD.net (offline).
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net (offline).ITU-R. 2000. Recommendation ITU-R S.733-2 (2000) Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

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