Over the past couple of years I’ve had a number of comments and questions about active antennas, instigated by my ARRL book, Receiving Antennas for the Radio Amateur.

The “main ingredient” of an active antenna (in this discussion, we’ll center on the very short WHIP), is the preamplifier, which generally takes the form of an FET source follower.

A true source follower (or ideal cathode follower) is theoretically capable of INFINITE power gain). In practice, modern FET input op-amps have an input resistance on the order of a teraohm or so, and an input capacitance of about a picofarad.

Although we can’t QUITE get to infinite power gain with a real FET (or FET input op amp), we can get EXTREMELY high power gains. Assuming an output (source) resistance of 1Kohm and an input resistance of 1 teraohm, a voltage follower will have a power gain of 10^21:1…..not too shabby. (This is assuming essentially a DC signal, where the input parallel capacitance can be ignored).

At this point in time, there has been no mention of noise… but it is key to the problem.

Let’s consider the case of a low noise preamplifier (assume Noise Figure 1dB) used ahead of a receiver with Noise Figure 6dB. We can calculate the system Noise Figure, ie the cascade of the two elements, vs preamplifier gain.

It is easier to solve this problem by working in equivalent Noise Temperatures, \(T_s=T_1+T_2/G_1\). So converting the two Noise Figures to Noise Temperatures, we can calculate system Noise Temperature vs preamplifier Gain and plot it.

Above is a plot of system Noise Temperature vs preamplifier Gain, also shown on the right hand axis is the system Noise Figure.

For this scenario, there is a significant improvement in Ts and NFs as Gain increases… up to about 20dB, after which further increase in Gain makes very little difference.

Above, zooming in on the results, the behavior is very clear. Note that it is dependent on the scenario, and the plot will be different for different scenarios.

We do not need to consider the antenna gain to find this point of diminishing returns of Ts and NFs vs preamplifier gain, and to show that for this scenario, a Gain of 20dB or 100 is sufficient to have achieved most of the benefit of a preamplifier with NF=1dB.

The bigger question is whether that system Noise Figure or Noise Temperature is ‘sufficient’ for a specific application.

Again, it is easier to work in equivalent Noise Temperature.

Consider a scenario of an antenna system, with gain -30dB (or 1/1000) at 3.5MHz. ITU P.372 suggests the expected external or ambient noise is 47350000K, and with an antenna system gain of 1/1000, the noise power presented to the preamplifier is \({T_e}^{\prime}=\frac{47350000}{1000}=47350 \text{ K}\).

A useful metric in system design is the extent to which the external S/N is degraded by the receiver system, I will call it Signal to Noise Degradation (SND).

\(SND=10 log\frac{\frac{S_{ext}}{N_{ext}}}{\frac{S_{ext}}{N_{int}+N_{ext}}}\)Simplifying this by dividing top and bottom by \(S_{ext}\) we get

\(SND=10 log\frac{N_{int}+N_{ext}}{N_{ext}}\).

So, SND gives us a metric that simply depends on the external noise and the receiver internal noise, a quantitative measure of the system in an application context.

Let’s take the system Noise Temperature with the above scenario and 20dB of preamplifier gain to be 84K, we can calculate SND due to receiver system internal noise to be \(SND=10 log\frac{N_{int}+N_{ext}}{N_{ext}}=10 log\frac{84+47350}{47350}=0.08 \text{dB}\).

So, in this scenario, the receive system equivalent noise temperature is so low that there is only a 0.08dB degradation in the off-air S/N ratio.

You might see that a system Noise Temperature of 5000K (NFs=12dB) is not going to degrade S/N much (<0.5dB).

But here is the problem…

The methods presented here apply to linear systems, they do not capture the effects of non-linear behavior such as IMD noise.

It is easy to build a preamplifier with high gain, harder to build one with low noise, and even harder to build a broadband one with very load IMD noise.

This article explains with graphs the relationship between Signal / Noise degradation (see Signal to noise degradation (SND) concept) and LNA gain in the configurations discussed in the original article. See The oft asked question of how much an LNA improves a 70cm weak signal station for documentation of the scenario assumptions.

The critical value for SND is a personal choice, but for the purpose of this discussion, let’s choose 1dB. That is to say that the S/N at the receiver output is less than 1dB lower than the ultimate that could achieved with the antenna system given the external noise environment.

The total line loss in the example configurations was 2.6dB. The model assumes that LNA Noise Figure is independent of LNA Gain, though in the real world, there is typically some small dependence.

Often the choice of LNA Gain drives the choice of a single stage or two stage LNA, which has cost implications.

Above is a chart showing SND vs LNA Gain. It can be seen that as LNA gain is increased, SND improves rapidly with a knee around 15dB LNA gain above which SND improvement is slower.

For SND lower than 1dB, one would choose LNA gain of more than 12dB for this scenario.

Above is a chart showing SND vs LNA Gain. It can be seen that as LNA gain is increased, SND improves rapidly with a knee around 20dB LNA gain above which SND improvement is slower.

For SND lower than 1dB, one would choose LNA gain of more than 18dB for this scenario.

Above is a chart showing SND vs LNA Gain. It can be seen that as LNA gain is increased, SND improves rapidly with a knee around 5dB LNA gain above which SND improvement is slower.

For SND lower than 1dB, one would choose LNA gain of more than 2dB for this scenario.

The bigger question for this scenario is whether there is worthwhile benefit in using an LNA at all. If very low LNA Gain is sufficient, no LNA is probably nearly as good… it is just not needed and likely to have significant downsides with negligible benefit.

Even for this simple practical scenario where all else is held constant, the SND response to changing LNA Gain depends on the external noise level, and the response is not a simple linear one, but one with a distinct knee.

It is not safe to simply use as much gain as possible / available as high gain amplifiers are more prone to IMD, and more likely to overload the following receiver creating IMD.

Excessive gain is not a safe solution.

In high noise environments it takes little effort to achieve low SND, in fact an LNA is probably not warranted.

At the other extreme, the very external low noise level of a satellite path means that a suitable LNA is vital to low SND, and it probably needs high gain to achieve low SND, even for an LNA with very very low Noise Figure.

It is complicated, and it is a multi-dimensional problem… and that is where the G/T spreadsheet may assist.

Rules of Thumb may not be reliable.

Be wary of over simplified rules, this is a complicated problem for linear systems, then candidate solutions need to be tested carefully to see whether they are unduly affected by IMD etc.

Since the kind of improvements made to achieve a high performance weak signal receive system tend to be expensive, a little time to make measurements and on desk studies to understand the problem and design a solution may be a good investment.

]]>This article focusses on just one question in a quite similar configuration, what is the advantage given by the LNA?

The scenario will be evaluated for both terrestrial and satellite paths.

Above is the assumed ambient noise environment, it has great bearing on the results. More on that later.

The system G/T statistic has been used to quantify comprehensively the performance of a receive station over many decades. It has widest application in weak signal / low noise receive systems, eg satellite paths. G/T is the ratio of system antenna gain to equivalent noise temperature, most often given in dB as dB 1/K or simply dB/K.

The article Effective use of a Low Noise Amplifier on VHF/UHF gives some insight into G/T and its application.

Let’s use my G/T spreadsheet to model the scenario.

Assumptions:

- feed line types and lengths as listed in the spreadsheet;
- ambient noise as given in table above;
- LNA option is a MVV-432-VOX;
- system is linear, ie no non-linearity, zero IMD.

Two key metrics are calculated in the spreadsheet, G/T and Signal to Noise Degradation (SND).

- G/T can be used to calculate the S/N ratio given a receive field strength; and
- SND is the degradation of the external S/N ratio by system internal noise (see Signal to noise degradation (SND) concept).

Either metric can be used to calculate the S/N improvement due to adding the LNA.

S/N is a measurable quantity, and an S-meter does not give S/N with any accuracy. Higher S-meter deflection is not synonymous with higher S/N ratio.

The following assumes an equivalent external noise temperature that is of the order of what might be expected to illustrate the analysis technique, but measured values should be used for a specific scenario.

Above is the baseline terrestrial model with provision for the LNA, but without it.

A perfect receive system would have SND=0dB, so at 6.67dB, this degrades ‘off-air’ S/N substantially.

Above is the terrestrial model with LNA.

A perfect receive system would have SND=0dB, so at 0.73dB, this degrades ‘off-air’ S/N by a quite small amount, and some 6dB improvement over the baseline terrestrial model with no LNA.

The following assumes an equivalent external noise temperature that is of the order of what might be expected to illustrate the analysis technique, but measured values should be used for a specific scenario.

Above is the baseline satellite model with provision for the LNA, but without it.

A perfect receive system would have SND=0dB, so at 16.64dB, this degrades ‘off-air’ S/N hugely.

Above is the satellite model with LNA.

A perfect receive system would have SND=0dB, so at 5.14dB, this degrades ‘off-air’ S/N substantially, but 12dB improvement over the baseline satellite model with no LNA.

The results above depend on an assumption that the system is linear, in particular this means insignificant IMD.

Note that many ham LNA designs and products lack front end selectivity which predisposes them to worse IMD due to the higher aggregate signal levels reaching the active device.

High gain antenna systems tend to be frequency selective and provide some measure of front end selectivity. It is worth evaluating S/N ratio with a low value precision attenuator inserted before the LNA, if S/N improves there is significant IMD… and addressing that improves internal noise.

As mentioned, external noise is scenario dependent, antenna pattern dependent, antenna azimuth and elevation dependent, and should be evaluated (see link below).

The model has many variables, and more system components could be added if needed. Any of these can be varied to answer questions like:

- what is the impact of less LNA gain;
- is optimal gain just sufficient to offset the coax loss;
- is a NF=0.8dB Gain=10dB LNA better;
- should I choose an LNA with more gain, or lower noise figure;
- what is the benefit of LDF4-50A feed line;

etc.

Whilst discussions on social media about with opinions and hand waving, it is quantitative analysis of your own scenario that gives the most valid answers.

]]>

For those who may have used or want to use my G/T spreadsheet tool I have released an improved version 1.12. This is not a bug fix.

An updated version of the spreadsheet GT.xlsm is at https://github.com/owenduffy/xl.

If Microsoft has frightened you off using spreadsheets with macros, you could use this with macros disabled, it just stops the green sort button working, all the cells still calculate properly.

]]>For this discussion, I will use the amplifier developed at A high performance active antenna for the high frequency band, but applied to the antenna described at Ambient noise measurement using whip on vehicle – #1 – estimate Antenna Factor.

Let’s assume that the antenna + amplifier will be used with a HF receiver with Noise Figure 6dB, Teq=864.5K.

From (Martinsen 2018) Fig 3.8, the amplifier internal noise at the output terminals is -118dBm in 100kHz @ 3.5MHz. That implies that the amplifier Noise Temperature is 857.93K. The amplifier has 6.4dB voltage gain which needs to be subtracted from the AF calculated for unity gain (at the amplifier input terminals).

Amplifier characteristics:

- Voltage gain 6.4dB;
- AF=6.05-6.4=-0.35dB/m;
- input Z=1MΩ||15pF;

From (Martinsen 2018) Fig 3.8, the amplifier internal noise at the output terminals is -118dBm in 100kHz @ 3.5MHz. The equivalent noise temperature is 857.9K.

The amplifier output terminals will be used as the reference plane for the following calculations.

Total internal noise (amplifier and receiver) \(T’=857.9+864.5=1722 \text{ K}\).

Using Field strength / receive power converter for measurements made in a 1kHz wide ENB,

we obtain:

The Ambient Noise Figure Fa is 57.5dB, similar to that predicted for a Residential precinct in ITU P.372-14.

It may be tempting to assume a simple linear relationship between the measure power and ambient noise figure.

In most cases, the measured power includes internal noise of the receive system (both active antenna and the receiver), and when external noise dominates, the relationship is close to linear.

Above is a plot of Fa vs measured (total) power for this (exact) scenario. In this case, Fa=Pt+174 is a good estimator for Pt>-145dBm or Fa>29dB. You would not expect to measure such low Fa in this scenario (frequency and equipment), but that may not be true of other scenarios… you need to check.

Field strength / receive power converter properly accounts for internal noise.

- Martinsen, W. Aug 2018. A high performance active antenna for the high frequency band. Cyber and Electronic Warfare Division

Defence Science and Technology Group DST-Group-TR-3522.

Ambient noise is commonly dominated by man made noise, and it often arrives equally from all directions. For measurement of such noise, the captured power depends on average antenna gain, and so the calculations below focus on gain averaged over the hemisphere.

Antenna Factor is often very convenient for field strength measurement as it relates the external E field strength to the receiver terminal voltage given a certain antenna (system). In fact, given a short vertical terminated by a high impedance amplifier, Antenna Factor is often fairly independent of frequency over several octaves of frequency.

Whilst it is easy to come up with Rules of Thumb or simple approximations for a short monopole over perfect earth conductor (PEC) either matched for maximum power transfer, or essentially unloaded, the case of a short vertical on the roof of a motor vehicle suspended above natural ground is not so easy.

Some underlying assumptions:

- a vertically polarised antenna will be most sensitive to ground wave noise on the lower HF bands (as horizontally polarised ground waves are more quickly attenuated with distance);
- the system uses an active antenna, the amplifier having a high input impedance and unity voltage gain; and
- reciprocity can be used to infer certain receive performance from transmit performance.

So, the approach is to:

- calculate the power captured by a lossless isotropic antenna, and the Thevenin source voltage for a given E field (1V/m);
- use an NEC model to find the (matched) average gain of the antenna system (so accounting for ground losses etc), source impedance, and radiation resistance (which is used as the Thevenin source impedance); and
- calculate the loaded voltage at the amplifier input terminals, and Antenna Factor at the amplifier input terminals.

An NEC-5.0 model was created for a 1.215m (4′) vertical mounted on the roof of a motor vehicle at 3.5MHz. The model was derived from a sample model supplied with NEC-5, the vertical was lengthened and moved to mid roof, and the unused antennas deleted. The model was changed to introduced real ground (σ=0.005, εr=13).

Above is a 3D pattern plot, the pattern is an almost omnidirectional donut.

Above is an elevation profile.

Above is the azmuth plot at θ=-70° (elevation 30°).

Some key values are extracted from the NEC output report.

The calculated equivalent series source capacitance Cs is given for interest sake, it is not used directly here, but is often estimated for so-called E-field probe antennas.

Thevenin source voltage of a lossless isotropic antenna is found by calculating the available power to be captured by a matched antenna given the excitation scenario (E=1V/m). The available power is given by the product of the effective aperture Ae and the power flux density S (for E=1V/m). Ae is calculated from average gain (unity for a lossless isotropic antenna) and frequency.

Having calculated available power, we can calculate the voltage in a matched load, and the Thevenin source voltage Vth is twice that.

The Thevenin source impedance is radiation resistance Rr calculated earlier from the NEC output.

We are interested in the Antenna Factor when the antenna is loaded by the high impedance amplifier. The amplifier is approximated as some resistance Rp in shunt with some capacitance Cp.

Antenna Factor is given by \(AF=20 log \frac{E}{V_{in}} \text{ dB}\) where E is the electric field strength and Vin is the amplifier input terminal voltage.

AF is quite sensitive to Cp, efforts need to be made in circuit configuration, device selection, and circuit layout to minimise Cp and achieve optimal AF.

The above discussion is based on a unity gain amplifier, if otherwise, the gain in dB should be subtracted from the calculated AF to get AF wrt the amplifier output terminals (ie, the input terminals to the following receiver).

]]>Above is an archived extract of a spreadsheet that was very popular in the ham community, both with antenna designers and sellers and end users (buyers / constructors). It shows a column entitled G/T which is actually the hammy calculation. The meaning possibly derives from (Bertelsmeier 1987), he used G/Ta.

Ta is commonly interpreted by hams to be Temperature – antenna. It is true that antennas have an intrinsic equivalent noise temperature, it relates to their loss and physical temperature and is typically a very small number. But as Bertelsmeier uses it, it is Temperature – ambient (or external), and that is how it is used in this article.

Let’s calculate the G/Ta statistic for the three scenarios in Do I ‘need’ a masthead preamp to work satellites on 2m? – space noise scenario.

Above is a calculation of the base scenario, G/T=-29.74dB/K.

Also shown in this screenshot is G/Ta=-23.98dB/K.

Above is a calculation of the masthead amplifier scenario, G/T=-25.21dB/K.

Also shown in this screenshot is G/Ta=-23.98dB/K.

Above is a calculation of the LNA at the receiver scenario, G/T=-25.754dB/K.

Also shown in this screenshot is G/Ta=-23.98dB/K.

Scenario | G/T (dB/K) | G/Ta (dB/K) |

Base | -29.74 | -23.98 |

With masthead LNA Gain=20dB NF=1dB | -25.21 | -23.98 |

With local LNA Gain=20dB NF=1dB | -25.75 | -23.98 |

Note that G/Ta is the same for all three configurations, it does not contain the important information that differentiates the performance of the three configurations.

Importantly, you cannot derive G/T from G/Ta without knowing either G or Ta (and some other important stuff), the G/Ta figure by itself cannot be ‘unwound’… so if you select an antenna ranked on a G/Ta value (even if mislabeled), the ranking of ‘real’ G/T may be different depending on many factors specific to your own scenario, ie the one with the better G/Ta might have the poorer G/T.

- Bertelsmeier, R. 1987. Equivalent noise temperatures of 4-Yagi-arrays for 432MHz. DUBUS..
- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net.
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net.
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- 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 .

Base scenario is a low end satellite ground station:

- 144MHz;
- terrestrial noise (satellite with omni antenna);
- IC-9700, assume NF=4.8dB;
- omni antenna;
- 10m of LMR-400.

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.

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net.
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net.
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- 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 .

Base scenario is a low end satellite ground station:

- 144MHz;
- satellite;
- IC-9700, assume NF=4.8dB;
- high gain (narrow beamwidth antenna);
- 10m of LMR-400.

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.

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net.
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net.
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- 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 .

In fact what is commonly measured is Signal + Noise to Noise ratio, and of course this ratio is one of powers. For this reason, specifications often give (S+N)/N.

This article discusses those metrics in the context of ‘conventional’ receivers and introduces the key role of assumed bandwidth through the concept of Equivalent Noise Bandwidth..

Let’s consider the raw S/N ratio of an ideal AM detector and ideal SSB detector.

Above is a diagram of the various vector components of an AM signal with random noise, shown at the ‘instant’ of a modulation ‘valley’. The black vector represents the carrier (1V), the two blue vectors are counter rotating vectors of each of the sideband components, in this case with modulation depth 30%, and the red vector is 0.095V of random noise rotating on the end of the carrier + sideband components.

In an ideal detector, the recovered modulation is proportional to the sum of the sideband vectors, amplitude here is 0.3V, and the noise is proportional to the noise vector 0.095V.

We can calculate the S/N ratio as \(\frac{S}{N}=20 log \frac{0.3}{0.095}=10 \;dB\). You can see now why the noise voltage of 0.095V was chosen.

We can calculate the (S+N)/N ratio as \(\frac{S+N}{N}=10 log \frac{0.3^2+0.095^2}{0.095^2}=10.4 \;dB\).

AM is commonly demodulated in an envelope detector, and their departure from ideal linearity is significant.

Above is a diagram of the same ‘signal’ and the same noise as presented to an SSB detector.

The black vector represents the carrier (1V) and the red vector is 0.095V of random noise rotating on the end of the signal component.

In an ideal detector, the recovered modulation is proportional to the signal vectors, 1.0V, and the noise is proportional to the noise vector 0.095V.

We can calculate the S/N ratio as \(\frac{S}{N}=20 log \frac{1}{0.095}=20.45 \;dB\).

We can calculate the (S+N)/N ratio as \(\frac{S+N}{N}=10 log \frac{1^2+0.095^2}{0.095^2}=20.48 \;dB\).

SSB detectors are not perfect either, but circuits that are principally mixers are typically closer to ideal than AM envelope detectors on AM. Envelope detectors used with a BFO for SSB depend on incidental mixing and are quite unpredictable.

On the basis of the above, we would expect the sensitivity figure for SSB at 10dB (S+N)/N to be 10.5dB lower (or about one third) that for the AM detector.

Yet specifications for real receivers tend to give differences more in the range of 15-20dB. Why?

Commonly, the IF bandwidth for SSB is considerably less than for AM. For communications quality we might expect 3dB less, for AM broadcast quality vs communications quality SSB, we might expect more like 6dB.

In a receiver where the noise power is dominated by the front end, the amount of noise power presented to an SSB detector from a 2.5kHz IF filter is substantially less than presented to an AM detector from a 10kHz IF filter, 6dB in this case, leading to an expectation that SSB sensitivity will be 16.5dB better than AM.

Detector non-linearity might cause a different difference.

If we know the sensitivity specification and Equivalent Noise Bandwidth we can calculate the receiver Noise Figure.

The problem is that receiver specifications tend to not give the Equivalent Noise Bandwidth, rather they may give the bandwidth between nominated points like -6dB, -60dB etc and that does not imply Equivalent Noise Bandwidth.

The difference in stated sensitivity for conventional communications receivers between AM and SSB modes is due to two main contributions:

- the fact that it is the amplitude of the AM sidebands that determine the S part of S/N rather than that of the carrier which is the stated sensitivity figure; and
- the Equivalent Noise Bandwidth applied to each mode by the receiver.