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.

Let’s work an example using Simsmith to do some of the calculations.

Scenario:

- 20m ground mounted vertical base fed against a 2.4m driven earth electrode @ 0.5MHz;
- 10m RG58A/U coax; and
- Receiver with 500+j0Ω ohms input impedance and Noise Figure 20dB.

An NEC-4.2 model of the antenna gives a feed point impedance of 146-j4714Ω and radiation efficiency of 0.043%, so radiation resistance \(Rr=146 \cdot 0.00043=0.0063\).

Above, the NEC antenna model summary.

Above is a Simsmith model of the system scenario.

R1 and G model the antenna, G uses Rr for Zo, and R1 contains the balance of the feed point impedance.

With the useZo source type, the source would deliver 1W or 0dBW to a conjugate matched load.

The next important figure is the power into the 500Ω load L. it is -58.3dBW. Simsmith has calculated the solution to the antenna loss elements, mismatches and coax loss under standing waves. Effectively, the average gain of the antenna system (everything to the right of L) is -58.3dB. Such an antenna is likely to have a Directivity of around 4dB, in fact the NEC model calculates 4.8dB. So the maximum gain is -58+4.8=-53.2dB.

The burning question is whether it is sufficiently good to hear most signals. Well, a better question is how much does it degrade off-air signal to noise ratio (S/N). All receivers degrade S/N, but how much degradation occurs in this scenario.

We need to think about the ambient noise. Lets use ITU-R P.372 for guidance on the expected median noise in a rural precint.

Above, ambient noise figure @ 0.5MHz is 75.54dB.

Now lets calculate the Signal to Noise Degradation (SND).

At 4.58 dB it is not wonderful, the weakest signals (ie those with low S/N) we be degraded significantly, stronger signals (those with high S/N) will be degraded by the SAME amount, but for instance reducing S/N from 20 to 15dB is not so significant.

Applying this to your own scenario

The information fed into the calculations included:

- Rr;
- feed point impedance;
- transmission line details;
- Rx input impedance and NF; and
- Ambient noise expectation.

To calculate your own scenario, you need to find these quantities with some accuracy.

Tools:

]]>- 1m active monopole;
- RTL-2832U v3 SDR dongle;
- RPi 3B+ running Spyserver; and
- SdrSharp client.

Above is the active whip antenna. Not optimal mounting, but as you can see from the clamps, a temporary mount but one that does not confuse results with feed line common mode contribution.

Above is the remote electronics, the RPi 3B+ and RDL SDR dongle, and underneath the power supply for the active monopole.

The initial trial was on 7MHz, and was a total failure due to extreme level of RFI from the RPi itself. The two RPi power supplies tested were noise tested on a dummy load and were OK, the noise comes from the digital signals on the RPi board. A Kenwood R-5000 receiver was connected to the active antenna, and noise floor was relatively low until the RPi was plugged in.

Above is the SdrSharp screen, extreme noise level and no signals could be heard (though a local transmitter on low power verified that the receiver was working).

The emissions from the RPi, were so high that it is really unsuitable for this purpose, it would be very difficult to reduce emissions by the needed more than 40dB.

]]>A first observation of listening to a SSB telephony signal is an excessive low frequency rumble from the speaker indicative of a baseband response to quite low frequencies, much lower than needed or desirable for SSB telephony.

The most common application of such a filter is reception of A1 Morse code.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is hardly an idealised rectangular filter response. Though the response might be well suited to Morse code reception, it is an issue when measurements make assumptions about the ENB. The response is not well suited to narrowband data such as RTTY etc.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 460-770Hz=310Hz.

ENB=224Hz with respect to gain at 610Hz (passband centre frequency).

ENB=222Hz with respect to gain at 590Hz (max gain frequency).

ENB=222Hz with respect to gain at 600Hz.

If we take the gain reference frequency to be 600Hz, there is 3.5dB less noise admitted by this filter than an idealised rectangular filter. Measurements such as the ARRL MDS that might assume 500Hz bandwidth will have 3.5dB error.

A 1000Hz filter might be well suited to narrow band data reception, many of the so-called ham digital modes.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is fairly close to an idealised rectangular filter response.

There appears to be no means to offset the filter at baseband frequency.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 110-950Hz=840Hz.

ENB=823Hz with respect to gain at 530Hz (passband centre frequency).

ENB=716Hz with respect to gain at 200Hz (max gain frequency).

ENB=800Hz with respect to gain at 500Hz.

If we take the gain reference frequency to be 500Hz, there is 0.97dB less noise admitted by this filter than an idealised rectangular filter.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is fairly close to an idealised rectangular filter response.

There appears to be no means to offset the filter at baseband frequency.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 110-2350Hz=2240Hz.

ENB=2353Hz with respect to gain at 1230Hz (passband centre frequency).

ENB=1829Hz with respect to gain at 210Hz (max gain frequency).

ENB=2255Hz with respect to gain at 1000Hz.

If we take the gain reference frequency to be 1000Hz, there is 0.27dB less noise admitted by this filter than an idealised rectangular filter.

SDR# does not appear to have a convenient facility to shift or offset the baseband response.

Above is the baseband response in 2400Hz USB mode as show in the SDR# window. Note that the response rolls off below 100Hz, whereas good conventional SSB Telephony receivers would have a 6dB response from say 250-2750Hz for a ENB of 2400Hz. The lower -6dB point for this response is 110Hz.

This leads to substantial low frequency component that is not a priority for SSB telephony, and in the case where the transmitter is band limited to 300-2700Hz, the filter admits unnecessary noise and the low end and cuts of a little of the high end. It is a hammy sammy approach where recognised speech characteristics, conventions and compatibility between transmitter and receiver are jettisoned.

The basic 1000Hz USB filter provides a response close to ideal, centred around 530Hz, and its ENB is 800Hz (-0.07dB on 1000Hz).

There appears no facility in SDR# to save a number of filter settings for later recall, so the process of configuring SDR# for measurement is a bit tedious.

My attention has been draw to the facility to drag the upper and lower limits of the IF passband, thanks Martin.

Above is an example where a 500Hz passband is centred on 1500Hz at baseband.

As soon as another mode is selected, the setting is lost and there appears no facility to save a set of settings for later recall. Note the inconsistency between the two displayed bandwidth figures.

Yes, it works but it is not convenient and not practical for save / recall of a standardised set of measurement or reception conditions.

]]>(Ikin 2016) proposes a different method of measuring noise figure NF.

Therefore, the LNA noise figure can be derived by measuring the noise with the LNA input terminated with a resistor equal to its input impedance. Then with the measurement repeated with the resistor removed, so that the LNA input is terminated by its own Dynamic Impedance. The difference in the noise ref. the above measurements will give a figure in dB which is equal to the noise reduction of the LNA verses thermal noise at 290K. Converting the dB difference into an attenuation power ratio then multiplying this by 290K gives the LNA Noise Temperature. Then using the Noise Temperature to dB conversion table yields the LNA Noise Figure. See Table 1.

The explanation is not very clear to me, and there is no mathematical proof of the technique offered… so a bit unsatisfying… but it is oft cited in ham online discussions.

I have taken the liberty to extend Ikin’s Table 1 to include some more values of column 1 for comparison with a more conventional Y factor test of a receiver’s noise figure.

Above is the extended table. The formulas in all cells of a column are the same, the highlighted row is for later reference.

A test setup was arranged to measure the noise output power of an IC-7300 receiver which has a sensitivity specification that hints should have a NF≅5.4dB. The relative noise output power for four conditions was recorded in the table below.

Ikin’s method calls for calculating the third minus second rows, -0.17dB, and looking it up in his table. In my extended table LnaNoiseDifference=-0.17dB corresponds to NF=3.10dB.

We can find the NF using the conventional Y factor method from the values in the third and fourth rows.

The result is NF=5.14dB (quite close to the expected value based on sensistivity specification).

Ikin’s so called dynamic impedance method gave quite a different result in this case, 3.10 vs 5.14dB, quite a large discrepancy.

The chart above shows the relative level of the four measurements. The value of the last two is that they can be used to determine the NF using the well established theory explained at AN 57-1.

The values in the first columns are dependent on the internal implementation of the amplifier, and cannot reliable infer NF.

- Hewlett Packard. Jul 1983. Fundamentals of RF and microwave noise figure measurement. AN 57-1
- Ikin, A. 2016. Measuring noise figure using the dynamic impedance method.

Let’s review of the concepts of noise figure, equivalent noise temperature and measurement.

Firstly let’s consider the nature of noise. The noise we are discussing is dominated by thermal noise, the noise due to random thermal agitation of charge carriers in conductors. Johnson noise (as it is known) has a uniform spectral power density, ie a uniform power/bandwidth. The maximum thermal noise power density available from a resistor at temperature T is given by \(NPD=k_B T\) where Boltzman’s constant k_{B}=1.38064852e-23 (and of course the load must be matched to obtain that maximum noise power density). Temperature is absolute temperature, it is measured in Kelvins and 0°C≅273K.

Noise Figure NF by definition is the reduction in S/N ratio (in dB) across a system component. So, we can write \(NF=10 log \frac{S_{in}}{N_{in}}- 10 log \frac{S_{out}}{N_{out}}\).

One of the many methods of characterising the internal noise contribution of an amplifier is to treat it as noiseless and derive an equivalent temperature of a matched input resistor that delivers equivalent noise, this temperature is known as the equivalent noise temperature Te of the amplifier.

So for example, if we were to place a 50Ω resistor on the input of a nominally 50Ω input amplifier, and raised its temperature from 0K to the point T where the noise output power of the amplifier doubled, would could infer that the internal noise of the amplifier could be represented by an input resistor at temperature T. Fine in concept, but not very practical.

Applying a little maths, we do have a practical measurement method which is known as the Y factor method. It involves measuring the ratio of noise power output (Y) for two different source resistor temperatures, Tc and Th. We can say that \(NF=10 log \frac{(\frac{T_h}{290}-1)-Y(\frac{T_c}{290}-1)}{Y-1}\).

AN 57-1 contains a detailed mathematical explanation / proof of the Y factor method.

We can buy a noise source off the shelf, they come in a range of hot and cold temperatures. For example, one with specified Excess Noise Ratio (a common method of specifying them) has Th=9461K and Tc=290K. If we measured a DUT and observed that Y=3 (4.77dB) we could calculate that NF=12dB.

This method of noise figure measurement is practical and used widely. Note that the DUT always has its nominal terminations applied to the input and output, the system gain is maintained, just the input equivalent noise temperature is varied.

Some amplifiers are not intended to be impedance matched at the input (ie optimised for maximum gain), but are optimised for noise figure by controlling the source impedance seen at the active device. Notwithstanding that the input is not impedance matched, noise figure measurements are made in the same way as for a matched system as they figures are applicable to the application where for example the source might be a nominal 50Ω antenna system.

So, NF is characterised for an amplifier with its intended / nominal source and load impedances.

Nothing about the NF implies the equivalent internal noise with a short circuit SC or open circuit OC input. The behaviour of an amplifier under those conditions is internal implementation dependent (ie variable from one amplifier design to another) and since it is not related to the amplifier’s NF, it is quite wrong to make inferences based on noise measured with SC or OC input.

So this raises the question of NF measurements made with a 50Ω source on an amplifier normally used with a different source impedance, and possibly a frequency dependent source impedance. An example of this might be an active loop amplifier where the source impedance looks more like a simple inductor.

Well clearly the measurement based on a 50Ω source does not apply exactly as amplifier internal noise is often sensitive to the source impedance, but for smallish departures, the error might be smallish.

A better approach might be to measure the amplifier with its intended source impedance. In the case of the example active loop antenna, the amplifier could be connected to a dummy equivalent inductor, all housed in a shielded enclosure and the output noise power measured with a spectrum analyser to give an equivalent noise power density at the output terminals. Knowing the AntennaFactor of the combination, that output power density could be referred to the air interface. This is often done and the active antenna internal noise expressed as an equivalent field strength in 1Hz, eg 0.02µV/m in 1Hz. For example the AAA-1C loop and amplifier specifies Antenna Factor Ka 2 dB meters-1 @ 10 MHz

and MDS @ 10MHz 0.7 uV/m , Noise bandwidth =1KHz and

to mean equivalent internal noise 0.022µV/m in 1Hz @ 10MHz at the air interface. 0.022µV/m in 1Hz infers Te=6.655e6K and NF=43.608dB again, at the air interface. These figures can be used with the ambient noise figure to calculate the S/N degradation (SND).

A spectrum analyser or the like can be used to measure the total noise power density at the output of the loop amplifier with the input connected to a dummy antenna network (all of it shielded) and to calculate the equivalent noise temperature and noise figure at that point. For example, if we measured -116dBm in 1kHz bandwidth, Te=1.793e+5K and NF=27.9dB. Knowledge of the gain from air interface to that reference point is needed to compare ambient noise to the internal noise and to calculate SND, that knowledge might come from published specifications or a mix of measurements and modelling of the loaded antenna.

The mention of a spectrum analyser invites the question about the suitability of an SDR receiver. If the receiver is known to be calibrated, there is no non-linear process like noise cancellation active, and the ENB of the filter is known accurately, it may be a suitable instrument.

In both cases, the instruments are usually calculated for total input power, ie external signal and noise plus internal noise, so to find external noise (ie from the preamp) allowance must be made for the instrument NF (ie it needs to be known if the measured power is anywhere near the instrument noise floor).

Field strength / receive power converter may assist in some of the calculations.

The foregoing discussion assumes a linear receiver, and does not include the effects of intermodulation distortion IMD that can be hugely significant, especially in poor designs.

Part of the problem of IMD is that the effects depend on the individual deployment context, one user may have quite a different experience to another.

There are a huge number of published active loop antenna designs and variant, and a smaller number of commercial products. Most are without useful specifications which is understandable since most of the market are swayed more by anecdotal user experiences and theory based metrics and measurement.

- Hewlett Packard. Jul 1983. Fundamentals of RF and microwave noise figure measurement. AN 57-1

The MGF1302 is a low noise GaAs FET designed for S band to X band amplifiers, and was very popular in ham equipment until the arrival of pHEMT devices.

An important characteristic of the MGF1302 is that matching the input circuit for maximum gain (maximum power transfer) does not achieve the best Noise Figure… and since low noise is the objective, then we must design for that.

The datasheet contains a set of Γ_{opt} for the source impedance seen by the device gate, and interpolating for 1296MHz Γ_{opt}=0.73∠-10.5°.

Lets convert Γ_{opt} to some other useful values.

The equivalent source Z, Y and rectangular form of Γ_{opt}= will be convenient during the circuit design phase.

The other important characteristic is Zin of the gate in the final circuit configuration, and that is derived from a model of the device in circuit. The value is 7.8-j164Ω. At low frequencies, the FET gate looks like an extremely high impedance, at higher frequencies more like tiny capacitance with very low equivalent series resistance (ESR), and still higher frequencies the capacitive reactance is lower and ESR higher, and still higher frequencies lead inductance comes into play and the gate looks inductive with even higher ESR.

A model of the antenna to gate circuit was built in SimSmith v16.9.

Above, the SimSmith model which includes a swept length of LDF4-50A transmission line.

The standard display was supplemented with impedance, admittance and Γ looking from the gate back towards the antenna. These make it easier to adjust the L and C components for the desired outcome. The G component of Y is most sensitive to adjustment of L and the B component to adjustment of C. So, they are both adjusted to approximately obtain Γ_{opt}=0.7178-j0.1330 from the conversions done earlier.

A sweep is shown for power from the source (antenna) and power into the FET gate for a range for transmission line lengths. Whilst loss between antenna and gate may seem high, the LNA delivers around NF<1dB and 13dB of gain from its input terminal (ie looking into L1) to output despite the lack of conjugate matching.

The behavior demonstrates the complex interaction of source, transmission line and load… worth studying.

The discussion is about a low noise receiving system where optimal results come from an input circuit that is not designed for maximum power transfer.

]]>## Effective Bandwidth

The contribution to the available output noise by the Johnson-noise sources in the signal generator is readily calculated for and ideal or square-top band-pass characteristic and it is GKTB where B is the bandwidth in cycles per second. In practice, however, the band is not flat; ie, the gain over the band is not constant but varies with frequency. In this case the total contribution is ∫G

_{f}KTdf where G_{f}is the gain at frequency f. The effective bandwidth B of the network is defined as the bandwidth of an ideal band-pass network with gain G that gives this contribution to the noise output.

Above is the response of the ‘factory’ 2400Hz soft filter in an IC-7300 (SDR) transceiver. It is not an ideal rectangular response.

To perform the calculation described by Friis, ∫G_{f}KTdf, we firstly need a G(f) dataset. The above plot is of the log of G(f) and to perform geometric operations to find the area under the curve is quite misguided.

Above is a plot of G(f) (measured with Gaussian noise integrated over a period), and we can find ∫G_{f}KTdf wrt G at some reference frequency (1kHz in the above example as that is what is used for sensitivity measurement).

In this case the filter -6dB response is 377-2616Hz=2239Hz, and Effective Bandwidth wrt gain at 1kHz is 2077Hz.

In my own articles and software I usually refer to this as the Equivalent Noise Bandwidth (ENB) to be clearer.

ARRL to be different refer to Equivalent Rectangular Bandwidth but they do not expose how they calculate it (it is a hammy thing).

The term Equivalent Noise Bandwidth is sometimes used.

- Friis, HT. Noise figures of radio receivers. Proceedings of the IRE, Jul 1944 p420.

(Friis 1944) suggested that temperature as reference temperature and it has been widely used since. One may also see 293K (eg in certain ITU-R recommendations), but in my experience, 290K is most commonly used and is for instance the basis for calibration of Keysight noise sources in Excess Noise Ratio (ENR).

The assumption in measurement of Noise Figure or of sensitivity is that the ‘cold’ source has a known source resistance with Johnson noise equivalent to 290K (16.85° C). That noise producing resistance is commonly achieved using a large attenuator at the generator output.

- Friis, HT. Noise figures of radio receivers. Proceedings of the IRE, Jul 1944 p420.
- Keysight. Jul 2018. Keysight 346A/B/C noise source operating and service manual.

The update corrects an error in conversion between ENR and temperature where Tcold<>290K.

- Duffy, O. 2007. Noise Figure Meter software (NFM). https://owenduffy.net/software/nfm/index.htm (accessed 01/04/2014).