Receiver sensitivity is commonly given as some signal level, say in µV, for a given Signal to Noise ratio (S/N), say 10dB. For AM, the depth of sinusoidal modulation is also given, and it is usually 30%. In fact these are power ratios in the context of and some nominal reference receiver input impedance.

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.

## Raw Signal/Noise

### AM 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. Continue reading Comparing sensitivity figures of an AM receiver and SSB receiver

I see online discussions struggling to try to work out if a receiving system is sufficiently good for a certain application.

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. Continue reading Quantifying performance of a simple broadcast receive system on MF

## Active monopole + RTL SDR + RPi Spyserver experiment

A brief experiment was conducted of a remote HF receiver using:

• 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. Continue reading Active monopole + RTL SDR + RPi Spyserver experiment

## SDR# (v1.0.0.1732) – channel filter exploration

With plans to use an RTL-SDR dongle and SDR# (v1.0.0.1732) for an upcoming project, the Equivalent Noise Bandwidth (ENB) of several channel filter configurations were explored.

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.

### 500Hz CW filter

The most common application of such a filter is reception of A1 Morse code. Above is a screenshot of the filter settings. Continue reading SDR# (v1.0.0.1732) – channel filter exploration

## Noise figure of active loop amplifiers – the Ikin dynamic impedance method

Noise figure of active loop amplifiers – some thoughts discussed measurement of internal noise with particular application of active broadband loop antennas.

(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. Continue reading Noise figure of active loop amplifiers – the Ikin dynamic impedance method

## Review of noise

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 kB=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

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

### Equivalent noise temperature

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.

### Y factor method

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. Continue reading Noise figure of active loop amplifiers – some thoughts

## SimSmith – looking both ways – an LNA design task

This article shows the use of SimSmith in design and analysis of the input circuit of an MGF1302 LNA.

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 Γopt for the source impedance seen by the device gate, and interpolating for 1296MHz Γopt=0.73∠-10.5°.

Lets convert Γopt to some other useful values. The equivalent source Z, Y and rectangular form of Γopt= will be convenient during the circuit design phase. Continue reading SimSmith – looking both ways – an LNA design task

## Noise Figure – Equivalent Noise Bandwidth

Harald Friis (Friis 1944) gave guidance on measuring the noise figure of receivers, and explains the concept of Effective Bandwidth.

#### 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 ∫GfKTdf where Gf 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.

## Is it 290K or 293K?

A reader of my articles commented on them and some of my calculators regarding the use of 290K as the reference temperature (T0) for Noise Figures.

(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.