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.

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.

### SSB

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.

### Comparison.

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?

## Equivalent Noise Bandwidth

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.

## Estimating Noise Figure from sensitivity

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.

## Conclusions

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.