2.4 Signal-to-Noise Ratio and Receiver Noise Performance

2.4 Signal-to-Noise Ratio and Receiver Noise Performance

ACMA Exam Focus: Syllabus item 5.15 asks you to recall, in simple terms, the meaning of 'signal to noise ratio' as applied to a receiver specification. The examinable idea is that a sensitivity figure only means something when it is quoted together with a signal-to-noise or SINAD figure.

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1. The Definition

Signal-to-noise ratio (SNR, or S/N) is the ratio of wanted signal power to unwanted noise power, measured at the same point in the receiver and normally expressed in decibels:

$\text{SNR}_{\text{dB}} = 10 \log_{10} \left( \frac{P_{\text{signal}}}{P_{\text{noise}}} \right)$

When you are working with voltages across the same impedance, use the voltage form:

$\text{SNR}_{\text{dB}} = 20 \log_{10} \left( \frac{V_{\text{signal}}}{V_{\text{noise}}} \right)$

A positive SNR means the signal is stronger than the noise. Roughly speaking, a 3 dB SNR is barely detectable, 10 dB gives comfortable copy on SSB, and 40 dB is armchair quality. Modern weak-signal digital modes decode successfully at negative SNRs, because forward error correction and very narrow processing bandwidths recover information a human ear cannot.

Worked example. A signal produces 2.0 microvolts at the receiver input and the noise in the same bandwidth measures 0.2 microvolts.

$\text{SNR} = 20 \log_{10} \left( \frac{2.0}{0.2} \right) = 20 \log_{10}(10) = 20\ \text{dB}$

2. Why a Sensitivity Figure Alone Is Meaningless

A receiver specification never says simply "sensitivity 0.2 microvolts". It says something like:

• "0.2 microvolts for 10 dB S/N" - typical of an SSB or CW specification;
• "0.25 microvolts for 12 dB SINAD" - the usual FM specification, where SINAD is the ratio of signal plus noise plus distortion to noise plus distortion, and so also accounts for the distortion an FM detector adds.

The reason is simple. Any receiver can be made to produce an audible output from an arbitrarily small input - just add gain. What gain cannot do is improve the ratio of signal to noise; amplifying the input amplifies the noise with it, and every stage adds a little noise of its own. A bare microvolt figure therefore tells you only how loud the receiver is, not how useful the output is. Adding the quality figure makes the number comparable between radios: the smaller the input voltage needed to reach the stated S/N or SINAD, the better the receiver.

Always check that two specifications you are comparing use the same quality figure and the same measurement bandwidth. A radio quoted at 10 dB S/N will look better than an identical radio quoted at 12 dB SINAD, purely because the test is easier.

3. Where the Noise Comes From

Noise at the receiver input has two origins.

External noise arrives down the feedline with the signal:

• Atmospheric noise - overwhelmingly lightning, which is why 160 and 80 metres are so noisy in an Australian summer.
• Galactic noise - broadband radio noise from the Milky Way, significant from about 20 MHz to a few hundred megahertz.
• Man-made noise - switch-mode power supplies, solar inverters, LED lighting, VDSL, plasma displays, electric fences and faulty power-line hardware.

Internal noise is generated inside the receiver itself:

• Thermal (Johnson) noise in every resistance, with power $P = kTB$, where $k$ is Boltzmann's constant, $T$ the absolute temperature and $B$ the bandwidth.
• Shot noise and device noise in semiconductors, summarised as the receiver's noise figure.

At room temperature the thermal noise floor is about -174 dBm in a 1 Hz bandwidth. In a 2.4 kHz SSB bandwidth that becomes:

$-174 + 10 \log_{10}(2400) = -174 + 33.8 \approx -140\ \text{dBm}$

A receiver with a 6 dB noise figure therefore has an internal noise floor of about -134 dBm in an SSB bandwidth. Remember that number: on HF the noise actually coming down the antenna is usually 20 to 40 dB above it.

4. Why a Preamplifier Helps at VHF but Not on HF

A preamplifier raises the signal and the noise already present by the same amount. It can only improve SNR by contributing less noise of its own than the stage it precedes - which matters only if receiver noise is what is limiting you.

On 40 metres the band noise heard on a decent antenna is far above the receiver's own noise floor. Adding a preamplifier lifts signal and band noise together, the SNR is unchanged, and the only real effect is to push the front end closer to overload and intermodulation from strong broadcast stations. Experienced HF operators frequently switch the attenuator in rather than the preamplifier: signals get quieter, but the ratio that matters is unchanged and the receiver behaves better.

On 144 MHz and above external noise is low, and the receiver's own noise figure - together with feedline loss ahead of it - is what sets the weakest workable signal. A low-noise preamplifier mounted at the masthead, ahead of the coaxial loss, genuinely lowers the system noise figure and can transform weak-signal work.

5. Bandwidth: The Operator's Best SNR Control

Noise power is proportional to bandwidth, but a signal only occupies its own bandwidth. Every hertz of receiver passband beyond what the signal needs admits noise and no extra signal. Narrowing the filter to match the mode therefore improves SNR by:

$\text{Improvement (dB)} = 10 \log_{10} \left( \frac{B_{\text{wide}}}{B_{\text{narrow}}} \right)$

Worked example. An operator copying weak CW switches from the 2.4 kHz SSB filter to a 250 Hz CW filter:

$10 \log_{10} \left( \frac{2400}{250} \right) = 10 \log_{10}(9.6) \approx 9.8\ \text{dB}$

Almost 10 dB of improvement, from a change of filter alone - more than doubling transmitter power would give the other station. This is the same selectivity discussed earlier in this chapter, seen from the noise side rather than the adjacent-signal side.

The limit is that you must not narrow the filter below the bandwidth of the signal itself. Squeezing a 250 Hz filter onto a 2.4 kHz SSB signal removes most of the intelligence along with the noise. Match the filter to the mode: roughly 2.4 kHz for SSB, 250-500 Hz for RTTY, 250-500 Hz for CW, and as little as 50 Hz for narrow digital modes handled in software.

6. S-Units, Decibels and Reports

By IARU convention, S9 on HF corresponds to 50 microvolts at the receiver's 50 ohm antenna terminals, which is -73 dBm, and each S-point below that represents 6 dB. At VHF and above the reference is 20 dB lower, S9 being 5 microvolts or -93 dBm. Real S-meters are only loosely calibrated, so treat readings as indicative.

Notice how this closes the loop with section 3. An S1 signal at -121 dBm sits about 13 dB above a -134 dBm receiver noise floor in a 2.4 kHz bandwidth - readable, but only because the receiver's internal noise is low enough to let it through.

Signal reports use the RST system: Readability 1 to 5, Strength 1 to 9, and Tone 1 to 9 for CW only. Readability is a direct verbal statement of signal-to-noise ratio as the ear perceives it, which is why "R5" and a high S-meter reading do not always go together - a strong signal buried in local noise can be S9 and barely readable.

A short decibel table is worth memorising for the exam, since the arithmetic appears throughout: