Signal to Noise Ratio
When a recording has an audible hiss behind quiet passages, when a sensor reading jitters in its last few digits, or when a weak signal on a spectrum analyzer barely rises above the grass, you are seeing a limited signal-to-noise ratio. The signal is there, but the noise is so close in level that it cannot be extracted cleanly. Signal-to-noise ratio, universally abbreviated SNR, is the single most important figure for describing how cleanly a system carries or recovers a signal. Noise figure, noise floor and dynamic range all ultimately exist to tell you something about SNR under specific conditions.
Unlike raw signal strength, SNR is a relative measurement. A strong signal is worthless if the noise is equally strong. A weak signal can be perfectly usable if the noise is even weaker. This lesson explains what SNR means, how to calculate it, what SNR different applications need, how to read SNR and SINAD on datasheets, and what you can do to improve it.
What is SNR? The Fundamental Definition
Signal-to-noise ratio is the ratio of the power of the desired signal to the power of the noise measured at the same point in the signal chain. It answers the question: how many times stronger is the signal than the noise? Expressing this ratio as a plain number is unwieldy because useful SNR values range from less than 0.001 (signal buried deep in noise) to more than 100,000 (crystal-clear signal far above the noise floor). Logarithms compress this range into manageable numbers, which is why SNR is almost always stated in decibels.
The decibel formula for SNR is:
Because power levels in RF systems are usually already expressed in dBm, this simplifies to:
SNR (dB) = Signal level (dBm) − Noise level (dBm)
This is one of the great conveniences of the dBm scale: subtraction of dBm values gives you SNR directly. If your signal is at −90 dBm and your noise floor is at −120 dBm, the SNR is simply −90 − (−120) = 30 dB. No logarithms to calculate by hand.
Interpreting SNR values
A few reference points help anchor your intuition:
- 0 dB SNR: Signal power equals noise power. The signal is right at the noise floor. Detection is barely possible and intelligibility is essentially zero for voice.
- 3 dB SNR: Signal power is twice the noise power. A tone is just visible on a spectrum display, but its amplitude cannot be measured accurately.
- 10 dB SNR: Signal power is 10 times the noise power. Speech is intelligible with effort; an amplitude reading is good to about half a decibel.
- 20 dB SNR: Signal power is 100 times the noise power. Comfortable speech; simple digital links run with few errors.
- 30 dB SNR: Signal power is 1000 times the noise power. Clean speech, and noise is no longer the main limit on most measurements.
Negative SNR values — where the signal is below the noise — are not only possible but are routinely exploited. A signal at −10 dB SNR has one-tenth the power of the surrounding noise, yet averaging, correlation and other processing can still recover it, as explained later in this lesson.
Worked example: calculating SNR from two dBm readings
SNR = −100 dBm − (−118 dBm) = 18 dB
The signal is clearly visible and its level can be read accurately — at 18 dB SNR the noise adds only about 0.07 dB to the reading. To measure a signal much weaker than this, narrow the resolution bandwidth or switch on the analyzer's preamplifier.
The power ratio form of SNR
Sometimes you need to convert dB SNR back to a plain power ratio, for example when calculating required signal levels for a specific performance target. The formula is:
For voltage ratios (which appear in some audio and RF calculations):
Vsignal / Vnoise = 10(SNR dB / 20)
The factor of 10 in the power formula versus 20 in the voltage formula reflects the fact that power scales as voltage squared. A 20 dB SNR means a power ratio of 102 = 100 and a voltage ratio of 101 = 10 simultaneously — both are correct descriptions of the same signal condition.
High SNR (left): the signal peak rises clearly above the noise floor. Low SNR (right): the signal is barely distinguishable from the noise. The SNR in dB is the gap between signal level and noise floor.
View LargerSNR Calculator
Enter the received signal level and the noise floor (both in dBm) to calculate SNR, voltage ratio, power ratio, and a readability assessment.
How Much SNR Is Enough?
Different applications need radically different SNR. The key factor is how much information has to be recovered from the signal, and how much processing can be applied to recover it. A human listener needs a fairly high SNR for comfortable speech; a hi-fi system needs far more for noise to be inaudible; a digital receiver that averages or correlates over time can work with very little.
| Application | Typical SNR needed | Notes |
|---|---|---|
| Seeing a tone on a spectrum display | 3 dB | Detectable, but the level reading is unreliable |
| Accurate amplitude measurement | 10 dB or more | Noise adds about 0.4 dB at 10 dB SNR, under 0.05 dB at 20 dB |
| Intelligible speech | 10–15 dB | Comfortable listening needs 20–30 dB |
| Simple digital link (FSK, BPSK) | 10–13 dB | For a low bit-error rate; error correction lowers this |
| 64-QAM Wi-Fi data rates | 25–30 dB | Denser modulation needs more SNR for the same error rate |
| Sensor reading to 1% | 40 dB | 0.1% resolution needs 60 dB |
| Analog video | 40–50 dB | Below about 30 dB the picture looks visibly grainy |
| Hi-fi audio playback | 90–100 dB | 16-bit audio has a theoretical SNR of 98 dB |
| Professional recording | 110–120 dB | Achievable with 24-bit converters and careful gain staging |
| GPS reception | about −20 dB | In the channel bandwidth; recovered by correlation |
Why some systems work far below 0 dB SNR
Noise is random. When you add many noise samples together, they partially cancel because some are positive and some are negative. The RMS noise grows only as the square root of the number of samples added, while a steady or predictable signal grows linearly. Averaging N samples therefore improves the power SNR by a factor of N: averaging 100 readings improves SNR by 20 dB, and averaging 10,000 improves it by 40 dB. This improvement is called processing gain.
Processing gain is how a lock-in amplifier measures a sensor signal buried 60 dB under noise, how an oscilloscope's averaging mode reveals a clean repetitive waveform, and how a GPS receiver recovers satellite signals about 20 dB below the noise by correlating with each satellite's known code. The price is always time or throughput: the receiver must collect data for longer, or send information more slowly, to gain the extra SNR.
Reading SNR on Datasheets
SNR figures appear on almost every datasheet for audio, conversion and sensing equipment, but they are only meaningful if you know what they are referenced to.
Signal level is not SNR
A large signal does not guarantee a good SNR. A recording made at full level on a noisy preamplifier, a sensor output with plenty of amplitude but lots of hum, or a strong RF signal sitting on a high noise floor can all be poor despite their size. What matters is the gap between signal and noise, measured in the same bandwidth at the same point in the system.
Audio SNR
Audio SNR is usually quoted as the ratio between a reference output level — the amplifier's rated power, or full scale (0 dBFS) for digital equipment — and the noise with no input signal, measured over 20 Hz to 20 kHz. Many specifications are A-weighted, filtering the noise to match the ear's sensitivity; this typically improves the figure by 2 to 5 dB, so compare weighted figures only with weighted figures. A specification of “100 dB, A-weighted, re rated output” means the hiss is 100 dB below full power — but at normal listening levels, 30 dB below full power, the real listening SNR is only 70 dB.
ADC SNR and ENOB
An ideal N-bit converter has an SNR of 6.02N + 1.76 dB for a full-scale sine wave. Real converters fall short, and datasheets give the measured SNR along with the effective number of bits (ENOB) — the number of bits an ideal converter would need to match it. A 16-bit ADC with 86 dB SNR performs like an ideal converter of about 14 bits; the last two bits are noise. Signals below full scale lose SNR decibel for decibel, so a signal using only a tenth of the input range gives up 20 dB.
Sensor noise density
Sensors such as accelerometers, gyroscopes and magnetometers specify noise as a noise density per square root of hertz. Multiply by the square root of the bandwidth to get the RMS noise.
Noise = 150 µg × √100 = 1,500 µg = 1.5 mg RMS
SNR = 20 × log10(1 g / 0.0015 g) = 20 × log10(667) = 56.5 dB
Reducing the bandwidth to 10 Hz would lower the noise by √10 and raise the SNR to 66.5 dB — at the cost of slower response.
SINAD — Signal Plus Noise Plus Distortion to Noise Plus Distortion
SINAD (pronounced “sigh-nad”) is a variant of SNR that counts distortion as well as noise. Both degrade a signal, and in many systems distortion matters as much as noise. The full name reveals the formula:
Or in dB:
SINAD (dB) = 10 × log10[(Signal + Noise + Distortion) / (Noise + Distortion)] (power ratio)
SINAD in ADC and audio specifications
Converter datasheets specify SINAD alongside SNR, and the effective number of bits is properly calculated from SINAD: ENOB = (SINAD − 1.76) / 6.02. A 12-bit ADC with a SINAD of 68 dB has an ENOB of (68 − 1.76) / 6.02 = 11.0 bits.
Audio equipment usually quotes the same quantity the other way up, as THD+N (total harmonic distortion plus noise) relative to the signal. A THD+N of 0.01% is −80 dB, equivalent to a SINAD of 80 dB.
The 12 dB SINAD sensitivity standard
SINAD is also the standard sensitivity measurement for FM receivers, such as two-way radios and pagers, because an FM demodulator produces heavy distortion as the signal weakens. The sensitivity is the input level that produces 12 dB SINAD in the recovered audio. This corresponds to roughly 25% noise and distortion, which sounds poor by hi-fi standards but marks the threshold of usable speech.
P = V² / R = (0.35 × 10−6)² / 50 = 1.225 × 10−13 / 50 = 2.45 × 10−15 W
P(dBm) = 10 × log10(2.45 × 10−15 / 10−3) = 10 × log10(2.45 × 10−12) ≈ −116 dBm
This is the input signal level at which the radio just reaches usable speech quality.
SINAD versus SNR: which should you use?
Use SNR when noise is the main limitation, as in sensitive amplifiers, sensor front ends and receivers working near their noise floor. Use SINAD (or THD+N) when distortion matters as well — audio amplifiers, ADCs and DACs, and FM receivers — because a system can have an excellent SNR and still produce a badly distorted output.
Improving SNR — What Works and What Does Not
Improving SNR means either increasing the signal relative to the noise or reducing the noise relative to the signal. Which approach works depends on what is limiting the SNR in the first place, so always identify the dominant noise source before spending money or effort.
1. Reduce the bandwidth — the most effective tool
Noise power is proportional to bandwidth. Halve the bandwidth and you halve the noise power — a 3 dB SNR improvement — while a signal that still fits within the bandwidth is unchanged.
Narrowing the bandwidth by 10:1 reduces noise by 10 dB.
In practice: filtering a sensor amplifier's output from 20 kHz down to the 1 kHz its signal needs improves SNR by 10 × log10(20) = 13 dB. Averaging, longer FFTs and narrower analyzer resolution bandwidths all work the same way.
2. Increase the signal early in the chain
Make the signal as large as possible before it meets the noisy parts of the system. Use the full input range of an ADC, apply gain early so later stages add proportionally less noise (good gain staging), raise the excitation voltage on a strain-gauge bridge where the sensor allows, and keep low-level signals away from long cables and noisy circuits.
3. Use a low-noise first stage — only when the amplifier noise dominates
A low-noise preamplifier improves SNR only when the amplifier chain's own noise is the limiting factor. If the noise arrives with the signal — a hissy source, a microphone in a noisy room, or an antenna picking up atmospheric noise — a quieter amplifier makes no difference, because it amplifies the noise along with the signal. The Friis formula from the Noise Figure lesson tells you which situation you are in.
4. Remove interference
In practice, much of the “noise” in real circuits is not random thermal noise but interference: mains hum, switching-supply ripple, digital clock harmonics and radio signals picked up by cables. Shielding, differential signalling, good grounding, ferrite chokes and moving circuits apart often improve SNR by tens of decibels — far more than any low-noise amplifier. The last five lessons of this module cover these techniques.
5. Use processing gain
For signals that are steady, repetitive or follow a known pattern, averaging, synchronous (lock-in) detection and correlation can gain 20 to 40 dB or more. The cost is time: the measurement or the data rate must slow down in proportion to the gain.
Frequently Asked Questions
Is a strong signal the same as a good SNR?
No. Signal strength is an absolute level; SNR is the ratio of signal to noise. A large signal can still have a poor SNR if the noise is also large, and a tiny signal can have an excellent SNR if the noise is smaller still. Always compare signal and noise measured in the same bandwidth at the same point in the system.
What SNR do I need?
It depends on the application. Detecting a tone needs only a few decibels; reading its level accurately needs 10 dB or more. Intelligible speech needs 10–15 dB and comfortable listening 20–30 dB. A sensor reading to 1% needs about 40 dB, and hi-fi audio needs 90 dB or more for the noise to be inaudible. Digital systems that use averaging or correlation can work below 0 dB.
Why does averaging improve SNR?
A steady signal is the same in every sample, so it adds up linearly when samples are summed. Random noise is different in every sample, so it adds up only as the square root of the number of samples. Averaging N samples therefore improves the power SNR by a factor of N (10 × log10N dB). Averaging is equivalent to narrowing the measurement bandwidth, which is why it only works for signals that do not change during the averaging time.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.