Noise Floor

The noise floor is the line in the sand below which signals become undetectable. It is the total noise in a signal chain — thermal noise from the source, plus the noise added by every amplifier, mixer and converter — expressed as an equivalent power or voltage at the input. Any signal smaller than the noise floor is buried in the noise and cannot be measured directly, whether the system is a spectrum analyzer, a radio receiver, an oscilloscope, a data-acquisition ADC or a sensor amplifier.

Knowing how to calculate a noise floor is not just academic. It tells you the smallest signal an instrument can show you, explains why a spectrum analyzer's baseline moves when you change its resolution bandwidth, lets you compare instruments and receivers objectively, helps you decide whether a preamplifier or a narrower filter will actually help, and shows how processing such as averaging and FFTs pulls signals out of noise.

The noise floor is the sum of three terms: the thermal noise density at room temperature (-174 dBm/Hz), the bandwidth factor (10 log of the bandwidth in Hz), and the system noise figure in dB.

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The Noise Floor Formula

For any system with a defined input impedance (usually 50 Ω for RF instruments and receivers), the noise floor is the noise power at the input, expressed in dBm. It is the signal power that would produce an output equal to the noise output — the level below which a signal is indistinguishable from noise. The formula combines everything from the previous two lessons:

Let's unpack each term:

−174 dBm/Hz is the thermal noise power density at room temperature (290 K), as derived in the Thermal Noise lesson. This floor exists before any hardware is considered — it is the noise generated by the thermal motion of electrons in the 50 Ω source resistance.

10 × log₁₀(BW) is the bandwidth factor. The total noise power in bandwidth BW is BW times the noise density per hertz. In dB, multiplying by BW becomes adding 10 × log₁₀(BW). For a 1 kHz bandwidth: 10 × log₁₀(1000) = 30 dB. For a 100 kHz bandwidth: 50 dB.

NF is the system noise figure in dB, from the previous lesson. Every real amplifier, receiver and instrument adds noise beyond the thermal floor. A 6 dB NF system has a noise floor 6 dB above that of a perfectly noiseless one.

Worked Examples

Noise Floor Calculator

Why Bandwidth Is the Key Variable

The bandwidth term in the noise floor formula is the one you can usually control — the noise figure is fixed by the hardware you own. Every time you halve the bandwidth, the noise floor drops by 3 dB. Every time you reduce the bandwidth by a factor of 10, it drops by 10 dB. A spectrum analyzer shows this directly: change the RBW and the whole noise baseline moves, while a steady sine-wave signal stays at the same level.

The sweep-time column explains why real analyzers do not simply use the narrowest RBW all the time: a swept analyzer would take hours to cover a wide span at 10 Hz. Modern analyzers get around this by switching to FFT processing at narrow RBWs, and by sweeping only a narrow span around the signal of interest.

The same principle applies outside RF. A sensor amplifier filtered to 10 Hz instead of 10 kHz has a noise floor 30 dB lower. Averaging N readings of a steady signal reduces random noise by √N — averaging 100 ADC readings lowers the noise by a factor of 10, or 20 dB in voltage terms — because averaging is simply a way of narrowing the bandwidth. Narrow-band digital communication modes and GPS receivers push this to the extreme, integrating over long periods to work with signals well below the noise in their channel bandwidth.

Minimum Discernible Signal (MDS)

The noise floor is the level at which signal power equals noise power — a 0 dB SNR point. But a signal at 0 dB SNR is barely detectable and cannot be measured accurately. To read a signal's amplitude on a spectrum analyzer to within about 0.5 dB, it should be at least 10 dB above the noise; to understand speech comfortably, a voice channel needs 10–15 dB SNR; a data link needs whatever SNR its modulation scheme requires for an acceptable error rate.

The minimum discernible signal (MDS) is the input signal that produces a specified SNR at the output. In receiver and instrument specifications, MDS is usually the signal that raises the output power by 3 dB above the noise alone — meaning the signal power equals the noise power (0 dB SNR). This is essentially the noise floor itself.

To convert MDS to a useful sensitivity for a specific job, add the SNR that job requires:

The Noise Floor of ADCs, Oscilloscopes and FFTs

Not every system has a 50 Ω input and a noise figure, but every system has a noise floor.

ADCs. An ideal N-bit converter digitizing a full-scale sine wave has a signal-to-quantization-noise ratio of 6.02N + 1.76 dB: about 74 dB for 12 bits and 98 dB for 16 bits. Real converters do worse because of thermal noise, reference noise and clock jitter; the datasheet's SNR or ENOB (effective number of bits) gives the true figure. A 16-bit audio interface with 96 dB SNR, for example, behaves like an ideal converter of about 15.7 bits.

FFT displays. The noise floor you see on an FFT is lower than the converter's SNR suggests, because the noise is spread across all the frequency bins. An M-point FFT has M/2 bins, so each bin holds only 2/M of the total noise — a processing gain of 10 × log₁₀(M/2). A 12-bit ADC with 74 dB SNR viewed through a 4,096-point FFT shows a noise floor about 74 + 33 = 107 dB below full scale. A longer FFT means narrower bins and a lower displayed floor, exactly like a narrower RBW on a spectrum analyzer.

Oscilloscopes. An oscilloscope's noise floor is quoted in volts RMS at each vertical setting. At its most sensitive range with full bandwidth, a typical general-purpose 8-bit scope shows a few hundred microvolts of noise. Because that noise is spread across the full bandwidth, switching on the 20 MHz bandwidth limit, using high-resolution acquisition mode or averaging repetitive waveforms lowers the visible noise considerably — once again, by narrowing the bandwidth.

Comparing Instruments and Receivers

When comparing two instruments or receivers, the noise floor calculation immediately shows which will see weaker signals. A system with 6 dB NF in a 10 kHz bandwidth has a noise floor of −174 + 40 + 6 = −128 dBm. A system with 15 dB NF in the same bandwidth has a noise floor of −174 + 40 + 15 = −119 dBm. The 6 dB NF system is 9 dB more sensitive. When comparing spectrum analyzers, always compare displayed average noise level (DANL) at the same RBW, or normalize both to 1 Hz.

However, this comparison only holds when the system is noise-limited, with no strong signals present. A system with a higher noise figure may handle strong signals far better, with higher dynamic range and a better intercept point, as later lessons in this module explain. The right choice depends on whether your application is limited by weak signals or by strong ones.

Practical Noise Floor Examples

Here are approximate noise floors for common equipment, to give a sense of real-world numbers:

The GPS line shows how far processing gain can go: GPS signals arrive at the earth's surface at about −130 dBm, some 20 dB below the receiver's noise floor, yet the receiver recovers them by correlating with the known spreading code of each satellite.

These values assume the external noise arriving at the input is below the system's own noise floor. That is not always true. A receiver connected to an antenna below about 30 MHz picks up atmospheric and man-made noise that often raises the effective floor by 10–30 dB, and a measurement circuit near a switching power supply or motor may see interference far above its thermal floor. In those cases, improving the noise figure is pointless until the external noise is dealt with — the subject of the EMI lessons later in this module.