How to determine noise figure: part 1

A noise figure consolidates the effects of various noise types to provide a single specification for the noise performance of a component or system.

In electronic circuits and systems, noise is an undesirable, inevitable disturbance in currents and voltages. Noise has many underlying fundamental causes. Thermal noise, also known as Johnson–Nyquist noise, results from random thermal motion of electrons and is generally white noise, with the noise power spectrum spread uniformly across the bandwidth of interest. Flicker noise results from conductive-channel irregularities or transistor bias currents. Pink noise, flicker noise, is also known as 1/f noise because its power spectral density is inversely related to frequency. Shot noise results from discrete electrons crossing a gap. These forms of noise are joined by partition noise, burst noise, transit-time noise, and others. These different forms of noise can all be treated individually, but having a single parameter that describes a component or system’s overall noise performance can be helpful. That parameter is called noise figure (NF).

I recall a series on phase noise. Should phase noise be added to the list above?

Phase noise results from some of the underlying noise sources listed. For example, a modulator can upconvert low-frequency flicker noise to the frequency of a carrier, which can contribute to phase noise.

What’s the definition of NF?

Back in the 1940s, the Danish-American radio engineer Harald Friis defined a device’s noise factor, labeled F, as the power signal-to-noise ratio (SNR) at a device or system input divided by the power SNR at the output, where S_IN, S_OUT, N_IN, and N_OUT are the input and output signal levels and the input and output noise levels, respectively:

Noise figure is generally expressed in decibels and relates to F as follows:

Because we know that division becomes subtraction in the logarithmic world of decibels, we can also express NF in decibels as follows, where S_IN, S_OUT, N_IN, and N_OUT are all decibel values:

Could you illustrate that with specific signals and noise levels?

See Figure 1, which represents the performance of an ideal amplifier. The blue trace indicates the input signal, with a peak of –55 dBm at 2.25 GHz and a noise floor of about –85 dBm. Consequently the input SNR ( equals –55 dBm – (–85 dBm) = 30 dB. The red trace illustrates the output of an ideal amplifier in response to the blue input trace. The red trace shows a signal peak of –45 dBm and a noise level of –75 dBm, so the amplifier has added 10 dB of gain to the noise and the signal. For the red trace, the output SNR () equals –45 dBm – (–75 dBm) = 30 dB. That’s the same as the input SNR, so the noise figure NF = 30 dB – 30 dB = 0.

Figure 1. Given the input indicated by the blue trace, an ideal amplifier adds 10 dB to both the signal and the noise (red trace).

What happens with a nonideal amplifier?

Figure 2 represents the more realistic scenario of a nonideal amplifier with a gain of 10 dB. This amplifier adds 10 dB to the signal, as in Figure 1, but also contributes an extra 5 dB of noise. For Figure 2, the input SNR remains 30 dB, but the output SNR equals –45 dB – (–70 dB) = 25 dB. The noise figure is, therefore, NF = 30 dB – 25 dB = 5 dB.

Figure 2. A nonideal amplifier (whose output trace is shown in red) adds 10 dB to the signal, as in Figure 1, but it also adds 5 dB of noise.

So, a low noise-figure value is good, and a higher one indicates poorer performance.

Right. An amplifier with a noise figure of 0 dB adds no noise of its own; it simply amplifies the input noise. In contrast, an amplifier with a nonzero noise figure amplifies the input noise and adds additional noise of its own.