# The Four Ws of Noise Figure

Blog Post created by benz on May 30, 2017

If you're going to optimize it you have to quantify it

Note from Ben Zarlingo: This is the second in our series of guest posts by Nick Ben, a Keysight engineer. Here he turns his attention to the fundamentals of noise figure.

In the previous edition of The Four Ws, I discussed the fundamentals of spurious emissions. This time I’m discussing the WHAT, WHY, WHEN and WHERE of characterizing your system’s noise figure (NF) to process low-level signals for improving product design.

What

Noise figure, also known as noise factor, can be defined as the degradation of (or decrease in) the signal-to-noise ratio (SNR) as a signal passes through a system network. In our case the “network” is a spectrum or signal analyzer (SA).

Basically, a low figure means the network adds very little noise (good) and a high noise figure means it adds a lot of noise (bad). The concept fits only those networks that process signals and have at least one input and one output port.

Figure 1, below, provides the fundamental expression for noise figure. Figure 1. Noise figure is the ratio of the respective signal-to-noise power ratios at the input and output when the input source temperature is 290 °K.

Additionally, noise figure is usually expressed in decibels:

NF (in dB) = 10 log (F) = 10 log (No) – 10 log (Ni)

Why and When

Noise figure is a key system parameter when handling small signals, and it lets us make comparisons by quantifying the added noise. Knowing the Noise Figure value, we can calculate a system’s sensitivity from its bandwidth.

It’s important to remember that a system’s noise figure is separate and distinct from its gain. Once noise is added to the signal, subsequent gain stages amplify signal and noise by the same amount and this does not change the SNR.

Figure 2.a, below, shows an input to an amplifier, and the peak is 40 dB above the noise floor; Figure 2.b shows the resulting output signal. Gain has boosted the signal and noise levels by 20 dB and added its own noise. As a result, the peak of the output signal is now only 30 dB above the noise floor. Because degradation in the SNR is 10 dB, the amplifier has a 10 dB noise figure. Figure 2: Examples of a signal at an amplifier’s input (a) and (b) its output. Note that the noise level rises more than the signal level due to noise added by the amplifier circuits. This change in signal and noise is the amplifier noise figure.

Where (& How)

The open question: Where are the system noise sources that affect noise figure? Most noise consists of spontaneous fluctuations caused by ordinary phenomena in the electrical equipment, and this noise is generally flat. We perform measurements on this noise to characterize noise figure. These noise sources fit into two main categories: thermal noise and shot noise.

One more note: It’s important to consider that some of the power measured in a noise figure measurement may be some type of interference rather than noise. Therefore, it’s critical to be alert for and guard against this by performing measurements in shielded rooms to ensure we’re seeing only the spontaneous noise we want to measure.

Wrapping Up

If you’d like to learn more about characterizing noise figure and improving your product designs, recent application notes titled Three Hints for Better Noise Figure Measurements and Noise and Noise Figure: Improving and Simplifying Measurements include great explanations and how-to techniques as well as pointers to additional resources. You’ll find both in the growing collection on our signal analysis fundamentals page.

I hope my second installment of The Four Ws of X provided some information you can use. Please post any comments – positive, constructive, or otherwise – and let me know what you think. If this post was useful, please give it a like and, of course, feel free to share.