Understanding noise figure

Signal to noise ratio (SNR)

To understand noise figure, we need to start with signal to noise ratio (SNR), which is simply the ratio of the power of a signal relative to the power of adjacent noise. Since power in radio frequency systems is normally reported in logarithmic units, SNR is also normally reported in logarithmic units, i.e., in decibels (dB). A high SNR is almost always desirable: the higher a signal is “above the noise,” the easier it is to both detect or “see” the signal. This also makes it easier to demodulate and extract information from the signal.

Ideal device

SNR cannot be improved by passing the input signal through an amplifier. This is because even an ideal amplifier would amplify both the signal and the noise by the same amount. The means that the SNRs of the signals entering and exiting the amplifier would be the same.

Real device

A real amplifier adds its own internal noise to the input signal. This added internal noise increases the amount of noise present in the amplified output signal. This means that the output SNR is always lower than the input SNR.

Although we’re using an amplifier as an example here, all active and even passive devices or components add noise to the signal and reduce output SNR. As such, it is helpful to quantify just how much noise a given device or component adds.

Noise figure

We can quantify SNR degradation by calculating the noise factor: the linear ratio of input SNR to output SNR. Since logarithmic units are much more widely used in RF than linear units, noise factor is usually then converted into logarithmic form, dB. This converted form is the noise figure.

Noise figure is typically measured with either a spectrum analyzer or vector network analyzer . These instruments use different methods to measure the noise figure. Here, we’ll only be covering noise figure measurement using a spectrum analyzer.

A special device called a noise source is used in conjunction with the spectrum analyzer to measure the noise figure. This source produces a known level of wideband noise, which is used as the DUT input signal. The amount of noise produced by the source is specified in terms of excess noise ratio (ENR).

This combination of a spectrum analyzer and noise source can be used to measure noise figure with the Y-factor method.

Y-factor method and spectrum analyzer noise measurement

The Y-factor method is the most widely used noise figure measurement method. A noise source is connected to the input of the device under test (DUT), and the DUT output is connected to a spectrum analyzer’s RF input. In almost all cases, the spectrum analyzer also controls and provides power to the noise source.

The difference in noise power at the DUT output and input is the Y-factor. Measurements are usually made and reported over a range of frequencies because the noise figure of a device tends to be a function of frequency. The gain of the DUT is often measured and reported as well.

The Y-factor method involves two measurements.

• Calibration or spectrum analyzer noise measurement: The noise source is attached to the spectrum analyzer input and used to measure the noise figure of the analyzer itself. This allows the analyzer’s noise factor to be mathematically removed from the DUT measurement result.
• Noise power: The noise power is measured, once with the noise source in the “off” state and another time with the noise source in the “on” state.

From here, you can calculate the Y-factor using a formula that gives you the linear ratio of the noise powers. Then, you use the Y-factor and ENR to calculate the noise figure of the DUT.

Additional noise figure measurement topics

Before we wrap up, let’s cover some additional details on noise sources: ENR, preamplifiers, noise figure measurement uncertainty and cascaded noise figure measurements.

The primary characteristics of noise sources are the supported frequency range and ENR, i.e., the level of noise the source can produce. Typically, noise source ENR values fall in the ranges of approximately 6 dB, 15 dB or 25 dB, with 15 dB being the most common. These are approximate values because a source’s ENR normally varies by a few dB over its frequency range.

Higher ENR values are needed to measure devices with higher noise figures, and the source’s ENR should also be at least 3 dB higher than the noise figure of the spectrum analyzers. The ENR-versus-frequency values of the noise source are referred to as calibration data. Modern noise sources often store this calibration data internally, and the analyzer can then read the ENR-versus-frequency values directly from the source. Such smart noise sources can also measure temperature changes, and this allows the analyzer to compensate for measurements that are not made at the “standard” noise figure temperature of 290 degrees Kelvin.

Preamplifiers also affect noise figure measurements. Accurate noise figure measurements almost always require the use of an external or internal preamplifier, and this is especially true when the DUT has a low noise figure and low gain. This is because the noise figure of the spectrum analyzer itself is often the largest contributor to measurement uncertainty. When the spectrum analyzer has a high displayed average noise level, or DANL, this can make it difficult to accurately measure small amounts of noise added by the DUT.

Most modern spectrum analyzers have an optional internal preamplifier, which (when enabled) reduces the DANL and thus also the noise figure measurement uncertainty. The preamplifier is treated as part of the measurement system, and the preamplifier’s own noise figure can easily be calibrated out of the measurement results.

Speaking of noise figure measurement uncertainty, most spectrum analyzers include an uncertainty calculator application, which takes user-entered values to automatically calculate the measurement uncertainty. These applications often also include guidelines on the recommended minimum values for ENR, spectrum analyzer noise figure, etc.

The last special topic we’ll touch on is cascaded noise figure. The combined noise figure of cascaded components can be calculated from the individual gain and noise figure of each component or “stage.” However, the combined noise figure is not a simple addition of each component’s noise figure. Instead, cascaded noise figure is calculated using the Friis equation. This equation uses linear terms and can be expanded to any arbitrary number of stages. As we can see in this example, even if the same amount of noise is added by each stage, the noise added by subsequent stages is a smaller percentage of the total noise. As a result, the noise figure of a cascade tends to be dominated by the first stage, meaning that the component with the lowest noise figure should always be placed at or near the front of the chain.