Three methods for noise figure measurement

Definition
The noise figure (noise factor) contains important information about the noise performance of a RF system. The standard definition is:

Many commonly used noise figure (noise factor) formulas can be derived from this definition.

The following table shows typical RF system noise figures:

The method for measuring noise figure varies from application to application. As can be seen from the table above, some applications have high gain and low noise figure (low noise amplifier (LNA) in high gain mode), some have low gain and high noise figure (mixer and LNA in low gain mode), and some have very high gain and a wide range of noise figures (receiver systems). Therefore, the measurement method must be carefully selected. This article will discuss the noise figure tester method and two other methods: the gain method and the Y-coefficient method.

Using a Noise Figure Tester
A noise figure tester/analyzer is shown in Figure 1.

A noise figure tester, such as the Agilent N8973A noise figure analyzer, generates a 28VDC pulse signal to drive a noise source (HP346A/B), which generates noise to drive the device under test (DUT). The output of the DUT is measured using a noise figure analyzer. Since the input noise and signal-to-noise ratio of the noise source are known to the analyzer, the noise figure of the DUT can be calculated internally and displayed on the screen. For some applications (mixers and receivers), a local oscillator (LO) signal may be required, as shown in Figure 1. Of course, certain parameters must be set in the noise figure tester before measurement, such as frequency range, application (amplifier/mixer), etc.

The most direct way to measure noise figure is to use a noise figure tester. It is also the most accurate in most cases. Engineers can measure the noise figure over a specific frequency range, and the analyzer can display both gain and noise figure to help with the measurement. Analyzers have frequency limitations. For example, the Agilent N8973A can operate from 10MHz to 3GHz. When measuring very high noise figures, such as noise figures exceeding 10dB, the measurement results are very inaccurate. This method requires very expensive equipment.

Gain Method
As mentioned earlier, in addition to using a noise figure tester directly, other methods can be used to measure noise figure. These methods require more measurements and calculations, but under certain conditions, these methods are more convenient and accurate. One commonly used method is called the "gain method", which is based on the definition of noise factor given above:

In this definition, noise is generated by two factors. One is interference arriving at the input of the RF system, which is different from the desired useful signal. The second is due to random perturbations of the RF system carrier (LNA, mixer and receiver, etc.). The second case is the result of Brownian motion. Applied to the thermal equilibrium in any electronic device, the available noise power of the device is: P _NA = kTΔF,
where k = Boltzmann's constant (1.38*10 ^-23 joules/ΔK),

So we have the following formula:

In the formula, P _NOUT is the measured total output noise power, and -174dBm/Hz is the power spectral density of the ambient noise at 290°K. BW is the frequency bandwidth of interest. Gain is the gain of the system. NF is the noise figure of the DUT. Each variable in the formula is logarithmic. To simplify the formula, we can directly measure the output noise power spectral density (dBm/Hz), and the formula becomes:

To measure noise figure using the gain method, the gain of the DUT needs to be predetermined. The input of the DUT needs to be terminated with a characteristic impedance (50Ω for RF applications and 75Ω for video/cable applications). The output noise power spectral density can be measured using a spectrum analyzer.

The gain method measurement device is shown in Figure 2.

As an example, we measure the noise figure of the MAX2700. The gain measured at the specified LNA gain setting and V _AGC is 80dB. Next, the instrument is set up as shown above, with the RF input terminated with a 50Ω load. The output noise power spectral density is read on the spectrum analyzer as -90dBm/Hz. To obtain a stable and accurate noise density reading, the optimal RBW (resolution bandwidth) and VBW (video bandwidth) are selected as RBW/VBW=0.3. The calculated NF is:
-90dBm/Hz + 174dBm/Hz - 80dB = 4.0dB.

The gain method can be applied to any frequency range as long as the spectrum analyzer allows it. The biggest limitation comes from the noise floor of the spectrum analyzer. From the formula, we can see that when the noise figure is low (less than 10dB), (P _OUTD - Gain) is close to -170dBm/Hz, and the gain of the LNA is usually about 20dB. This requires us to measure the noise power spectral density of -150dBm/Hz, which is below the noise floor of most spectrum analyzers. In our example, the system gain is very high, so most spectrum analyzers can accurately measure the noise figure. Similarly, if the noise figure of the DUT is very high (for example, above 30dB), this method is also very accurate.

The Y -factor
method is another commonly used method for measuring noise figure. In order to use the Y-factor method, an ENR (redundant noise ratio) source is required. This is the same noise source mentioned in the previous noise figure tester section. See Figure 3 for the setup diagram:

ENR heads usually require a high voltage DC power supply. For example, the HP346A/B noise source requires 28VDC. These ENR heads can operate over a very wide frequency band (for example, 10MHz to 18GHz for the HP346A/B) and have standard noise figure parameters at specific frequencies. The following table gives the specific values. The noise figure at frequencies between the labels can be obtained by extrapolation.

Table 1: ENR of noise head

In this formula, ENR is the value given in the table above. Usually the NF value of the ENR head is listed. Y is the difference in the output noise power spectral density when the noise source is turned on and off. This formula can be obtained from the following:

The ENR noise head provides a noise source with two noise temperatures:
hot temperature T = TH (when DC voltage is applied) and cold temperature T = 290°K. The ENR noise head is defined as:

The redundant noise is obtained by biasing the noise diode. Now consider the ratio of the power output of the amplifier (DUT) at the cold temperature T = 290 ° K and at the hot temperature T = _TH
: Y = G (Th + Tn) / G (290 + Tn) = (Th / 290 + Tn / 290) / (1 + Tn / 290).
This is the Y factor method, and its name comes from the above formula.

According to the definition of noise factor, F=Tn/290+1, F is the noise factor (NF=10*log(F)), so Y=ENR/F+1. In this formula, all variables are linearly related, and the above noise factor formula can be obtained from this formula.

We will again use the MAX2700 as an example to demonstrate how to use the Y-factor method to measure noise figure. The setup diagram is shown in Figure 3. Connect the HP346A ENR to the RF input. Connect a 28V DC voltage to the noise source. We can monitor the output noise power spectral density on a spectrum analyzer. By turning the DC power on and off, the noise spectral density changes from -90dBm/Hz to -87dBm/Hz. So Y=3dB. To get a stable and accurate noise power spectral density reading, RBW/VBW is set to 0.3. From Table 2, ENR=5.28dB at 2GHz, so we can calculate the NF value to be 5.3dB.

Summary
In this article, three methods for measuring the noise figure of RF devices were discussed. Each method has its advantages and disadvantages and is suitable for specific applications. The following table summarizes the advantages and disadvantages of the three methods. In theory, the measurement results of the same RF device should be the same, but due to the limitations of RF equipment (availability, accuracy, frequency range, noise floor, etc.), the best method must be selected to obtain correct results.