Detailed explanation of the two methods of noise figure measurement, do you get it?
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Noise Figure Basics at a Glance There are many ways to quantify noise figure and noise factor. One of the earliest definitions was given by Harold Friis in the 1940s. In Friis's definition, the noise factor (the linear equivalent of noise figure) is the reduction in the signal-to-noise ratio (SNR) of a given signal passing through a given component. Both noise factor and noise figure are unitless quantities, with noise factor expressed linearly and noise figure expressed logarithmically. Equation 1. Noise Factor as a Function of SNR As shown in Equation 1, if the SNR of the signal at the LNA input is 100dB and the noise figure is 5dB, then the SNR at the output is 100-5dB = 95dB. As shown in Figure 10, a “black box” component with a noise figure of XdB will degrade the SNR by XdB. Figure 10. The noise figure is the sum of the intrinsic noise power and the thermal noise power of the component. Another definition of noise figure is the additional noise power introduced by specific active and passive devices at a normal temperature thermal noise power of -174dBm/Hz, expressed in dB. This definition is consistent with the IEEE definition of noise factor, which has been widely accepted and is expressed in Equation 2.
where k represents the Ertzmann constant T0 represents normal temperature B represents bandwidth G represents the gain of the DUT Equation 2. Formal Definition of Noise Factor In Equation 2, kTo is simplified to the thermal noise at room temperature, which is -174dBm/Hz. Therefore, the noise factor is equal to the signal power plus the noise power introduced by the components. For example, with an antenna connected to an LNA, the noise power at the LNA input is -174dBm/Hz. At the output of the LNA, the noise power is -174dBm/Hz plus the noise figure of the LNA. In this case, a noise figure of 5dB will produce an output noise power of -169dBm/Hz. Note that in this case, since the noise figure is expressed logarithmically, the noise power is directly equal to 5dB plus -174 dBm/Hz. Noise Unit Conversion Before introducing the noise figure measurement in detail, it is necessary to first clarify the definitions of some commonly used units and terms for noise measurement. The most common measurement parameters include noise figure, noise factor and noise temperature. The noise figure (NF) is equal to the noise power of the device plus the thermal noise power, expressed in dB. The noise factor (F) is a linear representation of the noise power introduced by the device on top of the thermal noise. NF can be converted to F and vice versa using equations 3 and 4. Equations 3 and 4. Conversion formulas between noise factor and noise coefficient "]A related expression for noise power is noise temperature. Since noise power is proportional to the Kelvin temperature of the device, noise temperature (Te) is the equivalent temperature of the device when it produces a certain amount of noise power. It is important to note that the equivalent noise temperature of the device is only a theoretical value and is only used to represent the theoretical temperature at which the passive device produces a specific noise power level. Equations 5 and 6 describe the relationship between noise temperature and noise figure.
Equation 5. Noise temperature is a function of noise factor Equation 6. Noise factor is a function of noise temperature and vice versa In Equations 5 and 6, T0 typically refers to room temperature or 290K. According to these two equations, a device with a noise factor of 4 or a noise figure of 6.02 dB has an equivalent temperature of 290 K (4-1) = 870 K. Based on this calculation, the inherent thermal noise of a device heated to 870 K is 6.02 dB higher than the thermal noise of a device at room temperature of 290 K. Therefore, an equivalent temperature of 870 dB is equivalent to a noise factor of 4 or a noise figure of 6.02 dB. The Friis formula used to calculate the noise factor of a cascaded RF system is very important for measuring noise factor. This is because when measuring the noise figure of a device, all measurement parameters must be taken into account, including the noise of the device under test and the noise of the instrument itself. The Friis formula applies to the cascaded RF system shown in Figure 11. Cascaded RF System Note that the Friis formula requires that both noise and gain be expressed in linear rather than logarithmic form. Also note that if the first component in the system has a high gain, such as an LNA, then the noise factor of the system can usually be ignored and only the first two terms in Equation 7 need to be considered, so Equation 7 can be simplified to Equation 8. Equation 8. Noise Factor for a Two-Stage Cascaded System Similarly, we can calculate the noise temperature of the cascade using a similar equation. Substituting the noise factor for the noise temperature in the equation shows that the noise temperature of the first component in the cascade system is equal to the system noise factor minus the noise of the second component, as shown in Equation 9. Equation 9. Noise Temperature for a Two-Stage Cascade System Noise Figure Measurement Although there are several methods for measuring noise figure,the two most commonly used methods are the cold source method (also called the gain method) and the Y-factor method. The basic principle of the gain method is to terminate the input of the device under test and then use a signal analyzer to measure the output noise of the DUT, as shown in Figure 12. In this case, the output noise power is the result of the inherent noise of the DUT amplified by the gain of the DUT. Figure 12. Using the cold source method requires terminating the input of the DUT. 51)]The cold source method is usually most effective for high-gain LNAs, because the signal analyzer can more accurately measure the noise power for signals that are significantly above its inherent noise floor. One disadvantage of the cold source method is that it is susceptible to uncertainty in the voltage standing wave ratio (VSWR). In addition, common methods of improving VSWR, such as using an external attenuator, will reduce the instrument's ability to measure low-power signals. Therefore, if the VSWR can be compensated, the cold source measurement technique will provide more accurate results. In fact, assuming the noise floor is low enough, a network analyzer can occasionally be used to measure noise figure because the network analyzer can reduce the uncertainty caused by VSWR. Y-Factor Method Based on Calibrated Noise Sources The second noise figure measurement method, perhaps the more common one, is the Y-factor method. This method introduces a calibrated noise source into the LNA or PA and measures the noise power when the noise source is turned on and off. The Y-factor method is simpler if the DUT and signal analyzer are part of a two-stage cascaded RF system, as shown in Figure 13.51, 51)]Figure 13. Connecting an LNA to a signal analyzer forms a cascaded RF system With the noise source (usually an LNA or demodulator) connected to the input of the DUT, the test system can be modeled as a two-stage system. In this case, the noise figure of the system includes the noise figure of the first component, the LNA, and the noise contribution of the RF signal analyzer. The Y-factor method aims to measure the noise figure of the DUT (F1) by first solving for the noise figure of the system (F12) and the gain of the DUT (G1). Therefore, the process of measuring the noise figure of an RF component using the Y-factor method consists of the following two steps: 1. Measure the noise figure of the signal analyzer. 2. Measure the noise figure of the system after connecting the DUT. An important component of a Y-factor test system is a calibrated noise source. A calibrated noise source is very useful when measuring noise figure because it provides a noise-like signal to the device under test (DUT) at a relatively low power level. The noise source has two settings, on and off, and its characteristic parameter is the excess noise ratio (ENR). The ENR can be expressed by Equation 10, where TsON and TsOFF represent the equivalent temperature and noise power for each setting. In actual measurements, it is usually assumed that TsOFF = T0 = 290K. The ENR of a noise source is usually printed directly on the device or noted in the specification document, and typical ENR values range from 5 dB to 30 dB, depending on the actual application. ENR is essentially the ratio of the power when the noise source is on to when it is off. Step 1: Analyze the Signal Analyzer’s Noise Figure Characteristics The first step in measuring noise figure using the Y-factor method is to measure the signal analyzer’s noise figure without the DUT connected. Note that the noise source typically requires a 28 VDC power supply provided through the 28 VDC port of the RF signal analyzer, as shown in Figure 14. Figure 14. Measuring the intrinsic noise figure of a signal analyzer by connecting a noise source directly to the signal analyzer. In the system shown in Figure 14, the Y factor is the ratio of two noise power levels, one measured with the noise source turned on and the other with it turned off. Therefore, the Y factor measurement is a function of the two power measurements, Non and Noff. Note that the ratio of Non to Noff must be expressed linearly, with the noise power in watts. This is shown in Equation 11.
Equation 11. The Y factor is the ratio of Non to Noff. Non and Noff can be measured using the channel power measurement function of an RF signal analyzer. Since the accuracy of noise figure measurements using an RF signal analyzer depends on the noise figure of the instrument itself, it is necessary to minimize the noise figure of the instrument by following the steps below: 1. Turn on the instrument's preamplifier (if any). 2. Set the reference level as low as possible, typically less than -50dBm. 3. Manually set the instrument's attenuation to 0dB. Note that for high-gain DUTs, the benefit of adjusting the instrument’s attenuation to greater than 0 dB may outweigh the noise floor reduction that can be achieved by zeroing the attenuation. Although the Y-factor method theoretically reduces the uncertainty introduced by the VSWR, a small amount of error introduced by the VSWR may still exist because the signal analyzers may not match each other during the calibration and measurement steps. After completing the above setup, the in-band power measurement method can be used to measure the noise power of the RF signal analyzer. The in-band power measurement provides a more accurate noise power measurement than simply measuring the noise floor using a marker. If you want to measure power in dBm, simply replace dBm in equation 12 with W. Equation 12. Power in Watts as a Function of dBm Because the in-band power measurement method measures the noise power over a large frequency bin, the bandwidth of the measurement can significantly affect the power measurement result. For example, -90dBm in a 1MHz bandwidth is equivalent to -100dBm in a 100kHz bandwidth. Therefore, noise power is usually expressed in dBm/Hz, as shown in Equation 13. Equation 13: Converting Measured Power to dBm/Hz It is important to note that while expressing noise power in dBm/Hz provides information about the signal analyzer noise floor, the measurement bandwidth will generally not affect the Y-factor ratio unless the measurement bandwidth is wider than the bandwidth of the noise signal itself. Assuming the same measurement bandwidth is used to measure Non and Noff, the units of the two bandwidths cancel each other out. A general rule of thumb is to make the measurement bandwidth narrower than the output bandwidth of the noise source and equal to or narrower than the bandwidth of the DUT signal to be amplified. Once the Y-factor is determined based on the power measurement method described above, the noise figure is simply a function of the ENR and the Y-factor, as shown in Equation 14. Equation 14. Noise Figure is a Function of ENR and Y Factor "]Or you can use noise temperature to express the noise, and then solve the noise coefficient and noise factor. Assume that the noise source is turned off T0 = 290K (room temperature), then the noise temperature of the noise source in the on state is a function of ENR. Using equations 15 and 16, we can first solve the noise temperature of the noise source for ENR. Then use this value and the measured Y factor to calculate the noise temperature of the signal analyzer. Equations 15 and 16. Using the Y Factor to Determine the Noise Temperature of a Signal Analyzer Step 2: Insert the DUT The noise figure/noise factor/noise temperature of the RF signal analyzer can be solved by connecting the noise source directly to the signal analyzer. The noise figure of the system with the DUT connected can then be measured. Therefore, the output of the noise source needs to be connected to the input of the DUT, as shown in Figure 15. Steps to measure the Y factor Figure 15. Measuring the noise figure of an RF system with the DUT connected After connecting the DUT between the noise source and the signal analyzer, the terms F12, G12, and T12 represent the noise figure, gain, and noise temperature of the entire system, respectively. Similar to the calibration step, the Y factor of the entire system needs to be calculated next. This step measures the system or cascaded Y factor, and then finally calculates Y12. Equation 17. The Y factor of the system is the ratio of the measured noise with the DUT connected. The noise figure or noise temperature of the system can also be calculated using Equations 18 or 19, respectively. Equation 18. Noise Figure Calculation Formula (in dB) 51)]Equation 19. Noise Temperature Calculation Formula (in Kelvin) Once the noise figure (NF12) or noise temperature (T12) of the entire system is determined, the Friis formula can be used to calculate the noise figure of the DUT. Step 3: Calculate Noise Figure After measuring the noise figure or noise factor of the signal analyzer and the measurement system connected to the DUT, it is almost possible to solve for the noise figure of the DUT. However, before doing so, the gain of the DUT must be calculated, as shown in Equation 20. Equation 20. Gain Calculated Based on Four Noise Power Measurements Once the system noise figure (F12) and the DUT gain (G1) are determined, the Friis formula can be used to solve for the noise figure of the DUT, as shown in Equation 21. It is important to note that the Friis formula expresses the noise figure in a linear manner, so any units of gain or noise figure must be converted to linear terms. Equation 21. Calculating the Noise Factor of the DUT Using the Measurement Results Alternatively, if all of the measurement results are expressed in terms of noise temperature, then Equation 22 can be used to solve for the noise temperature of the DUT. Equation 22. Calculating the Noise Temperature of the DUT Using the Measured Results Again, the gain must be expressed linearly. Once the equivalent noise temperature of the DUT (T1) is calculated, it can be converted to a noise figure using Equation 23. Equation 23. Conversion of noise temperature to noise factor at T0 = 290K "]The Y-factor method for measuring noise figure is a relatively accurate method for measuring LNA or even RF noise figure. Although understanding noise figure, noise factor, and noise temperature requires a certain theoretical foundation, as long as you master the basic knowledge, you can accurately measure the noise figure. BlinkMacSystemFont, "]Equation 21. Calculating the Noise Factor of the DUT Using Measurement Results Alternatively, if all measurement results are expressed in terms of noise temperature, equation 22 can be used to solve for the noise temperature of the DUT. Equation 22. Calculating the Noise Temperature of the DUT Using the Measured Results Once again, the gain must be expressed in a linear fashion. Once the equivalent noise temperature of the DUT (T1) is calculated, it can be converted to a noise factor using Equation 23. Equation 23. Converting Noise Temperature to Noise Factor at T0 = 290K The Y-factor method for measuring noise figure is a relatively accurate method for measuring LNA and even RF noise figure. Although understanding noise figure, noise factor and noise temperature requires a certain theoretical foundation, as long as you master the basic knowledge, you can accurately measure the noise figure. BlinkMacSystemFont, "]Equation 21. Calculating the Noise Factor of the DUT Using Measurement Results Alternatively, if all measurement results are expressed in terms of noise temperature, equation 22 can be used to solve for the noise temperature of the DUT. Equation 22. Calculating the Noise Temperature of the DUT Using the Measured Results Once again, the gain must be expressed in a linear fashion. Once the equivalent noise temperature of the DUT (T1) is calculated, it can be converted to a noise factor using Equation 23. Equation 23. Converting Noise Temperature to Noise Factor at T0 = 290K The Y-factor method for measuring noise figure is a relatively accurate method for measuring LNA and even RF noise figure. Although understanding noise figure, noise factor and noise temperature requires a certain theoretical foundation, as long as you master the basic knowledge, you can accurately measure the noise figure.
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