37W-30477-0 Noise Figure WP
Noise FigureOverview of Noise Measurement MethodsIntroductionNoise, or more specifically the voltage and current fluctuations caused by the random motion ofcharged particles, exists in all electronic systems. An understanding of noise and how itpropagates through a system is a particular concern in RF and microwave receivers that mustextract information from extremely small signals. Noise added by circuit elements can concealor obscure low-level signals, adding impairments to voice or video reception, uncertainty to bitdetection in digital systems and cause radar errors.Measuring the noise contributions of circuit elements, in the form of noise factor or noisefigure is an important task for RF and microwave engineers. This paper, along with itsassociated appendices presents an overview of noise measurement methods, with detailedemphasis on the Y-factor method and its associated measurement uncertainties.1White Paper
Noise FigureOverview of Noise Measurement MethodsContentsNoise Measurements . 4Noise Factor, Noise Figure and Noise Temperature . 5Active Devices . 5Passive Devices . 8Noise Figure of Cascaded Stages . 9Effective Noise Temperature of Cascaded Stages . 10Noise Figure Measurements . 10Y-factor Method . 10Cold Source or Network Analyzer Method . 12Signal Generator (Twice Power) Method . 13Direct Noise Measurement Method . 13Noise Figure Measurements in Frequency Converters . 14Frequency Converters with Image Rejection. 14Image-reject Filter Included in the Measurement . 16Image-reject Filter Excluded in the Measurement . 18The Nature of Random Noise . 22Thermal Noise . 22Power Spectral Density of Thermal Noise . 22Shot Noise. 23/ Noise . 24Noise Power Spectral Density Graph . 25Noise in Electronic Components . 26Resistors . 26Capacitors . 26Inductors . 27Active Devices . 27Conclusion . 282White Paper
Noise FigureOverview of Noise Measurement MethodsAppendicesAppendix 1: Noise of a Resistor, Capacitor and Inductor. 29Resistors . 29Capacitors . 30Piezoelectric Effects in Capacitors . 32Inductors . 32Appendix 2: Shot Noise . 33Computing Shot Noise . 33Derivation Assuming a Poisson Distribution . 33Appendix 3: Bandwidth Equivalent of Averaging . 35Appendix 4: Avalanche Diode Noise Sources . 36Avalanche Breakdown. 36Noise Mechanism . 37A Practical Noise Source. 37Appendix 5: Error Analysis of the Y-factor Method . 38Y-factor Measurements . 38Noise Factor of a Measurement Receiver . 38Noise Factor of the DUT Cascaded with the Measurement Receiver . 38Uncertainty in Noise Factor Measurements . 39Sensitivities to Measurement Errors . 44Computing the Sensitivities for Device Gain . 51Sensitivity ofto Power Measurement Errors. 51Computing the Gain Sensitivities to the Power Measurement Errors . 52Summary of Errors . 57Errors in Measuring Noise Factor . 57Errors in Measuring Device Gain . 57Statistical Distribution of Measurement Errors . 59ENR . 59Receiver Gain Error . 59Mismatch Errors . 60Coverage Factor . 61Example of Contributions to Noise Figure Measurement . 623White Paper
Noise FigureOverview of Noise Measurement MethodsNoise MeasurementsThe noise contribution from circuit elements is usually defined in terms of noise figure, noisefactor or noise temperature. These are terms that quantify the amount of noise that a circuitelement adds to a signal. They can be measured directly using available test equipment aswell as modeled using both system and circuit simulation SW.Figure 1. Example of an amplifier with signal, thermal noise and additive noiseConsider the amplifier1 shown schematically in Figure 1. Its intended job is to amplify the signalpresented at its input and deliver it to the load. The thermal noise that is present at the input isamplified along with the input signal. The amplifier also contributes additional noise. The loadreceives a composite signal made up of the sum of the amplified input signal, the amplifiedthermal noise and the additional noise contributed by the amplifier. Noise figure, noise factorand noise temperature are figures of merit used to quantify the noise added by a circuit element,the amplifier in this case.14This paper assigns all added noise to the output of the amplifier. Other derivations exist where the added noiseis modeled at the DUT input.White Paper
Noise FigureOverview of Noise Measurement MethodsNoise Factor, Noise Figure and Noise TemperatureNoise factor is defined as the signal-to-noise ratio at the input divided by the signal-to-noiseratio at the output. Noise factor is always greater than unity as long as the measurementbandwidth is the same for the input and output.Equation 1Noise figure is Noise Factor expressed in dB .Equation 2The definitions for noise figure and noise factor are valid for any electrical network, includingfrequency converting networks that contain mixers and IF amplifiers (up-converters or downconverters).Active DevicesIf we consider an electrical network such as amplifier or frequency converter with input signalwe have, voltage gainand additive noise referred to the output of ,is the noise present at the input to the system. The parentheticalis used towhereindicate that these are frequency-dependent quantities. For simplicity, we will drop thisfunctional notation in the remainder of the paper unless it is needed for clarity. ,Equation 3An important case exists when the noise at the input is thermal noise, .has a flat .refers to Boltzmann’spower spectral density with power level of constant, to the absolute temperature in degrees Kelvin and to the system bandwidthexpressed in Hertz.at 300 Kelvin has a value of 4.14X10-21 W or -174 dBm whenmeasured in a one Hz bandwidth.5White Paper
Noise FigureOverview of Noise Measurement MethodsSimilarly, the signal-to noise ratio at the output is given by ,Equation 4where is the voltage gain of the device under test (DUT) andthe DUT. The noise factor can be computed by taking the ratio.is the noise voltage added by Equation 5 It is often more practical to use power gain instead of voltage gain. Let the power gain of thesystem be Equation 5 becomes Equation 6In the case where the input noise is thermal noise or in the above equation refers to a standard temperature, usually 290K.6White PaperEquation 7
Noise FigureOverview of Noise Measurement MethodsNoise factor and noise figure are an indication of the excess noise (beyond the system thermalnoise) contributed by a functional block in a system.Effective noise temperature refers to the temperature that a matched input resistance wouldrequire to exhibit the same added noise. Equation 8Effective noise temperature can be related to noise factor by Equation 9.Equation 10is the reference temperature, usually 290K. Figure 2. Noise Temperature vs. Noise Figure shows agraph of Noise Temperature versus Noise Figure. A noiseless device has a noise temperatureof absolute zero or 0 K, while a 4 dB noise figure is equivalent to a noise temperature ofapproximately 430 K.Noise Temperature VS Noise FigureReference Temp 290KNoise Temperature (K)10001001010123Noise Figure (dB)Figure 2. Noise Temperature vs. Noise Figure7White Paper45
Noise FigureOverview of Noise Measurement MethodsPassive DevicesPassive devices, those composed only of resistive or reactive elements, have a power gain lessthan or equal to unity and contribute no additive noise beyond thermal noise. The noise powerat the output when the input is terminated is always. Applying Equation 5 and Equation 6we have Equation 11 The above equation states that the noise figure of a passive device is the reciprocal of its powergain. A 3 dB attenuator (8White Paper) for example would have a 3 dB noise figure.
Noise FigureOverview of Noise Measurement MethodsNoise Figure of Cascaded StagesConsider a two-port network consisting of two stages. The first stage has thermal noise presentat its input. This thermal noise is amplified by the first stage gain and has any additive noiseproduced by the first stage added to it. The noise at the output of the first stage is then . Equation 12The second stage has the output of the first stage presented to it. The second stage amplifiesthe input and contributes additional noise. . Equation 13The principle illustrated above can be extended for multiple stages. Equation 14The noise factor is the ratio of the SNR at the input to the SNR at the output. For a given inputsignal, the ratio for a cascade of k stages is Equation 15 Equation 16Applying Equation 6 to Equation 16 yields the noise figure calculation for a system consisting of kcascaded stages. Consider K stages in a system. The kth stage has power gainand noisefactor . Both the signal and the noise from previous stages arrive at the input of the kth stage.The contribution of the kth stage is reduced by the gain preceding it. Noise Figure calculation forthe cascade of K stages can be found from .Equation 17. Equation 17is often called the Friis formula2for cascaded stages. It is named after Danish-American electrical engineer Harald T. Friis.29Friis, H.T., Noise Figures of Radio Receivers, Proc. Of the IRE, July, 1944, pp 419-422.White Paper
Noise FigureOverview of Noise Measurement MethodsEffective Noise Temperature of Cascaded StagesThe same equation can be manipulated to give the effective noise temperature for cascadedstages. If we replace the noise factors of each stage by their effective noise temperature we get11 .Equation 18Noise Figure MeasurementsY-factor MethodThe Y-factor method uses a noise source that can be switched off and on. It is based ontwo power measurements, each performed with the same port impedances3 and the samemeasurement bandwidth. The Noise source has a specified amount of excess noise. This isspecified as the Excess Noise Ratio or ENR. ENR is the ratio of noise from the source to thesystem thermal noise or kTB, often expressed in dB. 1 Equation 19 1Equation 20Making a noise figure measurement using the Y-factor method involves the use of a switchablenoise source and four power measurements. The first two measurements are used tocharacterize the noise behavior of the receiver used to make measurements., is the power, is the powermeasured by the measuring receiver with the noise source in the OFF state.measured by the measuring receiver with the noise source in the ON state. The device undertest (DUT) is inserted between the noise source and the receiver for the next two powerandare the power measurements made at the DUT output with themeasurements.noise source turned OFF and ON respectively.There are then three steps in making the measurement. The first, often called the calibrationstep, is to measure the noise figure of the RF receiver used to make the power measurements.The second step is to make a noise figure measurement on the cascaded receiver and DUT.The next step is to de-embed the two measurements.Let the receiver noise figure be.3Equation 21Noise sources with a port impedance that changes between the “ON” and “OFF” states contribute additionalerrors to the noise figure measurement.10White Paper
Noise FigureOverview of Noise Measurement MethodsThe noise figure for the cascade of DUT and receiver has aEquation 22The power gain of the DUT is measured by taking the ratioEquation 23From the cascaded noise figure equation we haveEquation 24111111Equation 25Substituting the power ratios for the Y-factors, we get1Equation 26Equation 26 expresses the noise figure of the device under test interms of the four power measurements in the Y-factor method. This method relying on a seriesof power measurements is ideally suited to low-level measurement receivers. It has beenimplemented in modern spectrum analyzers as a cost-effective method of making noise figuremeasurements.11White Paper
Noise FigureOverview of Noise Measurement MethodsCold Source or Network Analyzer MethodThe cold source method essentially measures the noise power at the output of a device with aninput that is at the reference temperature (cold). It depends on very accurate knowledge of thedevice gain. Network Analyzers can measure gain with extreme accuracy, making them ideal forthis method. Like the Y-factor Method, the cold source method requires a calibration step todetermine the measurement receiver’s noise figure. This is done with the use of a calibratednoise source and a method similar to what is described in Equation 21.The gain of the device under test is then measured as a function of frequency using the usualnetwork analyzer methodology. A power measurement is then made as function of frequencybe the noise added bywith the cold source connected to the device under test. If we letbe the noise added by the receiver then the measured power isthe device under test and 1 1 Equation 27 Equation 28Some network analyzers4 offer a noise figure measurement option that includes low noisepreamplifiers in their receivers, calibrated noise sources and the software to makemeasurements. The Network Analyzer’s ability to make accurate transmission and reflectionmeasurements means that complete characterization of devices can be made that includeNoise Figure and S-parameters, making Network Analyzer measurements ideal for inclusionin software-based system models.4Agilent Application Note: High Accuracy Noise Figure Measurements Using the PNA‐X Series Network Analyzer.12White Paper
Noise FigureOverview of Noise Measurement MethodsSignal Generator (Twice Power) MethodMeasuring devices with a high noise figure presents a problem for the popular Y-factor method.The Y-factor approaches unity as the noise figure approaches the source ENR. This affects theaccuracy of the Y-factor measurement. The twice-power method uses a signal generator and ameasuring receiver with an accurately known noise BW such as a spectrum analyzer. The inputto the device under test is terminated with a load at approximately the reference temperature(usually 290K). A signal generator is then connected to the device under test until the measuredpower is exactly 3 dB or twice the power measured with the input terminated. At this point thesinusoidal power is exactly the same as the noise power and the noise factor can be calculated.Knowledge of receiver bandwidth is critical but of knowledge of device gain is not needed. Thenoise factor of the cascaded DUT and receiver can be computed fromEquation 29The noise factor for the DUT can be dis-embedded using the formula for cascaded noise figurein Equation 24.Direct Noise Measurement MethodDevices with high noise figure can be measured with directly with a spectrum analyzer or otherreceivers with accurately known bandwidths as long as the gain is known. The input to deviceunder test is terminated in a source that is near the reference temperature (290K). The noisepower at its output is measured and noise factor can be computed fromEquation 30Knowledge of receiver bandwidth is required, as is knowledge of device gain. The noise factor ofthe cascaded DUT and receiver can be computed from the formula for cascaded noise figure inEquation 24.13White Paper
Noise FigureOverview of Noise Measurement MethodsNoise Figure Measurements in Frequency ConvertersThe super-heterodyne receiver is at the core of most RF communi
Noise Figure Overview of Noise Measurement Methods 4 White Paper Noise Measurements The noise contribution from circuit elements is usually defined in terms of noise figure, noise factor or noise temperature. These are terms that quantify the amount of noise that a circuit element adds to a signal.
7 LNA Metrics: Noise Figure Noise factor is defined by the ratio of output SNR and input SNR. Noise figure is the dB form of noise factor. Noise figure shows the degradation of signal's SNR due to the circuits that the signal passes. Noise factor of cascaded system: LNA's noise factor directly appears in the total noise factor of the system.
Figure 1: Power spectral density of white noise overlaid by flicker noise. Figure 2: Flicker noise generated from white noise. 1.1 The nature of flicker noise Looking at processes generating flicker noise in the time domain instead of the frequency domain gives us much more insight into the nature of flicker noise.
the noise figure of the receiver. Noise figure has nothing to do with modulation or demodula-tion. It is independent of the modulation format and of the fidelity of modulators and demodulators. Noise figure is, therefore, a more general concept than noise-quieting used to indicate the sensitivity of FM receivers or BER used in digital .
extract the noise figure of the DUT from the overall system noise measurement. This step is referred to as second-stage noise correction, as the DUT’s mea-sured noise figure is corrected based on the gain and noise figure of a second stage, which in this case is the test instrument’s noise receiver.
A noise factor of 1, no degradation in signal to noise, produces a noise figure of 0 dB. HF receiver noise figures will range from about 10 to 20 dB. VHF and UHF receivers will often exhibit a lower noise figure, 8 to 15 dB, to take advantage of the lower atmospheric noise environment found there. The receiver noise figure is primarily a .
Where F rx is the receiver noise figure, F LNA is the LNA noise figure. F MIX is the mixer noise figure, GLNA is the LNA gain. Assuming that the LNA and mixer are the dominant contributors of noise, if the mixer noise figure is assumed to be 10dB, the maximum noise figure of the LNA is 4.5dB. Maximum swing at ADC output is 0.5V.
The Noise Element of a General Plan is a tool for including noise control in the planning process in order to maintain compatible land use with environmental noise levels. This Noise Element identifies noise sensitive land uses and noise sources, and defines areas of noise impact for the purpose of
Acceptance testing for AngularJS is done via the Protractor tool, which is a framework developed by the team behind AngularJS. It is worth noting that Protractor uses by default Jasmine as the testing framework and it was not until recently that CucumberJS was integrated to Protractor. You should also be aware of the fact that CucumberJS does not cover all the features provided by the standard .
