Spectrum Analyzer CW Power Measurements and the Effects of Noise

Spectrum Analyzer CW Power Measurements and the Effects of Noise
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Spectrum Analyzer CW Power Measurements and the Effects of Noise

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    1The following article appeared in the December 2012 edition of NCSLI Measure: TheJournal of Measurement Science, with all rights under copyright of NCSL International.Spectrum Analyzer CW Power Measurementsand the Effects of NoiseThe frequency discrimination capability of spectrum analyzers make...

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    2continuous wave (CW) signal of known frequency in the presence of noise. It is important toremember the assumption of a CW signal, as different results will be obtained for other signalssuch as those with pulsed or spread-spectrum characteristics [4].The model of a spectrum analyzer signal + noi...

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    3Noise MeasurementsGiven the noise voltage.ܰ=ටܰ୧ଶ+ܰ୯ଶ,thedistributionofthenoisevoltagewillbedescribedby the Rayleigh distribution which can be expressed as݂(ݔ)=௫ఙమ݁ି௫మଶఙమ/.(1)where e = 2.71828… (Euler’s number).Figure 2. The Rayleigh distribution.To measure t...

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    4The variance of power averaging is given byvar(݌)=∫ (݌−݌̅)ଶஶ଴ PDF(ݒ)݀ݒ=න ቀ௩మோ−ଶఙమோቁଶஶ଴௩ఙమ݁ି௩మଶఙమ/݀ݒ,(3)where p is the power, which equalsଵோమఙమ∫ (ݒହ−4ݒଷߪଶ+4ߪସ)ஶ଴݁ି௩మଶఙమ/݀ݒ=൫଼ఙల...

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    5Converting the standard uncertaintyටସି஠஠intodecibelswillequalටସି஠஠20logଵ଴݁=4.54dB(10)Logarithmic averagingIn theory we could compute the average power when measuring noise using logarithmic poweraveraging by evaluating݌logതതതതത=න 10logቀ௩మோቁஶ଴PD...

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    6whereRsns = signal + noise to signal voltage ratiom= signal to noise power ratio.When measuring the log of the power the measurement bias equalsrsns=10logଵ଴݁ቆ−ln݉−ߛ+݁ି௠෍ ௠ೖ௞!ஶ௞ୀଵ ቀ1+ଵଶ+ଵଷ+⋯+ଵ௞ቁቇ, (14)wheresns = signal + noise to signal log...

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    7Figure 4. Signal + noise measurement bias (logarithmic scale).Standard Deviation of Signal + Noise MeasurementsAs described in the Application Note, Spectrum and Signal Analyzer Measurements andNoise[3], the noise can be broken into two components: one in-phase with the signal and anotherout of ...

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    8ߪ=20logଵ଴݁ቀ10ିSNRశయమబቁ=8.69ቀ10ିSNRశయమబቁdB.(16)Recognizing that the signal to noise power ratio is defined by݉=10SNRభబ(17)and rearranging some terms, we can restate Eq. 8,(16) asߪ=ටଶ௠10logଵ଴݁ dB(18)For large signal to noise ratios, this result i...

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    9݌̅=௏౩మାଶఙమோ.(22)Combining Eq. 8,(19), 8,(21), and 9,(22) into Eq. 8,(20) producesvar(݌)=ଵோమප ൫4ܸୱଶݒ୧ଶ+4ܸ௦ݒ୧ଷ+4ܸ௦ݒ୧ݒ୯ଶ−8ܸୱݒ୧ߪଶ+ݒ୧ସ+2ݒ୧ଶݒ୯ଶ−4ݒ௜ଶߪଶ+ݒ୯ସ−ஶିஶ4ݒ୯ଶߪଶ+4ߪସ൯ଵఙ߮...

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    10Voltage and logarithmic power averagingThe calculations for the variance of a CW signal measured in the presence of noise when usingvoltage or logarithmic power averaging are significantly more challenging than that for poweraveraging. However, equations based onpwr that model the behavior f...

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    11Figure 5. Signal + noise measurement standard deviation.Measurement Standard Deviation and AveragingThe equations derived so far apply to individual measurements. If multiple measurement samplesare averaged together the expected measurement bias does not change but the standard deviationwill de...

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    12A simplified spectrum analyzer block diagram is shown in Fig. 6 (see the application note,Spectrum Analyzer Basics [7], for more information). Each of the major components will beexamined in turn for their impact on signal + noise measurements.Figure 6. Simplified spectrum analyzer block diagra...

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    13Frequency spanIf the signal frequency is known, then performing a frequency sweep serves no useful purpose –all measurement time should be spent at the frequency of interest. The frequency reference of thespectrum analyzer should be locked to that of the signal source and the spectrum analyze...

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    14What happens when the resolution bandwidth is decreased by a factor of 10? The backgroundnoise level should decrease 10 dB, reducing the uncertainty for a single measurement (thenumerator in Eq. 13,(34)) by a factor of√10.However,giventhatthenoisebandwidthisnominally proportional to the reso...

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    15Detector typeThe amplitude display of the spectrum analyzer is broken into a number of separate ‘buckets’,also referred to as sweep points. For each bucket a certain number of measurement samples arecollected by the envelope detector. The sample(s) used to produce the amplitude displayed is...

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    16sweep. This non-measurement time can be especially significant for small resolution bandwidths.If possible, the required measurement integration time should be pre-calculated based on thesignal to noise ratio, the sweep time set to this value, and a single sweep should be performed.Optimizing N...

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    17SummarySignal + noise measurementsWhen measuring signal + noise, the measurement parameters in Table 3 are recommended. Themeasurement bias and standard uncertainties of signal + noise measurements are given in 17,Table 17,4and Table 5.ParameterSettingFrequency SpanZeroDetector TypeAverageAve...

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    186.14ቀ10ିೄಿೃమబቁdB(37)For time averaged measurements, the standard uncertainty is reduced by the square root of theproduct of the measurement time and the equivalent noise bandwidth of the spectrum analyzer.For example, for large signal to noise ratios the standard uncertainty wou...

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    19ConclusionsWhen measuring CW signals of known frequency, and noise is a concern, a spectrum analyzershould be configured for a zero span measurement using the average detector. If necessary, thenormalized noise floor can be efficiently determined using power averaging and a wideresolution bandw...