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Spectrum Analyzer CW Power Measurements
and Noise
2012 NCSL International Workshop and Symposium
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
Overview
• Signal + Noise Model
• Bias & Variance of Noise and Signal + Noise Measurements
• Variance of Averaged Measurements
• Spectrum Analyzer Block Diagram and Measurement Recommendations
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Signal + Noise Model
Signal
Noise = Ni + jNq
Signal+Noise
Ni distribution
Nq distribution
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Spectrum Analyzer Averaging Methods
• Averaging Types:
• Voltage
• Power
• Log Power
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Voltage Power Log Pwr(mV) (mW) (dBm)
Meas 1 16 0.01 -22.81Meas 2 79 0.12 -9.09Meas 3 84 0.14 -8.48Meas 4 762 11.62 10.65Meas 5 178 0.64 -1.97Meas 6 817 13.36 11.26Meas 7 964 18.60 12.70Meas 8 648 8.39 9.24Meas 9 923 17.02 12.31Meas 10 541 5.85 7.67Average 501 7.57 2.15Voltage 501 615 286Power 5.02 7.57 1.64Log Pwr 7.01 8.79 2.15
Noise – Measurement Bias
Averaging Bias (dB) Notes
Power 0 by definition
Voltage -1.05 -
Log Power -2.51 -
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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= Euler’s constant: 0.577216…
Noise – Standard Deviation of Discrete Measurements
Averaging Std Dev (dB) Notes
Power 4.34
Voltage 4.54
Log Power 5.77 Monte Carlo
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Signal + Noise – Measurement Bias
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Averaging Bias (dB)
Power
Voltage
Log Power
m = signal-to-noise ratio (W/W) = Euler’s constant: 0.577216…
Signal + Noise – Measurement Bias
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Signal + Noise – Standard Deviation of Discrete Measurements
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Averaging Std Dev (dB)
Power
Voltage (model based on Monte Carlo)
Log Power (model based on Monte Carlo)
m = signal-to-noise ratio (W/W)
Signal + Noise – Standard Deviation of Discrete Measurements
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Standard Deviation of Averaged Measurements
• Averaging Discrete Measurements – reduced by
• N = number of samples.
• Time Averaged Measurements – reduced by
• tint = integration (measurement) time
• NBW = noise bandwidth
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Filter Type Application NBW/RBW
4-pole sync Most SAs analog 1.128
5-pole sync Some SAs analog 1.111
FFT/digital FFT/digital IF swept SAs 1.056
Spectrum Analyzer Block Diagram
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Spectrum Analyzer Block Diagram – Input Attenuator and Preamplifier
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Attenuation = 0 dBPreamplifier On
but… don’t overdrive the mixer!
Spectrum Analyzer Block Diagram – Preselector
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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set based on impact to noise floor
Spectrum Analyzer Block Diagram – Frequency Span & Sweep Time
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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span = zerosweep time = based on noise uncertainty
Spectrum Analyzer Block Diagram – RBW
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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Signal + Noise: set RBW to give at least 8 dB SNR. Reducing RBW beyond this does not give any benefit (assumes log power averaging)
Noise: set RBW wide
(power averaging)
Spectrum Analyzer Block Diagram – RBW (Signal + Noise)
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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SNR > 8 dB produces negligible bias when using log power averaging
Spectrum Analyzer Block Diagram – RBW (Signal + Noise)
2012 NCSL International Workshop and Symposium
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SNR approximated by
Spectrum Analyzer Block Diagram – RBW (S+N)• Standard Uncertainty of discrete measurements
approximated by:
•
• m = SNR (W/W) =
• For time-averaged measurements:
• But
• Therefore: (time-averaged, SNR > 8 dB)
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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For time-averaged measurements, changing RBW does not change uncertainty due to noise
Spectrum Analyzer Block Diagram – Envelope Detector
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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detector = average
Spectrum Analyzer Block Diagram – Video Filter
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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video filter = “wide open”
Spectrum Analyzer Block Diagram – Averaging Type
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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averaging typenoise: powersignal + noise: log power
Spectrum Analyzer Block Diagram – Trace Averaging & Trace Points
Inputsignal
InputAttenuator
Preamplifier
Preselector
Mixer
Local Oscillator
Sweep Generator
Processing and Display
IF (Resolution Bandwidth) Filter
Video Filter
Envelope Detector
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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trace averages = 1trace points = anyfunction: average entire trace
Spectrum Analyzer Block Diagram – Summary of Recommendations
Function Noise Signal + Noise
Input Attenuation 0
Preamplifier On
Preselector based on impact to noise floor
Frequency Span Zero
Resolution Bandwidth widenarrow enough for SNR > 8 dB
Detector average
Video Bandwidth wide
Averaging Type power log power
Trace Averages 1
Trace Points n/a
Function average entire trace
2012 NCSL International Workshop and Symposium
Spectrum Analyzer CW Power Measurements and Noise
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