8/9/2015 frequency domain methods. time domain worldfrequency domain worldfourier transform: f...
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![Page 1: 8/9/2015 Frequency Domain Methods. Time domain worldFrequency domain worldFourier Transform: F Inverse Fourier Transform: F --1 Oscilloscope Spectrum](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649d9f5503460f94a8a31d/html5/thumbnails/1.jpg)
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Frequency Domain Methods
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Time domain world Frequency domain worldFourier Transform:
F
Inverse Fourier
Transform: F--1
OscilloscopeSpectrum Analyser
This transformation coud be made in real
time by using hardware or in a post procesing
scheme using software
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Time Domain Frequency Domain)2sin( iiii tfAV
time
Am
plitu
de
frequencyA
mpl
itude
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Why go to the Frequency Domain
• Frequency analysis can show characteristics of oscillator:– Noise processes– Side bands (modulation, parasitic)
• Spectrum analyzer easy to use to show noise far from the nominal frequency.– Limited by the bandwidth of the measuring
system.
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Detection of parasitic signals
• Parasitic signals simply adds to the signal
• Parasitic signal modulates the signal
• In either case, if the signal is far enough from the carrier (greater than the resolution of the spectrum analyser available) it can be resolved.
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Sideband detection
frequency
Sy(f)
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Line width problems
frequency
Sy(f)
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Increase time of measurement
frequency
Sy(f)
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Solution to limited spectrum analyzers
• Record the data for a very long time using a time measurement system
• Feed your data to a proper analyzer software.
• Convert the time data into frequency data.
• Interpret the results
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Time Domain => Frequency Domain
;frequencynormalized
2
''2
;frequency"eoustantanins"2
1
domain timein the signal))(2sin()(
00
0
0
0
0
0
ttty
dttt
dt
tdt
tvAtx
t
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Noise in frequency domain
dfffSyy
dardSIEEEperfS
fSfBW
fS
dffS
kky
y
RMS
BW
RMS
4
02
0
21
2
2
02
2
sin2
2
1
domainfrequency and
domain in time noisebetween iprelationsh
1139tan,2
1f
L
Spectral density of the phase fluctuations
Spectral density of the frequency fluctuations
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Noise in frequency domain
• Not very useful to calculate the Allan variance from the spectral density of the noise
• Very useful to detect anomalies in the noise pattern of a device
dfffSyy kky
4
02
0
21
2 sin2
2
1
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Common types of noise
4
3
2
1
0
)(
f
f
f
f
f
fS
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Common types of noise
22
42
11
31
00
20
11
11
22
02
20
frequency walk random
frequency flicker
frequency white
phaseflicker
phase white
)( noise of Type
fhfh
fhfh
fhfh
fhfh
fhfh
fSfS y
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Types of phase noise
fL
fS 20)(
3:frequency flicker f
4:frequency walk random f
0: phase white f
1: phaseflicker f
2:frequency white f
frequencyLog scale
Log
scal
e
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Types of frequency noise)( fS y
1:frequency flicker f
2:frequency walk random f
2: phase white f
1: phaseflicker f
0:frequency white f
frequencyLog scale
Log
scal
e
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y()
-1
0
Noise type: Whitephase
Flickerphase
Whitefreq.
Flickerfreq.
Randomwalk freq.
-1/2 1/2
Power Law Dependence of y()
As measured byAllan Deviation
1/f noise
-3/2
real noise
2
2
1tt yy
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Frequency Analysisusing a spectrum analyser
• Advantages of frequency analysis– Good detector of modulation/parasitic signals– Easier to look at high frequency noise– Can discriminate between white and flicker
phase noise!
• Disadvantages– Not very good for noise very close to the carrier
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Some examples stressing the differences between time domain and
frequency domain analysis
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White vs flicker phase noise
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White vs Flicker phase noise
Slope = -1Slope -
1
ADev() ADev()
Not very
different
Time domain
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White versus Flicker phase noise
f 0f -1
S(f) S(f)
f f
Frequency domain
No ambiguity
here!
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White and flicker phase noise
• They are often present over the same time scale and are difficult to separate.
• ADev is unable to do it.
• FFT will tell quickly if white phase noise is present, which is very likely for most oscillators on short time interval.
• This is true generally at high frequency offset from the nominal frequency.
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Hydrogen maser example I
• Case of a “sick” hydrogen maser
• It has excess white or flicker phase noise.
• ADev method of evaluation reveals higher than normal noise at short term. Unable to sort out white from flicker noise.
• FFT of phase signal sorts out the type of noise
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Hydrogen maser example II
f0 or f-1
Which one?
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Hydrogen maser example III
f-3
f-2
f0
No f-4 No flicker phase noise f-1
??
ampl
itude
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Hydrogen maser example IV
• Frequency analysis has resolved the type of noise affecting the performance of the maser.
• Frequency analysis has also revealed the presence of parasitic signals.– Some of it is due to some 4 seconds cycle
operation within the phase comparator itself
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Another way of looking at data:the moving FFT
• Easy to implement
• Can reveal intermittent problems
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Moving FFT I
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Moving FFT II
Moving FFT over sixty days of phase residuals of two hydrogen masers reveals strange parasitic signal.
Modulation period = one week
Parasitic frequency not stable
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Parasitic signal
It turns out that this signal is generated in the path between one maser and the phase comparator.
There are three buffer amplifiers and distribution boxes along the path.
The one week amplitude modulation tends to point out to interference with normal activities in the building.
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Conclusion
• Frequency domain methods should be used as well as time domain methods
• Both methods are complement of each other
• Never miss the opportunity to look at your data from all angles possible.