# Frequency Domain Methods 10192021 Amplitude Time Domain Frequency

- Slides: 31

Frequency Domain Methods 10/19/2021

Amplitude Time Domain Frequency Domain time 10/19/2021 frequency

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. 10/19/2021

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. 10/19/2021

Sideband detection Sy(f) frequency 10/19/2021

Line width problems Sy(f) frequency 10/19/2021

Increase time of measurement Sy(f) frequency 10/19/2021

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 10/19/2021

Time Domain => Frequency Domain 10/19/2021

Noise in frequency domain Spectral density of the phase fluctuations Spectral density of the frequency fluctuations 10/19/2021

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 10/19/2021

Common types of noise 10/19/2021

Common types of noise 10/19/2021

Log scale Types of phase noise Log scale 10/19/2021 frequency

Log scale Types of frequency noise Log scale 10/19/2021 frequency

Power Law Dependence of y( real noise As measured by Allan Deviation y( ) -3/2 1/f noise -1 -1/2 0 1/2 Noise type: White phase 10/19/2021 Flicker phase White freq. Flicker Random freq. walk freq.

Frequency Analysis using 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 10/19/2021

Some examples stressing the differences between time domain and frequency domain analysis 10/19/2021

White vs flicker phase noise 10/19/2021

Time domain White vs Flicker phase noise ADev(t) Slope @ -1 Slope = -1 Not very different t 10/19/2021 t

Frequency domain White versus Flicker phase noise Sf(f) f -1 f 0 f 10/19/2021 No ambiguity here! f

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. 10/19/2021

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 10/19/2021

Hydrogen maser example II f 0 or f-1 Which one? 10/19/2021

Hydrogen maser example III amplitude f-3 No f-4 No flicker phase noise f-1 ? ? f-2 f 0 10/19/2021

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 10/19/2021

Another way of looking at data: the moving FFT • Easy to implement • Can reveal intermittent problems 10/19/2021

Moving FFT I 10/19/2021

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 10/19/2021

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. 10/19/2021

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. 10/19/2021

- Frquency domain
- Amplitude wavelength and frequency
- Amplitude modulation vs frequency modulation
- Amplitude modulation vs frequency modulation
- Z domain to frequency domain
- Properties of roc in dsp
- Z transform integrator
- Time frequency domain
- Time frequency domain
- Time frequency
- Jablonski diagram
- Wax pattern in fpd
- Start time end time and elapsed time
- Frequency response methods and stability
- What is a joint relative frequency
- Frequency vs relative frequency
- Power of sine wave
- Vmax=aw
- Relative frequency bar chart
- Marginal frequency table
- Marginal frequency table
- Laplace frequency domain
- Equation of fourier transform
- Circular convolution definition
- Band pass filter in image processing
- Frequency domain image
- Image processing frequency domain
- Mechanical waves examples
- Cos wave formula
- O que é o clima equatorial
- Small amplitude oscillatory shear
- Rarefaction on a wave