# Presentation: 660820

## Frequency Domain Methods

## Time Domain  Frequency Domain

**Notes:**
In time domain, all signals are mixed. Frequency information appears to be lost.
In the frequency domain the phase information may be lost completely. Be careful.

## 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.

## 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.

## Sideband detection

- frequency

- Sy(f)

## Line width problems

- frequency

- Sy(f)

## Increase time of measurement

- frequency

- Sy(f)

**Notes:**
Increasing the duration of the measurement will help but most spectrum analyzers are limited in time.

## 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

## Time Domain => Frequency Domain

## Noise in frequency domain

- Spectral density of the phase fluctuations

- Spectral density of the frequency fluctuations

## 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

## Common types of noise

**Notes:**
You can already see that the time scale involved is inversely proportional to the frequency.

## Common types of noise

## Types of phase noise

- frequency

- Log scale

- Log scale

## Types of frequency noise

- frequency

- Log scale

- Log scale

## Power Law Dependence of y()

******y****(********)**

- -1

- 0

**Noise type:**

**White**
**phase**

**Flicker**
**phase**

**White**
**freq.**

**Flicker**
**freq.**

**Random**
**walk freq.**

- -1/2

- 1/2

**Power Law Dependence of ********y****(********)**

*As measured by*
*Allan Deviation*

- 1/f noise

****

**Notes:**
 Below the flicker of frequency noise (i.e., the “flicker floor”) region,
crystal oscillators typically show -1 (white phase noise) dependence.  Atomic standards show -1/2 (white frequency noise) dependence down to about the servo-loop time constant, and  -1 dependence at less than that time constant.  Typical ’s at the start of flicker floors are: 1 second for a crystal oscillator, 103s for a Rb standard and 105s for a Cs standard.

“Characterization of Clocks and Oscillators,” edited by D.B. Sullivan, D.W. Allan, D.A. Howe, F.L. Walls, NIST Technical Note 1337, March 1990.

## 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

## Some examples stressing the differences between time domain and frequency domain analysis

## White vs flicker phase noise

**Notes:**
Not that easy to discriminate between the two.

## White vs Flicker phase noise

*ADev(****)*

*ADev(****)*

**

**

- Not very different

- Time domain

**Notes:**
ADev is not sensitive enough

## White versus Flicker phase noise

*f **0*

*f **-1*

*S****(f)*

*S****(f)*

*f*

*f*

- Frequency domain

- No ambiguity here!

**Notes:**
FFT of the data or long integretation time will show the difference.

## 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.

## 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

## Hydrogen maser example II

- f0 or f-1

- Which one?

## Hydrogen maser example III

- No f-4

- No flicker phase noise f-1

- ??

- amplitude

## 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

## Another way of looking at data:the moving FFT

- Easy to implement
- Can reveal intermittent problems

## Moving FFT I

## 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

## 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.

## 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.