# Presentation: 530023

## Noise Evaluation of a Commonly Used Fluxgate Magnetometer for One-second Data

- T J Shanahan and C W Turbitt

**Notes:**
SO TODAY, ON THE SAME THEME OF 1 SECOND DATA, I’M GOING TO TALK ABOUT A METHOD I USED TO MEASURE THE NOISE IN A FLUXGATE MAGNETOMETER AND HOW THIS PROCESS HIGLIGHTED  SOME CLEAR ADVANTAGES IN USING SIGMA-DELTA DIGITISERS FOR DATA ACUISITION

## Motivation

- INTERMAGNET 1-Second data standard almost defined:
- BGS operates 7 observatories comprising 13 fluxgate magnetometer systems
- What are the current capabilities of our instrumentation – resolution and frequency response
- Establish method for evaluating noise of a fluxgate magnetometer under normal operating conditions or “under load”
- Establish method for evaluating frequency response of fluxgate with 1-Second standards in mind
- Highlight methods of filtering with regard to the new standard

**Notes:**
THE MOTIVATION FOR UNDERTAKING THIS WORK HAS BEEN DRIVEN BY THE INCREASING MOMENTUM IN THE MOVE TO INTERMAGNET STANDARD FOR 1 SECOND DATA THAT WHICH SETS THE RESOLUTION AT 0.01 NT

WITH THIS IN MIND WE DECIDED TO INVESTIAGE THE CURRENT CAPABILITIES OF OUR INSTRUMENTATION

AS BGS OPERATES 13 FLUXGATE MAGNETOMETERS WE WERE INTERESTING IN THE IDEA OF BEING ABLE TO MODIFY OUR EQUIPMENT TO MEET THE NEW STANDARD RATHER THAN STARTING WITH NEW INSTRUMENTATION

## INTERMAGNET 1-Second Data

**INTERMAGNET 1-Second Data**

***Key specifications:***
** ****Data resolution: 0.01 nT****RMS**
-  Timing accuracy: 10 ms
-  Output rate: 1 Hz
-  Filtering preferences: linear phase
***For 1 Hz, required SNR (in 0.5 Hz bandwidth):***
***ADC resolution:***

*For DMI FGE fluxgate with +/- 4000 nT dynamic range*

**Notes:**
THE KEY REQUIREMENTS OF THE INTERMAGNET STANDARD FOR 1 SECOND DATA AS IT STANDS ARE LISTED HERE

GIVEN A DYNAMIC RANGE OF +- 4000 NT, THE REQUIRED SIGNAL TO NOISE IS OF THE ORDER OF 109 DB WHICH TRANSLATES TO APPROXIMATELY 19 BITS OF DIGITAL RESOLUTION

ABOVE 16 BITS OF RESOLUTION TYPICAL SUCCESSIVE APPROXIMATION DIGITERS BECOME EXPENSIVE TO MANUFACTURE AND INCREASINGLY SIGMA DELAT CONVERTERS ARE NOW BEING USED FOR HIGH RESOLUTION APPLICATIONS

## ADC Selection For Noise Tests

**Specifications**
**Type: Seismic**
**Dynamic range: ~ 130 dB @ 1 SPS**
**Manufacturer: Guralp**
**Converter type: Delta-Sigma**
**Output format: 24 bits**
**Output rates: 1 SPS to 200 SPS**
**Timing: GPS **
**Sampling rate: 32 kHz**
**Anti-alias: 3-pole**
**Stop-band attenuation: ~ 140 dB**
**Digital filter: FIR (Sinc)**

## Delta-Sigma ADC Operation

- High resolution is achieved by:

-  Over-sampling
-  Noise ‘shaping’
-  Digital filtering

*Anti-alias filter cut-off*
*can be much higher*

## Typical Signal Processing

- FLUXGATE OUTPUT
- LOW PASS FILTER

- ANTI-ALIAS LOWPASS
-  FILTER

- 50/60 Hz NOTCH FILTER

- DIGITISATION

- DIGITALFILTER
- AND DECIMATION

**MAGNETC FIELD**

**DIGITAL DATA**
**SAMPLES**

*DELTA-SIGMA CONVERTER*

- Benefits of Delta-Sigma converter:
-  Some analog filter stages can be replaced
-  Digital filtering performed by converter
-  Anti-alias requirements are relaxed by over-sampling
-  High quality digital filter with linear phase

**Notes:**
THE TYPICAL SIGNAL PROCESSING STAGES FOR A DATA AQUISTION SYSTEM USING A STANDARD DIGITISER ARE SHOWN HERE WITH SEVERAL ANALOG FILTERING STAGES FOLLOWED BY A DIGITAL FILTER 

BY USING A SIGMA DELTA CONVERTER BOTH THE ANALOG AND DIGITAL FILTERING STAGES CAN BE SUBSTITUTED BY A SINGLE SYSTEM THAT PROVIDES MORE DESIREABLE FREQUENCY RESPONSE CHARACHTERISTICS

## Noise Evaluation Method

- FLUXGATE

- FLUXGATE

- N1

- N2

- SIESMIC
- DIGITISER
- 1 SPS OUTPUT

- ∑

- MEASURED
- MAGNETIC
- FIELD INPUT

- -

**+**

- CH2

- CH1

*< 10 m*
*separation*

- NT

**Notes:**
2 magnetometer systems run concurrently to enable removal of the common measured signal whilst providing ‘load’ conditions (real feedback current)

High resolution sigma-delta digitiser used with implicitly high sampling rate allows all potential noise sources to be represented and alleviates aliasing issues

Digital filter removes unwanted signals and the two data sets are used to remove common measured signal

Standard deviation represents the rms noise contributed by both systems and noise of single magnetometer easily estimated

## Slide 8

## Noise Power Spectral Density

## Noise Results Summary

**Sampling D channel @ 1 SPS (un-biased):**
**Sampling Z channel @ 1 SPS (bias current present):**

-    1 min:	 N = 0.03 nTrms

- 1 hour: N = 0.04 nTrms

- 1 day: N = 0.09 nTrms

- 1 min: N = 0.04 nTrms

- 1 hour: N = 0.06 nTrms

-          1 day: N = 0.12 nTrms

*Bias current in Z channel contributes additional noise*

*Resolution is dependent on long term stability*

- 0.02 nTrms/√Hz @ 0.25 Hz

## Testing Frequency Response

**Testing Frequency Response**

- GPS

- STEP
- GENERATOR
- (BLACK BOX)

- DELTA-SIGMA
- DIGITISER
- 200 SPS

- DFT

- 1 PPS

- FREQUENCY
- RESPONSE

- DD

*f*

*A*

- FLUXGATE

- HELMHOLTZ
- COILS

***~ 400 nT step***
***input***

**Notes:**
AS A PRECURSOR TO MEASURING THE NOISE IN THE MAGNETOMETER WE DECIDED IT WOULD BE USEFUL TO INVESTIGATE THE FREQUENCY RESPONSE OF THE INSTRUMENT BY INJECTING AN IMPULSE INTO THE FLUXGATE SENSOR

## Frequency Response (Phase)

## Frequency Response (Amplitude)

## Summary

- Delta-Sigma converter is good digitiser choice
- Implements over-sampling which relaxes anti-alias selection
- Sophisticated digital filter can substitute analog equivalents
- Provides necessary dynamic range for 1-Second data
- Over-sampling is a good option in any case
- Encouraging results from tests of FGE magnetometer
- 0.02 nTrms / √Hz @ 0.25 Hz
- Linear phase up to ~ 1 Hz with analog output filter
- Linear phase up to ~ 10 Hz with out analog output filter
- Flat amplitude response well above 1 Hz with filter removed

## Sigma-Delta ADC Components

- N-BITS DATA STREAM

*Transfer functions show the modulator acts as a low-pass filter for the input signal and high-pass filter for the quantisation noise*

## Sigma-Delta ADC operation

- Noise is ‘shaped’ by the high-pass filtering nature of the system transfer function

- ∑

- QUANTISATION NOISE

**X**

- ∑

- ANALOG FILTER
- H(f) = 1/f

**Y**

**Y**

**Q**

**X-Y**

**(X-Y) / f**

- Input (X) is low-pass filtered
- Quantisation noise (Q) is high-pass filtered (‘noise shaping’)

- TRANSFER FUNCTION

## Sigma-Delta ADC Anti-aliasing

- Fs

- 3Fs

- 2Fs

- f

- f

- 1⁄2Fs

- 1⁄2MFs

- OVERSAMPLE BY FACTOR M

- ANTI-ALISAS TRANSITION
- CAN BE RELAXED

- ANTI-ALISAS STOPBAND
- IS FLEXIBLE

- QUANTISATION NOISE IS ‘SPREAD’ OVER WIDER FREQUENCY RANGE

- H(f)

- H(f)

- 1⁄2Fs

- (NYQUIST)

- (NYQUIST)