Noise budget

• based on the data sheet values, sensor noise should dominate. However, measured noise is similar to front-end circuit noise
• circuit noise is dominated by reference/DAC/OpAmp
• noise of the sense resistor and the differential amplifier can be neglected

Sensor

• Sensor gain: 0.5mA/A * 6 turns = 3mA/A
• Sense resistor: 10 Ohms
• Equivalent sensor gain: 30mOhm
• Typical coil current = 60A, gives ~2V at sensor

Data sheet noise numbers

Frequency range	specified sensor noise	equivalent voltage/field noise
0-10Hz	20uA rms MAX	600nVrms, 50uG rms
0-100Hz	200uA rms MAX	6uVrms, 500uG rms
0-1kHz	400uA rms MAX	12uVrms, 1mG rms

Frequency range	measured noise
1.5Hz-10Hz	<=16uG rms (0.2uV rms)
1.5Hz-100Hz	<=45uG rms (0.6uV rms)
1.5Hz-1kHz	<=75uG rms (1uV rms)

Measurement resistor

• thermal (Nyquist) noise: 0.4nV/rtHz (13nVrms in 1kHz BW = 1uG rms)
• thermal (kTC) noise for 4.7nF: 1uVrms in 100kHz BW. (in 1kHz: 10nVrms = 0.75uG rms)

First stage OpAmp

• ADA4004:
• LF voltage noise: 0.1Hz-10Hz - 150nVpk-pk TYP (~50nVrms = 4.3uG rms)
• vn at 1kHz 1.8nV/rtHz TYP (60nVrms for 1kHz, gives 5uG rms)
• in at 10Hz 3.5pA/rtHz TYP (110nVrms for 1kHz and 1k load, = 9uG rms)
• in at 200Hz 1.2pA/rtHz TYP

DAC

• 1nV V_DAC noise corresponds to 1nV DIFF_SIG noise
• (1uV V_DAC rms = 80uG rms, and equally 1uV DIFF_SIG rms = 80uG rms)

Reference

• () = compared to 2V
• 0.1Hz-10Hz - 0.25ppm pk-pk TYP (0.5uV pk-pk ~<175nV rms = 14uG rms) -10Hz-1kHz - 0.67ppm rms TYP (1.34uV rms = 110uG rms)

Reference buffer OpAmp

-AD8628

• LF voltage noise: 0.1Hz-1Hz - 160nVpk-pk TYP (~60nVrms = 4.6uG rms)
• LF voltage noise: 0.1Hz-10Hz - 500nVpk-pk TYP (~175nVrms = 14uG rms)
• vn at 1kHz 22nV/rtHz TYP (700nVrms for 1kHz BW, = 57uG rms)
• in at 10Hz 5fA/rtHz TYP (1.4nVrms for 1kHz and min 9k DAC load, = 0.1uG rms)

DAC

• 0.1Hz-10Hz - 134nV pk-pk TYP (~<48nV rms = 4uG rms)
• 10Hz-1kHz - 375nV rms TYP (30uG rms)

Lowpass filter after DAC

• 4.7kOhm, 1.0uF (pole at 34Hz), ADA4004 buffer
• kTC-noise: 65nVrms (5uG rms)
• opamp in: 3.5pA/rtHz TYP (100nVrms for 34Hz amd 4k7 load, = 8uG rms)
• reduces (reference + buffer + DAC) noise in 100-1000Hz by 1 order of mag.

Stability/drift budget

• Sensor drift is expected to be similar to OpAmp Voff/Ib drift.
• Overall system temp. co. should be ~250uG/K.

Sensor

• Temp. Co. 1ppm/K MAX (146uG/K)
• 1ppm/month MAX (146uG/month)

Measurement resistor

• Temp. Co: 0.2ppm/K TYP (30uG/K)

First stage OpAmp

• ADA4004-4
• Voff - 1uV/K MAX (73uG/K MAX)
• Ib = 90nA MAX (90uV for 1k load, = 7.3mG)
• Ib stability (from eye-balling Fig 11 on data sheet) 0.4nA/K (32uG/K)

Reference:

• Temp Co: 2ppm/K MAX for B grade (300uG/K)
• Long term: 60ppm/rtkHr MAX (1.5mG/day) (n.b. this should drop off after a few weeks!)

Reference buffer OpAmp

• AD8628
• Voff - 0.02uV/K MAX (1.6uG/K MAX)
• Ib = 100pA MAX (900nV for min 9k DAC load, = 73uG)
• Ib stability (from eye-balling Fig 6 and Fig 12 on data sheet) 0.15pA/K (0.1uG/K)

DAC

• gain error temp co: +/-0.1ppm/K TYP (16uG/K)
• zero-code temp co: +/-0.05ppm/K TYP (8uG/K)

Lowpass filter after DAC

• 1kOhm, 1.5uF (pole at 100Hz), ADA4004 buffer
• opamp Ib: 0.4nA/K (for 1k load: 0.4uV/K = 32uG/K)