Calibration
ADU-08e
HF Board 08e
The theoretical transfer function for the HF-channel is given below:
\(F_{HF - Channel} = G_{1} \cdot F_{1} \cdot F_{2} \cdot F_{3} \cdot F_{4}\)
with
\(G_{1} = 1 \ or\ 4, 8, 16\) depending on gain setting of first stage
\(F_{1} = \frac{1}{1 + P_{1}}\); \(P_{1} = i \cdot \frac{f}{338 kHz}\)
\(F_{2} = \frac{1}{1 + P_{2}}\); \(P_{2} = i \cdot \frac{f \cdot G_{1} }{100 MHz}\)
\(F_{3} = \frac{1}{1 + P_{3}}\); \(P_{3} = i \cdot \frac{f}{1.59 MHz}\)
\(F_{4} = \frac{P_{4}}{1 + P_{4}}\); \(P_{4} = i\frac{f}{482 Hz}\) if high-pass is switched on.
\(F_{4} = 1\) if high-pass is switched off.
(gains and input divider are calibrated into the LSB, you don’t see them)
LF Board 08e
\(F_{LF - Channel} = G_{1} \cdot G_{2} (\cdot G_{3}) \cdot F_{1} \cdot F_{2} \cdot F_{3} \cdot F_{4}\)
\(G_{1} = 1 \ or\ 4, 8, 16\) depending on gain stage 1 settings
\(G_{2} = 1 \ or\ 4, 8, 16, 32, 64\) depending on gain stage 2 settings, inside the ADC; (32, 64 not set by software, only manually)
Gains and input divider do not appear in the ats file, they are calibrated into the LSB
\(G_{3} = 2\) is a fixed gain and can’t be changed; this gain is invisible in the time series
\(F_{1} = \frac{1}{1 + P_{1}}\); \(P_{1} = i\frac{f}{318 kHz}\)
\(F_{2} = \frac{1}{1 + P_{2}}\); \(P_{2} = i\frac{f \cdot G_1 }{2 MHz}\)
\(F_{3} = \frac{1}{1 + 1.414 \cdot P_{3} + P_{3}^{2}}\); \(P_{3} = i \cdot \frac{f}{4Hz}\) if 4 Hz Low-pass is switched on
and
\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot \frac{f}{10.5 kHz}\) if RF-2 on & DIV-8 = on (default for coil, not used for E)
\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot \frac{f}{30 kHz}\) if RF-1 on & DIV-8 = on (not used for E)
\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot 2 \pi f \cdot (R_{sensor} + 200) \cdot 7.27E^{-9}Hz\) if RF-2 on & DIV-1 = on (default for electrodes < 1500 Ohm contact resistance, default for buffer electrodes, not used for H) )
\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot 2 \pi f \cdot (R_{sensor} + 200) \cdot 470E^{-12}Hz\) if RF-1 on & DIV-1 = on ( electrodes > 1500 Ohm contact resistance, not used for H)
in old manuals the equations were written like
\(P_{4} = i \cdot \frac{f}{\frac{0.159}{(R_{sensor} + 200) \cdot 7.27E^{-9}Hz}}\)
\(P_{4} = i \cdot \frac{f}{\frac{0.159}{(R_{sensor} + 200) \cdot 470E^{-12}Hz}}\)
ADU-10e
LF Board 10e
\(F_{LF - Channel} = G_{1} \cdot F_{1} \cdot F_{4}\)
\(G_{1} = 1 \ or\ 4, 8, 16, 32, 64\)
The \(G_{1}\) (inside ADC) is a chopper stabilized gain. The SW shall set 1 as default, for E this means \(\pm\) 2.5 V input range .
Gains and input divider do not appear in the ats file, they are calibrated into the LSB
\(F_{1} = \frac{1}{1 + P_{1}}\); \(P_{1} = i\frac{f}{318 kHz}\)
and
\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot \frac{f}{7.8 kHz}\) if DIV-8 = on (default for coil, not used for E)
\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot 2 \pi f \cdot (R_{sensor} + 200) \cdot 6.8E^{-9}Hz \) if DIV-1 = on (default for electrodes, not used for H) )
(in old manuals the equation was written like \(P_{4} = i \cdot \frac{f}{\frac{0.159}{(R_{sensor} + 200) \cdot 6.8E^{-9}Hz}}\) )
ADU-07e
HF Board 07e
The theoretical transfer function for the HF-channel is given below:
\(F_{HF - Channel} = G_{1} \cdot G_{2} \cdot F_{1} \cdot F_{2} \cdot F_{3}\)
with
\(G_{1} = 1 \ or\ 8\) depending on gain setting of first stage
\(G_{2} = 1 \ or\ 8 \ or\ 64\) depending on gain setting of second stage
\(F_{1} = \frac{1}{1 + P_{1}}\); \(P_{1} = i \cdot \frac{f}{7.7 MHz}\) if \(G_1 \ne 1\)
\(F_{2} = \frac{1}{1 + P_{2}}\); \(P_{2} = i \cdot \frac{f}{7.7 MHz}\) if \(G_2 \ne 1\)
\(F_{3} = \frac{P_{3}}{1 + P_{3}}\); \(P_{4} = i\frac{f}{1 Hz}\) if high-pass is switched on.
(gains and input divider are calibrated into the LSB, you don’t see them)
LF Board 07e
\(F_{LF - Channel} = G_{1} \cdot G_{2} \cdot F_{1} \cdot F_{2} \cdot F_{3}\)
\(G_{1} = 1 \ or\ 2, 4, 8, 16, 32, 64\) depending on gain stage 1 settings
\(G_{2} = 1 \ or\ 2, 4, 8, 16, 32, 64\) depending on gain stage 2 settings, inside the ADC; (32, 64 not set by software, only manually)
\(F_{1} = \frac{1}{1 + P_{1}}\); \(P_{1} = i \cdot \frac{f}{4 kHz}\) if \(G_1 \ne 1\)
\(F_{3} = \frac{1}{1 + 1.414 \cdot P_{3} + P_{3}^{2}}\); \(P_{3} = i \cdot \frac{f}{4Hz}\) if 4 Hz Low-pass is switched on
MF Board 07e
tbd.
MFS Coils
OLD Calibration Files are normalized by f!
e.g. the MFSXXX.txt files.
The JSON files are using mV (as the time series data) and are not normalized by f.
If you normalize the calibration you end up with a constant \(\frac{200 mV}{nT \cdot Hz}\) and 90°
phase below 0.1 Hz for the MFS-06e and \(\frac{20 mV}{nT \cdot Hz}\) and 90° for the MFS-07e.
The term \(P_{1}\) is the cut-off frequency generated by the feedback coil.
The other terms \(P_{2}\), \(P_{3}\), \(P_{4}\) are result of the pre-amplifier components[1][2].
MFS-06e
\(P_{1} = i \cdot \frac{1}{4 Hz}, \enspace P_{2} = i \cdot \frac{1}{9645 Hz} \enspace\) \(P_{3} = i \cdot \frac{1}{0.72 Hz},\enspace P_{4} = i \cdot \frac{1}{23897 Hz}\)
Chopper on
\(F_{on}(f) = \frac{ mV}{nT} = 800 \enspace \frac{mV}{nT} \cdot \frac{P_1}{1+P_1} \cdot \frac{1}{1+P_2} \cdot \frac{1}{1+P_4} \)
Chopper off
\(F_{off}(f) = \frac{ mV}{nT} = 800 \enspace \frac{mV}{nT} \cdot \frac{P_1}{1+P_1} \cdot \frac{1}{1+P_2} \cdot \frac{P_3}{1+P_3} \cdot \frac{1}{1+P_4} \)
MFS-07e
\(P_{1} = i \cdot \frac{1}{32 Hz}, \enspace P_{2} = i \cdot \frac{1}{45150 Hz} \enspace\) \(P_{3} = i \cdot \frac{1}{0.72 Hz},\enspace P_{4} = i \cdot \frac{1}{49735 Hz}\)
Chopper on
\(F_{on}(f) = \frac{ mV}{nT} = 640 \enspace \frac{mV}{nT} \cdot \frac{P_1}{1+P_1} \cdot \frac{1}{1+P_2} \cdot \frac{1}{1+P_4} \)
Chopper off
\(F_{off}(f) = \frac{ mV}{nT} = 640 \enspace \frac{mV}{nT} \cdot \frac{P_1}{1+P_1} \cdot \frac{1}{1+P_2} \cdot \frac{P_3}{1+P_3} \cdot \frac{1}{1+P_4} \)