Calibration

ADU-08e

HF Board

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

\(F_{LF - Channel} = G_{1} \cdot G_{2} (\cdot G_{3}) \cdot F_{1} \cdot F_{2} \cdot F_{3} \cdot F_{4}\)

\(G_{1} = 1 \ or\ 4, 8, 16\) 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)

\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot \frac{f}{\frac{0.159}{(R_{sensor} + 200) \cdot 7.27E^{-9}Hz}}\) if RF-2 on & DIV-1 = on (default for electrodes < 1500 Ohm contact resistance, default for buffer electrodes, not used for H) )

\(F_{4} = \frac{1}{1 + P_{4}}\); \(P_{4} = i \cdot \frac{f}{\frac{0.159}{(R_{sensor} + 200) \cdot 470E^{-12}Hz}}\) if RF-1 on & DIV-1 = on ( electrodes > 1500 Ohm contact resistance, not used for H)


ADU-10e

LF Board

\(F_{LF - Channel} = G_{1} \cdot F_{1} \cdot F_{2}\)

\(G_{1} = 1 \ or\ 4, 8, 16, 32, 64\) depending on gain stage 1 settings, here tge gain is inside the ADC like gain 2 for old ADUs

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

\(F_{2} = \frac{1}{1 + P_{2}}\); \(P_{2} = i \cdot \frac{f}{7.8 kHz}\) if DIV-8 = on (default for coil, not used for E)

\(F_{2} = \frac{1}{1 + P_{2}}\); \(P_{2} = i \cdot \frac{f}{\frac{0.159}{(R_{sensor} + 200) \cdot 6.8E^{-9}Hz}}\) if DIV-1 = on (default for electrodes < 1500 Ohm contact resistance, default for buffer electrodes, not used for H) )

alt: \(P_{2} = i \cdot 2 \pi f \cdot (R_{sensor} + 200) \cdot 6.8E^{-9}Hz \)


ADU-07e

HF Board

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

\(F_{LF - Channel} = G_{1} \cdot G_{2} \cdot F_{1} \cdot F_{2} \cdot F_{3}\)

\(G_{1} = 1 \ or\ 2, 4, 8, 16, 32, 64\) 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