Analog Devices ADuCM356 Reference Manual page 159

Reference Manual
USE CASE CONFIGURATIONS
Step 5: Calculate the Impedance of
Electrochemical Sensor Sensing Electrode
Node
Calculate the magnitude and phase of Step 2, Step 3, and Step 4.
The following code example and equations show how to calculate
the magnitude and phase of each step:
// Get RMS result of each step based on DFT
REAL and IMAG outputs
DFT_Mag[i] = DFTREAL* DFTREAL+ DFTI►
MAG* DFTIMAG;
DFT_Mag[i] = sqrt(DFT_Mag[i]);
// Use atan2 function to get phase result
of each step based on DFT REAL and IMAG outputs
Phase[i] = atan2(DFTIMAG,
DFTREAL); // returns value between -pi to +pi
(radians) of ATAN2(IMAG/Real)
= I(s)
In Step 4,
V(s)
CAL
Z CAL(magnitude)
where:
V(s) is the signal voltage.
I(s) is the calibration current.
CAL
Z (magnitude) is the magnitude of the impedance of the calibra-
CAL
tion.
V(s) = I(s) × Z
Therefore,
CAL
= I(s)
In Step 2,
V(s)
RE + RLOAD02
Z RE + RLOAD02
where:
Z is the impedance of the sensor and Load Resistor 2.
RE + RLOAD02
I(s) is the current flowing through the sensor and Load
RE + RLOAD02
Resistor 2.
Z =
Therefore,
V(s)
RE + RLOAD02
I(s) RE + RLOAD02
= I(s)
In Step 3,
V(s)
RLOAD02
Z RLOAD02
where:
Z is the impedance of Load Resistor 2.
RLOAD02
I(s) is the current flowing through Load Resistor 2.
RLOAD02
Z =
Therefore,
V(s)
RLOAD02
I(s) RLOAD02
analog.com
Z =Z
Therefore, based on Step 2 through Step 4,
RE RE + RLOAD02
=I s × Z
CAL
=I s × Z
CAL
If Z (magnitude) = 200 Ω and Z
CAL
Z (magnitude) = Z
obtain the following equations:
RE
= 200 × I(s)
CAL
×
I(s) RLOAD02 − I(s) RE + RLOAD02
I(s) RE + RLOAD02 × I(s) RLOAD02
where:
Z (magnitude) is the magnitude of the impedance of the sensor.
RE
Z pℎase =Ang
I(s) values can be replaced by DFT results.
RE
(12) =0 + Ang
where:
Z (phase) is the phase part of the impedance measurement of the
RE
sensor.
Ang() is the function to calculate phase.
(13)
(14)
(15)
(16)
(17)
ADuCM356
− Z =
V s
RLOAD02
I s RE + RLOAD02
× −
1
CAL
I s RE + RLOAD02
×
I s RLOAD02 − I s RE + RLOAD02
CAL
I s RE + RLOAD02 × I s RLOAD02
(phase) = 0, it is possible to
CAL
− Z
RE + RLOAD02 RLOAD02
Z RE + RLOAD02 − Z RLOAD02
+ Ang
I s CAL I s RLOAD02 − I s RE + RLOAD02
Rev. A | 159 of 312
−
V s
I s RLOAD02
1
I s RLOAD02
(18)
(19)
(20)