Datasheet
P
C
Q R
L
9
SENSOR
2
1 1 5 10 1
¦
2 LC Q LC 2 LC
Q
|
S S
Copyright © 2016, Texas Instruments Incorporated
C
PAR
Coil Series
Resistance (Rs)
Eddy
Current
Target Resistance
M(d)
Distance-dependent coupling
C
PAR
+ C
TANK
L(d)
R
P
(d)
Parallel Electrical
Model, L-C Tank
Distance (d)
I
35
LDC1612
,
LDC1614
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SNOSCY9A –DECEMBER 2014–REVISED MARCH 2018
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Application Information (continued)
Figure 50. Electrical Model of the L-C Tank Sensor
A resonant oscillator can be constructed by combining a frequency selective circuit (resonator) with a gain block
in a closed loop. The criteria for oscillation are: (1) loop gain > 1, and (2) closed loop phase shift of 2π radians.
The R-L-C resonator provides the frequency selectivity and contributes to the phase shift. At the resonance
frequency, the impedance of the reactive components (L and C) cancels, leaving only R
P
, the lossy (resistive)
element in the circuit. The voltage amplitude is maximized at this frequency. The R
P
can be used to determine
the sensor drive current for a given oscillation amplitude. A lower R
P
requires a larger sensor current to maintain
a constant oscillation amplitude. The sensor oscillation frequency is given by:
where:
• C is the sensor capacitance (C
SENSOR
+ C
PARASITIC
)
• L is the sensor inductance
• Q is the quality factor of the resonator. Q can be calculated by: (1)
where:
• R
P
is the AC parallel resistance of the LC resonator at the operating frequency. (2)