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AN3394 Datasheet, PDF (24/29 Pages) STMicroelectronics – Antenna design and impedance matching guidelines for CR95HF multiprotocol contactless transceiver IC
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Demonstration of C11 and C22 calculation
AN3394
Equation (A.I.4)
Xtot= –ω × C11 × -R----e---q---2(--R--×---e--(-q-1---×--–---C--L--1-P--1--A--×--×---ω--ω--)--2-2---×-×----C(---1--2--2-–--)--L-(--1-P---A-–----×-L---P-C---A-2---2×----×-ω----ω2----2×---)--(2---C-+---2--(-2--ω--+--2---C-×---1--L-1---P)---A)----+-×----ωC----2-1---1×---)--L2---P----A---2-
Neglecting ω2 x LPA2, then resolving the numerator leads to two different resonance
pulsation ω0 and ω1:
Equation (A.I.5)
ω0 = L----P----A----×-----(--C----1-2---2----+-----C----1---1---)-
Equation (A.I.6)
ω1 = L----P----A----1×-----C-----2--2-
Finally inserting Equation (A.I.5) in Equation (A.I.3) leads to:
Equation (A.I.7)
C11 = R-----e---q---1-×-----ω----0- ×
⎛
⎝
R-R----o-e--u-q--t
–
1⎠⎞
Equation (A.I.8)
Equation (A.I.9)
C22 = L----P----A----1×-----ω----0---2- – C11
C22 = L----P----A----1×-----ω----0---2- – C11 – Cinput – p
In addition, Cinput-p is in parallel with C22, and Cinput-p has to be subtracting to C22.
A.2 Serial to parallel equivalence RL impedance, and example of
RL load
Figure 23. Serial-to-parallel RL equivalent circuit
2!
:LOAD
,!
:LOAD0
20! ,0!
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Doc ID 018754 Rev 5
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