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Micrel Inc.
Matching Calculations
Capacitor C3 and inductor L2 form the L-shaped
matching network. The capacitor provides additional
attenuation for low frequency outside band noise and
the inductor provides additional ESD protection for the
antenna pin. Two methods can be used to find these
values, which are matched close to 50 ? . One method
calculates the values using the equations below, and
another by using a Smith chart. The Smith chart is
made easier by using software that plots the values of
the components C3 and L2, such as WinSmith by
Noble Publishing.
To calculate matching values, you need to know the
input impedance of the device. Table 3 shows the
input impedance of the MICRF221 receiver and
suggested matching values for the most used
frequencies. These suggested values may be different
if your layout is different from the layout for the
QR221BPF evaluation board.
MICRF221
Freq (MHz)
C3 (pF)
L2(nH)
Z device ( ? )
868.35
915.0
916.5
1.2
1.2
1.2
9.5, Coilcraft
8.7, Coilcraft
8.7, Coilcraft
9.4-j71.8
9.0-j67.4
8.5-j68.0
Figure 6. Device’s Input Impedance, Z = 9.0 – j67.4 ?
Because stray parasitic elements can be caused by
both the printed circuit board as well as the
components themselves, the values plotted are
Table 3. Matching Values for the Most Used
Frequencies
For the frequency of 915.0MHz, the input impedance
is Z = 9.0-j67.4 ? . The matching components are
calculated by:
Equivalent parallel = B = 1/Z = 1.95 + j14.6 msiemens
slightly different from the calculated ones. Therefore,
one plots the shunt inductor (8.7nH, from Coilcraft)
and the series capacitor (1.2pF) for the desired input
impedance (Figure 7). One can then see the matching
leading to the center of the Smith Chart or close to
50 ? .
Rp = 1 / Re (B);
Xp = 1 / Im (B)
Rp = 513 ? ; Xp = 68.5 ?
Q = SQRT (Rp/50 + 1)
Q = 3.35
Xm = Rp / Q
Xm = 153.1 ?
Resonance Method For L-shape Matching Network:
Lc = Xp / (2×Pi×f);
Lp = Xm / (2×Pi×f)
L2 = (Lc×Lp) / (Lc + Lp); C3 = 1 / (2×Pi×f×Xm)
L2 = 8.2nH
C3 = 1.14pF
Doing the same calculation, example with the Smith
Chart, it would appear as follows:
First, plot the input impedance of the device
(Z = 9.0 – j67.4) ? @ 915.0MHz.(Figure 6).
October 2008
13
M9999-100108
(408) 955-1690
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