MICRF221 datasheet(13/26 Pages) MICREL

13 / 26 page

Micrel Inc.

MICRF221

October 2008

M9999-100108

(408) 955-1690

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 50Ω. 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.

Freq (MHz)

C3 (pF)

L2(nH)

Z device (Ω)

868.35

1.2

9.5, Coilcraft

9.4-j71.8

915.0

1.2

8.7, Coilcraft

9.0-j67.4

916.5

1.2

8.7, Coilcraft

8.5-j68.0

Table 3. Matching Values for the Most Used

Frequencies

For the frequency of 915.0MHz, the input impedance

is Z = 9.0-j67.4Ω. The matching components are

calculated by:

Equivalent parallel = B = 1/Z = 1.95 + j14.6 msiemens

Rp = 1 / Re (B);

Xp = 1 / Im (B)

Rp = 513Ω;

Xp = 68.5Ω

Q = SQRT (Rp/50 + 1)

Q = 3.35

Xm = Rp / Q

Xm = 153.1Ω

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)Ω @ 915.0MHz.(Figure 6).

Figure 6. Device’s Input Impedance, Z = 9.0 – j67.4Ω

Because stray parasitic elements can be caused by

both the printed circuit board as well as the

components themselves, the values plotted are

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

50Ω.

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