# Matching Circuit Design

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```					                                          Matching Circuit Design

Design a matching circuit which matches a whip antenna to a pre-amplifier with the following
specifications

a) Frequency: matching is to be achieved for f 0 = 8.1 MHz

b) Bandwidth: ∆f = 0.7 MHz

c) Antenna impadace: Z A = R A ∠ jX A = 36 ∠ j15 Ω at f 0 ;

d) Input inpedance: pre-amplifier has input impedance of Z L = R L = 200 Ω .

Design

Since the antenna has capacitive impedance and its resistance R A = 36 Ω is less than the the input
resistance of the pre-ampplifier, the Series C (type 2) circuit can be used (see Fig. 6.16 in the textbook [1]
or Fig on the page 4-5 in the course notes [2]). Notatios from [1] are used.

In order to provide required bandwidth the circuit has to have the following quality factor Q

f0    8.1MHz
Q = ---- = ------------------- ≈ 11.6
-                     -                                                          (1)
∆f     0.7MHz

Using equation (6.-25) in [1] one can calculate intermediate parameters A and B of the matching
circuit

4.88 kΩ
A = R A ( Q 2 + 1 ) = 36Ω × ( 11.6 2 + 1 ) ≈ 4.88 kΩ , B =               ( A ⁄ RL ) ∠ 1 =   ------------------- ∠ 1 ≈ 4.3
-             (2)
0.25 kΩ

This allows to calculate necessary reactances of the matching circuit according to equations (6.26):

X L = QR A + X A = 11.6 × 36Ω + 15Ω ≈ 433 Ω                                                         (3)

A             4.88 kΩ
X C = -------------- = ------------------------ ≈ 669 Ω
-                          -                                                (4)
1  Q∠B              11.6 ∠ 4.3

X C = BR L = 4.3 × 250 Ω ≈ 1.08 kΩ                                                             (5)
2

Finally, reactance allows to calculate values of the elements since the frequency is also known

433 Ω
L = X L ⁄ ω = ------------------------------ ≈ 8.5 µH
-                                                   (6)
2π ⋅ 8.1MHz

-1-

```
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