# pi-matching

A -match network is shown in Figure-1. Two back-to-back connected l-match circuits form a -match network. The additional element in -match, compared with L-macth, allows independently setting impedance transformation ratio() and Q-factor of the circuit.

The analysis of -match circuit shown in Figure-1 can be simplified by redrawing the circuit into two L-match sections as shown in Figure-2.

If is the voltage at the input of L-match circuit, and is the impedance seen looking into each L-match circuit, then current flowing through inductor of each L-match circuit is .

The Q-factor looking into each parallel R-X branch is given by

(1)

By series-to-parallel transformation as shown in From Fig.3,

(2)

(3)

(4)

Rearranging Eq.(3)

(5)

The total of the circuit is given by

(6)

At resonant frequency, and . Therefore,

(7)

This equation can be used as a sanity check for the calculated T-matching network element values.

### DESIGN PROCEDURE

1. Find using Eq.(6) from given , and .

2. Calculate and using Eq.(5)

3. Lowpass -match
Find and using Eq.(1). and
Find and using Eq.(??).
.

.
.
4. Highpass -match
Find and using Eq.(1). and
Find and using Eq.(??)