# Tapped Capacitor Matching

The impedance transformation ratio ( ) and bandwidth/Q-factor of the circuit can be set independently.

STEP-1
The Q-factor( ) of parallel  branch is,

(1) At resonant frequency( ), the parallel  branch can be represented with series equivalent  as shown if Figure 1(b)

STEP-2

After parallel to series transformation,

(2) (3) (4) The total capacitance in the branch (  -R_{Lp}^{‘}) is

(5) The Q-factor of the branch (  -R_{Lp}^{‘}) is

(6) When ,

(7) STEP-3

To present the circuit in parallel resonant form, series to parallel transformation is performed. The equivalent circuit is shown in Figure 1(c).

(8) (9) (10) (11) When and , from Eq.(7) and Eq.(9),

(12) Therefore the impedance transformation ratio is mainly a function of capacitance tap ratio. Hence tapped-capacitor matching network.

DESIGN PROCEDURE

• Find Q of the circuit, from the desired bandwidth, • Determine and from Eq.(8)
• Find from Eq.(10)
• Knowing , now find the value of from Eq.(1)
• Finally find the value of using Eq.(4)

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