# Tapped Capacitor Matching

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

Figure 1. Tapped capacitor impedance matching network

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

(1)

At resonant frequency(), the parallel Â branch can be represented with series equivalentÂ  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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