Tapped-C Transformer Matching

Description

The Tapped-C transformer uses a shunt-series-shunt arrangement of one inductor and two capacitors to achieve impedance matching at a target frequency. The loaded Q controls the bandwidth. Unlike the Tee and Pi networks there is no LP/HP mask — the component placement is fixed by the impedance ratio alone.

When to Use

RF frequencies.
Narrow bandwidth.
Small area to be implemented.
Typically used in some RF oscillators.

Design Equations

When RL > RS the roles of the two ports are internally swapped before computing component values, and L and C2 are placed on opposite sides of the network (see Topology section).

Auxiliary Q Factor

\[Q_2 = \sqrt{\frac{R_L}{R_S}(Q^2 + 1) - 1}\]

Component Values

\[L = \frac{R_S}{\omega_0\, Q}\]

\[C_2 = \frac{Q_2}{R_L\, \omega_0}\]

\[C_1 = \frac{C_2\,(Q_2^2 + 1)}{Q\,Q_2 - Q_2^2}\]

Minimum Q Constraint

\[Q > Q_{\min} = \sqrt{\frac{\max(R_S, R_L)}{\min(R_S, R_L)} - 1}\]

Values of Q below Qmin make Q2 imaginary and the design is invalid.

Parameters

Parameter	Description
Z0	Source impedance RS (Ω)
ZL	Load impedance (Ω)
Frequency	Matching frequency (Hz)
Q	Loaded Q factor (Q > Qmin)

Tapped-C vs Tapped-L

The Tapped-C and Tapped-L are duals of each other. Both use a shunt-series-shunt Pi arrangement with one reactive element type forming the series arm and the other split across the two shunt arms:

	Tapped-C	Tapped-L
Series element	C1 (capacitor)	L1 (inductor)
Shunt elements	L and C2	C and L2
Preferred use	Tank circuits, oscillators

Limitations

Q constraint must be given -> Narrowband.
Only real-to-real matching.