Tapped-L Transformer Matching

Description

The Tapped-L transformer uses a shunt-series-shunt arrangement of two inductors and one capacitor to achieve impedance matching at a target frequency. It is the dual of the Tapped-C: the series element is always an inductor (L1), and the single capacitor C is split across the two shunt arms together with a second inductor L2. The loaded Q controls the bandwidth.

When to Use

RF frequencies.
Narrow bandwidth.
Small area to be implemented.

Design Equations

When RL > RS the roles of the two ports are internally swapped before computing component values, and C and L2 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

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

\[L_2 = \frac{R_L}{Q_2\, \omega_0}\]

\[L_1 = \frac{L_2\,(Q\,Q_2 - Q_2^2)}{Q_2^2 + 1}\]

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.