Design of the Frequency-Tunable CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 81

Fig. 6.3 Tunable
π -matching network

6.2.1.1 Finite Q u Inductors

An important non-ideality of an impedance matching network is the finite unloaded
quality factor ( Q u ) of the passive components. For the π -matching network, the
inductor in the series path is the most critical component. We express the unloaded
quality factor of an inductor as the ratio between its reactance and its parasitic series
resistance:

X L
R Ls =

ωL
R Ls

Q u = . (6.12)

An inductor with finite Q u in the series path of an output matching network
reduces the output power of the PA. We distinguish two contributions:

1. The mismatch due to the presence of a resistor R Ls in series with the inductor
L 1 in Fig. 6.2 . If this resistor is not taken into account correctly, it will produce
an impedance mismatch which in turn will provoke a deviation of the impedance
seen by the PA from its optimum value.
2. The power dissipation in the series resistor R Ls due to the output RF current
flowing from the PA to the antenna.

Hence, the quest for high- Q u inductors in CMOS technology has its motivation
also on the design of PAs.

6.2.2 Tunable Output Impedance Matching

The tunable output impedance matching network is based on the coupled-inductor
technique introduced in Chap. 5.A π -type network using an inductor as the tunable
element was chosen according to the analysis made in Sect. 6.2.1 . A schematic of
this network is shown in Fig. 6.3 .
The terminals of L 2 are connected to a control circuit providing a current I ctrl
that satisfies (5.6)onp.69. The design of the coupled inductors and the control
circuit is the subject of Sect. 6.4 .