Design of the Frequency-Tunable CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 84

Fig. 6.6 φ domain in

quadrants

values of the phase φ between the two currents. The Cartesian plane is divided in
four quadrants and it can be seen that the region of interest encloses the first and
second quadrants because the corresponding equivalent resistance is lower than the
original value R Ls — Q enhancement—and the inductance can be greater or lower
than the original value L —inductance tuning. Operation in these quadrants imposes
that β> 0or0° <φ< 180°.
The value of r is limited by the efficiency of the circuit. The higher r is, the
higher the control current is. Therefore, the target is r< 1 and as close to zero as
possible.

6.4.2.1 Design of the Coupled Inductors

The design of coupled inductors (transformers) is a complex subject treated in sev-
eral articles, thesis, and textbooks like [ 9 , 12 , 15 , 19 , 25 ]. An analysis of the various
types of integrated transformers can be found in [ 12 , 15 ]. To choose the type of the
transformer to design the coupled inductors, we identify two main requirements:
high coupling factor and 4-terminal configuration.
The following types of transformers were analyzed:

1. Tapped : consists of two concentric windings for which only one turn of each
winding is adjacent to a turn of the other winding. This limits the coupling factor
to values between 0.3 and 0.5. It is suitable for 3-terminal applications.
2. Interleaved : also known as Frlan transformer [ 12 ], because it was first proposed
by Frlan in [ 8 ]. It consists of two interwound coils implemented with the same
metal layer. Coupling factors from 0.6 to 0.8 can be achieved [ 12 , 15 ] and it is
appropriate to 4-terminal applications. Because of the distance between the turns
of the same winding, the self-inductance is usually low.
3. Stacked : also known as overlay or Finlay transformer [ 12 ]. It is composed of
two windings that are implemented each in a different metal layer. By exploiting
both lateral and vertical magnetic coupling, this type of transformer achieves the