Frequency-Tunable Capability - Linear CMOS RF Power Amplifiers for Wireless Applications - page 70

Fig. 5.5 Example of circuit
for current control used
in [ 57 ]

The equivalent inductance seen by the RF circuit and the corresponding quality
factor are

L eq =

+

L( 1 αk), (5.11)

ωL( 1 + αk)

Q eq =

βkQ u ) ,

(5.12)

R Ls ( 1 −

where Q u = ωL/R Ls is the unloaded quality factor of inductors L 1 and L 2 .

Equations ( 5.9 ), ( 5.11 ) and ( 5.12 ) can be written in polar notation as follows:

R eq =− ωLkr sin φ + R Ls , (5.13)

L eq = L( 1 + kr cos φ), (5.14)

ωL( 1 + kr cos φ)

Q eq =

− kr sin φQ u ) .

(5.15)

R Ls ( 1

Equations ( 5.14 ) and ( 5.15 ) show that the equivalent inductance and quality fac-
tor are determined by the choice of the magnitude and the phase of the ratio be-
tween the currents flowing through the inductors—refer to ( 5.7 ). Pehlke et al. in
[ 41 ] demonstrated, with a measurement setup including a directional coupler, an
amplifier, a variable attenuator, and a variable phase shifter, that an inductor with a
TR of 67% (0.8-1.6 nH) could be achieved with integrated silicon coupled induc-
tors at 2 GHz. They also showed that a quality factor of 2000 could be reached at
a particular amplitude and phase of the control current. The coupled inductors were
integrated in a 0.18 µm CMOS technology and a photograph of the tunable inductor
can be found in [ 41 ,Fig.2].
Although in [ 41 ] tuning and Q enhancement were demonstrated, a current con-
trol circuit viable for an IC implementation was not presented. Wu and Chang in [ 57 ]
proposes a CMOS control circuit (Fig. 5.5 ) to use the coupled-inductor technique
exclusively as a Q -enhancement technique. The input voltage applied at the tunable
inductor terminals appears equally at the gate of M 1 and at the primary winding of