Design of the Frequency-Tunable CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 85

≈

0 . 9). The drawback is the high
capacitance between winding terminals which translates to a lower SRF.
4. StackedInterleaved : by using windings stacked in two different metal layers, but
with both windings being interleaved in each layer, coupling factors of the order
of 0.7 can be achieved [ 15 ]. The advantage over the interleaved topology is the
increased inductance density.
5. Rabjohn : first proposed by Rabjohn in [ 25 ], this transformer has interwound
windings and exhibits perfect symmetry when center tapped and, hence, is suit-
able for application as a balun [ 12 ].

highest self-inductance and coupling factor ( k

A decision for an interleaved transformer is justified by its suitability for applica-
tion in a 4-terminal configuration and because of its relatively high coupling factor.
Although the stacked configuration offers a higher coupling factor, it was not chosen
because of a possible lower SRF.

Interleaved Transformer Design and Simulation The design of the transformer
was an iterative process using Matlab [ 14 ], VeloceRF [ 11 ], and ADS Momen-
tum [ 2 ]. The geometrical parameters for the layout were obtained using the Matlab
function indspi from the MLib toolbox developed by Pisani in [ 22 , 23 ]. The formu-
lae used in this function are based on the works reported in [ 3 , 16 ]. The geometrical
parameters were then entered in VeloceRF which generated the layout for the trans-
former. This layout was then imported into ADS Momentum where a 2.5D planar
electromagnetic simulation was performed.
In order to generate the initial geometrical parameters for the transformer, we
calculated the mutual inductance using the method described by Mohan in [ 15 ].
In this method, two inductances are associated to the transformer. The first one,
L L 2 , is the inductance of the primary and secondary windings. The second

one, L T , is the inductance of a single spiral containing all the segments of both
windings. The mutual inductance can be written as

= L 1 =

L T − L 1 − L 2

M = . (6.16)

2

The coupling factor ( k ) can be directly determined from ( 6.16 ):

M
√ L 1 L 2 k = . (6.17)

Table 6.3 shows the parameters obtained using the indspi function considering
L 1 = L 2 = 0 . 8 nH. The definition of the geometrical parameters is provided in

Fig. 6.7 . The choice of the value for the self-inductances L 1 and L 2 depends on
the design of the control circuit and is treated in Sect. 6.4.3 . It is important to note
that the coupling factor given by ADS Momentum was not available at the time the
circuit was designed. This result was obtained after applying the model described in
Sect. 7.3 on p. 104. This investigation was carried out to find out the causes of the
malfunctioning of the circuit. Hence, for the design, we considered k =

0 . 7, which
is lower than that obtained with ( 6.16 ), thereby providing a safety margin.
The layout of the interleaved transformer was generated using VeloceRF with
the geometrical parameters of Table 6.3 . A Patterned Ground Shield (PGS) and