Design of the Dynamic Supply CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 30

Fig. 3.14 Rollett stability factor simulation

the signal reflected in port 1 is higher than the incident signal, which, by its turn,
means that the real part of the impedance at port 1 is negative. The same is valid for
port 2.
However, the Rollett criteria are valid only under a proviso stated by Rollett
in [ 26 ], but often overlooked:

. . . the characteristic frequencies of the twoport with ideal terminations (infinite immit-
tances, i.e., open or short circuits, as appropriate) lie in the left half-plane.
This is known as the Rollett's proviso and, although it does not represent a prob-
lem for single active device circuits, it is important for circuits with multiple active
devices [ 18 ]. Hence, the Rollett criteria can only be used to determine whether a
multiple transistor PA is stable if no poles fall on the Right-Half Plane (RHP). The
proviso can be verified using the Normalized Determinant Function (NDF) [ 18 , 23 ].
With ADS and performing an S-parameter analysis, the factors K and B 1 were
simulated and the results are shown in Figs. 3.14 and 3.15 . In these figures, three
cases are shown: without any stability components, with R stab1 only, and with R stab1 ,
R stab2 , and C stab . Figure 3.15 reveals that the auxiliary condition B 1 > 0 is respected
in the three cases. However, without any stability components, Fig. 3.14 shows that
the condition K> 1 is not respected for frequencies above 200 MHz.
We begin by solving this problem with source and load stability circles
[ 15 , Chap. 3] to insure that K> 1 at the operating frequency of 5.2 GHz. The
simulated stability circles for the “no stability components” case are shown in
Fig. 3.16 (a). When the load and source stability circles fall partially inside the
Smith chart, the amplifier is potentially unstable. In order to push these circles