Design of the Frequency-Tunable CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 91

Table 6.4 Script
tunable_ratio.fl

vin iscx -(gm1+k*gm2)
vin iscy -gm2
iscx vx (s*L)/(1+s^2*L*C1)
iscy vy s*L
vx iscout 1/(s*L)
vin iscout k*gm2
iscout vout (s*RL*L)/(RL+s*L+RL*L*C2*s^2)
vout iscy k*(1/RL+s*C2)
vout iscx 1/(s*L)

for the

flow_t tool

.pre syms s gm1 gm2 RL C1 C2 L k

.tf vin vout

Table 6.5 Matlab commands
used with the flow_t tool

H=flow_tf('tunable_ratio.flw');
syms s gm1 gm2 RL C1 C2 L k;
Iratio=-gm2*(RL/(1+s*RL*C2))*(1/H.sym{1});
pretty(Iratio);

Replacing the expression for H(s) calculated with the flow_t tool into ( 6.26 )
yields

s 2 LC 1 + s 3 R L LC 1 C 2 ] g m2 [

+

sR L (C 1 +

+

I ctrl
I RF =−

1 C 2 )

. (6.27)

s 2 g m2 kLC 1 )

( 1 + sR L C 2 )( − g m1 +

The script used with flow_t is shown in Table 6.4 and the Matlab commands to
run the script and calculate the final current ratio are shown in Table 6.5 .

6.4.3.2 Design of the Control Circuit

Equation ( 6.27 ) provides a relationship between the components of the circuit of
Fig. 6.9 and the current ratio ( I ratio ) between I ctrl and I RF . It was seen that the phase
and amplitude of I ratio determines the effective inductance and resistance seen by
the RF circuit between the two terminals of L 1 . Agilent's ADS simulator provides
a direct calculation of the current ratio.
In order to establish a design procedure for the control circuit, we identify three
main points of the problem:

1. Determination of the tuning range required for the inductance.
2. Determination of α and β (or r and φ ).
3. Feasibility of the circuit for the required variation of α and β .

For the first point, the knowledge of five variables is required: R opt , C 1 , C 2 ,the
nominal value of L 1 , and its unloaded quality factor. The determination of these