Design of the Frequency-Tunable CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 90

Fig. 6.13 Signal-flow graph of the circuit of Fig. 6.9

1 + sR L C 2

R L

I RF =− v out , (6.22)

i X M
sL =

k, (6.23)

and, hence, ( 6.20 ) can be rewritten as
⎧
⎨

1

i SCx =− g m1 v in − kg m2 v in +

sL v out ,

k 1 + sR L C 2
R L

i SCy =− g m2 v in + v out , (6.24)

⎩

1

i SCout = kg m2 v in +

sL v x .

The voltages of the nodes in the circuit with an associated auxiliary source are de-
termined by multiplying the driving-point impedance by the short-circuit current—
v n = Z DPn ×

i SCn . The voltages of the remaining nodes are determined by the sum
of the auxiliary and existing voltage sources.
Once the driving-point impedances and short-circuit currents have been deter-
mined, the SFG of Fig 6.13 can be drawn—the symbol “ ” represents a parallel

circuit combination. From this graph it is possible to determine the transfer function
of the circuit:

v out
v in

H(s) = . (6.25)

However, we are interested in obtaining the ratio between the control and RF
currents. Division of ( 6.21 )by( 6.22 ) yields the desired current ratio as a function
of H(s) :

I ctrl
I RF =−

R L

H(s) − 1 . g m2 (6.26)

1 + sR L C 2

Graph algebra and graph reduction techniques can be used to simplify the SFG of
Fig. 6.13 and determine H(s) . Alternatively, an SFG analysis tool for Matlab called
flow_t [ 17 , 18 ] can generate automatically the transfer function between two nodes
of an SFG from the circuit equations.