Design of the Frequency-Tunable CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 80

Table 6.2 π -matching
network for a target
R opt = 18 .Low- Q 0 case:
C 1 = 2 . 39 pF and
C 2 = 1 . 84 pF

freq (GHz) L 1 (nH) Q 0 R opt () X opt () Γ opt (dB)

3.7 1.212 1.56 17.92 0 − 53 . 2

3.8 1.169 1.62 18.07 0.30 − 41 . 2

3.9 1.124 1.67 18.03 0.60 − 35 . 6

4.0 1.082 1.72 18.00 0.88 − 32 . 2

4.1 1.042 1.77 17.98 1.14 − 29 . 9

4.2 1.004 1.82 17.95 1.40 − 28 . 1

4.3 0.965 1.86 17.75 1.66 − 26 . 5

4.4 0.931 1.91 17.73 1.90 − 25 . 4

4.5 0.898 1.96 17.70 2.13 − 24 . 4

4.6 0.867 2.01 17.68 2.36 − 23 . 5

4.7 0.837 2.06 17.66 2.57 − 22 . 7

4.8 0.807 2.11 17.47 2.79 − 21 . 9

4.9 0.780 2.16 17.45 2.99 − 21 . 3

5.0 0.755 2.21 17.44 3.19 − 20 . 8

5.1 0.729 2.25 17.25 3.39 − 20 . 1

5.2 0.706 2.30 17.23 3.57 − 19 . 7

C 1 and C 2 are kept fixed. If we choose a low- Q 0 network, with C 1 = 2 . 39 pF and

C 2 = 1 . 84 pF, Table 6.2 shows that the value of R opt can still be kept close to 18

throughout the whole frequency range from 3.7 to 5.2 GHz. This is again achieved
by varying just L 1 whereas C 1 and C 2 are kept fixed.
For both cases, the transformed impedance Z opt is close to the desired value of
18 , but for the high- Q 0 case ( Q 0 > 8) it is much closer than for the low- Q 0 case
(1 . 5 <Q 0 < 2 . 5) as reveals the column Γ opt —which presents a maximum value of
−

19 . 7dBforlow Q 0 . This column shows the reflection
coefficient as if a port with a characteristic impedance ( Z 0 )of18 were connected
to the output matching network in place of the power amplifier—refer to ( 6.11 ).
Hence, the most negative the reflection coefficient is, the closer the transformed
impedance is to the target resistance. Therefore, we can state that a higher Q 0 is
preferred in the case in which the inductor is varied and the capacitors are kept
constant.

31 . 2 dB for high Q 0 and −

20 log

Z opt − Z 0
Z opt +

Γ opt (dB) = . (6.11)

Z 0

Arrangements of inductors and capacitors, other than that of Fig. 6.2 , can also
be used to form narrowband π -matching networks as described in [ 1 , Chap. 3].
In [ 7 ], a procedure for the design of a π -matching network resulting in a relatively
wideband operation is discussed.