Radio Frequency Integrated Circuit Design - Webs

358 Radio Frequency Integrated Circuit Design
We can find the dc component and the fundamental component by
determining the Fourier series of this waveform. Note that the tuned circuit
will give us the fundamental component (if tuned to f 0).
I dc = 1
2� � �
= 1
� � �
−�
Power supplied is given by
0
(ICC cos �t − I CQ)d(�t)
[ICC(cos �t − cos � )]d(�t) (10.8)
= ICC
[sin � − � cos � ]
�
PCC = VCC I dc = VCC ICC (sin � − � cos � ) (10.9)
�
The fundamental current i 1 given by
i 1 = 4
2� � �
0
(ICC cos �t − I CQ) cos �t d(�t) = ICC
(2� − sin 2� )
2�
Output power is given by
Pout = i 2 1 R L
2
= vpeak √2 � ipeak √2 (10.10)
(10.11)
The maximum possible vpeak is when the output swings from about 0V
to 2VCC or vpeak = VCC . Thus,
Pout,max = VCC i1
�
√2 √2 = VCC ICC
(2� − sin 2� ) (10.12)
4�
Efficiency for this maximum possible voltage swing is given by
� max = P out,max
P dc
=
2� − sin 2�
4(sin � − � cos � )
(10.13)