Design of the Dynamic Supply CMOS RF Power Amplifie - Linear CMOS RF Power Amplifiers for Wireless Applications - page 24

Fig. 3.9 Anti-overlapping timing diagram

Fig. 3.10 LC filter used in
the output of the modulator

3.2.3 LC Filter

The LC filter of Fig. 3.3 attenuates the switching frequency component of the PWM
signal v sw and passes the envelope frequency components. In this way, the signal
v out will be a copy of the modulator's input signal which is the processed envelope
of the input RF signal. The filter action is not perfect and, hence, the switching
frequency component will be always present at the output signal. In the time domain,
this is commonly referred to as ripple. For a dynamic supply RF PA, the switching
frequency must be about 10 times the maximum frequency of the envelope so that
the ripple in the output signal does not disturb the operation of the system [ 17 , 28 ].
The LC filter, shown in detail in Fig. 3.10 , has the following transfer function:

1

H LC (s) =

s 2 LC ,

(3.4)

s R p + 1 +

where R p is the load of the LC filter, that is, the resistance seen by the LC filter
when looking at the power amplifier supply pin.
Equation ( 3.4 ) is a typical transfer function of a 2nd-order system and can be
rewritten as [ 24 , Chap. 9]:

1

H(s) = , (3.5)

ω 2
ω n

i2 ξ ω n − 1 +

where ξ is the damping ratio, ω is the angular frequency, and ω n is the undamped
natural frequency.