TABLE OF CONTENTS The voltage gain of a tuned amplifier in the s-domain was given as
From Fig. 4.14(a) it can be seen that in the vicinity of the resonance frequency and for s 0 ? s p1, ( s ? s p2) 
2 s and 
. Therefore (4.38) can be simplified as
and with A v( ? 0) = ? g m R eff and Q eff = ? 0 CR eff,
If n identical stages are connected in cascade, the total voltage gain becomes
and the bandwidth of the amplifier shrinks to
This is the appropriate solution if a high-gain and narrow-band amplifier is needed. But in some cases a relatively broad bandwidth and a flat frequency characteristic in this band are needed. It can be understood intuitively that tuning the stages of this multi-stage amplifier to slightly different frequencies around the center frequency of the band can lead to a feasible solution. In this case the gain of this multi-stage amplifier can be written as
which has n poles.
The appropriate positions of the poles of the transfer function (the voltage gain in our case) to obtain a desired frequency characteristic are investigated in depth in classical filter theory [28]. It is known that the number of poles and their relative positions determine the bandwidth and the shape of the frequency characteristics. Among several possibilities for...
