A Gain-Bandwidth Limitation for Parametric Amplifiers with n-Varactor Diodes

A gain-bandwidth limitation is derived in this paper for parametric amplifiers incorporating an arbitrary number of varactor diodes. For
n
varactors with parameters
C_{0\tau}
, and
C_{1\tau},\tau = 1,2,\cdots,n
, the optimum gain-bandwidth limitation is given by
(G_{T})_{n}\leq \cosh^{2}[\frac{\pi\sqrt{\omega_{s0}\omega_{i0}}} {\omega_0} \Sum_{r=1}^{n} \frac {C_{1\tau}} {C_{0\tau}}]
, where
(G_{T})_{n}
- is the maximum flat transducer power gain,
\omega_{c}
is the equivalent low-pass bandwidth, and
\omega_{s0}
and
\omega_{i0}
are the signal and idler band-center frequencies, respectively. This result is based on the three-frequency model for the varactor device and is essentially a generalization of the gain-bandwidth limitation for single-varactor parametric amplifiers published recently by the author [2].