A Broad-Banding Theory for Varactor Parametric Amplifiers-Part II

Fundamental gain-bandwidth limitations are derived in this paper for parametric amplifiers using varactors. These limitations are fundamental in that they are independent of the associated circuitry. For a single varactor parametric amplifier with ideal flat response, the optimum gain-bandwidth limitation is derived as
G_{T\max} = \cosh^2(\frac{\pi\sqrt{\omega_{s0}\omega_{i0}C_{1}}} {\omega_c C_0})
, where
G_{T\max}
is the maximum flat transducer power gain,
\omega_c
is the equivalent low-pass bandwidth,
\omega_{s0}
and
\omega_{i0
are the respective signal and idler band-center frequencies, and
C_0
and
C_1
denote the first two coefficients of a linear variable capacitor. Explicit formulas are presented for the design of modified Butterworth and Chebyshev characteristics of arbitrary orders and it is shown that both approach the ideal flat response over the prescribed band as the order is increased. When the series parasitic inductance
L
of the varactor is considered, there is an additional limitation given by
G_{T\max} = \cosh^2[\frac{\pi\sqrt{\omega_{s0}\omega_{i0}} C_{1}(3C_{0} - \omega_{s0}\omega_{i0}C_{1}^{2}L} {\omega_{c}^{3}LC_{0}^{3}}]
.