Optimum Synthesis of Wide-Band Parametric Amplifiers and Converters

This paper derives the theoretical limitation on gain and bandwidth for parametric amplifiers and inverting-type up-converters. It shows that the transducer power gain of an amplifier or a converter can be related to the reflection coefficient of a simple matching network as
G_a \approx \frac {\omega_0} {\omega_{0}\prime} G_c \aaprox \frac {1} {4 |p|^2}
where
G_a
and
G_c
are the power gain of the amplifier and the converter, respectively,
\omega_0
and
\omega_0 \prime
are the center frequencies of the signal and the idler bands, respectively, and
\rho
is the reflection coefficient which is limited in bandwidth by the following formula:
\frac {B} {\omega_0} \ln \arrowvert \frac {1} {\rho} \arrowvert \leq \frac {\pi} {2} \frac {C_1} {C_0} \sqrt{\frac {\omega_0 \prime} {\omega_0}}
B
is the bandwidth, and
C_0 + 2 C_1 \cos\overline{\omega} t
represents the variable capacitance. Optimum Butterworth filters are used as the coupling networks. Condition for optimum matching is determined together with element values of the circuit. The theoretical limitation on bandwidth can be approached if the number of elements in the coupling network is increased. The design of optimum wide-band amplifiers and converters becomes straightforward, thus eliminating any cut and try process.