Negative Resistance Devices Using A Multiple Number of Tunnel Diodes or Varactors

The critical need for simple high-gain, low-noise microwave amplifiers and frequency converters, required for space communication and improved ground communication systems, appears to be met by the solid-state tunnel diode and varactor devices. The incorporation of these low-noise negative resistance devices results in significant improvement in the performance of communication systems where sensitivity is of importance. Past attention has been concentrated mainly on negative resistance devices using a single tunnel diode or varactor. This paper will present some results on devices using a multiple number of tunnel diodes or varactors. The behavior of devices using an arbitrary number of diodes in either a nonreciprocal or reciprocal environment is studied and compared with the single-diode configurations. For an amplifier using
n
tunnel diodes with parameters (
- R_{1}, C_{1}
), (
-R_{2}, C_{2}
), ...,(
- R_{n}, C_{n}
), the optimum gain-bandwidth limitation for a nonreciprocal configuration is given by
(G_{T})_{n}\leq \exp [\sum \min{r=1} \max {n} \frac{2\pi}{\omega_{c}R_{r}C_{r}]
where
(G_{T})_{n}
is the fiat transducer power gain and ω
c
is the bandwidth in rad/s for the amplifier using
n
tunnel diodes. This optimum gain-bandwidth limit can be realized by cascading
n
stages of the optimum nonreciprocal single-diode amplifiers. For the reciprocal realization of the tunnel diode amplifiers, it can be shown that irrespective of the number of tunnel diodes employed, the optimum nonreciprocal matching can never yield more than 6 dB over the optimum reciprocal equalization. Thus, the fiat gain for the reciprocal case is given by
(G_{T})_{n} \leq \frac{1}{4}[1+ exp (\sum \min{r=1} \max{n} \frac{\pi}{\omega_{c}R_{r}C_{r})]^{2}
. For
n
varactors with parameters C
or
and
C{1r}, r
= 1,2, ...,
n
, the optimum nonreciprocal parametric amplifier must satisfy the following limitation
(G_{T})n \leq \cosh^{2} [\frac{\pi}{\sqrt{\omega_{so}w_{io}}{\omega_{c}}(\sum \min{r=1} \max{n} \frac {C_{1r}}{C_{or}})]
where
\omega_{s0}
and
\omega_{i0}
denote the signal and idler band-center frequencies respectively. This result is a generalization of the gainbandwidth limitation for single-varactor parametric amplifiers published recently by the author [1]. Besides the results on gain-bandwidth limitations, the stability of the negative-resistance devices using an arbitrary number of tunnel diodes or varactors is also studied. Since both the tunnel diode and the varactor are two-terminal active elements, they must be capable of operating in a stable manner under at least one passive termination. Although a complete stability theory for tunnel diode and varactor devices is not as yet available, some useful sufficient conditions are derived in the paper for the stability of these negative resistance devices. Results presented in the paper on the important gain-bandwidth limitations and stability conditions are useful in the design and synthesis of stable, broadband, low noise tunnel diode and varactor parametric amplifiers incorporating a multiple number of diodes. Among the many possible applications for this theory, one can cite the phased-array systems and the pseudo-passive satellite techniques. In the latter application, a large number of tunnel diode amplifier units are integrated in an antenna structure to enhance the scattering cross-section of a moderate-size structure.