In this paper we investigate how to use controlled circuit instability in the filtering and amplification of narrow pulses. The basic circuit consists of a first-order RC network coupled to a negative resistance controlled by an external quench generator, which yields alternating periods of stability and instability. The study shows that when the circuit acts as a signal generator it can produce narrow exponential or Gaussian pulses, depending on the quench waveform applied. Included as a receiver front end, the circuit behaves as a highgain narrow-pulse filter. We also estimate the circuit parameters required to generate and receive sub-nanosecond pulses.