A small‐signal theory of a field‐emission‐array distributed amplifier consisting of two microstriplike transmission lines is developed to calculate the premodulation in the input channel and the gain in the output channel. A first‐order perturbation analysis is used to treat the beam‐wave coupling in this device within the framework of a cold fluid model. The dependence of the linear gain on frequency, beam voltage, beam current, and the circuit parameters is derived to determine the parameter range for operation of the device. It is found that the height of the circuit is restricted to lie between 80 and 120 &mgr;m to maintain high electronic gain and low loss arising from the finite conductivity of the metal surfaces. In an output line having a substrate with a relative dielectric constant, &egr;r=4, a net gain of 7 dB/cm is calculated with a beam voltage of 60 V and a beam current of 2.14 A/cm in each wedge of a seven‐wedge emitter array. As the beam voltage is increased in the range 60–100 V, the net gain decreases from 7.0 to 3.0 dB/cm, while the frequency for maximum gain increases from 50 to 80 GHz with a corresponding increase in the bandwidth. The small‐signal instantaneous bandwidth is in excess of 60%.