We present a method of automatically generating circuit designs using evolutionary search and a set of circuit constructing primitives arranged in a linear sequence. This representation has the desirable property that virtually all sets of circuit-constructing primitives result in valid circuit graphs. While this representation excludes certain circuit topologies, it is capable of generating a rich set of them including many of the useful topologies seen in hand-designed circuits. Our system allows circuit size (number of devices), circuit topology, and device values to he evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. In all tasks, our system is able to generate circuits that achieve the target specifications. Although the evolved circuits exist as software models, detailed examinations of each suggest that they are electrically well behaved and thus suitable for physical implementation. The modest computational requirements suggest that the ability to evolve complex analog circuit representations in software is becoming more approachable on a single engineering workstation.