In this article, we present a generative adversarial network (GAN) design framework for circuit synthesis design. While the existing methods, such as domain knowledge-and metaheuristic-based methods have been applied successfully in circuit synthesis, they are suited for certain types of circuits and thus limited. Recent advances in efficient circuit topology enumeration methods have proven to be useful for circuit synthesis problem with moderately-sized component catalogs; enumeration methods, however, cannot be used as a solution method for problems with large catalogs. Here we present a strategy based on Generative Adversarial Networks (GANs) that facilitates solution of synthesis problems that are too large for enumeration. A GAN is a generative unsupervised learning model where a lower-dimensional latent space is predefined as an abstract representation of the circuit topology space. The GAN is trained to learn the mapping from the latent space to circuit topology space. Circuit topologies can be produced using the generator, and a discriminator helps to improve generator quality. A comparative study is conducted using several recent GAN models, including GANs, DCGANs, WGANs, and improved WGANs. We designed and carried out a series of numerical experiments to evaluate the ability of these GANs to generate new circuit topologies and support design exploration. Two circuit synthesis case studies are presented here: frequency response matching and low-pass filter realizability. The work presented here is an effort to leverage recent advancements in artificial intelligence to 1) create the ability to solve larger synthesis problems than previously possible, and 2) gain deeper design insights into engineering synthesis problems.