In this paper, we propose the use of GANs as learned, data-driven knowledge database that can be queried for rapid synthesis of suitable antenna designs given a desired response. As an example, we consider the problem of designing the Log-Periodic Folded Dipole Array (LPFDA) antenna for two non-overlapping ranges of Q-factor values. By representing the antenna with the vector of its structural parameters and considering each desirable range of the Q-factor as a class, we transform our problem to that of generating new samples from a given class. We develop two alternative models, a Conditional Wasserstein GAN and a label-switched library of vanilla Wasserstein GANs and train them with a dataset of features and their associated labels (parameter vectors and Q-factor range). The main component of these models is a generator network that learns to map a normally distributed noise vector along with a binary label to the vector of parameters of candidate structures. We demonstrate that in inference mode, these models can be relied upon for fast generation of suitable designs.