Dear Friend,
the dimensions of a quarter wave transformer depend on two main paramenters: the impedence to match and the dielectric characteristics. Supposing to match an impedence Zin and the load RL, the impedence of the quarter wave transformer is Z1^2 = RL * Zin. For example if RL = 50ohm and Zin = 100 Ohm the impedence is 70.7 ohm. Established the impedence you have to design the width as function of the dielectric characteristics (dielectric constant, dielectric height, loss tangent,...) and the length as function of your wavelength.
I hope that it is useful
BR