An Murali-Lakshmanan-Chua circuit is the simplest second order non-autonomous nonlinear circuit exhibiting chaos. The strange nonchaotic attractor behaviour of the circuit when subjected to quasiperiodic forcing is studied analytically. An explicit analytical solution for a system exhibiting strange nonchaotic attractor behaviour in its dynamics is presented here for the first time, with phase portraits showing the Heagy-Hammel and fractalization routes to chaos.