 Solution

For elliptical polarization from circular and linear components, use coherent waves of the same frequency, propagation direction and fixed relative phase. Let the circular component be $A(\hat{\mathbf{x}}\cos \psi +\hat{\mathbf{y}}\sin \psi )$ and the linear component $B\hat{\mathbf{x}}\cos \psi$, with $A,B>0$. Their sum has $E_x=(A+B)\cos \psi$ and $E_y=A\sin \psi$, soThe tip of the electric field traces an ellipse with unequal semiaxes $A+B$ and $A$. Coherence is necessary: averaging unrelated phases does not create this fixed polarization ellipse.