Q: Why can you couple the inductors on the Cuk Converter, but not on the Buck with an input filter?
A: To couple, the waveforms on the inductors must be the the same. The Buck's output inductor supports triangular ripple, while its input inductor passes only second order ripple. This is because there is a square wave voltage across L2, but only triangular ripple voltage across L1.

Q: How do I design the coupled inductor?
A: 1)Design it as if it were the output inductor of the Cuk Converter, but for twice the current.

2)Find the resulting wire size, then find a wire size with half the copper area.

3)Wind the original number of turns with this wire, close to the core on the bobbin. This is the output inductor winding.

4)Find the wire size with 1/Nsquared the area of the output winding wire, where N is the turns ratio of the isolation transformer.

5)Wind N times the number of turns of the output winding farther from the core on the bobbin. This is the input inductor winding.

6)Install this inductor in your breadboard. Remember that for a coupled inductor, DC current flows INTO BOTH DOTS.

7)Reduce the number of turns on the input winding one by one, until the output ripple is zero.

Q: What about this "second order ripple" I've heard about coming out of the coupled inductor.
A: Second order ripple comes from the triangular (first order) ripple voltage on the ETC. This appears across the remaining leakage inductance when zero ripple has been accomplished. It appears as third order voltage ripple on the output capacitor.

Since the original square-wave of current has, by that time been integrated 3 times, the resulting RMS value and harmonic content are negligible.

Q: Is line rejection lost when the inductors are coupled?
A: Yes. The open loop line to load transfer function features only two poles, instead of four, as in the uncoupled topology. These come from the output capacitor, and the leakage inductance of the coupled inductor.

Q: Should I worry?
A: No. I only recommend the Coupled Inductor converter for use as a power amplifier. In the back-to-back, or differential mode, line disturbances tend to cancel out, since both converters deliver the same hum to each side of the speaker.