By the end of 1960s, the US government made new laws enforcing strict emission standards. As a result, more and more electronic ignition systems were developed, and starting from 1970s all smaller engines installed CDI system to replace the contact point system, including Honda Cub which began to use AC-CDI system.
A typical CDI module consists of a small transformer, a charging circuit, a triggering circuit and a main capacitor. First, the system voltage is raised up to 400-600 V by a transformer inside the CDI module. Then, the electric current flows to the charging circuit and charges the capacitor. The rectifier inside the charging circuit prevents capacitor discharge before the ignition point. When the triggering circuit receives triggering signals, the triggering circuit stops the operation of the charging circuit, allowing the capacitor to discharge its output rapidly to the low inductance ignition coil, which increase the 400-600 V capacitor discharge to up to 40 kV at the secondary winding at the spark plug. When there's no triggering signal, the charging circuit is re-connected to charge back the capacitor.
The amount of energy the CDI system can store for the generation of a spark is dependent on the voltage and capacitance of the capacitors used, but usually it's around 50 mJ.
Most CDI modules are generally of two types:
Note that not all small engine ignition systems are CDI. Some older engines, and engines like older Briggs and Stratton use magneto ignition. The entire ignition system, coil and points, are under the magnetized flywheel.
Another sort of ignition system commonly used on small off-road motorcycles in the 1960s and 1970's was called Energy Transfer. A coil under the flywheel generated a strong DC current pulse as the flywheel magnet moved over it. This DC current flowed through a wire to an ignition coil mounted outside of the engine. The points sometimes were under the flywheel for two-stroke engines, and commonly on the camshaft for four-stroke engines. This system worked like all Kettering (points/coil) ignition systems... the opening points trigger the collapse of the magnetic field in the ignition coil, producing a high voltage pulse which flows through the spark plug wire to the spark plug.
If the engine was rotated while examining the wave-form output of the coil with an oscilloscope, it would appear to be AC. But you must consider that since the charge-time of the coil corresponds to much less than a full revoltion of the crank, the coil really 'sees' only DC current for charging the external ignition coil.
There exist some electronic ignition systems that are not CDI. Some systems use a transistor to switch the charging current to the coil off and on at the appropriate times. This eliminated the problem of burned and worn points, and provided a hotter spark because of the faster voltage rise and collapse time in the ignition coil.
Since the CDI system only provides a short spark, it's also possible to combine this ignition system with ionization measurement. This is done by connecting a low voltage (about 80 V) to the spark plug, except when fired. The current flow over the spark plug can then be used to calculate the temperature and pressure inside the cylinder.