The story of current transformers and vacuum cleaners

Q: In a recent RAQ I mentioned a current transformer, what is it and how do I use it? 
 
A: A current transformer is just a different use of an ordinary transformer. You can find it in textbooks, but many engineers seem to ignore it! I use a current transformer to start my vacuum cleaner.

The transformer in the general concept consists of two magnetically coupled coils: a primary coil and a secondary coil, with a turns ratio of 1: N. If the AC signal voltage on the primary coil is V, then a signal voltage N×V will be generated on the secondary coil.

When a transformer is used as a current transformer, an alternating current is passed through the primary coil. For the legendary "ideal transformer", the short-circuit secondary current is proportional to the input current and inversely proportional to the turns ratio.

If the secondary is not shorted but connected to a resistor (assuming the resistor is not too large), the above relationship still holds true. This provides a method of measuring the AC current in the secondary, from which the AC current in the primary can be derived, and allows us to measure AC current using an isolated current.

The design of the current transformer is usually unimportant, although extreme cases (AC plus DC measurements, high voltage, low loss measurements, etc.) require attention. For power line and audio frequencies, a small iron core transformer found in a junk box or Radio Shack, modified slightly to wrap a new 1:5 primary with hook-up wire around the existing coil (assuming there is enough space to make such a coil), is usually sufficient. Commercial current transformers usually consist of a wire-wound toroidal core with the primary being the wire running through the center of the torus. The torus is sometimes hinged so that it can be opened to insert the primary.

The secondary resistance must be small enough to prevent the transformer core from saturating. The lower the resistance, the lower the possible operating frequency of the transformer. If the transformer output is applied to the inverting input of an op amp with resistive feedback, the resistance will be very low, so the minimum operating frequency will also be very low. Often people just use a miniature current transformer rated for 10kHz with a 200Ω load, and down to 50/60Hz with an op amp as load.

In addition to measuring AC current, current transformers can also detect current for control purposes. For example, a current transformer is used to detect the current in a woodworking saw to operate a vacuum cleaner. In fact, current transformers are widely used in household power monitors.