A current transformers (CT) is a device that can detect a current through a wire passing through its center. This wire
constitutes a one-turn primary for the transformer, and the winding on the CT constitutes the secondary of the transformer. If the secondary winding is terminated to a suitable resistor, then a current will be generated in the secondary winding which is  proportional to the current in the one-turn primary, as well as to the ratio of the transformer. This current in turn generates a voltage VL across the terminating resistor which is  proportional to the value of the terminating resistor. Thus a desired output voltage can be obtained for a specific input current by a suitable selection of the turns ratio and the terminating resistor.

Theory of Operation

A current Ip through the CT will generate a current Is in the winding of the transformer according to the relation

Is = Ip / N

Where N is the ratio of the CT.

When the secondary is terminated to a load resistor RL, the voltage drop across RL is given by

VL = Is X RL

      = Ip X RL / N

Hence the voltage VL is a linear indicator of the line current Ip within the linear range of the CT.

The limits to this range are set by the saturation point of the core material at the high end, and by its ability to respond to low magnetic fields at the low end.

By selecting a suitable value for RL, a desired voltage range corresponding to the input current range can be obtained.

For example, if it is desired to generate 2V at 20A line current, and if transformer ratio is 1000:1, then

RL = VL X N / Ip

     = 2 X 1000 / 20

     = 100 ohms.

Then the current to be measured will be given by

Ip = N X VL / RL

   = 1000 X VL / 100

    = 10 X VL  Amps.

The resistor rating is given by

W = Is^2 X RL

     = Ip^2 X RL / N^2 watts.

     =  0.04 W for the example above.