Compared to conventional transformers (which are intended to alter the voltage between their respective windings), current transformers are designed differently. More specifically, we all know that:
In other words, the ratio of the operating voltages between any pair of (mutually coupled) windings is directly proportional to the ratio of turns comprising each winding.
Since (even practically speaking) transformers are essentially constant power devices - that is the input power is equal to the output power:
Knowing that the power developed//transmitted in any winding is given by:
As a result, we can see to conserve the power transferred between two dissimilar windings we must vary both the voltage and the current. If we substitute the transformer equation used above into our power conservation equation we can begin to develop the underlying concept utilized by current transformers.
It is then clear that the relationship of currents within each respective winding - that is, the current transformation ratio, is proportional to only the turns ratio:
Those with a keen eye will notice that the voltage and current transformation ratios are inversely proportional, which makes sense in order for power to be conserved.
It should now be very clear that a step-down current transformer is essentially a step-up voltage transformer in disguise...it has to be! Under normal operating conditions the secondary winding of a C.T. is shorted, and thus no hazardous voltages can be developed at the terminals. This healthy region of operation is defined/dictated by the current transformation ratio. The voltage transformation ratio, whilst still technically maintained internally (within the windings themselves), is not practically realizable at the terminals since a short exists across them (ideally).
An unhealthy operating condition is realized merely through opening/breaking the secondary circuit of the C.T.. In this regime the voltage transformation ratio dominates as the C.T. attempts to maintain secondary current (up to a point). Severe saturation occurs, heavily distorting both the current and voltage developed at the secondary. In large, high ratio C.T.'s this typically results in the generation of terminal voltages exceeding many kilovolts! Destruction of the C.T.'s and/or associated equipment can result.
This condition is to be avoided at all costs! This aspect of C.T. secondaries is so critical that NO overcurrent protection of any kind shall exist or be installed within a C.T. secondary loop. Additional joule heating from excess secondary current is greatly preferred over the generation of uncontrolled high voltages.