All interruption devices absorb energy from the circuit in which they operate.  Even a simple mechanical switch absorbs energy within its switching arc during the time period the arc is present.  How much energy the switching device can absorb, and still function in additional operations, is a measure of the device’s interrupt rating.  For example, the on/off switch in a laboratory power supply is rated to switch x number of amps at a given level of input line voltage.  Such a switch, however, is not designed to interrupt high levels of overcurrent and could fail (i.e. be destroyed) if it is used to do so.  The switching contacts in a circuit breaker, however, are designed for overcurrent interruption.  And thus, a breaker in series with an on/off switch would have a higher interrupt rating than that of the switch. 

A portion of the energy absorbed during the operation of an overcurrent protection device is used in the overcurrent detection process.  Since detection is a binary trip/no trip decision process, there must exist a threshold portion of the total absorbed energy within the device which will trigger the device’s interruption process.

In a fuse, the threshold is reached when the fuse element melts and begins to vaporize within a portion of its length.  In a thermal circuit breaker, the threshold is reached when a certain level of thermally induced expansion or deflection is attained within the thermal element.  In a magnetic circuit breaker, the threshold is reached when a movable armature has been magnetically attracted to a certain position.

We will term the detection threshold value of energy W_dt.  The time period between the initiation of the circuit overcurrent, and the time at which the absorbed energy within the detection mechanism of the protection device surpasses W_dt, is termed the detection period t_d (see Figure 1.5).  If the overcurrent is initiated at time t=0, we then have

where W_d is the total amount of energy absorbed within the protection device during the detection period.  v_B is the voltage drop across the device terminals, and i_B is the device current.  Note that in all cases                                                                                                                                          W_d > W_dt

 but only slightly, due to inefficiencies within the protection device internal circuitry.  Such inefficiencies include contact resistance losses, wiring resistance losses, conduction heat transfer away from thermal elements, etc.

The interruption period of a protection device begins immediately after the detection energy threshold has been exceeded.  Within this period, metal vaporization evolves into an arc in a fuse, and contacts separate and initiate an arc in a circuit breaker. The total energy absorbed by the device during this period, W_i, is given by where t_c is the total clearing time of the interruption device (see Figure 1.5).  Within the interruption period t_i = t_c-t_d, is the arc time t_a, where t_a ≤ t_i.  The energy absorbed within the arc, W_a, is given by

 where v_a is the voltage drop across the device arc.  In all practical devices, the arc voltage drop dominates the device voltage so that v_a =~ v_B, and the dominant portion of the total energy absorbed during the interruption period is consumed in the arc.  Thus, W_a =~ W_i.

The total clearing energy absorbed, W_c, by the protection device during the total clearing time t_c, is then given by            

It is this total absorbed energy W_c which doubly concerns the protection device designer.  In many cases the designer would like the detection threshold energy W_dt to be small, such that for large overcurrents the detection period can be short and the total W_c small.  But the designer would also like the device to be tough, (i.e. be able to interrupt very large overcurrents, with their associated large W_c’s), and survive.  Within these two conflicting goals lies a compromise design.

Nowhere is this compromise more evident than in the design of a thermal circuit breaker.  It is obvious that the detection of overcurrents by thermal means can be fast.  A high speed semiconductor fuse is, in fact, the fastest electromechanical protection device available.  But a fuse can afford to be fast, since it is designed to self-destruct when it operates.  It is deliberately designed to have a low thermal mass.  Thus, it can reach its operation (melting and vaporization) temperatures in very short periods of time.  A thermal circuit breaker, must have sufficient thermal mass that it will not self-destruct during operation.  This additional mass slows the response time to such a degree that the action of a pure magnetic circuit breaker can be significantly faster.  A thermal circuit breaker designer is forced, therefore, to trade off device speed for device survivability. 

In many respects survivability is the essence of protection science.  The application engineer – the one who specifies the particular overcurrent protection device to be used in a particular circuit – is concerned with the survivability of the circuit components.  He or she must choose the protection device which will, under a set of known fault or overload conditions, limit the amount of destructive overcurrent energy that is absorbed by the circuit components.

A nearly universal measure of the potential for damage in an overcurrent situation is the total i²t that a particular circuit component can absorb, and still survive.  It is only natural then that overcurrent protection devices would also be characterized by the amount of i²t that they let-through in a given overcurrent condition.  Mathematically, the let-through i²t of a protection is given by

 Note that we are concerned with the aggregate heating current, integrated over the total clearing period.  To emphasize this, we define a mean square current < i_B²>

 The protection device let-through i²t is thus given by < i_B² > t_C.

Note that the i²t value is an average value.  Many times two different overcurrent waveforms can have the same i²t value, yet one can be potentially more destructive than the other.  For example, the thermal mass of a semiconductor device is so low that the device junction temperatures are nearly proportional to the instantaneous square of the device current.  Thus, peak squared currents for semiconductor devices are also a measure of potential device damage.  To be safe, when device i²t limits are specified, the actual current waveform should always be specified,   i.e. DC, sinusoidal, offset sinusoidal, pulse, triangular, etc.