For a fault in a DC circuit, the prospective (available) short circuit current is the final constant value V_{DC} /R, where V_{DC }is the source voltage and R is the resistance of the circuit. After a fault occurs, the current in the circuit increases exponentially, as shown in figure 1, with a circuit time-constant L/R, where L is the circuit inductance.

**Figure 1.** *DC short circuit current*

When a DC fault occurs the rate of rise (*di/dt*) of current is dependent on the circuit time constant (L/R). For a typical DC motor armature circuit, the L/R time constant is around 40ms, which yields a lower rate of rise of current (*di/dt*) under short circuit conditions as compared to an AC short circuit. With the lower *di/dt*, the fuse takes longer to melt compared with AC conditions, which also leads to a relatively long arcing time. These conditions, together with the absence of natural current zeroes, make the interruption of DC faults more difficult for the fuse than AC faults if L/R is high. As the L/R time constant in a circuit increases, the DC voltage capability of the fuse decreases. Therefore, for DC applications it is essential to know the value of L/R. The voltage rating of a typical semiconductor fuse is affected by the circuit time constant.

It is often difficult to obtain a precise value for L/R in practice. In the absence of better information, Table 1 gives some typical guideline values.

**Table 1.** *Typical values of L/R*

* It is never recommended to fuse a DC motor field circuit

The arc energy produced in a DC circuit also varies with test current in a manner similar to that shown in figure 2.

**Figure 2.** *Total time and prearcting time versus prospective current*

So for a given L/R there exists a maximum breaking current, minimum breaking current, and current which gives maximum arc energy. The V vs. L/R characteristic is published for the maximum fuse arc energy condition. Minimum breaking currents for DC applications are published separately in a table.

**Figure 3.** *Maximum L/ R versus DC operating voltage (left);minimum interrupting capacity (right)*

Semiconductor device manufacturers publish surge current withstand in terms of a half cycle surge rating, characterized by the peak amplitude (I_{FSM}) of a single sinusoidal half-cycle pulse which the device can withstand. The duration of the test pulse (t_{0}) is usually 8.33 ms or 10 ms, corresponding to 60Hz or 50Hz half-cycles. Two withstand values are sometimes published :

(a) with full rated voltage reapplied to the device immediately after the surge has finished

(b) with zero reapplied voltage.

When fuse protection is provided, the fuse must clear the circuit current before the device is damaged. Value (b) can normally be used, because after the fuse arcs have extinguished, the residual fuse resistance increases rapidly. Often the surge withstand is given as an I²t value (“for fusing”). The r.m.s. value I_{0 }for a half-sine wave is given by:

**I _{0 }= I_{FSM }/√2**and the corresponding I²t value is

**I²t (for fusing) = I**

_{0}²t_{0}However, semiconductor devices in the ON state have very nonlinear I-V forward characteristics, and the instantaneous power dissipation within the device is not proportional to the square of the current. For this and other reasons, the I²t withstand of the semiconductor device is not constant, but decreases as the duration of the surge becomes shorter. Figure 4 illustrates the variation of I_{FSM} and the corresponding I²t value for a typical thyristor. A simple model of single-cycle surge withstand can be used to show that the withstand line can be represented by I_{O}^{N}t = constant.

**Figure 4.** *variation of IFSM and I²t for a power semiconductor*

Many device manufacturers give I_{FSM }at two different times (often 8.33 ms and 1.5 ms), and when such data is plotted in the form of figure 4, the value of N for real devices is found to lie within the range of 2.5-4.0. The value N = 4 is the worst possible value. In figure 4, the “device exponent” N is approximately 3.0.

In the absence of better information, a device exponent of 3.0 can be used for diodes and thyristors. In other words, the device withstand is approximately a constant I³t, and the device withstand I²t should be adjusted by using a constant I³t for the actual fault duration. Then when the fuse interrupts a fault it is necessary to check the total clearing time and to calculate the diode or thyristor I²t for that time and then compare it to the fuse total I²t. Since the fuse I²t curve is very often a constant value it is sufficient to check the total clearing time of the fuse for the largest fault as it will give the shortest total clearing time.

**Case rupture I²t (explosion I²t):** in some fuse applications (converter with several semiconductors in parallel per arm), the fuse must avoid the explosion of the case of the semiconductor. This data is usually not published and it is then necessary to contact the semiconductor manufacturer. This I²t is constant. It can be 3 to 4 times the junction I²t value at 10 ms.

**For more information, please read:**

Introduction to Current Rating for Fuses

Time-Current Characteristic for Fuses

I²t Curves and Operating Times for Fuses