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# Calculating Pull-in & Drop-out Voltages at High or Low Temperatures

Most of Kilovac's specifications are for a 25°C ambient temperature. However, a well known phenomena of electrical circuits is the rise in resistance of a current path as temperature is increased. The temperature rise may be caused by current flow or by changes in ambient temperature, but the effect in either case is increased resistance. Therefore, you can expect coil resistance, pull-in, and drop-out values to change over the operating temperature range of the relay.

Change in Pull-In Voltage Over Temperature

Figure 47.

The coil resistance (Rt ) after a specific temperature rise (Tr ) is calculated using the formula:

Rt = R 25°C (1+.003853 Tr )

Where:

Rt = New resistance at elevated temperature
R 25°C = Coil resistance at room temperature (25°C)
Tr = Rise in temperature from 25°C

Pick-up voltage varies directly with the change in coil resistance caused by a change in temperature. The basis for this is Ohms Law:

E/I = R

Since a relay coil is a current-driven device, as the coil resistance varies with temperature, so must the pick-up voltage (I=V/R). Thus, the same formula we used above to calculate the change in resistance with a change in temperature can be used to calculate pick-up voltage by substituting pick-up voltage for resistance. For example, assume that you have selected a relay that has a maximum pick-up voltage of 16 Vdc at 25°C, a standard value for a relay with a 26.5 Vdc coil, and you want to operate it in a 85°C environment. Using the formula, we find:

Vt = 16 Vdc (1+.003853 X 60°C) = 19.7 Vdc

If the ambient temperature is raised to 100°C, the new pick-up voltage will be:

Vt = 16 Vdc (1+.003853 X 75) = 20.6 Vdc

If the power supply you are using is rated at 20 Vdc, the relay would operate in an 85°C environment but not in a 100°C environment.

This same formula works for a decrease in temperature. For instance, at -25°C the pick-up voltage will drop to 12.9 Vdc, as follows:

Vt = 16 Vdc (1 + .003853 X -50) = 12.9 Vdc

If you want your circuit to operate properly over its entire temperature range, it is essential that you make the necessary calculations to ensure that the available voltage exceeds the temperature-adjusted relay specification.