Speed of Operation

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Since coils are made of wires, they have an internal resistance associate with it. Let's model the primary side of the relay with the following circuit:

For this relay, the coil has different resistances depending on the operating voltage.

When the switch is closed for a long period of time (DC conditions), the inductor acts like a short circuit.

The circuit becomes a simple resistor in series with the voltage source. Applying ohm's law to find the current in the circuit you get the nominal current values on Table 6 of the datasheet.

Example: with a coil voltage of 12V, you have a 320 ohm resistance. The nominal current in the circuit at DC is

Ok, at DC things are easy to calculate but how do we model the transient of this circuit (opening and closing of the switch).

The model that we are using is a simple RL circuit. An RL circuit as the mathematical expression below, where t is going to be related with the switching times that we are trying to model.
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Note: If you are curious where this equation is coming from, you can find that information in any circuits book or on this online course under "Write the differential equation governing RC and RL circuits".

•  is the current in the circuit after closing the switch and waiting for the circuit to be steady. In this case will match the value that we calculated for the nominal current before = 37.5 mA.
•  is the current in the circuit before closing the switch, which in this case will be equal to zero assuming that there is no initial energy in the system.
•  is called time constant and it is equal to .

Let's plug the values that we have so far and see what parameters are we missing:
Simplifying the equation to:

Remember that we are trying to find a value of t that relates with how fast the relay can operate. We can't plot this equation yet because we are missing 3 parameters, ,  and .

However, if we find the value of , we can plot and  and start understanding the dynamics of the relay.

Unfortunately, there is no information on the datasheet but we can try and measure the using an RCL meter. There is a lot that goes into measuring inductors, but we are going to keep things simple for now and get a value to work with.

In the lab, we have two RCL meters available, a vintage Fluke PM6303 and a more modern one the Keysight E4980AL.

• The vintage meter is very easy to use but it has the limitation that the user cannot apply different voltages or frequencies to the externals components, in this case the coil of the relay.
• From the datasheet, this meter measures everything at 1kHz and 2.

• Measuring the coil of the relay with this meter we get an .

• On the other hand, the Keysight meter is a bit more complex to operate but the user has a lot more control on what it can measure.
• Setting the same frequency and voltage used with the Fluke meter, we get an .

I am going to use the average value between these two measurements and plug that value in the equation below:

Let's plot  and see what we get:

Ok, we have a plot now but which value of current is important to us? Normally, we would look at when the current in the coil is at 90% of the final value (33.75 mA) which will give us a around 0.45 ms. However, the datasheet actually provides a minimum amount of current needed to trigger the switch.

If you go to Table 3 on the datasheet, you can find a coil sensitivity parameter.

We can use the power equation to find the minimum amount of current needed to trigger the coil at 12V.

According to the plot, the relay takes to reach 30 mA. This is super fast (around 3.125 kHz), way higher than the 0.5 Hz switching electrical time from the datasheet.

Some of the reasons why the manufacture recommends operating at much lower switching rates is because:

• Mechanically the switch can't switch that fast, so it is not worth to document an electrical timing that is ridiculously higher than the mechanical timing.
• And the mechanical parts of the switch will ware and tare over time, so if we operate at much lower speeds the relay can be used for longer.