# Comprehensive Relay Kickback Voltage Analysis

Relay is made up of two elements; the coil and the contact. The coil needs to be energized so that the contact will change state. For detailed analysis on how to drive the relay coil for it to energize read this. In this topic we will jump directly to relay kickback voltage analysis.

As mentioned, relay has a coil. This coil has an inductance and from what we know in the properties of an inductor is that it will resist to a sudden change in current by producing a counter EMF.

### Relay Kickback Voltage Analysis

Considering below circuit, once the driving voltage V2 is interrupted, the coil will be de-energized and the current will be interrupted. The coil will not allow a sudden current change and therefore it will oppose it and as a result a very high voltage spike will be experienced by the MOSFET S1. By the way, the component enclosed in green is the relay and the left side that has 10u is the coil while the right side is the contact. To know more about relay, about the parameters to take in design or understanding relay datasheet, read this.

The analysis is somewhat difficult especially to those who are not really working in design for years. In practice, it is best to measure the actual kickback voltage experienced by the MOSFET at turn off then install a protection to avoid the circuit device from damage. However this approach is sometimes destructive especially when the level of the spike voltage is very high. I will demonstrate to you how to analyze and compute for the possible level of the MOSFET drain voltage at turn off so that you have a point to start. Figure 2 – simplified version of our demo circuit wherein we did not include anymore the contact side of the relay since it is not anymore relevant in this particular analysis.

At normal operation (say the MOSFET is operating at saturation and the relay coil is energized), the current will flow from V1 to the relay coil, to the MOSFET and to the circuit ground to complete the path. During this condition, the upper side of the relay coil (the side connected to V1) has a positive sign while the lower part of the coil has a negative sign as shown in the figure above.

When the supply V2 is interrupted and the MOSFET will turn off, the relay coil will reversed its polarity to resist the change in current and try to maintain it in a short period of time. The circuit will now look like below. Figure 3 – Relay coil polarity reverses when V2 is interrupted

Then the voltage seen in the VDS node is can be expressed by doing KVL from V1. Expressing VDS Based from above equation, the voltage that MOSFET will see is the sum of the supply V1 and the coil voltage at the instance the current is interrupted. The voltage across an inductor is So the VDS equation is can be re-written as below Since we are accounting the instance the MOSFET is turned off, the current di during this time is still the normal current that flow through the coil. However, the challenging part here is how to determine the time dt. I prepare an illustration in Figure 4 to discuss the determination of the time dt very well. Figure 4 – Voltage and current waveform of the MOSFET during turn off

The upper waveform of Figure 4 is the current on the MOSFET while the lower one is the VDS. While the MOSFET is running at saturation the current is steady and this is labeled as the running current in the figure. When the MOSFET is turned off, the current will start to drop and then oscillate until it will rest to zero. On the other hand, while the MOSFET is ON, the VDS is zero since the MOSFET is operating in saturation. When the MOSFET is off and the current starts to decay, the VDS will start to increase and has its maximum level when the current is zero.

Hence, it is clear that the change in current di is the difference of zero and the running current (0 – running current). And now the change in time (dt) that the current is changing from the running current value to zero is the difference between point A and B in the above figure. When we extend the point the running current starts to decay in such a way the same with the dashed orange line in the above figure (point C), we can have a sine wave signal with a period from point C to point E.

Where these oscillations come from? These oscillations are due to the resonance action of the coil inductance and output capacitance (Coss) of the MOSFET. A combination of L and C will always creates ringing. And now, if we can get the frequency from point C to point E, we can get the period and then we can get dt since it is just a quarter of the period. But the question is how to get the frequency? The resonance frequency of L and C is can be expressed using below equation.

L is the coil inductance and C is the total drain capacitance which includes the layout and output capacitance of the MOSFET. If the layout is good, what will dominate is the Coss of the MOSFET. And also, a smaller value of C will give the worst case VDS, so the layout factor is may be neglected here.

Supposing we use AO6408 MOSFET which typical output capacitance is 232pF and we assumed a 10µH inductance for the relay coil, thus we can compute for the frequency as below. (Note: In Figure 4, the final current is zero and the initial current is the running current and the change in current di must be negative. However, we already accounted the negative sign into the coil voltage in our equation derivation, so the change in current is no longer negative. The running current is just 12V/68Ω, neglecting the on state voltage drop of the MOSFET.)

The maximum drain to source voltage that AO6408 MOSFET can handle is only 20V; hence it is expected to be damaged with the level of drain voltage which is reaching to 35.3V. To avoid damaging the device, you should install a protection. The most common protection is to use a freewheeling diode (Figure 5). Another method is to use a TVS across the MOSFET (Figure 6). The former has slower response than the latter. A diode with a 1A, 60V rating is already enough. For the TVS, the clamping voltage must be less than the minimum breakdown voltage of the MOSFET.

### Verify the Analysis through Simulation

We will check our computation how close it with the simulation result. Figure 7 is the circuit model with a coil of 10uH inductance and 68Ω resistance (internal). The MOSFET used is AO6408 which is the same with what we used above. The analysis method used is transient wherein the stop time is 4m seconds and we started all the supply from zero. We set V2 as a pulse with initial voltage zero and turn on level of 5V.

Figure 8 shows the simulated level of the drain voltage (VDS) which is around 33V. The simulation and the computation have close result.