There is an overvoltage on the relay coil due to its inductance and the rate of current decay in the circuit:
$$e=-L*\frac{di}{dt}$$ di / dt - means current increase / decrease over time, measured in A / s
When the relay is turned off, the disappearing magnetic field induces a voltage in the relay coil. It is directed against the voltage drop across the energized relay, i.e. it adds to the supply voltage of the relay. At the end of the controlled relay (the second one is connected directly to the power supply), there will be a voltage pin with an amplitude:
Up = Ucc + UL
Up - overvoltage (peak) voltage
Ucc - supply voltage
UL - induced voltage in the coil
Example. Omron G2R relay for 12V.
http://downloads.components.omron.eu/OCB/Prod...lays/Up%20to%2030A/G2R/K013/K013-E2-12A-X.pdf Coil R = 275?
Coil L = 2.29H (with anchor attracted, 1.15H is released)
When powered by 12V, the current in the coil circuit is:
$$Il=\frac{12V}{275\Omega}=43.6mA$$ Now let's say that within 0.5ms this current drops to zero, i.e. the overvoltage at the end of the coil will be:
$$Up=Ucc+L\frac{di}{dt}=12V+2.29H*\frac{43.6mA}{0.5ms}=211.7V$$ If the switch-off time is even shorter, the overvoltage will be even greater (this phenomenon, unfavorable in relay circuits, is used in voltage-increasing converters, where the output capacitor is charged via a diode with such a controlled overvoltage, but the switching takes place with a much greater frequency).
Since the above-mentioned and calculated overvoltage can damage (break through) the control transistor, for example, diodes connected in parallel to the relay coil are used, which limit the overvoltage on the coil to its forward voltage.
Over-voltage suppression has the side effect of lengthening the deceleration time of the relay. This is due to the fact that although we do not supply current to the relay, due to self-induction, the current now flows in the relay coil-diode circuit.
The decaying current in the coil-diode circuit is described by an approximate formula:
$$Ild=\frac{Ucc-Ud}{R}*e^{-\frac{t}{\tau}$$ Ucc - supply voltage (12V)
Ud - voltage drop across the diode (0.8V)
R - relay coil resistance
L - relay coil inductance
t - time in seconds
? - circuit time constant RL = L / R
e - 2.718 ... the base of the natural logarithm
The above-mentioned relay releases when the current in the coil drops to 0.15 of the nominal value (in the data sheet it is given as release voltage)
Solving the equation:
$$0.15*I0=I1*e^{-\frac{t}{\tau}}$$ Where
I0 = Ucc / R
I1 = (Ucc-Ud) / R
we get that the current in the coil circuit will reach the release current level after time (for the above-mentioned data):
$$t=1.83*\frac{L}{R}=1.83*\frac{2.29H}{275\Omega}=15.2ms$$ Without a diode, the deceleration time is (for the G2R relay for DC voltage):
so-called = 5ms
with diode:
Tcałk_zw = so-called + td = 5ms + 15.2ms = 20.2ms
Of course, this is a theoretical value that does not take into account the scattering of parameters of individual relays
In some applications, this increase in deceleration time can hurt us.
It can be prevented by using several diodes in series instead of a single diode or a Zener diode in series with a rectifying diode. As a result, the overvoltage on the coil will be limited to safe values and at the same time will shorten the time of current flow in the overvoltage discharge circuit.
Uz + Ud + Ucc
. 