## Optimum Turn-Off RCD Snubber

#### Design of optimum Turn-Off RCD snubber with online calculator and live simulation.

Let's start the discussion about snubber circuits and their use in switching converters with this first post about turn-off snubbers, specifically the turn-off RCD rate of voltage rise control snubber.

One of the losses present in power electronics circuits are the switching losses. They occur at both turn-on and turn-off commutation. The turn-off switching transition loss is caused by the fact that the switch voltage Vds rises before the off current Id has fallen to zero. One book that very well explains the various commutation phases and associated losses is Switching Power Supplies A - Z.
For a clamped inductive load the turn-off waveforms are showed in Fig. 1. If we denote the switch voltage rise time with tr and the current (Id) fall time with ts_off the energy dissipated by the switch at turn-off is given by the formula:

$E_{loss} = \frac {V_o*I_{in}} {2}*(t_r+t_{s off})$
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 Figure 1
Notice that the voltage rises to Vd before the current begins to fall, in fact the current path would only switch through the diode, but the diode has its cathode on Vo~=Vds and so the current cannot flow through the diode until it is positively polarized.
If make use of an RCD snubber as shown in Circuit 1, to control the rate of voltage rise the result is the waveforms on Fig. 2, where the voltage now begins to rise slowly and it overlaps the current waveform transition. The key element in this type of RCD snubber circuit is the capacitor Cs, the diode Ds and resistor Rs are only to limit the capacitor discharge current during switch turn-on. The capacitor Cs provides another path to the switch current to flow through. You are invited to open the circuit project and follow the instructions to see the snubber effect on the circuit waveforms.
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 Figure 2
The energy dissipated by the switch during turn-off with the snubber in place and approximating Vds with the voltage across the snubber capacitor Cs is derived as:

$E_{loss}= \int_0^{t_f} i_D v _{DS}\,dt=\frac {1} {12}*\frac {I^2_D*t^2_{s off} } {2*Cs}$

$P_{loss}= \int_0^{t_f} i_D v_{DS}\,dt=\frac {1} {12}*\frac {I^2_D*t^2_{s off }} {2*Cs}*f_{sw}$

As can be seen from the formulas above the switching loss could be ideally brought to zero given a sufficiently large capacitor. Unfortunately there is a downside, during switch turn-on the energy accumulated in the snubber capacitor Cs is dissipated through resistor Rs. In other words increasing the snubber capacitance decreases the switch losses but increases the snubber losses. The value of Rs should be chosen such that the RsCs time constant is about one fifth of the switch minimum turn-on time, thus assuring that Cs gets discharged during this time interval. The energy stored in the snubber capacitor is:

$E_{C_s}=\frac {Cs*V^2_{DS}} {2}$

The case where Vds = Vmax when Id = 0 is called a normal snubber, Cs = Cn:

$C_n=\frac {I_D*t_{s off}} {2*V_{max}}$

According to [1] it can be shown that there exists an optimal value of Cs for which the total loss (switch + snubber) is reduced to 53% of what it would have been without the snubber present in the circuit. The current fall time ts_off is mainly dependent on the mosfet driver voltage Vg, driver resistance Rg and mosfet gate capacitance Cg=Ciss and can be calculated as described in [2]:

$t_{s off}= Rg*C_{iss}*log(\frac{\frac{I_D}{g_{fs}}+V_{th}}{V_{th}})$

gfs =mosfet transconductance, Vth = gate threshold voltage

Although it is possible to calculate ts_off from mosfet datasheet parameters and application parameters it turns out to be more complicated as it may seem. In fact the mosfet capacitances are not constant but are voltage dependent and Vth is also not precisely defined in datasheets. I will address this in more detail in one of the next posts. For this purpose we will rather determine ts_off using a simulation or via oscilloscope measurement (using a shunt resistor, for example).
The calculator at the bottom of the page calculates the optimum RCD snubber values and generates a spice netlist that can be used for verification. In fact due to device parasitic elements some tuning may be needed to find the optimal value. Additionally a test netlist may be generated for measuring ts_off (current fall time) for the actual circuit that can be used for calculating the snubber.﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿
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Circuit 1

Optimum RCD Turn-Off Snubber Calculator

 Id = A --inductor current at turn-off Vds = V --output voltage at turn-off Vg = V --gate drive voltage Rg = Ohm --gate driver internal+external resistance ts_off = ns --switch current fall time (enter or MEASure) ton_min = ns --minimum turn-on time (duty-cycle related) f_sw = kHz --switching frequency Cs = nF Rs = Ohm Rs = mW
Snubber test circuit SPICE NETLIST

<---Click to open snubber circuit simulation template
1. William McMurray, SELECTION OF SNUBBERS AND CLAMPS TO OPTIMIZE THE DESIGN OF TRANSISTOR SWITCHING CONVERTERS, IEEE IAS transactions, Vol. IA-16, No. 4, July/August 1980, pp. 513-523
2. S. Maniktala, Switching Power Supplies A - Z, Second Edition, 2012