## 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

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

*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

$E_{loss} = \frac {V_o*I_{in}} {2}*(t_r+t_{s off})$

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~=

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

The energy dissipated by the switch during turn-off with the snubber in place and approximating

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

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

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

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

The case where

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

According to [1] it can be shown that there exists an optimal value of

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

gfs =mosfet transconductance, Vth = gate threshold voltage

Although it is possible to calculate

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

Circuit 1

**tr**and the current (**Id**) fall time with**ts_off**the energy dissipated by the switch at turn-off is given by the formula:$E_{loss} = \frac {V_o*I_{in}} {2}*(t_r+t_{s off})$

Figure 1 |

**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.

Figure 2 |

**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.

Circuit 1

__Optimum RCD Turn-Off Snubber Calculator__- 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
- S. Maniktala, Switching Power Supplies A - Z, Second Edition, 2012