« Previously: Snubber design: Choosing the proper Rsnb value  
As explained in the introduction, the bigger the snubber capacitance, the smaller the amplitude of the oscillations. At the same time, the energy required to charge and discharge the capacitor increases (Eq.(3)), affecting the efficiency. The optimum value for the capacitor is then the one which provides the right ringing attenuation without wasting any additional power.

One approach to find the optimum value for Csnb is to follow a rigorous mathematical approach, similar to what was done in the previous paragraph for Rsnb. Solving the equations in the time domain would lead to a third-order differential equation whose solution (finding the first oscillation peak and solving on Csnb) would be far more complicated.

A different approach, presented in this paper, consists of exploiting the power of numerical computation to solve those equations using Simplis to simulate the previous circuit under different conditions. The goal, similar to what was done for Rsnb, provides a simple equation to calculate the optimal value for the snubber capacitor. Let’s first define the gain introduced by the snubber and ratio between the maximum voltage with the snubber over the maximum voltage without the snubber. Since the snubber is supposed to reduce the voltage ringing, this number will be smaller than one, hence an attenuation of the ringing.

20170713_EDNA_Maxim-snubber_03_01 (cr)

Note that Eq.(32) is not a function Rsnb under the assumption that the optimum value defined by Eq.(31) is used. In simple words, the value of Gsnb tells how much ringing voltage is left after adding the snubber. Gsnb = 0.8, for example, means that the ringing amplitude with the snubber is reduced to 80% of the original value.

The first round of simulations consists in keeping the value of the inductor L1 constant (1.5nH) while varying the value of C1 and its ratio with Csnb. The data from these simulations (one subset of which is reported in Figure 1 as reference) is shown in Table 1, where the left side reports the raw data expressed in terms of maximum ringing voltage and the right side reports the attenuation calculated with Eq. (32).

20170713_EDNA_Maxim-snubber_03_02 (cr) Table 1: Result of the simulation with L1 = 1.5nH and Rsnbopt.

20170713_EDNA_Maxim-snubber_03_03 (cr) Figure 1: Increasing Csnb reduces the oscillation. (C1 = 0.5nF, L1 = 1.5nH, Rsnbopt)

Plotting this data as a function of Csnb\C1 (Figure 2) brings to light the fact that the attenuation is quite independent from the value of C1 itself and can be simplified as:

20170713_EDNA_Maxim-snubber_03_04 (cr)

20170713_EDNA_Maxim-snubber_03_05 (cr) Figure 2: Effect of the Csnb/C1 ratio on the Attsnb (L1 = constant)

The next step is intended to determine how the value of L1 affects this curve. Using a similar approach, C1 is kept constant (0.5nF) and L1 is varied. Interestingly, the results reported in Figure 3 show how L1 also does not significantly affect the amount of the gain.

20170713_EDNA_Maxim-snubber_03_06 (cr) Figure 3: Effect of the Csnb/C1 ratio on the Attsnb (C1 = constant)

20170713_EDNA_Maxim-snubber_03_07 (cr)

The only step that is left to take now is to express this curve with an equation. To do this, let’s first focus on Csnb\C1 ≤ 5. This is the most interesting region for the snubber design. Using a snubber capacitor so much bigger than C1 would certainly cause a big efficiency drop and indicates that the layout or the choice of the components needs to be reviewed.

A reasonable starting point to get the attenuation equation (34) is to use Eq.(29), which describes the gain of the circuit at ω03. From Figure 3, we know:

20170713_EDNA_Maxim-snubber_03_08 (cr)

20170713_EDNA_Maxim-snubber_03_09 (cr) Figure 4: Change y axis label

Figure 4 shows how well Eq. (38) tracks the simulation data.

Finally:

20170713_EDNA_Maxim-snubber_03_10 (cr)

 
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