Boost Converter Efficiency Through Accurate Calculations

Sep 1, 2008 12:00 PM
By Travis Eichhorn, Senior Applications Engineer, National Semiconductor, Grass Valley, Calif.

In developing this model, consider the power balance in the boost regulator P_IN = P_LOSS + P_OUT. This states that the total input power is equal to the output power plus the power lost in each of the circuit's components. Again, using a typical asynchronous boost converter, the dc losses in the NFET switch, the diode and the inductor are used to generate a power-balance equation given by P_IN = P_{SWITCH +} P_DIODE + P_INDUCTOR + P_OUT.

Substituting I_IN = (I_OUT/1 - D), as was done before in the first-order model, leads to the modified power-balance equation:

Instead of using the ideal duty-cycle ratio D = (V_OUT - V_IN)/V_OUT, the power-balance equation is now used to solve directly for D. Multiplying by (1 - D)² and collecting the terms on one side gives a second-order polynomial for the duty cycle:

D² ´ (V_F ´ I_OUT + V_OUT ´ I_OUT + R_D ´ I_OUT²) + D ´ (R_N ´ I_OUT² + V_IN ´ I_OUT - 2 ´ V_F ´ I_OUT - 2 ´ V_OUT ´ I_OUT) + (R_L ´ I_OUT² + V_F ´ I_OUT + V_OUT ´ I_OUT - V_IN ´ I_OUT) = F(D)².

This becomes the second-order model that generates two solutions for D, one of which is correct (the first zero crossing of F(D) versus increasing D) and the other (the second crossing) is not. This can be solved using the quadratic formula.

Since only the dc losses are accounted for in this model, the efficiency estimate is only accurate when the converter operates in the continuous-conduction mode (CCM) with relatively small inductor current ripple and when the dc losses are much bigger than the switching losses. However, when this is not the case and the peak-peak inductor current ripple approaches (2 ´ I_OUT)/1 - D and/or switching losses begin to approach or surpass the dc conduction losses, this model begins to deviate from the actual efficiency, much the same way as the first-order model did.

To show the error in the first- and second-order models, consider an asynchronous boost converter such as National Semi's LM3528, which is designed to power two strings of white LEDs in an LCD backlight (Fig. 1). With the given circuit parameters, the measured efficiency is 83%.

Using the first-order model, the estimated duty cycle is:

The input current is calculated as:

The dc conduction losses in the NFET become:

D ´ I_IN² ´ R_N = 18 mW.

The diode losses become:

V_F ´ I_OUT + I_OUT² ´ R_D = 19.2 mW.

And the inductor loss becomes:

I_IN² ´ R_L = 15.6 mW.

This gives an approximated efficiency of:

The second-order estimate should yield a closer approximation to the actual efficiency since the circuit's internal losses are included in calculating the duty cycle. Taking the converter's parameters and using the quadratic formula to solve for D in the equation F(D²) gives a duty cycle of 0.825. This results in a slightly lower efficiency:

However, this efficiency is still quite a ways off from the actual value.

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