Similarly, we can perform this power analysis for LED applications. For a prototypical LED array, we relate the supply voltage to the forward current at the corresponding voltage as follows, where N is the number of series LEDs per string and M is the parallel strings.

A CREE JB2835B 3-V, 0.5-W class LED I-V characteristic is shown below. Because diode voltage and current change with time due to the slewed waveform of Vvs, the LED power dissipation is better to be analyzed with via modeling than by calculating by hand. We can simplify the V-I curve by 1st order least-squares regression which gives a turn-on voltage of ~2.6 V and which matches the true performance of the device with little variance.

For most purposes, assuming the current is already at its peak as soon as the diodes become forward biased is fairly accurate and enables quick estimation.

The main difference from the restive load case is that no current and thus no power is delivered before the supply potential can forward bias the LED string. The LED string(s) begin conducting once the output voltage exceeds the sum of the LED forward voltages N?V_F.

Average power for one cycle is based on the number of parallel LED strings as well, the time-dependent LED forward current, and the HSS output voltage which is distorted by slew rate and PWD, where M is the number of parallel LED strings and N the number of series LEDs.

LED current of Cree JB2835D G-class LED string was modeled in a computational tool, according to the design target below

• Supply voltage: V_vs = 12 V
• # of Series LED: N =4
• # of Parallel Strings: M = 1
• LED operating point: V_F(OP) = 2.75 V , I_F(OP) = 95 mA
• Current limiting resistor: R_LED = 3 Ω
• HHS Slew rate: SR_ON = 0.36 V/ μs

LED current in the string is shown in Figure 3-12 to Figure 3-14. As pulse-width decreases, either by increasing the PWM frequency or decreasing duty cycle, the LEDs spend less and less time of the output pulse above their forward voltage. In Figure 3-13, the diodes can no longer become forward biased during the ON pulse and stay off.

This design was recreated on the bench with a > 500-mA LED forward current and run for several PWM frequencies across several duty cycles.

These results match the Cree model at input pulse widths of 50 μs. At 1 kHz and up, PWD was noticeably worse and would no longer conduct.