Driving a light-emitting diode (LED) or LED array is not without its challenges. The LEDs require a well-designed constant-current source for controlled brightness. More specifically, the output capacitor in the traditional buck converter that serves to drive the LEDs can have a significant effect on control-loop characteristics, and the capacitor type as well as the output circuit configuration is often critical. Placing the capacitor in parallel with the LEDs, versus from output to ground, for example, can make the difference between using the simpler type-two compensation circuit and a type-three circuit for reduced parts count, a more linear and stable loop transfer function, and ease in design.

Ultimately, output capacitor sizing and type is determined by what is best for the intended application, and there are several options. The output capacitor can be ceramic or aluminum; sometimes the designer may choose to omit the output capacitor entirely. SPICE circuit modeling provides a good way to validate and confirm the design.

Overview
The use of LEDs in automotive and outdoor lighting applications and the like has grown substantially, largely due to the availability of more efficient, white high-power devices. Luminous efficacies of greater than 175 lumens/watt in white LEDs are now commercially available. Operational lifetimes of greater than 50,000 hours and compact size are driving their increased usage.

An LED has a forward V-I characteristic curve that is similar to a diode. Below the LED turn-on threshold, which for a white LED is approximately 3.5 volts, very little current will flow through it. Above that threshold, current flow increases rapidly for incremental increases in forward voltage. The rise in current is exponential. Thus the LED can be accurately modeled in SPICE, for a given operating current, as a voltage source in series with a resistor. That is, for accurate modeling the resistor's value depends on the amount of current flowing through the LED. Figure 1 shows the measured impedance of a 1-watt white LED. The slope of the LED's V-I curve essentially represents the LED's dynamic impedance as a function of the load current.

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Figure 1: 1-watt dynamic LED impedance measurement

A 1-watt LED illuminates at currents as low as 1 mA, although not very brightly. Additionally, at large forward currents, the LED operates at a high power level, which in turn begins to heat the die. As a result, the LED's forward drop increases, as does its dynamic impedance. It is critical to consider the thermal environment when the LED's impedance is determined.

Modeling the converter
The LED's driving source must be designed very carefully. Consider, for example, the voltage-mode buck converter in Fig. 2 using the TPS40200 controller, with the converter designed to drive three series LEDs at a constant current of 1 amp. It regulates the voltage across the current sense resistor (R8) at a constant 0.7 volts. In essence, R8 programs the current regulated in the LED string.

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Figure 2: Voltage-mode buck converter, constant-current mode

The output from the converter is equal to the voltage across the LED string, plus the reference voltage (0.7 volt). For three white LEDs, the output is approximately (3.5)(3) + 0.7 = 11.2 volts. In a typical buck converter, the output capacitor (C8) is connected from the output-to-ground. However, in this circuit the output capacitor is connected across the LEDs. Although this may seem like a minor difference, it greatly simplifies stabilizing the control loop. Figure 3 shows the SPICE model of the AC control loop. The modulator "gain" block is internally set to a fixed gain of 8V/V (minimum), as programmed by the TPS40200 controller. This gain is constant over input voltage due to the voltage feed-forward feature of the controller, which changes the oscillator ramp amplitude in proportion to any input voltage variations. From Fig. 1, the dynamic impedance of a single LED driven with 1 amp is 0.5 ohms. Three LEDs are modeled as a lump sum of three series 0.5-ohm resistors and three series 3.5 volt sources. Note that the resultant 10.5-volt DC source has no effect on the AC control loop model (SPICE shorts out all DC voltage sources in AC loop analyses). To measure the closed loop gain and phase margin, we break the feedback path and insert an AC voltage source (V_ac) at the current regulation point (R8).

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Figure 3: SPICE model for LED buck converter