Simplified analysis of DCM boost converters that drive LED strings

Part 1: Theoretical analysis

Fixed frequency boost converters are ideal for driving LED strings in constant current mode. Operating in discontinuous conduction mode (DCM), this converter can be effectively used for fast dimming operations, providing superior transient response over competing devices operating in continuous conduction mode (CCM). When the LED is turned on, DCM operation provides fast transient performance and recharges the output capacitor, thus minimizing the analog dimming of the LED. In order to properly stabilize the DCM boost converter, there is a small signal model. However, the AC analysis of the boost converter that drives the LEDs is different from the AC analysis of a boost converter using a standard resistive load. Since series diodes require DC and AC load conditions, care must be taken when deriving the final transfer function.

This article (ie, Part 1) does not use the traditional small-signal model of the discontinuous conduction mode (DCM) boost converter, but instead uses a simplified method based on the output current expression of the converter under study. In Part 2 (actual considerations), we will delve into the application, verify the measurement accuracy, and compare it with theoretical derivation.

Boost converter for powering LED strings

Figure 1 shows a simplified circuit diagram of a constant frequency peak current mode boost converter that drives a string of LEDs. The output current is continuously monitored by the sense resistor Rsense. A corresponding output voltage is applied to the control circuit to continuously adjust the on-time of the power switch to provide a constant LED current Iout. This is the controlled output variable.

In Figure 1, when the LED string is driven to emit light, the output current is stabilized to the set point value, and the LED string generates a voltage across the LED connection. This voltage depends on the threshold voltage VT0 associated with each LED technology and its dynamic impedance rd. Therefore, the total voltage drop across the LED string is the sum of the threshold voltages of the LEDs VZ, while the dynamic impedance rLEDs represent the LED series dynamic impedance. with. Figure 2 shows the equivalent circuit used. You can characterize the LED string voltage drop and its total dynamic impedance yourself. For measurement purposes, the LED string current is biased to its rated current IF1. Once the LED is thermally stable, measure the total voltage drop across the LED string Vf1. Change the current to a slightly lower value IF2 and measure the new voltage drop VF2.

The current source actually refers to the current that is transmitted from the input supply to the output without loss. The current source can be adjusted up or down by the control voltage Vc, and Vc sets the inductor peak current cycle by cycle. The controller uses the boost converter to switch the current sense resistor Ri to observe the inductor peak current and operate accordingly. When the voltage across the Ri matches the control voltage, the power switch is turned off.

If we are considering an AC circuit diagram now, we should consider the capacitor and its parasitic components, as shown in Figure 4. The Zener component itself has no effect because its voltage remains constant during AC modulation: only its dynamic impedance rLEDs need to be considered and integrated into the Rac.

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