Jeff Falin, Senior Applications Engineer, Texas Instruments
Mathematical models have always helped determine the best compensation components for a particular design. However, compensating for a white LED current-regulating boost converter is slightly different than compensating for the same converter that is set to regulate the voltage. Measuring the control loop in a conventional manner is quite inconvenient because the impedance of the feedback (FB) pin is not high and the upper FB resistor is lacking. A simple small-signal control loop model was demonstrated at Ray Ridley for boost converters with current mode control. The following explains how the Ridley model should be modified to work with a white LED current-regulating boost converter. It also shows how to measure the control loop of the boost converter.
Loop component
As shown in Figure 1, any adjustable DC/DC converter can be modified to provide a higher or lower regulated output voltage from the input voltage. In this type of configuration, if ROUT is assumed to be purely a resistive load, then VOUT = IOUT × ROUT. When the DC/DC converter is used to power the LED, it regulates the current through the LED by adjusting the lower FB resistor, as shown in Figure 2. The traditional small-signal control loop formula is no longer applicable because the load itself (LED) replaces the upper FB resistor. DC load impedance is
and
The VFWD from the diode data sheet or from the measurement is the forward voltage of the ILED, and n is the number of LEDs in series.
Figure 1: Adjustable DC/DC Converter for Regulating Voltage
Figure 2: Adjustable DC/DC Converter for Adjusting LED Current
However, from a small signal point of view, the load impedance includes REQ and the LED dynamic impedance rD at the ILED. While some LED manufacturers offer rD standard values ​​for different current quantities, the best way to determine rD is to derive this value from the LED IV standard curve provided by all manufacturers. Figure 3 shows an example of an IV curve for an OSRAM LW W5SM high power LED. The rD value is the number of dynamic (or small signals) defined as the voltage change divided by the current change, ie rD = ΔVFWD/ΔILED. To derive rD from Figure 3, simply draw a straight tangent from the beginning of VFWD and ILED and calculate the slope. For example, using the dashed line cut out in Figure 3, you get rD = (3.5– 2.0 V) / (1.000 – 0.010 A) = 1.51 W, and ILED = 350 mA.
Figure 3: IV curve of OSRAM LW W5SM
Small signal model
For the small-signal model, the TPS61165 peak-current model converter is used here to drive three series-connected OSRAM LW W5SM parts. Figure 4a shows the equivalent small-signal model of the current-regulated boost converter, while Figure 4b shows a simplified model. Equation 3 shows the frequency (s) model used to calculate the DC gain of the current regulated boost converter and the voltage regulated boost converter:
The general variable is
as well as
Figure 4: Small Signal Model of a Current-Regulated Boost Converter
Calculate the load cycle D of both circuits and the way VOUT and REQ are modified. Sn and Se are the naturally occurring inductor slope and compensation slope of the boost converter, respectively, and fSW is the switching frequency. Regarding the small-signal model of the voltage-regulated boost converter and the model of the current-regulating boost converter, the real difference between the two is derived from the resistance KR multiplied by the transconductance term (1–D)/Ri and the main electrode wp. . These differences are summarized in Table 1. See reference 1 for details. Since the RSENSE value is generally much lower than the ROUT value in a regulator that regulates the voltage, the gain of the current-regulating converter (where ROUT = REQ) is almost lower than the gain of the voltage-regulating converter.
Table 1: Differences between the two converter models in Equation 3
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