Compensating and measuring the control loop of a high-power LED driver

Mathematical models have always been helpful in determining the best compensation components for a particular design, however, compensating a WLED current regulating boost converter is slightly different than compensating the same converter set to regulate voltage. Measuring the control loop using traditional methods is quite inconvenient because the feedback (FB) pin has low impedance and lacks an upper FB resistor. In reference 1, Ray Ridley presents a simple small signal control loop model for a boost converter with current mode control. The following article shows how the Ridley model should be modified to work for a WLED current regulating boost converter, and also shows how to measure the control loop of a boost converter.

Circuit components

As shown in Figure 1, any adjustable DC/DC converter can be modified to provide a higher or lower regulated output voltage from an input voltage. In this configuration, if ROUT is assumed to be a purely resistive load, then VOUT = IOUT × ROUT. When a DC/DC converter is used to power an LED, it controls the current through the LED by adjusting the lower FB resistor, as shown in Figure 2. Since the load itself (LED) replaces the upper FB resistor, the traditional small signal control loop equations no longer apply. The DC load impedance is

and

VFWD, obtained from a diode data sheet or from measurement, is the forward voltage of ILED, and n is the number of LEDs in series.

Figure 1. An adjustable DC/DC converter for voltage regulation.

Figure 2. Adjustable DC/DC converter for regulating LED current.

However, from a small signal perspective, the load impedance consists of REQ and the dynamic impedance of the LED at ILED, rD. Although some LED manufacturers provide standard values ​​of rD at different current levels, the best way to determine rD is to derive it from the standard IV curves for LEDs 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 a dynamic (or small signal) quantity defined as the change in voltage divided by the change in current, or rD = ΔVFWD/ΔILED. To derive rD from Figure 3, simply draw a straight tangent line from the beginning of VFWD and ILED and calculate the slope. For example, using the dotted line cut in Figure 3, we 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 will be used as an example, which can drive 3 OSRAM LW W5SM parts in series. Figure 4a shows the equivalent small signal model of the current regulated boost converter, while Figure 4b shows a more simplified model

as well as

Table 1. Differences between the two converter models in Equation 3

The same method is used to calculate the duty cycle D and the modified values ​​of VOUT and REQ for both circuits. Sn and Se are the natural inductance slope and compensation slope of the boost converter, respectively, and fSW is the switching frequency. The real difference between the small signal model of the voltage-regulated boost converter and the current-regulated boost converter comes from the impedance 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 the voltage-regulated converter, the gain of the current-regulated converter (where ROUT = REQ) is almost always lower than that of the voltage-regulated converter.

Measuring circuit

To measure the control loop gain and phase of a voltage regulating converter, a network or dedicated loop gain/phase analyzer typically uses a 1:1 transformer to inject a small signal into the loop through a small impedance (RINJ). The analyzer then measures and compares the injected signal at point A to the returned signal at point R as a function of frequency, and reports the ratio of the amplitude difference (gain) to the time delay (phase). This impedance can be inserted anywhere in the loop as long as the impedance at point A is much lower than the impedance at point R, otherwise the injected signal will be too large and interfere with the operating point of the converter. As shown in Figure 5, the high impedance node is where this impedance is typically inserted and is where the FB resistor senses the output voltage at the output capacitor (low impedance node).

Figure 5. Control loop measurement of a voltage regulation converter.

In a current regulation configuration, if the load itself is the upper FB resistor, the injection resistor cannot be inserted in series with the LED. The converter’s operating point must be changed before the resistor can be inserted between the FB pin and the sense resistor, as shown in Figure 6. In some cases, a non-inverting unity-gain buffer amplifier may be required to lower the impedance at the injection point and reduce measurement noise.

Figure 6. Control loop measurement for a current-regulated converter.

The loop was measured using a Venable loop analyzer with the same setup as in Figure 6 but without the amplifier and with RINJ = 51.1 W. The model of the current regulating converter was built in Mathcad® using the datasheet design parameters of the TPS61170, with the same core as the TPS61165. The model produces the expected loop response of the TPS61165EVM when VIN = 5 V and ILED is set to 350 mA, as shown in Figure 7, for easy comparison with the measured data.

Figure 7. Measured and simulated loop gain and phase at VIN = 5 V and ILED = 350 mA

Observing the changes in the WLED's dynamic impedance and referring to standard LED IV curves and chip-to-chip variations in IC amplifier gain can easily explain the difference between the measured and simulated gain.

in conclusion

Although the mathematical model is not completely accurate, it is a preliminary approach that designers can use when designing a WLED current regulated boost converter. Designers can also measure the control loop using one of these methods.