Power Management Texas Instruments Incorporated Compensating and measuring the control loop of a high-power LED driver By Jeff Falin Senior Applications Engineer A mathematical model is always helpful in determining the optimal compensation components for a particular design. However, compensating the loop of a WLED currentregulating boost converter is a bit different than compensating the same converter configured to regulate voltage. Measuring the control loop with traditional methods is cumbersome because of low impedance at the feedback (FB) pin and the lack of a top-side FB resistor. In Reference 1, Ray Ridley has presented a simplified, small-signal control-loop model for a boost converter with current-mode control. The following explains how to modify Ridley’s model so that it fits a WLED current-regulating boost converter; it also explains how to measure the boost converter’s control loop. Figure 1. Adjustable DC/DC converter used to regulate voltage VIN VIN VOUT VOUT Adjustable DC/DC Converter GND R OUT VFB FB Loop 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 we assume ROUT is a purely resistive load, then VOUT = IOUT × ROUT. When used to power LEDs, a DC/DC converter actually controls the current through the LEDs by regulating the voltage across the low-side FB resistor as shown in Figure 2. Because the load itself (the LEDs) replaces the upper FB resistor, the traditional small-signal control-loop equations no longer apply. The DC load resistance is REQ = VOUT /ILED, Figure 2. Adjustable DC/DC converter used to regulate current through LEDs (1) VIN VIN Adjustable DC/DC Converter GND with VOUT VOUT FB VFB VOUT = n × VFWD + VFB. (2) R SENSE VFWD, taken either from the diodes’ datasheet or from measurements, is the forward voltage at ILED; and n is the number of LEDs in the string. 14 High-Performance Analog Products www.ti.com/aaj 4Q 2008 Analog Applications Journal Power Management Texas Instruments Incorporated ILED for the application and compute the slope. For example, using the dotted tangent line in Figure 3, we get rD = (3.5 – 2.0 V)/(1.000 – 0.010 A) = 1.51 W at ILED = 350 mA. Figure 3. I-V curve of OSRAM LW W5SM OHL02520 Forward Current, ILED (mA) 1000 Small-signal model TA = 25ºC As an example of a small-signal model, the TPS61165 peakcurrent-mode converter driving three series OSRAM LW W5SM parts will be used. Figure 4a shows an equivalent small-signal model of a current-regulating boost converter, while Figure 4b shows an even more simplified model. Equation 3 shows a frequency-based (s-domain) model for computing DC gain in both the current-regulating and the voltage-regulating boost converters: 350 100 1 + s 1 − s × ω z ω RHP 1 ( − D) GP(s) = K R × × , (3) Ri 1 + s s s2 + × 1+ ω p Qpω n ω 2 n 10 2.0 2.5 3.0 3.5 4.0 Forward Voltage, VFWD (V) 4.5 where the common variables are ωz = However, from a small-signal standpoint, the load resist ance consists of REQ as well as the dynamic resistances of the LEDs, rD, at the ILED. While some LED manufacturers provide typical values of rD at various current levels, the best way to determine rD is to extract it from the typical LED I-V curve, which all manufacturers provide. Figure 3 shows an example I-V curve of an OSRAM LW W5SM highpower LED. Being a dynamic (or small-signal) quantity, rD is defined as the change in voltage divided by the change in current, or rD = ∆VFWD/∆ILED. To extract rD from Figure 3, we simply drive a straight tangent line from the VFWD and Qp = 1 , ESR × COUT 1 S π 1 + e (1 − D) − 0.5 S n , ω n = π × fSW , and ω RHP = R EQ (1 − D)2 × L . Figure 4. Small-signal model of current-regulating boost converter L VOUT VOUT n VIN (1 – D) Ri COUT D + + – × rD n × rD COUT REQ – – Ri ESR R SENSE + Σ VREF R SENSE ESR – + VREF (a) Complete (b) Simplified 15 Analog Applications Journal 4Q 2008 www.ti.com/aaj High-Performance Analog Products Power Management Texas Instruments Incorporated Table 1. Differences in Equation 3 terms for two converter models TERM EVALUATION OF CURRENT-REGULATING BOOST CONVERTER EVALUATION OF VOLTAGE-REGULATING BOOST CONVERTER KR REQ REQ + n × rD 1+ RSENSE ROUT 2 1+ wp n × rD + RSENSE REQ 2 (ROUT +ESR) × COUT (n × rD + RSENSE +ESR) × COUT Measuring the loop The duty cycle, D, and the modified values for VOUT and REQ are computed the same way for both circuits. Sn and Se are the natural inductor and compensation slopes, respectively, for the boost converter; and fSW is the switching frequency. The only real differences between the smallsignal model for the voltage-regulating boost converter and the model for a current-regulating boost converter is the resistance KR—which multiplies by the transconduct ance term, (1 – D)/Ri —and the dominant pole, wp. These differences are summarized in Table 1. See Reference 1 for more information. Since the value of RSENSE is typically much lower than that of ROUT in a converter configured to regulate voltage, the gain for a current-regulating converter, where ROUT = REQ, will almost always be lower than the gain for a voltageregulating converter. To measure the control loop gain and phase of a voltageregulating converter, a network or dedicated loop-gain/ phase analyzer typically uses a 1:1 transformer to inject a small signal into the loop via a small resistance (RINJ). The analyzer then measures and compares, over frequency, the injected signal at point A to the returned signal at point R and reports the ratio in terms of amplitude difference (gain) and time delay (phase). This resistance can be inserted anywhere in the loop as long as point A has relatively much lower impedance than point R; otherwise, the injected signal will be too large and disturb the converter’s operating point. As shown in Figure 5, the high-impedance node where the FB resistors sense the output voltage at the output capacitor (low-impedance node) is the typical place for such a resistor. Figure 5. Control-loop measurement for voltageregulating converter VOUT VIN Adjustable DC/DC Converter Configured as a Voltage Regulator GND Low Z VOUT 1:1 C OUT R INJ k High Z FB A AC Source R Network or Loop-Gain Analyzer k 16 High-Performance Analog Products www.ti.com/aaj 4Q 2008 Analog Applications Journal Power Management Texas Instruments Incorporated Figure 6. Control-loop measurement for currentregulating converter ILED VIN VOUT Adjustable DC/DC Converter Configured as a Current Regulator GND C OUT Optional R INJ (50 to 100 Ω) + FB – R SENSE 1:1 A R AC Source Network or LoopGain Analyzer Figure 7. Measured and simulated loop gain and phase at VIN = 5 V and ILED = 350 mA Conclusion 30 Reference 1. Ray Ridley. (2006). Designer’s Series, Part V: Current-Mode Control Modeling. Switching Power Magazine [Online]. Available: http:// www.switchingpowermagazine.com/ downloads/5%20Current%20Mode %20Control%20Modeling.pdf Measured Phase 20 120 60 10 Gain (dB) While not exact, the mathematical model gives the designer a good starting point for designing the compensation of a WLED current-regulating boost converter. In addition, the designer can measure the control loop with one of the alternate methods. 180 Simulated Phase 0 Simulated Gain –10 0 Measured Gain Phase (°) In a current-regulating configuration, with the load itself being the upper FB resistor, the injection resistor cannot be inserted in series with the LEDs. The converter’s operating point must first be changed so 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 necessary to lower the impedance at the injection point and reduce measurement noise. With the measurement setup in Figure 6 but without the amplifier, and with RINJ = 51.1 W, a Venable loop analyzer was used to measure the loop. The model of a current-regulating converter was constructed in Mathcad ® using the datasheet design parameters of the TPS61170, which has the same core as the TPS61165. With VIN = 5 V and ILED set to 350 mA, the model gives the predicted loop response for the TPS61165EVM as shown in Figure 7, which provides an easy comparison with measured data. We can easily explain the differences between the measured and simulated gain by observing variations in the WLED dynamic resistance and using the typical LED I-V curve as well as chip-to-chip variations in the IC’s amplifier gain. –60 –120 –20 –30 100 –180 1000 10000 Frequency (Hz) 100000 Related Web sites power.ti.com www.ti.com/sc/device/TPS61165 www.ti.com/sc/device/TPS61170 17 Analog Applications Journal 4Q 2008 www.ti.com/aaj High-Performance Analog Products IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications, enhancements, improvements, and other changes to its products and services at any time and to discontinue any product or service without notice. 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