8.1.1 Duty Cycle Considerations

The switch duty cycle, D, defines the converter operation and is a function of the input and output voltages. In steady state, the duty cycle is derived using expression:

Buck:

Equation 2.

Boost:

Equation 3.

Buck-Boost:

Equation 4.

The minimum duty cycle, D_MIN, and maximum duty cycle, D_MAX, are calculated by substituting maximum input voltage, V_IN(MAX), and the minimum input voltage, V_IN(MIN), respectively in the previous expressions. The minimum duty cycle achievable by the device is determined by the leading edge blanking period and the switching frequency. The maximum duty cycle is limited by the internal oscillator to 93% (typ) to allow for minimum off-time. It is necessary for the operating duty cycle to be within the operating limits of the device to ensure closed-loop LED current regulation over the specified input and output voltage range.

8.1.2 Inductor Selection

The inductor peak-to-peak ripple current, Δi_L-PP, is typically set between 10% and 80% of the maximum inductor current, I_L, as a good compromise between core loss and copper loss of the inductor. Higher ripple inductor current allows a smaller inductor size, but places more of a burden on the output capacitor to smooth the LED current ripple. Knowing the desired ripple ratio RR, switching frequency ƒ_SW, maximum duty cycle D_MAX, and the typical LED current I_LED, the inductor value can be calculated as follows:

Buck:

Equation 5.

Equation 6.

Boost and Buck-Boost:

Equation 7.

Equation 8.

As an alternative, the inductor can be selected based on CCM-DCM boundary condition specified based on output power, P_O(BDRY). The choice of inductor ensures CCM operation in battery-powered LED driver applications that are designed to support different LED string configurations with a wide range of programmable LED current setpoints. The output power should be calculated based on the lowest LED current and the lowest output voltage requirements for a given application.

Equation 9.

Buck:

Equation 10.

Boost:

Equation 11.

Buck-Boost:

Equation 12.

The saturation current rating of the inductor should be greater than the peak inductor current, I_L(PK), at the maximum operating temperature.

Equation 13.

8.1.3 Output Capacitor Selection

The output capacitors are required to attenuate the discontinuous or large ripple current generated by switching and achieve the desired peak-to-peak LED current ripple, Δi_LED(PP). The capacitor value depends on the total series resistance of the LED string, r_D, the switching frequency, ƒ_SW, and on the converter topology (that is, step-up or step-down). For the Buck and Cuk topology, the inductor is in series with LED load and requires a smaller capacitor than the Boost, Buck-Boost, and SEPIC topologies to achieve the same LED ripple current. The capacitance required for the target LED ripple current can be calculated based on following equations.

Buck:

Equation 14.

Boost and Buck-Boost:

Equation 15.

When choosing the output capacitors, it is important to consider the ESR and the ESL characteristics as they directly impact the LED current ripple. Ceramic capacitors are the best choice due to their low ESR, high ripple current rating, long lifetime, and good temperature performance. When selecting ceramic capacitors, it is important to consider the derating factors associated with higher temperature and DC bias operating conditions. TI recommends an X7R dielectric with voltage rating greater than maximum LED stack voltage. An aluminum electrolytic capacitor can be used in parallel with ceramic capacitors to provide bulk energy storage. The aluminum capacitors must have necessary RMS current and temperature ratings to ensure prolonged operating lifetime. The minimum allowable RMS output capacitor current rating, I_COUT(RMS), can be approximated:

Buck:

Equation 16.

Boost and Buck-Boost:

Equation 17.

The expressions (Equation 14 to Equation 17) are best suited for designs driving a fixed LED load, with known output voltage and LED current. For applications that are required to support different LED string configurations with a wide range of programmable LED current setpoints, the previous expressions are rearranged to reflect output capacitance based on the maximum output power, P_O(MAX), to ensure that LED current ripple specifications are met over the entire range of operation. Typical Buck-Boost LED Driver provides the details for Buck-Boost LED driver.

8.1.4 Input Capacitor Selection

The input capacitors, C_IN, smooth the input voltage ripple and store energy to supply input current during input voltage or PWM dimming transients. The series inductor in the Boost, SEPIC, and Cuk topology provides continuous input current and requires a smaller input capacitor to achieve desired input ripple voltage, Δv_IN(PP). The Buck and Buck-Boost topology have discontinuous input current and require a larger capacitor to achieve the same input voltage ripple. Based on the switching frequency, ƒ_SW, and the maximum duty cycle, D_MAX, the input capacitor value can be calculated as follows:

Buck:

Equation 18.

Boost:

Equation 19.

Buck-Boost:

Equation 20.

X7R dielectric-based ceramic capacitors are the best choice due to their low ESR, high ripple current rating, and good temperature performance. For applications using PWM dimming, TI recommends an aluminum electrolytic capacitor in addition to ceramic capacitors to minimize the voltage deviation due to large input current transients generated in conjunction with the rising and falling edges of the LED current.

Figure 28. VIN Filter

For most applications, TI highly recommends to bypass the VIN pin with a 0.1-µF ceramic capacitor placed as close as possible to the device and add a series 10-Ω resistor to create a 150-kHz low-pass filter and eliminate undesired high-frequency noise.

8.1.5 Main Power MOSFET Selection

The power MOSFET should be able to sustain the maximum switch node voltage, V_SW, and switch RMS current derived based on the converter topology. TI recommends a drain voltage V_DS rating of at least 20% greater than the maximum switch node voltage to ensure safe operation. The MOSFET drain-to-source breakdown voltage, V_DS, and RMS current ratings are calculated using the following expressions.

Buck:

Equation 21.

Equation 22.

Boost:

Equation 23.

Equation 24.

Buck-Boost:

Equation 25.

Equation 26.

Where the voltage, V_O(OV), is the overvoltage protection threshold and the worst-case output voltage under fault conditions.

Select a MOSFET with low total gate charge, Q_g, to minimize gate drive and switching losses. The MOSFET R_DS resistance is usually a less critical parameter because the switch conduction losses are not a significant part of the total converter losses at high operating frequencies. The switching and conduction losses are calculated as follows:

Equation 27.

Equation 28.

C_RSS is the MOSFET reverse transfer capacitance. I_L is the average inductor current. I_GATE is gate drive output current, typically 500 mA. The MOSFET power rating and package should be selected based on the total calculated loss, the ambient operating temperature, and maximum allowable temperature rise.

8.1.6 Rectifier Diode Selection

A Schottky diode (when used as a rectifier) provides the best efficiency due to low forward voltage drop and near-zero reverse recovery time. TI recommends a diode with a reverse breakdown voltage, V_D(BR), greater than or equal to MOSFET drain-to-source voltage, V_DS, for reliable performance. It is important to understand the leakage current characteristics of the Schottky diode, especially at high operating temperatures because it impacts the overall converter operation and efficiency.

The current through the diode, I_D, is given by:

Equation 29.

The diode should be sized to exceed the current rating, and the package should be able to dissipate power without exceeding the maximum allowable temperature.

8.1.7 LED Current Programming

The LED current is set by the external current sense resistor, R_CS, and the analog adjust voltage, V_IADJ. The current sense resistor is placed in series with the LED load and can be located either on the high side (connected to the output, V_O), or on the low side (connected to ground, GND). The CSP and CSN inputs of the internal rail-to-rail current sense amplifier are connected to the R_CS resistor to enable closed-loop regulation. When V_IADJ > 2.5 V, the internal 2.42-V reference sets the V_(CSP-CSN) threshold to 172 mV and the LED current is regulated to:

Equation 30.

The LED current can be programmed by varying V_IADJ between 140 mV to 2.25 V. The LED current can be calculated using:

Equation 31.

The output voltage ripple should be limited to 50 mV for best performance. TI recommends a low-pass common-mode filter consisting of 10-Ω resistors is series with CSP and CSN inputs and 0.01-µF capacitors to ground to minimize the impact of voltage ripple and noise on LED current accuracy (see Figure 20). A 0.1-µF capacitor across CSP and CSN is included to filter high-frequency differential noise.

8.1.8 Switch Current Sense Resistor and Slope Compensation

The switch current sense resistor, R_IS, is used to implement peak current mode control and to set the peak switch current limit. The value of switch current sense R_IS is selected to achieve stable inner current loop operation based on the magnitude of slope compensation ramp, V_SL, and to protect the main switching MOSFET under fault conditions. The lower of the two values calculated using the following equations should be selected for R_IS.

Equation 32.

Equation 33.

The internal slope compensation voltage, V_SL is fixed at 200 mV (typ). A resistor can be placed in series with the IS pin to increase slope compensation, if necessary. The peak switch current limit is set based on the internal current limit threshold of 525 mV (typ) and adjusted based on slope compensation to ensure reliable operation while PWM dimming.

Figure 29. IS Input Filter

The use of a 1-nF and 100-Ω low-pass filter is optional. If used, the resistor value should be less than 500 Ω to limit its influence on the internal slope compensation signal.

8.1.9 Feedback Compensation

The open-loop response is the product of the modulator transfer function (shown in Equation 34) and the feedback transfer function. Using a first-order approximation, the modulator transfer function can be modeled as a single pole created by the output capacitor, and in the boost and buck-boost topologies, a right half-plane zero created by the inductor, where both have a dependence on the LED string dynamic resistance, r_D. Because TI recommends a ceramic capacitor, the ESR of the output capacitor is neglected in the analysis. The small-signal modulator model also includes a DC gain factor that is dependent on the duty cycle, output voltage, and LED current.

Equation 34.

Table 1 summarizes the expression for the small-signal model parameters.

The feedback transfer function includes the current sense resistor and the loop compensation of the transconductance amplifier. A compensation network at the output of the error amplifier is used to configure loop gain and phase characteristics. A simple capacitor, C_COMP, from COMP to GND (as shown in Figure 30) provides integral compensation and creates a pole at the origin. Alternatively, a network of R_COMP, C_COMP, and C_HF, shown in Figure 31, can be used to implement proportional and integral (PI) compensation and to create a pole at the origin, a low-frequency zero, and a high-frequency pole.

Table 1. Small-Signal Model Parameters

	DC GAIN (G0)	POLE FREQUENCY (ωP)	ZERO FREQUENCY (ωZ)
Buck	1		—
Boost
Buck-Boost

The feedback transfer function is defined as follows.

Feedback transfer function with integral compensation:

Equation 35.

Feedback transfer function with proportional integral compensation:

Equation 36.

The pole at the origin minimizes output steady-state error. High bandwidth is achieved with the PI compensator by placing the low-frequency zero an order of magnitude less than the crossover frequency. Use the following expressions to calculate the compensation network.

Figure 30. Integral Compensation

Figure 31. Proportional-Integral Compensation

Buck with integral compensator:

Equation 37.

Boost and Buck-Boost with proportional integral compensator:

Equation 38.

Equation 39.

Equation 40.

The loop response is verified by applying step input voltage transients. The goal is to minimize LED current overshoot and undershoot with a damped response. Additional tuning of the compensation network may be necessary to optimize PWM dimming performance.

8.1.10 Soft-Start

The soft-start time (t_SS) is the time required for the LED current to reach the target setpoint. The required soft-start time, t_SS, is programmed using a capacitor, C_SS, from SS pin to GND, and is based on the LED current, output capacitor, and output voltage.

Equation 41.

8.1.11 Overvoltage Protection

The overvoltage threshold is programmed using a resistor divider, R_OV2 and R_OV1, from the output voltage, V_O, to ground for Boost and SEPIC topologies, as shown in Figure 24 and Figure 25. If the LEDs are referenced to a potential other than ground, as in the Buck-Boost or Buck configuration, the output voltage is sensed and translated to ground by using a PNP transistor and level-shift resistors, as shown in Figure 27 and Figure 26. The overvoltage turn-off threshold, V_O(OV), is:

Boost:

Equation 42.

Buck and Buck-Boost:

Equation 43.

The overvoltage hysteresis, V_OV(HYS) is:

Equation 44.

8.1.12 PWM Dimming Considerations

When PWM dimming, the TPS92691/-Q1 requires another MOSFET placed in series with the LED load. This MOSFET should have a voltage rating greater than the output voltage, V_O, and a current rating at least 10% higher than the nominal LED current, I_LED.

It is important to control the slew-rate of the external FET to achieve a damped LED current response to PWM rising-edge transitions. For a low-side, N-channel dimming FET, the slew-rate is controlled by placing a resistor in series with the GATE pin. The rise and fall times depend on the value of the resistor and the gate-to-source capacitance of the MOSFET. The series resistor can be bypassed with a diode for fast rise time and slow fall times to achieve 100:1 or higher contrast ratios. If a high-side P-channel dimming FET is used, the rise and fall times can be controlled by selecting appropriate resistors for the level-shift network, R_LS1 and R_LS2, as shown in Figure 26.

8.2.1 Typical Boost LED Driver

Figure 32. Boost LED Driver With High-Side Current Sense

8.2.1.2 Detailed Design Procedure

This procedure is for the boost LED driver application.

8.2.1.2.1 Calculating Duty Cycle

Solve for D, D_MAX, and D_MIN:

Equation 45.

Equation 46.

Equation 47.

8.2.1.2.2 Setting Switching Frequency

Solve for R_T:

Equation 48.

The closest standard resistor of 20 kΩ is selected.

8.2.1.2.3 Inductor Selection

The inductor value should ensure continuous conduction mode (CCM) of operation and should achieve desired ripple specification, Δi_L(PP).

Equation 49.

Solving for inductor:

Equation 50.

The closest standard inductor is 27 µH. The expected inductor ripple based on the chosen inductor is:

Equation 51.

The inductor saturation current rating should be greater than the peak inductor current, I_L(PK).

Equation 52.

8.2.1.2.4 Output Capacitor Selection

The specified peak-to-peak LED current ripple, Δi_LED(PP), is:

Equation 53.

The output capacitance required to achieve the target LED current ripple is:

Equation 54.

Considering 40% derating factor under DC bias operation, four 4.7-µF, 100-V rated X7R ceramic capacitors are used in parallel to achieve a combined output capacitance of 18.8 µF.

8.2.1.2.5 Input Capacitor Selection

The input capacitor is required to reduce switching noise conducted through the input wires and reduced the input impedance of the LED driver. The capacitor required to limit peak-to-peak input ripple voltage ripple, Δv_IN(PP), to 70 mV is given by:

Equation 55.

A 4.7-µF, 50-V X7R ceramic capacitor is selected.

8.2.1.2.6 Main N-Channel MOSFET Selection

The MOSFET ratings should exceed the maximum output voltage and RMS switch current given by:

Equation 56.

Equation 57.

A 60-V or a 100-V N-channel MOSFET with current rating exceeding 3 A is required for this design.

8.2.1.2.7 Rectifying Diode Selection

The diode should be selected based on the following voltage and current ratings:

Equation 58.

Equation 59.

A 60-V or a 100-V Schottky diode with low reverse leakage current is suitable for this design. The package must be able to handle the power dissipation resulting from continuous forward current, I_D, of 0.5 A.

8.2.1.2.8 Programming LED Current

LED current is based on the current shunt resistor, R_CS and the V_(CSP-CSN) threshold set by the voltage on the IADJ pin V_IADJ. By default, IADJ is tied to VCC via an external resistor to enable the internal reference voltage of 2.42 V that then sets the V_(CSP-CSN) threshold to 172 mV. The current shunt resistor value is calculated by:

Equation 60.

Two 0.68-Ω resistors are connected in parallel to achieve R_CS of 0.34 Ω.

8.2.1.2.9 Setting Switch Current Limit and Slope Compensation

The switch current sense resistor, R_IS, is calculated by solving the following equations and choosing the lowest value:

Equation 61.

Equation 62.

A standard value of 0.1 Ω is selected.

8.2.1.2.10 Deriving Compensator Parameters

The modulator transfer function for the Boost converter is derived for nominal V_IN voltage and corresponding duty cycle, D, and is given by the following equation. (See Table 1 for more information.)

Equation 63.

The proportional-integral compensator components C_COMP and R_COMP are obtained by solving the following expressions:

Equation 64.

Equation 65.

The closet standard capacitor of 33 nF and resistor of 2.15 kΩ is selected. The high frequency pole location is set by a 100 pF C_HF capacitor.

8.2.1.2.11 Setting Start-up Duration

The soft-start capacitor required to achieve start-up in 8 ms is given by:

Equation 66.

The closet standard capacitor of 100 nF is selected.

8.2.1.2.12 Setting Overvoltage Protection Threshold

The overvoltage protection threshold of 50 V and hysteresis of 5 V is set by the R_OV1 and R_OV2 resistor divider.

Equation 67.

Equation 68.

The standard resistor values of 249 kΩ and 6.34 kΩ are chosen.

8.2.1.2.13 PWM Dimming Considerations

A series dimming FET is required to meet PWM dimming specification from 100% to 4% duty cycle. A 60-V, 2-A N-channel FET is suitable for this application.

As an alternative, a 60-V, 2-A P-channel FET could be used to achieve PWM dimming. An external level-shift circuit is required to translate the DDRV signal to the gate of the P-channel dimming FET. The drive strength of 5 mA and gate-source voltage of 15 V are set by the 1-kΩ and 2-kΩ level-translator resistors and a small-signal N-channel MOSFET, whose gate is connected to DDRV.

By default, the PWM pin is connected to VCC through a 100-kΩ resistor to enable the part upon start-up.

8.2.1.3 Application Curves

These curves are for the boost LED driver.

Figure 33. Efficiency vs Input Voltage

     Ch1: Input voltage; Ch2: Soft-start (SS) voltage;
     Ch3: Input current;
     Ch4: LED current; Time: 2 ms/div

Figure 35. Startup Transient

     Ch1: GATE voltage; Ch2: External CLK signal;
     Ch3: Switch sense current resistor voltage;
     Ch4: LED current; Time: 1 µs/div

Figure 37. Clock Synchronization

     Ch1: DDRV voltage; Ch2: PWM input;
     Ch3: Switch sense current resistor voltage;
     Ch4: LED current; Time: 4 µs/div

Figure 39. PWM Dimming Transient (Zoomed)

     Ch1: Switch node voltage;
     Ch3: Switch sense current resistor voltage;
     Ch4: LED current; Time: 1 µs/div

Figure 34. Normal Operation

     Ch1: Output voltage;
     Ch2: Soft-start (SS) voltage;
     Ch4: LED current; Time: 200 ms/div

Figure 36. Overvoltage Protection

     Ch1: DDRV voltage; Ch2: PWM input;
     Ch3: Switch sense current resistor voltage;
     Ch4: LED current; Time: 2 ms/div

Figure 38. PWM Dimming Transient

     Ch1: Input voltage;
     Ch2: IMON voltage;
     Ch4: LED current; Time: 2 ms/div

Figure 40. Step Input Voltage Transient and IMON Behavior

8.2.2 Typical Buck-Boost LED Driver

Figure 41. Buck-Boost LED Driver

8.2.2.2 Detailed Design Procedure

8.2.2.2.1 Calculating Duty Cycle

Solving for D, D_MAX, and D_MIN:

Equation 69.

Equation 70.

Equation 71.

8.2.2.2.2 Setting Switching Frequency

Solving for R_T resistor:

Equation 72.

8.2.2.2.3 Inductor Selection

The inductor is selected to meet the CCM-DCM boundary power requirement, P_O(BDRY). Typically, the boundary condition is set to enable CCM operation at the lowest possible operating power based on minimum LED forward voltage drop and LED current. In most applications, P_O(BDRY) is set to be 1/3 of the maximum output power, P_O(MAX). The inductor value is calculated for maximum input voltage, V_IN(MAX), and output voltage, V_O(MAX):

Equation 73.

The closest standard value of 33 µH is selected. The inductor ripple current is given by:

Equation 74.

The inductor saturation rating should exceed the calculated peak current which is based on the maximum output power using the following expression:

Equation 75.

8.2.2.2.4 Output Capacitor Selection

The output capacitor should be selected to achieve the 5% peak-to-peak LED current ripple specification. Based on the maximum power, the capacitor is calculated as follows:

Equation 76.

A minimum of four 10-µF, 50-V X7R ceramic capacitors in parallel are needed to meet the LED current ripple specification over the entire range of output power. Additional capacitance may be required based on the derating factor under DC bias operation.

8.2.2.2.5 Input Capacitor Selection

The input capacitor is calculated based on the peak-to-peak input ripple specifications, Δv_IN(PP). The capacitor required to limit the ripple to 70 mV over range of operation is calculated using:

Equation 77.

A parallel combination of four 10-µF, 50-V X7R ceramic capacitors are used for a combined capacitance of 40 µF. Additional capacitance may be required based on the derating factor under DC bias operation.

8.2.2.2.6 Main N-Channel MOSFET Selection

Calculating the minimum transistor voltage and current rating:

Equation 78.

Equation 79.

This application requires a 60-V or 100-V N-channel MOSFET with a current rating exceeding 3 A.

8.2.2.2.7 Rectifier Diode Selection

Calculating the minimum Schottky diode voltage and current rating:

Equation 80.

Equation 81.

This application requires a 60-V or 100-V Schottky diode with a current rating exceeding 1.5 A. TI recommends a single high-current diode instead of paralleling multiple lower-current-rated diodes to ensure reliable operation over temperature.

8.2.2.2.8 Setting Switch Current Limit and Slope Compensation

Solving for R_IS:

Equation 82.

Equation 83.

A standard resistor of 0.1 Ω is selected based on the lower of the two calculated values. The resistor ensures stable current loop operation with no subharmonic oscillations over the entire input and output voltage ranges.

8.2.2.2.9 Programming LED Current

The LED current can be programmed to match the LED string configuration by using a resistor divider, R_ADJ1 and R_ADJ2, from V_CC to GND for a given sense resistor, R_CS, as shown in Figure 21. To maximize the accuracy, the IADJ pin voltage is set to 2.1 V for the specified LED current of 1.5 A. The current sense resistor, R_CS, is then calculated as:

Equation 84.

A standard resistor of 0.1 Ω is selected. Table 4 summarizes the IADJ pin voltage and the choice of the R_ADJ1 and R_ADJ2 resistors for different current settings.

Table 4. Design Requirements

LED CURRENT	IADJ VOLTAGE (VIADJ)	RADJ1	RADJ2
500 mA	700 mV	10.2 kΩ	100 kΩ
750 mA	1.05 V	16.2 kΩ	100 kΩ
1.5 A	2.1 V	39.2 kΩ	100 kΩ

8.2.2.2.10 Deriving Compensator Parameters

A simple integral compensator provides a good starting point to achieve stable operation across the wide operating range. The modulator transfer function with the lowest frequency pole location is calculated based on maximum output voltage, V_O(MAX), duty cycle, D_MAX, LED dynamic resistance, r_D(MAX), and minimum LED string current, I_LED(MIN). (See Table 1 for more information.)

Equation 85.

The compensation capacitor needed to achieve stable response is:

Equation 86.

A 100 nF capacitor is selected.

A proportional integral compensator can be used to achieve higher bandwidth and improved transient performance. However, it is necessary to experimentally tune the compensator parameters over the entire operating range to ensure stable operation.

8.2.2.2.11 Setting Startup Duration

Solving for soft-start capacitor, C_SS, based on 8-ms startup duration:

Equation 87.

A 100-nF soft-start capacitor is selected.

8.2.2.2.12 Setting Overvoltage Protection Threshold

Solving for resistors, R_OV1 and R_OV2:

Equation 88.

Equation 89.

The closest standard values of 249 kΩ and 7.87 kΩ along with a 60-V PNP transistor are used to set the OVP threshold to 40 V with 5 V of hysteresis.

8.2.2.2.13 PWM Dimming Consideration

A 60-V, 2-A P-channel FET is used in conjunction with an external level-shift circuit to achieve PWM dimming. The drive strength of 5 mA and gate-source voltage of 15 V are set by the 1-kΩ and 2-kΩ level-translator resistors and a small-signal N-channel MOSFET, whose gate is connected to DDRV.

8.2.2.3 Application Curves

These curves are for the buck-boost LED driver.

Figure 42. Line Regulation (3 LEDs at 1.5 A and 9 LEDs at 500 mA)

VIN = 14 V

Figure 44. Efficiency from 100 mA to 1.5 A

VIN = 14 V

Figure 43. LED Current vs IADJ Voltage