# Step-by-Step Design Process for the MAX16833 High-Voltage High-Brightness LED Driver, Part 2

Abstract:

This application note details a step-by-step design process for the MAX16833 high-voltage high-brightness LED driver. This process can speed up prototyping and increase the chance for first-pass success. A typical design scenario is presented, along with example calculations based on the design constraints. Component selection trade-offs are discussed. A spreadsheet calculator (XLS) is included to help calculate external component values. This application note focuses on the buck-boost converter topology. However, the same process can be applied to other topologies as long as the underlying equations are understood. For a boost converter design example, see application note 5571, “Step-by-Step Design Process for the MAX16833 High-Voltage High-Brightness LED Driver, Part 1.”

## Introduction

*Figure 1. Typical operating circuit.*

## Inductor Selection (Buck-Boost)

(Eq. 1) |

_{LED}is the forward voltage of the LED string in volts, V

_{D}is the forward drop of the rectifying diode (approximately 0.6V), V

_{INMIN}is the minimum input-supply voltage in volts, and V

_{FET}is the average drain-to-source voltage of the switching MOSFET in volts when it is on (assume 0.2V initially).

(Eq. 2) |

(Eq. 3) |

_{L}is the peak-to-peak inductor current ripple in amperes.

(Eq. 4) |

(Eq. 5) | |

(Eq. 6) | |

(Eq. 7) | |

(Eq. 8) |

_{MIN}as possible without going under. Recalculate the peak inductor current and ripple using the chosen inductor value. These numbers are necessary for additional calculations going forward.

L_{ACTUAL} = 8.2µH |
(Eq. 9) |

(Eq. 10) | |

(Eq. 11) |

_{P}. Typically, 20% headroom is used for inductor peak current.

## Switching MOSFET Selection

V_{DS} = (V_{LED} + V_{INMAX} + V_{D}) × 1.2 |
(Eq. 12) |

(Eq. 13) |

_{DRMS}is the switching MOSFET’s drain RMS current in amperes.

## Rectifier Diode Selection

I_{D} = IL_{AVG} × (1 - D_{MAX}) × 1.2 |
(Eq. 14) |

_{LED}+ V

_{INMAX}), the maximum expected reverse voltage across the diode.

## Dimming MOSFET Selection

_{LED}.

## Input Capacitor Selection

(Eq. 15) |

_{Q_IN}is the portion of input ripple due to the capacitor discharge.

(Eq. 16) |

_{ESR_IN}is the input ripple due to ESR.

_{INMIN}). Also, assume that 95% of this input ripple comes from the bulk capacitance. This assumption may need to be revisited if the calculated values are not easily attained with actual components. Based on the stated design specifications, the input capacitor is calculated as follows:

(Eq. 17) | |

(Eq. 18) |

*at the operating voltage*(capacitance can decrease substantially with a change in voltage in ceramic capacitors).

## Output Capacitor Selection

(Eq. 19) |

_{Q_OUT}is the portion of output ripple due to the capacitor discharge.

_{ESR_OUT}, comes from the output capacitor ESR, which can be calculated as follows:

(Eq. 20) |

^{1}

_{LED}. Also, assume that the dynamic impedance of the chosen LED is 0.2Ω (0.8Ω total for the 4 LED string). The total output voltage ripple is then calculated as follows:

V_{OUTRIPPLE} = 0.1A × 0.8Ω = 80mV |
(Eq. 21) |

(Eq. 22) | |

(Eq. 23) |

*at the operating voltage*(capacitance can decrease substantially with a change in voltage in ceramic capacitors).

## Overvoltage Protection

_{OVP}exceeds 1.23V, NDRV is forced low until V

_{OVP}discharges to 1.16V.

_{OV}trip point chosen should be above the maximum output voltage expected during normal operation.

V_{OV} > V_{INMAX} + V_{LEDMAX} |
(Eq. 24) |

(Eq. 25) |

_{OV}of 42V is desired. Choose R

_{OVP2}to be 10kΩ, then

(Eq. 26) |

## Current Sensing

### LED Current Sensing

_{ICTRL}> 1.23V, the internal reference regulates the voltage across R

_{CS_LED}(V

_{ISENSE+}- V

_{ISENSE-}) to 200mV. Therefore, the current-sense resistor R

_{CS_LED}sets the LED current.

(Eq. 27) |

_{ICTRL}< 1.23V, then the LED current is determined by R

_{CS_LED}and V

_{ICTRL}. This allows the LEDs to be dimmed with an analog voltage.

(Eq. 28) |

_{ICTRL}= 1.23V, both equations are the same.

### Switching FET Current Sensing and Slope Compensation

_{SC}from CS to the source of the switching MOSFET). Internal to the MAX16833, there is a current source that feeds current through R

_{SC}to create a voltage V

_{SC}. This voltage is added to the voltage across R

_{CS_FET}and the result is compared to a reference.

V_{CS} = V_{SC} + V_{CS_FET} |
(Eq. 29) |

V_{SCMIN} = 0.5 × (inductor current downslope - inductor current upslope) × R_{CS_FET} |
(Eq. 30) |

_{CS_FET}, has both the switching MOSFET current and the slope compensation current flowing through it.

*Figure 2. Slope compensation.*

(Eq. 31) |

(Eq. 32) | |

(Eq. 33) |

(Eq. 34) |

(Eq. 35) |

_{CS_FET}has been determined, R

_{SC}can be calculated as follows:

(Eq. 36) |

(Eq. 37) | |

(Eq. 38) |

(Eq. 39) |

## Error Amplifier Compensation

_{ZRHP}and the instability caused by the RHP zero can be avoided. The error amplifier must be compensated to ensure loop stability over all expected variations in operating conditions. The worst case RHP zero frequency is calculated as follows:

(Eq. 40) |

_{P2}, can be calculated as follows:

(Eq. 41) |

_{OUT}is the bulk output capacitance calculated above and R

_{OUT}is the effective output impedance.

(Eq. 42) |

_{LED}is the dynamic impedance of the LED string at the operating current in ohms.

_{COMP}and C

_{COMP}) from COMP to SGND. R

_{COMP}sets the crossover frequency and C

_{COMP}sets the integrator zero frequency. For optimum performance, use the following equations:

(Eq. 43) | |

(Eq. 44) |

_{COMP}and the output impedance of the error amplifier set the dominant pole frequency according to the following equation:

(Eq. 45) |

_{EA}is much greater than R

_{COMP}. ROUT

_{EA}is not specified in the MAX16833 data sheet, but it can be calculated from the transconductance and open-loop gain of the error amplifier. First, convert the open-loop gain of 75dB from decibels to volt/volt.

(Eq. 46) |

_{EA}can be calculated as follows:

(Eq. 47) |

(Eq. 48) | |

(Eq. 49) | |

(Eq. 50) | |

(Eq. 51) |

(Eq. 52) |

(Eq. 53) |

## Loop Response and Phase Margin

_{M}) as follows:

(Eq. 54) |

_{ZRHP}, setting the integrator zero (f

_{ZI}) at f

_{P2}, and assuming f

_{P1}is much less than f

_{C}, the equation simplifies to the following:

Φ_{M} = 90° - tan^{-1}(0.2) = 79° |
(Eq. 55) |

**Figure 3**shows a simulated Bode plot based on the above external component choices. The crossover frequency is 5.5kHz and the phase margin is 79°. The crossover frequency is slightly below the hand calculated value but well within the expected range.

*Figure 3. Bode plot simulation.*

*after*the prototype has been assembled.

**Figure 4**for a typical gain and phase measurement setup.

*Figure 4. Setup for measuring the gain and phase response of the loop.*

## Designing a Circuit to Accommodate Multiple Applications

*Figure 5. Generic MAX16833 solution allowing boost or buck-boost configuration.*

## Output Capacitor Connection

_{IN}.

**Figure 6**shows both options for connecting the output capacitor of a buck-boost LED driver. Option A is the standard method and will usually provide the best EMI performance. However, because the LED cathode is connected to the input, the LED voltage is vulnerable to line-transient conditions. By connecting the output capacitor across the LEDs, the line-transient vulnerability is reduced. Option B has the drawback of changing the input current from continuous to discontinuous, increasing voltage ripple on the input and hurting EMI performance.

*Figure 6. Two different options for connecting the output capacitor of a buck-boost LED driver.*

## Conclusion

**Figure 7**. By following the step-by-step design process outlined in this application note, significant time can be saved during the debug and test phase of the project.

*Figure 7. Typical application circuit based on example calculations.*

#### References

- For information on acoustic noise and capacitors for acoustic noise reduction, see www.murata.com/products/capacitor/solution/naki.html.