# How to Design an Efficient DC-DC Converter Using the DS1875 PWM Controller

Abstract: The DS1875 features a pulse-width modulation (PWM) controller that can be used to control a DC-DC converter. The DC-DC converter can then be used to generate the high bias voltages necessary for avalanche photodiodes (APDs). This application note describes the operation of a boost converter that uses the DS1875. Discussion covers the selection of the inductor and switching frequency, and the selection of components that improve the efficiency of the converter. Test data are presented.

## Overview

**Figure 1**shows a simple boost converter using the DS1875 PWM controller.

*Figure 1. Diagram of a DC-DC converter using the DS1875 PWM controller. Note that R1 and C3 were set to 0 for this application note. Refer to the DS1875 data sheet for information about selecting these filter components.*

## Boost Converter Operation

**Figure 2**shows the inductor current and inductor voltage during both the charging and discharging phases.

_{IN}, across the inductor L1. Diode D1 prevents capacitor C2 from discharging to ground through Q1. Because the input voltage is DC, the inductor current rises linearly as seen in Figure 2. The equation for the inductor current is given by:

_{PK}is the peak current that flows in the inductor. This current occurs at the end of the charging phase. Using Equation 1, this peak current can be calculated as:

_{L}needs to be greater than the voltage at V

_{OUT}.

_{L}when the inductor current begins to flow through the diode. Now that there is a large negative voltage across the inductor, the slope of the current through the inductor reverses. Because of the large voltage across the inductor, the current in the inductor will quickly decrease to zero. Once all of the energy stored in the inductor has been injected into the output, inductor current decreases to zero. Because there is no more current to sustain the voltage at V

_{L}, this node drops back down to the input voltage, V

_{IN}. The inductor current during the discharge phase is given by:

*Figure 2. Inductor current and voltage.*

## Efficiency in a DC-DC Converter

_{OUT}. This node also has the transistor's drain-to-source capacitance and the capacitance of the anode that both need to be charged before diode conduction can begin.

## Minimizing Efficiency Losses

**Figure 3**shows three inductors (1, 2, and 4 Henrys, respectively), each with 1V applied to them, charging until they store 2 Joules of energy. The 4H inductor takes twice as long, or twice the duty cycle, as the 1H inductor to charge to the same stored energy level of 2 Joules.

**Figure 4**shows the current flowing in these three inductors as they are charging. It can be seen that the 1H inductor requires 2A of current, but the 4H inductor only requires 1A of current. This illustrates how choosing a larger inductor and increasing the duty cycle of a DC-DC converter reduces inductor current.

*Figure 3. Stored inductor energy.*

*Figure 4. Inductor current.*

**Figure 5**shows the efficiency versus load current for a DC-DC converter using the DS1875's PWM controller. This graph shows that increasing the inductance, which increases the duty cycle, increased the efficiency. It also shows that a longer time period resulted in a higher efficiency because the switching losses were reduced. This example converter uses a BSSS123 n-channel FET and a 1N4148 diode.

**Table 1**shows parameters for the two inductors used.

*Figure 5. Efficiency of a DC-DC converter generating 76V from 3.3V.*

Table 1. Inductor Parameters | |||

Inductor Value (µH) | Current Rating (mA) | DC Resistance (Ω) | Package Size (mils) |

47 | 390 | 0.67 | 1210 |

22 | 175 | 0.44 | 1007 |

## Selection of Inductor, Duty Cycle, and Time Period

## Example Calculations for Typical DC-DC Converters

Requirements | Initial Assumptions |

V_{IN} = 3.3V |
D = 80% |

V_{OUT} = 76V |
T = 1/262.5kHz |

I_{OUT} = 5mA |
η = 0.5 |

**Table 2**shows other common DC-DC converter configurations using the DS1875 as the PWM controller. The table shows the calculated inductance and the switching frequency that were selected. This table is calculated using an efficiency of 50% and a target duty cycle of 80%.

Table 2. Parameters for Common DC-DC Converter Configurations | ||||

V_{IN} (V) |
V_{OUT} (V) |
I_{OUT} (mA) |
Switching Freq (kHz) | Inductor (µH) |

3.3 | 76 | 5 | 262.5 | 15 |

3.3 | 38 | 5 | 525 | 15 |

12 | 76 | 5 | 1050 | 56 |

## Diode Selection

_{PK}) can be several hundred milliamps. Third, to minimize power loss when the diode is conducting, the forward voltage should be as small as possible. Some applications may even use Schottky diodes because they have a much lower forward voltage. Finally, choosing a diode with a short reverse-recovery time will limit the output charge lost back to the input when the diode switches from the conducting to the nonconducting stage.