Application note, Rev 0.2, November 2007 Define PWM duty cycle to stabilize light emission Application note By Stéphane Fraissé Automotive Power PWM for lamps Abstract 1 Abstract Note: The following information is given as a hint for the implementation of the device only and shall not be regarded as a description or warranty of a certain functionality, condition or quality of the device. This application note intends to provide information about duty cycle determination, necessary to drive lamps in PWM, function of the measured battery voltage. 2 Introduction .The purpose of the PWM is to maintain the light emited by the lamp constant, regardless of the battery voltage applied. Maintaining a constant light has for consequence to maintain the electrical power constant. 2.1 Normalization of the wattage Every bulb used in automotive applications is standardized based on its wattage. The wattage is defined at a predetermined voltage and has a given power accuracy. Table 1 sums up the commonly used lamps in the automotive environment. Each lamp is defined as a certain voltage and the lamp’s accuracy is also function of the wattage. Table 1 Electrical parameter of the automotive bulb lamp Power accuracy in % Voltage definition in VREF 5 10 13.5 7 10 12.8 10 10 13.5 15 10 13.5 21 6 12 27 6 12.8 55 6 13.2 65 6 13.2 Official power of the lamp in W 2.2 ILamp behavior in DC operation The current flowing through a lamp is not proportional to the battery voltage and thus cannot be approximated by Ohm's law. Equation (1) is a better description of the non-linearity of the lamp current, taking into account the battery and reference voltages. The equation is derived from observed measurements. Figure 1 sketches the 27W bulb current. I lamp = lamp Vbat- × P ----------------------V REF V REF Application note PWM for lamp (1) 2 Rev 0.2, 2007-11-16 PWM for lamps Introduction 27W bulb current with and without PWM Lamp current (A) 3,0 27W bulb without PWM min 2,8 27W bulb without PWM typ 2,6 27W bulb without PWM max 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 5 6 7 8 9 10 11 12 13 14 Battery voltage (V) Figure 1 27W bulb current 2.3 PWM influence on the lamp behavior 15 16 17 18 19 20 27Wbulbcurrent.vsd The lamp resistance is linked to the filament temperature. That’s the reason why the current in the lamp is root means squared dependant of the battery voltage during DC operation. As soon as the lamp is in PWM, and with the purpose to maintain the electrical power constant, the resistance is not influenced by the battery voltage and it’s frozen to the voltage where the PWM starts. 2.4 Electrical parameters at the starting PWM voltage If we call VPWM the voltage where PWM starts to operate, the current IPWM, value of the current in the lamp at this VPWM voltage is getting easy to determine. I PWM = V PWM P lamp --------------- × ------------V REF V REF (2) Let’s call K, the parameter K = P lamp 1 - × ----------------------V REF V REF K is only lamp’s type dependant. Simplified like this, Equation (2) looks as follow : I PWM = K × V PWM (3) The lamp resistance is then Equation (4): V PWM R PWM = -------------------K (4) And last but not least, the power in the lamp at the starting PWM voltage VPWM is Equation (5): Application note PWM for lamp 3 Rev 0.2, 2007-11-16 PWM for lamps Power in the lamp during PWM 2 P PWM 2 V PWM V PWM = ------------------ = K × -------------------R PWM V (5) PWM 3 Power in the lamp during PWM 3.1 Power in the lamp when the VBAT above the PWM starting voltage VPWM To compute the average power in the lamp during PWM, the idea is to compute the energy during one PWM cycle and multiplied by the frequency F at which the PWM operates. Please refer to Figure 2 for details. P(W) TON P T P PWM power in the lamp.vsd Figure 2 t PWM energy, function of time. The energy during the ON time is equaled to the surface of the square. E = P × T ON (6) From Equation (6) and Equation (4), the energy in the lamp is then : 2 V BAT E = ---------------- × T ON R PWM (7) And thus the average power in the lamp is then, with d = TON / T, definition of duty cycle. 2 V BAT P = -------------------- × d × K V PWM 3.2 (8) Duty cycle deduction As said before, the target is to have P = PPWM. The quantity of Equation (8) and Equation (5) has to be equaled. It results : Application note PWM for lamp 4 Rev 0.2, 2007-11-16 PWM for lamps Dimming a lamp to substitute lower wattage 2 2 V BAT V PWM P = -------------------- × d × K = -------------------- × K V PWM V PWM Symplifying both quantities, it results the duty cycle is defined by : 2 V PWM d = -----------------2V BAT 3.3 Conclusion To perform PWM on lamps, with the goal to maintain a constant light emission, the duty cycle is independant of the lamp wattage, independant of the PWM frequency, and depends only on the square of the battery voltage. 4 Dimming a lamp to substitute lower wattage It is sometimes requested to dim a defined wattage to substitute lower wattage. For example, to dim the 27W break light to replace a broken 5W park light. The following chapter will defined the way to proceed. Let’s call Lbreak the lamp we want to simulate, and Ldim, the lamp we’re using as spare. Same convention will be used for all others parameter such as Kbreak is the K factor of the broken lamp. In Chapter 2.4, we have defined the a factor, called K, which is lamp specific. A very simplistic way to proceed would be to say that d, the duty cycle we are looking for is Equation (9). K break d dim = --------------K dim (9) With such a formula, the defined duty cycle will be as sumed up in Table 2: Please note dimming of a lamp can only reduce the power and obviously not increasing it so performing PWM to dim a 5W bulb to generate a 27W is non sense . Table 2 Duty cycle definition for dimming in percent Broken lamp Lbreak Lamp to dim Ldim 5 7 10 15 21 27 55 7 66 100 10 50 76 100 15 33 51 67 100 21 20 30 40 60 100 27 17 26 34 51 86 100 55 9 13 18 26 44 51 100 65 7 11 15 22 37 44 85 By using such a fixed duty cycle, the effect is the light emission is no more stabilized, in regards to battery voltage. this is usually sufficient, assuming that we’re already in a faded mode. Application note PWM for lamp 5 Rev 0.2, 2007-11-16 PWM for lamps Revision History 5 Revision History Define PWM duty cycle to stabilize light emission Revision History: Rev 0.2, 2007-11-16 Previous Version(s): Rev. 0.0, 2007-09-20 Page Subjects (major changes since last revision) 2 Modification of the Abstract text Application note PWM for lamp 6 Rev 0.2, 2007-11-16 Edition 2007-11-16 Published by Infineon Technologies AG 81726 Munich, Germany © 2007 Infineon Technologies AG All Rights Reserved. LEGAL DISCLAIMER THE INFORMATION GIVEN IN THIS APPLICATION NOTE IS GIVEN AS A HINT FOR THE IMPLEMENTATION OF THE INFINEON TECHNOLOGIES COMPONENT ONLY AND SHALL NOT BE REGARDED AS ANY DESCRIPTION OR WARRANTY OF A CERTAIN FUNCTIONALITY, CONDITION OR QUALITY OF THE INFINEON TECHNOLOGIES COMPONENT. THE RECIPIENT OF THIS APPLICATION NOTE MUST VERIFY ANY FUNCTION DESCRIBED HEREIN IN THE REAL APPLICATION. INFINEON TECHNOLOGIES HEREBY DISCLAIMS ANY AND ALL WARRANTIES AND LIABILITIES OF ANY KIND (INCLUDING WITHOUT LIMITATION WARRANTIES OF NON-INFRINGEMENT OF INTELLECTUAL PROPERTY RIGHTS OF ANY THIRD PARTY) WITH RESPECT TO ANY AND ALL INFORMATION GIVEN IN THIS APPLICATION NOTE. Information For further information on technology, delivery terms and conditions and prices, please contact the nearest Infineon Technologies Office (www.infineon.com). Warnings Due to technical requirements, components may contain dangerous substances. For information on the types in question, please contact the nearest Infineon Technologies Office. Infineon Technologies components may be used in life-support devices or systems only with the express written approval of Infineon Technologies, if a failure of such components can reasonably be expected to cause the failure of that life-support device or system or to affect the safety or effectiveness of that device or system. Life support devices or systems are intended to be implanted in the human body or to support and/or maintain and sustain and/or protect human life. If they fail, it is reasonable to assume that the health of the user or other persons may be endangered.