### Define PWM duty cycle to stabilize light emission

```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
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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
Infineon Technologies AG
81726 Munich, Germany
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