Abstract:
A method for driving a non-linear load element. On account of the non-linear interrelationship between the voltage and the current at the load element and the related non-linear dependence of the power loss on the quantities “voltage” and “current”, an adjustment of the switching speed only on the basis of the power loss in the switching element cannot be carried out with non-linear load elements without being confronted with undesirable switching losses and related electromagnetic noise fields. Therefore, the load current currently flowing in the load element is picked up in addition to the currently determined power loss in the switching element, and the switching speed of the switching element is controlled in dependence on the determined power loss and on the current picked up. The switching speed can be optimally adjusted when driving the non-linear load elements by means of PWM.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is the U.S. national phase application of PCT International Application No. PCT/DE2008/001391, filed Aug. 23, 2008, which claims priority to German Patent Application No. DE 10 2007 040 783.3, filed Aug. 28, 2007, the contents of such applications being incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The invention relates to a method for driving a non-linear load element. 
     BACKGROUND OF THE INVENTION 
     Many electric load elements, particularly electric load elements in motor vehicles, such as lamps, heating spirals etc., are driven by means of pulse-width modulation (PWM), wherein the power delivered to the load element can be regulated or controlled, wherein it is possible to minimize the losses in the drive electronics by the switching operations. 
     However, when driving load elements in motor vehicles by means of pulse-width modulation, electromagnetic fields that may interfere with the radio reception in the vehicle are emitted via the battery supply lines and the load supply lines. Therefore, appropriate limiting values have been laid down in various standards, such as IEC, ISO, CISPR, said limiting values reducing the interference with the radio receiver in the corresponding spectra to a tolerable degree. These emitted fields may be reduced by filtering at the inputs and outputs of the control device, for example. The new methods actively influence the switching edges, as it is described in the unexamined application W02005/057788, for example, which is incorporated by reference. 
     In the new series of vehicles, the lamps are being increasingly replaced by light emitting diodes (LED). However, the non-linearity of their current-voltage characteristic results in a sudden break-off of the current and so in increased interfering emissions. 
     Conventional methods attenuate the high-frequency alternating currents in the supply lines by means of filters in the input lines and output lines. However, the disadvantage of the filters consists in the fact that they are very expensive and require a lot of space, whereby they raise the price of the electronic components, and that they cannot be miniaturized (integration in silicon). 
     Another possibility of reducing electromagnetic radiation is the reduction of the switching speed in the switching element, whereby the high-frequency current portions can be reduced to the necessary degree, but here the undesirable switching losses heating up the electronic components are increasing with decreasing switching speed. 
     In the new methods, for example according to WO2005/057788, the switching speed of the switching element is varying in dependence on the instantaneous power loss.  FIG. 1  shows the normalized power loss in a switching element when driving an ohmic load element (linear load element) as well as a stepped convergence of the course of the rate of change of the output voltage according to WO2005/057788. 
     However, such methods, as disclosed in said application, fail when driving load elements that show a non-linear behaviour within a switching process (load elements with a non-linear voltage-current interrelationship, such as LEDs). 
     On account of the non-linear interrelationship between the voltage and the current in the load element, the power loss in the switching element is not linearly dependent on the output voltage or the load current, respectively. Therefore, when driving the non-linear load elements, an adjustment of the switching speed of the switching element that is only related to the power loss or output voltage at the switching element or to a quantity depending thereon is not applicable without being confronted with increased switching losses or a bad electromagnetic radiation, respectively. This difference between linear and non-linear load elements is illustrated in  FIG. 5 , for example. With an ideal linear load element (e.g. linear resistor), the current changes proportionally to the voltage at the load element (see dashed line L 1  in  FIG. 6 ). Thus, with a linear load element, there is a quadric-polynomial interrelationship between the power loss P V  at the switching element and the output voltage U a : P V ˜(U a ) 2 , i.e. the power loss P V  is linearly proportional to the square of the output voltage U a , as shown in  FIG. 1  (see continuous polynomial curve). 
     On the other hand, with a non-linear load element, the current flowing in this non-linear load element does not change proportionally to the output voltage (see continuous line L 2  in  FIG. 6 ). Therefore, there is no linear interrelationship between the power loss and the current or the voltage, respectively. This is illustrated in  FIGS. 2 and 8 , wherein  FIG. 2  shows a non-linear interrelationship in the L-range of the output voltage and  FIG. 8  a non-linear interrelationship both in the L-range and in the H-range of the output voltage. As a result of the non-linear interrelationship between the voltage and the current, an adjustment of the switching speed only on the basis of the power loss or the output voltage is not practicable with the non-linear load elements, which means that the radiation of electromagnetic noise fields cannot be reduced effectively by means of the method according to WO2005/057788. 
     SUMMARY OF THE INVENTION 
     It is therefore object of the present invention to set forth a method of the abovementioned type, by means of which the radiated electromagnetic fields with the non-linear load elements can be reduced effectively by means of a load-dependent, active influencing of the switching edges of the switching device and the valid standards can be met. 
     On account of the non-linear interrelationship between the voltage and the current at the load element and the related non-linear dependence of the power loss on the quantities “voltage” and “current”, an adjustment of the switching speed only on the basis of the power loss or the voltage, respectively, cannot be carried out with non-linear load elements without being confronted with undesirable switching losses and related electromagnetic noise fields. 
     Therefore, according to aspects of the invention, the load current currently flowing in the load element is picked up in addition to the currently determined power loss at the switching element, and the switching speed of the non-linear load elements is controlled in dependence on the determined power loss and on the measured load current. 
     By including the current flowing in the load element as a further measured quantity in addition to the quantity “power loss”, the switching speed of the non-linear load elements can be optimally adjusted, wherein the switching speed of the non-linear switching element is controlled as follows:
         the switching speed is set high in the range where the current-voltage characteristic of the load element dI a /dU a  is approximately zero;   the switching speed is set high in the range where the current-voltage characteristic of the load element dI a /dU a  is not approximately zero and the power loss is high; and   the switching speed is set low in the range where the current-voltage characteristic of the load element dI a /dU a  is not approximately zero and the power loss is low.       

     The present invention is based on an active influencing of the switching speed of the switching element in such a manner that the switching element is operated at a high switching speed in that range where both the output voltage and the current in the load element have exceeded the respective lower threshold. Accordingly, the switching element is operated at a reduced switching speed when the output voltage and the current in the load element are below the respective threshold. 
     For optimally adjusting the switching speed, two thresholds each are used for the power loss at the switching element and for the load current. For the power loss, the output voltage is picked up as a measured quantity, and two voltage thresholds are used as a reference quantity for the output voltage. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following, the invention will be explained in greater detail on the basis of the exemplary embodiments and with the aid of the figures in which 
         FIG. 1 : shows the relative power loss in dependence on the relative output voltage with a linear load element, shown in a right-handed coordinate system, wherein the right-hand abscissa axis is the relative output voltage U a /U KL30  and the upward ordinate axis is the relative power loss P V /P V max ; 
         FIG. 2 : shows the relative power loss in dependence on the relative output voltage with a non-linear load element, shown in a right-handed coordinate system, wherein the right-hand abscissa axis is the relative output voltage U a /U KL30  and the upward ordinate axis is the relative power loss P V /P V max ; 
         FIG. 3 : shows the variations in time/the switching behaviour of the relative power loss, of the relative load current and of the relative output voltage with a non-linear load element according to  FIG. 2 , shown in three right-handed coordinate systems, wherein the first coordinate system shows the variation in time of the relative load current I a /I a max , the second coordinate system shows the variation in time of the relative output voltage U a /U bat , and the third coordinate system shows the variation in time of the relative power loss P V /P V−max ; 
         FIG. 4 : shows an equivalent circuit diagram of a circuit arrangement for carrying out the method according to  FIG. 3 ; 
         FIG. 5 : shows the course of the normalized current-voltage characteristic of a linear and of a non-linear load element, wherein the maximum current with this non-linear load element has an upper limit, shown in a right-handed coordinate system, wherein the right-hand abscissa axis is the relative output voltage U a /U KL30  and the upward ordinate axis is the relative load current I a /I a max ; 
         FIG. 6 : shows the variations in time/the switching behaviour of the relative power loss, of the relative load current and of the relative output voltage with a non-linear load element, wherein the maximum current with this load element is limited according to  FIG. 5 , shown in three right-handed coordinate systems, wherein the first coordinate system shows the variation in time of the relative load current I a /I a max , the second coordinate system shows the variation in time of the relative output voltage U a /U bat , and the third coordinate system shows the variation in time of the relative power loss P V /P V−max ; 
         FIG. 7 : shows the variations in time/the switching behaviour of the relative power loss, of the relative load current and of the relative output voltage with a non-linear load element according to  FIG. 8  with the current limitation according to  FIG. 5 , shown in three right-handed coordinate systems, wherein the first coordinate system shows the variation in time of the relative load current I a /I a max , the second coordinate system shows the variation in time of the relative output voltage U a /U bat , and the third coordinate system shows the variation in time of the relative power loss P V /P V−max ; 
         FIG. 8 : shows the relative power loss in dependence on the relative output voltage with a non-linear load element with the current limitation according to  FIG. 5 , shown in a right-handed coordinate system, wherein the right-hand abscissa axis is the relative output voltage U a /U bat  and the upward ordinate axis is the relative power loss P V /P V max ; 
         FIG. 9 : shows an equivalent circuit diagram of a circuit arrangement for carrying out the method according to  FIG. 7 ; 
         FIG. 10   a : shows the switching behaviours in an inventive method for adjusting the switching speed of the switching element when driving a non-linear load element, with a course of the relative power loss relative to the relative output voltage according to  FIG. 8  according to Table 1, shown in four right-handed coordinate systems, wherein the first coordinate system shows the variation in time of the relative gate voltage U g /U g max , the second coordinate system shows the variation in time of the relative output voltage U a /U bat , the third coordinate system shows the variation in time of the relative load current I a /I a max , and the fourth coordinate system shows the variation in time of the relative power loss P V /P V−max ; 
         FIG. 10   b : shows the variation in time of the relative load current I a /I a max  with the associated pulse duration for the switching behaviour according to Table 1 and  FIG. 10   a;    
         FIG. 10   c : shows the switching behaviours in an inventive method for adjusting the switching speed of the switching element when driving a non-linear load element, with a course of the relative power loss relative to the relative output voltage according to  FIG. 8  according to Table 2, shown in four right-handed coordinate systems, wherein the first coordinate system shows the variation in time of the relative gate voltage U g /U g max , the second coordinate system shows the variation in time of the relative output voltage U a /U bat , the third coordinate system shows the variation in time of the relative load current I a /I a max , and the fourth coordinate system shows the variation in time of the relative power loss P V /P V−max ; 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows the change of the relative power loss P V /P V max  in dependence on the relative output voltage U a /U KL30  with a linear load element, wherein P V  is the instantaneous power loss, P V max  is the maximum power loss, U a  is the output voltage, and U KL30  is the supply voltage. According to that, the relative power loss P V /P V−max  shows a quadric polynomial of the output voltage U a /U KL30 , which is a result of the linear interrelationship between the output voltage U a  and the current I a  in a linear load element. 
       FIGS. 2 and 8 , on the other hand, show a non-linear interrelationship between the power loss P V  and the output voltage U a  in a non-linear load element. This non-linear interrelationship between the power loss P V  and the output voltage U a  is a result of the non-linear interrelationship between the output voltage U a  and the current I a  in the load element, which is the case with a non-linear load element. Consequently, such a non-linear load element, such as an LED (light emitting diode), cannot be operated by means of a method as described in WO2005/057788 without causing increased interfering radiation or increased switching losses. 
     As shown in  FIG. 2 , the curve of the relative power loss P V /P V−max  has a range (range B 1  in the figure) where the power loss P V  is zero in spite of the increasing output voltage U a . Outside this range B 1 , in range B 2 , the relative power loss P V /P V31 max  shows an approximately linear interrelationship with the relative output voltage U a /U KL30 . The transition point between these two ranges B 1  and B 2  is the lower voltage threshold U au  of the output voltage U a  that is still to be determined. 
     Since the voltage threshold U au  of the LED is not exactly known or is varying in dependence on the operational conditions, the current currently flowing in the load element (load current I a ) is introduced as a new physical measured quantity as against the known method according to WO2005/057788. Also, a current threshold I lim1  is introduced for the currently flowing load current I a . 
     So, the switching element is operated at a high switching speed in that range where both the output voltage U a  and the load current I a  have exceeded the lower thresholds U au  and I lim1 , respectively. Accordingly, the switching speed is reduced when the output voltage U a  and the load current I a  are below the thresholds U au  and I lim1 , respectively. The variations in time are illustrated in  FIG. 3 . The range of high power loss is dependent on the voltage threshold U au  of the LED. 
       FIG. 2  shows the basic course of the relative power loss P V /P V31 max  in the switching element. As in the method that is already known, the switching speed is adjusted to the instantaneous value of the power loss P V , wherein the dashed curves S 1  and S 2  represent a stepped convergence of the switching speed to the ideal curve with different numbers of steps, whereby the emitted spectrum can be reduced in the high-frequency ranges also for non-linear load elements without significantly increasing the switching losses. 
       FIG. 4  shows a possible realization of this switching process according to  FIG. 3  with a circuit arrangement. As the non-linear load element, an LED with a series resistor  110  is shown. In this circuit arrangement, when switching, the gate of the MOSFET switching element  200  is supplied with currents of varying amperage in dependence on the power loss P V , namely the output voltage U a , and on the load current I a , and so the switching speed, within the switching process, is specifically adjusted to the instantaneous values of the measured quantities power loss P V /output voltage U a  and load current I a . 
     The switching speed is set high in the range of high power loss P V  and in the range of small change dI a /dU a  of the load current I a  compared to the change of the output voltage U a . The switching speed is set low in the range of low power loss P V  and of great change dI a /dU a  of the load current I a  compared to the change of the output voltage U a . 
     By means of the controllable power sources  400  and corresponding control logic  300 , the transitions between the high and the low switching speeds can be preset very precisely and, if necessary, a very fine adjustment of the switching speed be realized. The functioning of the control logic  300  is illustrated in Tables 1 and 2. 
     In order to extend the service life of the LEDs and/or to control the brightness/the colour spectrum independently of the supply voltage, it is also usual to operate LEDs in series with power sources  120  for current limitation. The continuous line L 2  in  FIG. 5  shows an exemplary course of the normalized current-voltage characteristic of such a load element. When driving such a load element, current limitation results in the following variations in time as in  FIG. 6 . The shown variations in time illustrate that the spectrum of the current includes considerable high-frequency portions. These portions can be reduced by reducing the switching speed shortly before reaching the threshold current of the current limitation. 
     Since the current threshold of the current limitation is not exactly known or is varying in dependence on the operational conditions, this current threshold has to be determined for the next falling/rising edge during operation, unless the course of the current has already been rounded off in the load element, wherein the lower current threshold I lim1  is a quantity that is dependent on the maximum current of the switching element and/or on the instantaneous load. 
     In addition to the lower current threshold I lim1  already described, an upper current threshold I lim2  is defined so that the switching element is operated at a high switching speed only when the current in the load element has fallen below this upper current threshold I lim2 . Accordingly, the switching speed is reduced when the current I a  in the load element has exceeded the upper current threshold I lim2 . The difference ΔI between the current threshold and the maximum current I max  in the load element is defined absolutely or with reference to the maximum current I max . The variations in time are illustrated in  FIG. 7 . 
     The range of high power loss is dependent on the current threshold I lim2  of the current limitation as well as on the voltage threshold U ao  of the LED.  FIG. 8  shows the basic course of the relative power loss in the switching element. 
     The threshold may be defined in advance or during operation. For determining the upper current threshold I lim2  during operation, the maximum value I max  of the current is first determined, for example by means of a so-called peak detector or by single or multiple sampling of the current, said sampling being synchronous with the PWM signal. From this maximum value I max , the current threshold I lim2  is then determined, as described above, and preferably continuously compared with the instantaneous load current I a . 
     However, those periods of time during switching in which the current is almost constant may negatively influence the pulse-pause ratio so that the pulse-pause ratio of driving deviates from that of the load current I a . As a countermeasure, a further sample-and-hold element may be used for measuring, synchronously with the upper current threshold I lim2  of the load current I a , the associated voltage value at the load element. In dependence thereon, the upper voltage threshold U ao  may be defined above this voltage value, above which the switching speed is increased in order to improve the correspondence between the set pulse-duty factor and the actual pulse-duty factor by reducing the dead times. In addition to that, the maximum value of the voltage of the load element of the same pulse or the voltage value occurring simultaneously with the maximum current, respectively, is determined and compared with the lower voltage threshold U ao . In dependence on the difference between the two values, the associated upper voltage threshold U ao  and the current threshold I lim2  are accepted as valid values or rejected in order to prevent that wrong thresholds are adopted when the current limitation is not reached on account of a low supply voltage. 
     Accordingly, when the lower current threshold I lim1  is reached, the associated voltage value at the load element may be measured and the lower voltage threshold U au  be defined just below it, below which the switching speed is increased as well. 
     At the beginning, the thresholds U au , U ao , I lim1 , I lim2  are fixed at the respective expected value or its minimum or maximum value, respectively. 
       FIG. 9  shows an equivalent circuit diagram of a circuit arrangement for carrying out the method for adjusting the switching behaviour according to  FIG. 7 . 
       FIGS. 10   a ,  10   b ,  10   c  show the detailed switching behaviour in an inventive method for adjusting the switching speed in a non-linear load element, with a course of the relative power loss relative to the relative output voltage according to  FIG. 8 . 
       FIG. 10   a  shows the switching behaviour as shown in Table 1. 
     
       
         
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Gate voltage: 
                 Output 
                 Switching 
                 Power loss 
               
               
                 Range 
                 U g   
                 current: I 
                 speed 
                 in this range 
               
               
                   
               
             
             
               
                 A 
                 U g  &lt; U gu   
                 I &lt; I lim1   
                 High 
                 Low 
               
               
                 B, C 
                 U gu  &lt; U g  &lt; U go   
                 I &lt; I lim1   
                 Low 
                 Low 
               
               
                 D 
                 U gu  &lt; U g  &lt; U go   
                 I lim1  &lt; I &lt; I lim2   
                 High 
                 High 
               
               
                 E, F 
                 U gu  &lt; U g  &lt; U go   
                 I &gt; I lim2   
                 Low 
                 Low 
               
               
                 G 
                 U g  &gt; U go   
                 I &gt; I lim2   
                 High 
                 Low 
               
               
                   
               
             
          
         
       
     
     Table 1 and  FIG. 10   a  show a first case, wherein the switching speed is set low in ranges B and F. Here, particularly with the transitions between B and C and between E and F, the thresholds U au  and U ao  are not used yet. 
       FIG. 10   b  shows the course of the current with the associated pulse duration for the switching behaviour according to Table 1 and  FIG. 10   a , and also the idealized course of the current for driving without pulse shaping and the pulse duration thereof. 
     It is obvious that the correspondence between the two pulse durations, and thus the duty cycle faithfulness, depends on the symmetry of ranges A, B, C with ranges G, F, E. The difference between the pulse durations results from the difference between the duration of ranges E, F, G and the duration of ranges A, B, C:
 
Δ T   on   =T   on-effektiv   −T   on-ideal   =t   E   +t   F   +t   G   −t   A   −t   B   −t   C  
 
     Since t F , the duration of range F, depends on the supply voltage and thus does not have to be constant for a short period of time during operation, this may cause interfering variations of brightness. 
     For this reason, the switching speed is to be increased in ranges B and F, as it has been done for ranges A and G for the same reason. The result of this is a further improved switching behaviour (see Table 2 and  FIG. 10   c ). According to that, the reduction of the times t B  and t F  also reduces their influence on the error of the pulse duration ΔT on . Here, the thresholds U gu  and U go  are not used any more. They are replaced by the thresholds U au  and U ao , respectively. 
     
       
         
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                   
                 Output 
                   
                 Switching 
                 Power loss in 
               
               
                 Range 
                 voltage: U a   
                 Output current: I 
                 speed 
                 this range 
               
               
                   
               
             
             
               
                 A 
                 U a  &lt; U au   
                 I &lt; I lim1   
                 High 
                 Low 
               
               
                 B 
                 U a  &lt; U au   
                 I &lt; I lim1   
                 High 
                 Low 
               
               
                 C 
                 U au  &lt; U a  &lt; U ao   
                 I &lt; I lim1   
                 Low 
                 Low 
               
               
                 D 
                 U au  &lt; U a  &lt; U ao   
                 I lim1  &lt; I &lt; I lim2   
                 High 
                 High 
               
               
                 E 
                 U au  &lt; U a  &lt; U ao   
                 I &gt; I lim2   
                 Low 
                 Low 
               
               
                 F 
                 U a  &gt; U ao   
                 I &gt; I lim2   
                 High 
                 Low 
               
               
                 G 
                 U a  &gt; U ao   
                 I &gt; I lim2   
                 High 
                 Low 
               
               
                   
               
             
          
         
       
     
     The switching element is operated at a high switching speed only when the current in the load element has exceeded a lower current threshold I lim1 , as it is the case in range D. 
     Accordingly, the switching speed is reduced when the current in the load element is below the lower current threshold I lim1 , as at the transition from range D to range C. 
     The upper current threshold I lim2  cannot be preset for changing loads or for loads where a change in temperature, for example, results in a variation of the current limitation of the load element. This threshold has to be determined during operation and can then be assumed as being temporarily constant. 
     For determining this current threshold I lim2  during operation, the maximum current I max  of a previous pulse is determined, and so the threshold I lim2  has to be just below this maximum value:
 
 I   lim2   =I   max   −ΔI.  
 
     ΔI may be a fixed value or a percentage value δ. If it is a percentage value δ, the upper current threshold I lim2  is determined as follows:
 
 I   lim2 =(1−δ)× I   max .
 
     If the load element is an LED with a series resistor without current limitation as in  FIG. 4 , the value I max  changes almost linearly with the supply voltage U bat . However, since the supply voltage U bat  can be measured continuously, it is more useful not to select the current threshold I lim2 , but to select a threshold U a2  (not U au  or U ao ) with reference to the output voltage U a  that depends on the supply voltage. U a2  is selected as follows:
 
 U   a2   =U   KL30   −R   DS-on   ×I−ΔU,  
 
with U bat : supply voltage,
         R DS-on ×I: voltage drop at switching element,   ΔU: fixed value, or percentage value relative to supply voltage.       

     On account of the small voltage drop at the switching element, also U a2  may be indicated as a percentage value:
 
 U   a2 =(1−δ)× U   KL30  
 
     The lower voltage threshold U au  is determined as follows. The current threshold I lim1  is already known. During the cycle of a pulse, the output voltage U a  and the current I are sampled simultaneously. At the point in time t 1 , the current I reaches the lower current threshold: I(t 1 )=I lim1 . At the same point in time, the output voltage U a  reaches the value U a (t 1 ). The voltage threshold U au  is fixed just below this value U a  (t 1 ): U au =U a (t 1 ) ΔU 1 . When fixing the magnitude of ΔU 1 , it has to be taken into consideration that the current I is still or already almost zero at the lower voltage threshold U au . 
     Similarly, the upper voltage threshold U ao  is determined as follows. The upper current threshold I lim2  is already known. During the cycle of a pulse, the output voltage U a  and the current I are sampled simultaneously. At the point in time t 2 , the current reaches the upper current threshold: I(t 2 )=I lim2 . At the same point in time, the output voltage U a  reaches the value U a (t 2 ). The voltage threshold U ao  is fixed just above this value U a (t 2 ): U ao =U a (t 2 )+ΔU 2 . When fixing the magnitude of ΔU 2 , it has to be taken into consideration that the current I is still or already almost the maximum value I max  at the upper voltage threshold U ao . 
     
       
         
               
             
               
               
             
           
               
                   
               
               
                 List of reference numerals 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 110 
                 Light emitting diode (LED) in series with series resistor 
               
               
                 120 
                 Light emitting diode in series with power source 
               
               
                 200 
                 MOSFET switching element 
               
               
                 300 
                 Control logic 
               
               
                 400 
                 Controllable power source 
               
               
                 510, 520, 530 
                 Schmitt trigger, comparator 
               
               
                 600 
                 Comparator 
               
               
                 700 
                 Inverter 
               
               
                 810, 820 
                 Switch 
               
               
                 K1 
                 Relative power loss P V /P V-max  as a function of the relative 
               
               
                   
                 output voltage U a /U KL30  with a linear load element 
               
               
                 K2 
                 Relative power loss P V /P V-max  as a function of the relative 
               
               
                   
                 output voltage U a /U KL30  with a non-linear load element 
               
               
                 K3 
                 Relative power loss P V /P V-max  as a function of the relative 
               
               
                   
                 output voltage U a /U KL30  with a non-linear load element, wherein 
               
               
                   
                 the maximum load current has an upper limit 
               
               
                 S1, S2 
                 Stepped convergence of the switching speed to the ideal curve K1, 
               
               
                   
                 K2 and K3, respectively, with different numbers of steps 
               
               
                 B1 
                 Range where the power loss P V  is zero in spite of the increasing 
               
               
                   
                 output voltage U a   
               
               
                 B2 
                 Range where the relative power loss P V /P V-max  shows an 
               
               
                   
                 approximately linear interrelationship with the relative output voltage 
               
               
                   
                 U a /U KL30   
               
               
                 B3 
                 Range where the load current I a  is limited by the power source the 
               
               
                   
                 light emitting diode 120 is connected in series with 
               
               
                 T1 
                 Separating line between ranges B1 and B2 
               
               
                 T2 
                 Separating line between ranges B2 and B3 
               
               
                 L1 
                 Normalized current-voltage characteristic of a linear load element 
               
               
                 L2 
                 Normalized current-voltage characteristic of a light emitting diode 
               
               
                   
                 120 that is operated in series with a power source 
               
               
                 A, B, C, D, E, F, G 
                 Individual range in the switching process