FI105620B - Coupling device for approximating a nonlinear transfer function - Google Patents

Abstract

A circuit arrangement for approximating a non-linear transfer function, particularly a logarithmic or antilogarithmic transfer function, is improved in such a manner that it obtains a much better temperature stability of its transfer characteristic. At the same time, analog/digital conversion or digital/analog conversion becomes possible. In this arrangement, the said converters are supplied with an analog reference quantity (Vref) and an analog (Vin) or digital/binary input signal (Win). The converters (20, 30) output a digital or analog output signal (Wout, Vout) on the basis of an essentially linear converter characteristic and a non-constant reference quantity (Vref) depending on the analog input or output signal (Vin, Vout) is input to the respective linear converter (20, 30). Furthermore, a method is shown, particularly for operating the aforementioned circuit arrangement and a lighting system using the aforementioned circuit arrangement. In the lighting system, the brightness of one or more light generators is changed to suit the eye. <IMAGE>

Description

105620

This invention relates to a coupling arrangement used to approximate a logarithmic or antilogarithmic / exponential transfer function according to the species definition of claim 1. It further relates to a lighting system according to claim 9 for controlling or controlling the brightness of one or more light sources.

The sensitivity of the human eye as well as human hearing is nonlinear. This non-linearity is approximately logarithmic. The use of linear control or adjustment systems to obtain the desired luminance or volume does not, at all, produce a corresponding line-v luminance or volume sensation in the human senses. Thus, starting from a predetermined luminance, for example, by multiplying the electric or the luminous efficacy,

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doubling of the impression of light. The same applies to the acoustic sensory impression.

· 25 Linear control systems are suitable. therefore, only to a limited extent to control and adjust the light and volume in a satisfactory • · · * · * * way. For example, analog amplifiers having a logarithmic transmission characteristic and an exponential transmission characteristic are used for this purpose. Connecting these analog amplifiers sequentially - · · · • y / manually produces a linear transmission characteristic again.

The logarithmic or exponential analog amplifiers mentioned here generally use an exponential current / voltage characteristic of a 2 105620 diode or transistor connected in the current direction. An operational amplifier having a feedback diode coupled to a feedback branch or an input branch has a logarithmic or exponential-5 transmission characteristic. However, due to the strong temperature dependence of the diode characteristic, this too is strongly temperature dependent. Along with temperature dependence, there are also balancing problems because the characteristics of the various diodes are not exactly consistent, and thus the operation of several parallel amplifiers with a logarithmic or exponential characteristic is unsatisfactory.

It is therefore an object of the present invention to provide a switching arrangement having a logarithmic or antilogarithmic (exponential) transfer characteristic and in which the temperature stability is improved. It is a further object of the invention to provide an approximation of an arbitrary predetermined nonlinear transfer function - | a method in which the above-mentioned temperature problems do not occur. Finally, it is a further object of the invention to provide a lighting system in which

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: the luminosity can be varied to the satisfaction of the eye, depending on the linearly variable control variable.

The first object is solved by a coupling arrangement according to the specification of claim 1 by the features of claim 1. The second object mentioned is solved by the method according to the species · · of claim 9, by means of the features shown in its character part • ·: * · '. Finally, the third task mentioned is solved by claim 13: V. a lighting system according to the species definition by means of the patent claim 13 ·.

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An essential effect of the teachings according to the invention is that a temperature stability is now obtainable for a once-set nonlinear, in particular 3,105,620 logarithmic or antilogarithmic transfer curve. At the same time, the invention enables analog-to-digital or digital-to-analog conversion of an analog or digital input signal having the above-mentioned characteristic. The digital control variables can thus be converted to analog control variables and given to the control variables for analog controls or controls having a linear characteristic curve. Similarly, according to the invention, it is possible to switch from analog control variables to digitally controlled or tuned systems while guaranteeing a logarithmic or exponential characteristic.

Another essential effect of the invention is the possibility of equalization by a plurality of parallel lighting systems controlled by a single analog or digital control variable. In addition to improved dormancy, temperature stability is also an essential factor in maintaining the temporal stability of the various lighting systems and the '1' * dormancy.

It is also an object of the invention to provide: savings in the implementation of analog-to-digital or digital-to-analog converters. A related effect of the invention is the increased resolution * .t:: accuracy of the more sensitive area within the same measuring range. This is equivalent to compressing the available digital words with a small lower luminance range .....

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If we first start with a linear system, the • · · 10% change in the digital control word corresponds to, for example, a 10% change in the power supplied to the luminaire.

• · · · .., · 30 A 10% change in the control variable thus regularly produces a 10% change in power. This applies throughout the power control range. For digital control variables, the range of values that the control signal may have is determined by the number of bits in the digital word. For example, using 8 bits 4 105620 allows 256 different values for single-pole (0 ... + 256) control variables. Thus, corresponding to the above linear transfer characteristic curve, 256 possible powers and thus 256 possible luminance steps are also obtained.

However, due to the non-linear sensitivity of the human eye, this linear dependence is not observed as a linear change in luminance. The 1% change in luminance must always be directly related to the current luminance (nominal value), not to the maximum 10 luminance values. A 1% change in luminance at only 10% of the maximum luminance is thus equivalent to the required 0.1% change in luminance in one tenth of the maximum luminance. This requires a reduction in the brightness por-15 check at lower luminance values. However, in linear systems this can only be achieved by increasing the overall resolution, i.e. by increasing the bit width of the digital control words used. In addition to increasing the resolution of the lower ranges of V ', the resolution is increased by a linear characteristic

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and at the same time in the upper areas of light, to the greatest: to light. However, in higher-brightness areas, this resolution is not required, although .'j '; greater overall staging is sought. In addition, it unnecessarily increases costs. In the above i <t>; the example would have the required 0.1% • * luminance gradient at the lower end of the luminance range now also available at the upper end of the luminous region *. There, this has no effect.

According to the invention, the power stepping is now increased as the luminance increases. This is achieved in the simplest case by two intersecting lines having different slopes. Particularly advantageous is the continuous change of the stepping to produce an approximately exponential or anti-logarithmic transfer function. In addition to using control and control systems, the method of the invention and the switching arrangement of the invention may also be advantageously used in light metering systems or electronic pre-switching devices to control the brightness of gas discharge lamps. Similarly, with current phase surgery dimming, satisfactory dimming of the eye is possible by the present invention.

Note that the mathematically correct exponential function with an abscissa value of 0 has an ordinate value of 10 1. However, with the control, measurement and control characteristic of the method and the coupling arrangement according to the invention, the transfer function normally leaves the origin. This corresponds to an approximately exponentially displaced transmission characteristic. The transfer function having the logarithmic characteristic 15 is displaced horizontally with respect to this, so that it also leaves the origin.

In addition to the advantageous use of a switching arrangement having a logarithmic or anti-logarithmic characteristic, the two mentioned switching arrangements may also be advantageously used to save costs and facilitate the required digital solutions. These must then be mirrored; the analog-to-digital converter generates a logarithmic function on the input side, internally the control or control system operates (using logarithmic quantities) in a linear fashion, the output transmission characteristic is implemented as an anti-logarithmic, i.e., exponential. In this way, in-system: · 'technically laborious multiplications and divisions • · · * ... * 30 are made possible by simple additions and subtractions. Functionally, both switching- ···. the systems must then be considered to be • series connected, thereby linearizing their overall effect.

6 105620

Preferred embodiments of the coupling arrangement according to the invention and the method according to the invention are set forth in the subclaims. This applies in particular to the analog side of the input signal (analog-to-digital converter), or 5-side connecting analog output signal (digital-to-analog converter yl) converter concerned, the relevant reference input. Hereby, as far as possible, an approximation according to the human visual characteristic is achieved in a particularly advantageous manner.

10 The digital-to-analog converter and the analog-to-digital converter can receive both voltages and currents as reference signals. The same goes for analog inputs and outputs.

The invention will now be described with reference to the Examples. In the drawings, Figure 1 illustrates a first embodiment of the invention as an analog-to-digital converter (ADM) for transmitting between an analog input variable and a digital data word.

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'tofunction is approximately logarithmic,' '' Figure 2 shows another embodiment of the invention, • i ·. '· as a digital-to-analog converter (DAM), whereby the transfer function between digital input · · · · and analog output is: · Fig. 3 shows a linear stepped transmission characteristic of a conventional commercial ADM or 25 DAM and possible characteristics according to the invention, Figs. 4 and 4 show the analogue input of the converter in Figs. or a «··: ...: 30 detailed circuit diagram of a switching arrangement used to combine the output signal as a reference signal.

; · * ·. Figure 1 illustrates a conventional commercial ADM 20 to which an analog reference signal Vref • and an analog input signal V ^ n can be supplied. The ADM 20 is connected to the positive auxiliary voltage Vcc and to ground GND. At its output 7, the 105620 ADM 20 outputs digital data words Wout having a predetermined bit width, for example, 8 bits, 10 bits, or 12 bits. These data words Wout in the digital representation correspond to the analog input signal V ^ n, with reference to the reference signal Vref · used for the digital conversion, the ADM has other control interfaces for, inter alia, . The reference input interface-10 Vref is connected to the output of the analog summing element 10. The summing member 10 has two analog inputs, one of which is supplied with a reference voltage Vg or a corresponding reference current Ig and the other is supplied with an analog input signal V1 through the gain member k 11. The sum-15 spindle member 10 can, as mentioned, sum up either currents or voltages. Similarly, reference currents or reference voltages may be provided to the ADM reference input Vref.

... This depends on the ADM type.

'] The analog input signal V ^ n, which may be a control magnitude or a measurement signal, now first controls the ADM's 20 · analog input and, via the relay element 11, an analog • summing amplifier 10. This gives its output a weighted weight! the sum of the analog input signal k * V ^ n and the reference signal Vg. The linear transfer characteristic of ADMs, m · ·: * · *: ^ out = ^ max * ^ in / ^ 0 '(1) • ·: **, the analog input signal V ^ n is converted to the corresponding digital output format Wout when the A / D conversion is required via a single control wire.The maximum digital value Wmax depends on the resolution of the ADM. It is determined by the bit width of the word, 8 bits Wraax = 256, 10 bits Wmax = 1024. This is true for single-pole input signals 8 105620 V ^ n> 0. If a symmetric bipolar input signal is to be used, the maximum output amplitude is halved in each case. -reet t tends to be presented digitally.

5 With linear ADM, the ratio factor k = 0, so the reference signal Vref = Vg. This corresponds to a constant and constant reference value, in particular a temperature constant. The analogue input value V ^ n is converted, within the bounds 0 <ν ^ η <νisinβ £, to the corresponding digital 10 words Wout in linear steps. If k> 0 is selected, a reference voltage Vref, which depends on the input signal V ^ n, is generated alternately. It depends - depending on the size of k - more or less strongly on the input signal.

15 Wout = Vin / (Vref + k1Vin) (2) now defines the conversion of the analogue V ^ to the digital representation Wout. This shift characteristic, i.e. the shift "·, · '· function is non-linear. If k is then selected for k of the ratio 11 of the ratio element 20, then the shift characteristic:' v can be obtained for one segment of the logarithm function | V; good approximation.

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This is represented by the natural logarithm of • 2 ln (x) Taylor's power series development: 25 o.snn (x) - ^ 1 ... (3). : 30 It represents a series logic of a natural logarithm that • · · converges when x> 0.

• a 1 φ 9 · 2 • · · 9 105620

Horizontal shift x 'replaces (x + l) (4) 5 gives the displaced logarithm function according to the following equation (x ^ ignored) ln (x + 1) - 1 + 0> 5χ + 3 (i + o, 5x * (5) 10

When x <1, the cubic expression becomes irrelevant compared to the linear part. The first term of equation (5) then corresponds to (2), whereby the transfer function of the ADM 20 coupled to the ratio element 11 and 15 to the summing amplifier 10 approximates the displaced logarithm function.

Other values of k can be used to approximate log slope functions with other slope or other nonlinear transfer functions r i · '. In dimensioning k, only the maximum value of the reference voltage Vref shall be taken into account. This must not be exceeded at the maximum input voltage V ^ n · '· * and the predetermined reference signal Vq. In this case, • i can be both the reference voltage Vq and the ratio factor k other /: *. wide limits.

Similarly, as described in Figure 1. generating a logarithmic transfer function to "mirror" the digital-to-analog converter (DAM) 30 of FIG. 2 ... to generate an antilogarithmic, or exponential, transfer characteristic. DAM 30 also has a reference input then. •; ***; 30 Vref and the control and ··· state inputs and outputs already described in connection with Figure 1. In Figure 2, only • · «·„; the direction of the data stream transmitting data is reversed. DAM: lie * · 'input digital data and output an analog output signal Vout. This, in turn, is supplied via a ratio 10 105620 by means 11 and a summing amplifier 10 to a comparator input Vref. As shown in Fig. 1, a reference voltage Vq is supplied to the summing amplifier 10 as a second input signal. In turn, it represents the sum of its 5 input signals. DAM 30 has an almost linear transmission characteristic compared to ADM 20. Here the ^ out = vref * Win / (Wmax + 1) vout "vref * ^ in / wmax (6) 10 The digital input data W ^ n is converted to analog output Vout according to (6). Wmax corresponds to that already shown in Figure 1. k = 0 provides a linear transmission characteristic, each digital input signal W 1 is converted to a linear 15 transmission characteristic (shown in Figure 3). appearing digital

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The effect of the V '· bit. This corresponds to an exponential 20 transfer characteristic ♦ • «•« · »V V ^ out = (v0 + ^ * vout) * Win / (wmax + 1) (7)«

With a value of k = 0.5, the power series development presented in connection with (3), (4) and (5) above is now mirrored. approximately an exponential transfer characteristic. This • · ... is the horizontal displacement corresponding to (4), now mirrored • vertically.

·· Ϊ '·· With increasing value of k, the transfer function formed by DAM 30 becomes steeper. As k approaches 0, the transfer characteristic approaches the linear transfer function of (6).

Such linear transfer characteristic is shown in Fig. 3 t · "stepwise.

11 105620

Figure 3 then shows, depending on whether the digital input signal is selected or the analog input signal, the idealized transfer function of ADM 20 (analog input signal on the abscissa) or DAM 30 (digital input signal 5 Win on the ordinate axis). Depending on the type of input signal selected, the corresponding digital or analog display format can be read from the second axis. The dashed lines depict two functions a) and b) corresponding to the transfer functions that can be accomplished by the coupling according to Figure 1 or Figure 2, a) representing the approximately logarithmic transfer function of the ADM 20 with summing amplifier 10 and ratio element 11. If kADM increases, the transmission characteristic loive-nee direction of the arrow.

Similarly, the transfer characteristic b) shows the approximately exponential transfer characteristic of the DAM 30 having the same summing amplifier 10 and the ratio element 11 of Figure 2. As kDAM increases, the plotted exponential transfer characteristic of ex-V 'becomes steeper.

Each function a) and b) approximates at k = 0 r (<< '1; ideal linear and stepwise converter characteristic' ').

«I> ·: A value of k = 0.5 gives a particularly advantageous transmission characteristic p <t> for each of the uses of Figures 1 and 2 for lighting, measuring, control and control purposes; curve (transfer function). If such a system • 9 ... uses both the analog / digital input • i · * of Figure 1. 2 to the digital / analog output j '·· conversion of Figure 2, the corresponding values of k 30 of the input and output conversion should be substantially equal. In this case, both characteristics a) and b) are mirror symmetric.

• <', .1 Both transfer characteristics, both of Fig. 1 and * · of Fig. 2, i.e., functions a) and b) in Fig. 3, start from the origin. This corresponds, according to (4), to a horizontal displacement of a logarithmic function and a vertical displacement of an approximately exponential function. Each function begins at the origin with a slope of approximately 45 °. If it is now desired to change the initial inclination, this can be achieved by selecting a voltage Vg or by varying the weight of the predetermined V0 in kg (fraction of Vg). Reducing the value of Vg or the fraction of Vg relative to a predetermined (datasheet) value of ADM 20 increases the initial inclination (in the origin) of the function a) of FIG. Similarly, the reduction of the reference voltage Vg of the DAM 30 relative to the value provided by the datasheet or the reduced weighting in the summing amplifier 10 reduces the initial inclination of the function b) of Figure 3.

By matching the ratio of the reduced / increased reference voltage 15 Vg to the ratio analogue input voltage Vin weighted by the ratio element 11 (ratio factor k), both the slope of its approximately logarithmic function a) and its maximum terminal value can be set. In this way, with the maximum analog input value 20 Vmax, it becomes possible to achieve the largest digital output word Wmax; with approximately a logarithmic characteristic. If the greatest «t i .'i; ' input voltage V ^ n = Vmax and if the nominal reference voltage • * 'Vref = 0 V' ni * n preferably the reduced reference voltage factor in kg is determined by the following equation • · · 25 ^ * ^ max + ^ 0 * ^ 0® ^ ref0 • e · · · 5, · 'vref0 represents the nominal value of the reference voltage Vref (the value given by the data ·· * leaf).

* »· * ... t 30 The above applies mutatis mutandis to the switching arrangement of Fig. 2; this is affected by the function b) of Fig. 3, whose initial inclination in the origin is «« «reduced compared to the linear transfer characteristic, whereby the same largest digital data word 13 105620 win = wmax the analog value vout at the DAM 30 output corresponds to the nominal or maximum value Vmax. Thus, in both of the latter cases, no loss of resolution is lost, and Wmax or Vmax is achieved in each of the 5 cases.

Finally, Fig. 4 shows a switching example for the ratio element 11 and the summing element 10 which generate the necessary variable reference voltage Vref. The analog input or output signal controls the inverting input of the operational amplifier 12 via a series connection of resistor R and potentiometer 10 r. In addition, a current Iq = Vq / R is supplied to the inverting input. The output of the operational amplifier 12 is connected via a second resistor R to a reversing input. At the output of the inverting summing amplifier 15 so connected, there is a sum of the reference voltage Vq and the weighted analog input or output voltage. When R = T, the ratio factor k = 0.5 described above is particularly advantageous. In the event that the inverted voltage signal at the output of the ADM 20 or DAM 30 operation amplifier::: 20 must be supplied in the form of a positive voltage or current, a second operational amplifier 13 may be connected thereafter. the two resistors R, which are the input and back • a switching resistors, switch • · # · ... so that its gain is -1. Its output • · · 25 controls either directly or via an added resistor. The reference voltage input Vref of the ADM 20 or the DAM 30 or the reference current input Iref. Preferably, in addition, V * can be used to filter the reference voltage signal Vref or the reference current signal Iref. This will even out the potential. 30 jumps to the coupled nonlinear ADM 20 or DAM

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30 transfer functions. Filtering can take place on an operational • i «* it | ' a feedback capacitance R of the timer 13 by means of a filter capacitor «· * ·· * connected in parallel; this filtering capacitor may also be connected in parallel with the operation resistor R of the operation amplifier 12.

Another advantageous conversion filtering only the variable part of the reference voltage signal Vref is provided by a T-filter at the input of the operational amplifier. Hereby, a second input of the filtering capacitor is connected between resistor R and potentiometer T, which in series forms a connection between the analog input or output signal ν ^ η, νουΐ and the inverse 10 of the operation amplifier 12. Its other input is connected to ground.

In a lighting system where power control is performed by means of an electronic pre-switching device (EVG), the switching arrangement of Figure 1 and Figure 2 can advantageously be used. The power control performed in the EVG generates the power supplied to the luminaire (gas discharge lamp). This is accomplished by conventional lamp-load circuits, which are series resonant circuits, by the change in the frequency of the output AC voltage output by the EVG. Power control requires reference setpoint comparison.

• ♦ · «This is performed with a predetermined reference power PQhje Ja. . with the actual output power P0i0 from the lamp or EVG · If (i * assume that the conditions are completely linear, ie.

· • · * that the EVG has a linear control characteristic, * * 25 predefined reference power gives the lamps a linear power output according to the linear V * dependence. This does not correspond to the human sense of light.

*! **! Therefore, a switching arrangement according to Fig. 2 can advantageously be connected to the reference channel. This has an approximate exponential curve of 30 to achieve • · · Satisfactory - according to human perception * t '·; · adjusted - luminance change. In this case, the setpoint can be given digitally, after DAM 30 of FIG. 2, an analog control variable occurs, which is then applied to an analog power control circuit including the 105620 EVG. It is preferable that the digital actual value be adjustable and that the conventional analog control circuit operates on the basis of an analog setpoint (polo) reference. This is particularly practical because the measured power is usually available as an analogue P010

Another advantageous variant - used in the switching arrangement of Figure 2 - is a digital setpoint comparison. In this case, the digital reference PDhp is given "subtracting the digital actual value P0i0 · The difference in the digital format now controls the EVG and the inverter in the EVG. This is particularly advantageous when the inverter is error-prone and its output frequency can be determined 15 digitally adjustable VCOs (voltage controlled oscillator) or digital counter controlled frequency generator.

Similarly, the measured analog output power is converted to a digital measurement value P0lo1 with the ADM · / ": 20 20 by the ADM · containing the summing element 10 and the ratio element 11. The measurement value thus has an approximate logarithmic characteristic. through the influence of the actual channel v ·.

... 25 The above-described control technical coupling arrangements • · · * · 1 1 constitute preferred embodiments. Changes in the resulting wiring diagrams are possible within the purely control mode transformations and are therefore not • • · ϊ.ϊ explained separately.

·· • · • · ·,, Ml «1« · * · • • • · ««

Claims (10)

16 105620 A switching arrangement for approximating a logarithmic or antilogarithmic transfer function to provide a digital-to-analogue conversion having an approximate logarithm or antilogarithmic transmission characteristic of a digital 5 input signal (Win), characterized in that the digital-to-analog converter (DÄM, 30) has an analog comparator (Vref) and a digital / binary (Win) input signal, the converter (20,30) generates an analog output signal (Vout) based on a substantially linear converter characteristic, 15 linear converters (30) are given a non-constant, analog output signal (Vout) a dependent reference variable (Vref), and an amplifier circuit controlled by an analog output signal (Vout) is provided, the output voltage (Vout) 20 of which provides both a analog output signal (Vout) and a feedback signal for analogue: · ··· (Vre £). • · • · · · · · · · The switching arrangement according to claim 1, characterized in that the non-constant reference variable (Vref) comprises a first part which is a constant reference variable (V0) when the switching arrangement is used and a second part which is a switching arrangement. when · ·, ···, the portion (k) of the variable output signal «« * t 30 (Vout) of the respective converter (30). A switching arrangement according to claim 2, characterized in that the first portion is substantially one and that the second portion (k) is substantially 105620 ti 0.5 to form a switching arrangement. (10,11,30) a substantially logarithmic or antilogarithmic transfer function curve. A switching arrangement according to any one of the preceding claims, characterized in that a summing circuit (10,11,12,13; 1) is used which provides the converter (30) with an analog reference variable (Vref) while supplying to it (1) an analog output signal 10 (Vout), the input amplitude of which is set by the first fixed resistor (R) and the adjustable resistor (T), so that the constant reference value (V0) through the second fixed resistor (R). A switching arrangement according to claim 4, characterized in that the summing switching arrangement (1) comprises a first summing amplifier / operational amplifier (12) for generating a current or voltage sum of the first and second portions of the reference variable (Vref) and depending on the reference magnitude required by the converter (30); ·; a reel (Vref) sign after the first amplifier (12) is coupled to a rotating second amplifier (13), «· • V. preferably having a gain of -1, whereby either the first amplifier (12) or the second amplifier (12) gives / r. to the converter (30), an analog or voltage reference analog (Vref) of the voltage or current signal. Coupling arrangement according to Claim 4 or Claim 5 ii ·, characterized in that the resistance value of the adjustable resistor (T) • · · * substantially corresponds to the resistance value of the first and second fixed resistances (R) of equal value or resistor: V (T) is the third equivalent fixed resistor (R). «· · • · • ·« «« 18 105620 A switching arrangement according to claim 4, characterized in that the analog output signal (Vout) 5 of the converter (30) consists of an output current and the amplifier is coupled to a current to voltage converter. The switching arrangement according to claim 4, characterized in that the summing switching arrangement (1) in the digital-to-analog converter (30) formed by the output current of the analog output signal (Vout) comprises a first amplifier (12) coupled to a current voltage converter and , a second amplifier (13) for the output signal portion of the first amplifier (12) and the portion of the reference variable (V0) as summing amplifier, wherein the gain determining factors are selected by fixed resistors (R) and / or adjustable resistors (T). , 30) 20 gives an approximate exponential dependence between the 4 4 4 · · · · digital input signal (Win) and the analog output voltage (Vout) provided by the first amplifier (12). • · • · * 4 · * · • · An illumination system, wherein the luminance (Polo) of one or more of the light sources, in particular one or more gas discharge lamps, is controlled or adjusted depending on the luminous or power reference (Bottom), characterized in that 4; The 30 luminance reference (Bottom) or actual size (Polo) are controlled by the switching arrangement according to claim 1. • · · 4 4 4 • · • · · • 4 105620 10. Lighting system according to claim 9, characterized in that, in power control, either the linearity of the power reference (Base) is changed to non-linear, in particular 5 exponential, or the linearity of the power (Polo) is changed, in particular to logarithm. • * · »· · • a a * m a • a • a a • · · • a a • a a • • a a #« «I I p t 2t ° k 105620