Patent Publication Number: US-9892682-B2

Title: Electroluminescent display device for reducing color distortion of low gray values and method of operating same

Description:
This application claims priority to Korean Patent Application No. 10-2015-0084503 filed on Jun. 15, 2015, and all the benefits accruing therefrom under 35 U.S.C. § 119, the content of which in its entirety is herein incorporated by reference. 
     BACKGROUND 
     1. Field 
     Exemplary embodiments of the invention relate to a display device, and more particularly to an electroluminescent display device for reducing color distortion of low gray values and a method of operating the electroluminescent display device. 
     2. Discussion of the Related Art 
     Recently, various display devices such as a liquid crystal display (“LCD”), a plasma display, and an electroluminescent display have gained popularity. Particularly, the electroluminescent display can be driven with quick response speed and reduced power consumption, using a light-emitting diode (“LED”) or an organic light-emitting diode (“OLED”) that emits light through recombination of electrons and holes. 
     As the electroluminescent display device is manufactured, an image quality of an end product (i.e., complete product) of the electroluminescent display device may not reach a target quality level because of deviations in a manufacturing process. In this case, the end product may be determined as a defective product, and the defective product may be discarded. However, discarding all end products determined as defective products is not efficient. Therefore, a post-correction for adjusting the image quality of the organic light emitting display device to reach the target quality level is required. Thus, a multi-time programmable (“MTP”) operation for repeatedly performing the post-correction in luminance and color coordinate for respective pixel circuits is performed in order to adjust the image quality of the electroluminescent display device to reach the target quality level. 
     The MTP operation may be performed by storing the respective gamma offsets based on comparison between a reference gamma curve and respective actual gamma curves that are generated based on a pixel gamma curve. 
     SUMMARY 
     It is difficult to implement a brightness of low gray values because a detecting device used in the manufacturing device has a limited sensitivity to the brightness. Accordingly color distortion of the low gray values may occur and thus the image quality of the display device may be degraded. 
     At least one exemplary embodiment of the invention provides a method of operating an electroluminescent display device capable of reducing color distortion of low gray values. 
     At least one exemplary embodiment of the invention provides an electroluminescent display device capable of reducing color distortion of low gray values. 
     According to exemplary embodiments, a method of operating an electroluminescent display device, includes, determining a first gamma offset corresponding to a first gamma reference voltage by performing a multi-time programmable (“MTP”) operation with respect to a first reference gray value, determining a second gamma offset corresponding to a second gamma reference voltage by performing the MTP operation with respect to a second reference gray value greater than the first reference gray value, determining a base gamma offset by performing the MTP operation with respect to a base reference gray value smaller than the first reference gray value and generating low gray voltages corresponding to low gray values smaller than the first reference gray value based on the base gamma offset, the first gamma offset and the second gamma offset. 
     In an exemplary embodiment, generating the low gray voltages may include determining a slope factor representing a trend of the low gray voltages based on the base gamma offset, the first gamma offset and the second gamma offset. 
     In an exemplary embodiment, the low gray voltages may be determined by performing an extrapolation of the first gamma reference voltage and the second gamma reference voltage using the slope factor as a weight value. 
     In an exemplary embodiment, generating the low gray voltages may further include calculating a minimum gamma reference voltage corresponding to a minimum reference gray value smaller than the base reference gray value based on the slope factor, the first gamma reference voltage and the second gamma reference voltage. 
     In an exemplary embodiment, generating the low gray voltages may further include generating the minimum gamma reference voltage based on a minimum gamma offset corresponding to the calculated minimum gamma reference voltage, generating the first gamma reference voltage based on the first gamma offset and generating the low gray voltages corresponding to the low gray values between the minimum reference gray value and the first reference gray value by linearly dividing the minimum gamma reference voltage and the first gamma reference voltage. 
     In an exemplary embodiment, the minimum reference gray value may correspond to a gray value of 1. 
     In an exemplary embodiment, a gray voltage corresponding to a gray value of 0 may have a fixed voltage regardless of the MTP operation. 
     In an exemplary embodiment, the minimum reference gray value may correspond to a gray value of 0. 
     In an exemplary embodiment, the slope factor may include a red slope factor corresponding to red pixels, a green slope factor corresponding to green pixels and a blue slope factor corresponding to blue pixels. 
     In an exemplary embodiment, each of the red slope factor, the green slope factor and the blue slope factor may include a plurality of values corresponding to a plurality of temperature intervals. 
     In an exemplary embodiment, each of the red slope factor, the green slope factor and the blue slope factor may include a plurality of values corresponding to a plurality of dimming brightness intervals. 
     According to exemplary embodiments, an electroluminescent display device includes a display panel including a plurality of pixels connected to a plurality of data lines, a gamma circuit and a data driver. The gamma circuit stores a plurality of gamma offsets corresponding to a plurality of gamma reference voltages. The gamma offsets is determined by performing a MTP operation with respect to a plurality of reference gray values. The gamma circuit generates the gamma reference voltages based on the stored gamma offsets. The data driver generates a plurality of gray voltages based on the gamma reference voltages, and drives the data lines based on image data and the gray voltages. The electroluminescent display device generates low gray voltages corresponding to low gray values based on a first gamma offset corresponding to a first reference gray value, a second gamma offset corresponding to a second reference gray value greater than the first reference gray value and a base gamma offset corresponding to a base reference gray value smaller than the first reference gray value. The low gray values are smaller than the first reference gray value. 
     In an exemplary embodiment, the gamma circuit may include a storage unit which stores and provides the base gamma offset, the first gamma offset and the second gamma offset, a calculation unit and a voltage generation block. The calculation unit may determine a slope factor based on the base gamma offset, the first gamma offset and the second gamma offset, where the slope factor represents a trend of the low gray voltages corresponding to the low gray values. The calculation unit may calculate a minimum gamma reference voltage corresponding to a minimum reference gray value smaller than the base reference gray value based on the slope factor, a first gamma reference voltage corresponding to the first gamma offset and a second gamma reference voltage corresponding to the second gamma offset, and may provide a minimum gamma offset corresponding to the calculated minimum gamma reference voltage. The voltage generation block may generate the minimum gamma reference voltage, the first gamma reference voltage and the second gamma reference voltage based on the minimum gamma offset, the first gamma offset and the second gamma offset. 
     In an exemplary embodiment, the data driver may generate the low gray voltages corresponding to the low gray values between the minimum reference gray value and the first reference gray value by linearly dividing the minimum gamma reference voltage and the first gamma reference voltage. 
     In an exemplary embodiment, the minimum reference gray value may correspond to a gray value of 1. 
     In an exemplary embodiment, a gray voltage corresponding to a gray value of 0 may have a fixed voltage regardless of the MTP operation. 
     In an exemplary embodiment, the minimum reference gray value may correspond to a gray value of 0. 
     In an exemplary embodiment, the slope factor may include a red slope factor corresponding to red pixels, a green slope factor corresponding to green pixels and a blue slope factor corresponding to blue pixels. 
     In an exemplary embodiment, each of the red slope factor, the green slope factor and the blue slope factor may include a plurality of values corresponding to a plurality of temperature intervals. 
     In an exemplary embodiment, each of the red slope factor, the green slope factor and the blue slope factor may include a plurality of values corresponding to a plurality of dimming brightness intervals. 
     The electroluminescent display device and the method of operating the electroluminescent display device according to exemplary embodiments may reduce color distortion of low gray values and enhance image quality of the electroluminescent display device by determining the slope factor representing trend of the low gray voltages based on the base gamma offset that is obtained through the MTP operation and by generating the low gray voltages based on the slope factor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments of the invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings. 
         FIG. 1  is a flow chart illustrating a method of operating an electroluminescent display device according to exemplary embodiments. 
         FIG. 2  is a block diagram illustrating an electroluminescent display device according to exemplary embodiments. 
         FIG. 3  is a circuit diagram illustrating an example of a pixel included in the electroluminescent display device of  FIG. 2 . 
         FIG. 4  is a block diagram illustrating an exemplary embodiment of a gamma circuit included in the electroluminescent display device of  FIG. 2 . 
         FIG. 5  is a block diagram illustrating an exemplary embodiment of a data driver included in the electroluminescent display device of  FIG. 2 . 
         FIG. 6  is a diagram illustrating exemplary embodiments of a gamma circuit. 
         FIGS. 7A and 7B  are diagrams for describing an operation of the gamma circuit of  FIG. 6 . 
         FIG. 8  is a diagram illustrating exemplary embodiments of a gamma circuit. 
         FIGS. 9A and 9B  are diagrams for describing an operation of the gamma circuit of  FIG. 8 . 
         FIGS. 10A and 10B  are diagrams for describing an effect of exemplary embodiments of reducing color distortion of low gay values according t. 
         FIG. 11  is a diagram illustrating an example mapping relation between gamma offsets and gamma reference voltages. 
         FIG. 12  is a block diagram illustrating exemplary embodiments of an electroluminescent display device. 
         FIG. 13  is a circuit diagram illustrating an example of a pixel included in the electroluminescent display device of  FIG. 12 . 
         FIG. 14  is a block diagram illustrating exemplary embodiments of a mobile device. 
         FIG. 15  is a block diagram illustrating exemplary embodiments of an interface included in a mobile device. 
         FIG. 16  is a block diagram illustrating an electronic device including exemplary embodiments of a display device. 
     
    
    
     DETAILED DESCRIPTION 
     The exemplary embodiments are described more fully hereinafter with reference to the accompanying drawings. Like or similar reference numerals refer to like or similar elements throughout. 
     The invention now will be described more fully hereinafter with reference to the accompanying drawings, in which various embodiments are shown. This invention may, however, be embodied in many different forms, and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like reference numerals refer to like elements throughout. 
     It will be understood that when an element is referred to as being “on” another element, it can be directly on the other element or intervening elements may be therebetween. In contrast, when an element is referred to as being “directly on” another element, there are no intervening elements present. 
     It will be understood that, although the terms “first,” “second,” “third” etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another element, component, region, layer or section. Thus, “a first element,” “component,” “region,” “layer” or “section” discussed below could be termed a second element, component, region, layer or section without departing from the teachings herein. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms, including “at least one,” unless the content clearly indicates otherwise. “Or” means “and/or.” As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. It will be further understood that the terms “comprises” and/or “comprising,” or “includes” and/or “including” when used in this specification, specify the presence of stated features, regions, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, regions, integers, steps, operations, elements, components, and/or groups thereof. 
     Furthermore, relative terms, such as “lower” or “bottom” and “upper” or “top,” may be used herein to describe one element&#39;s relationship to another element as illustrated in the Figures. It will be understood that relative terms are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. In an exemplary embodiment, when the device in one of the figures is turned over, elements described as being on the “lower” side of other elements would then be oriented on “upper” sides of the other elements. The exemplary term “lower,” can therefore, encompasses both an orientation of “lower” and “upper,” depending on the particular orientation of the figure. Similarly, when the device in one of the figures is turned over, elements described as “below” or “beneath” other elements would then be oriented “above” the other elements. The exemplary terms “below” or “beneath” can, therefore, encompass both an orientation of above and below. 
     “About” or “approximately” as used herein is inclusive of the stated value and means within an acceptable range of deviation for the particular value as determined by one of ordinary skill in the art, considering the measurement in question and the error associated with measurement of the particular quantity (i.e., the limitations of the measurement system). For example, “about” can mean within one or more standard deviations, or within ±30%, 20%, 10%, 5% of the stated value. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the invention, and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     Exemplary embodiments are described herein with reference to cross section illustrations that are schematic illustrations of idealized embodiments. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments described herein should not be construed as limited to the particular shapes of regions as illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. In an exemplary embodiment, a region illustrated or described as flat may, typically, have rough and/or nonlinear features. Moreover, sharp angles that are illustrated may be rounded. Thus, the regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the precise shape of a region and are not intended to limit the scope of the claims. 
       FIG. 1  is a flow chart illustrating a method of operating an electroluminescent display device according to exemplary embodiments. 
     Referring to  FIG. 1 , a first gamma offset OFS 1  (refer to  FIGS. 4 and 6 ) corresponding to a first gamma reference voltage GRV 1  (refer to  FIG. 4 ) is determined by performing a multi-time programmable (“MTP”) operation with respect to a first reference gray value RG 1  (refer to  FIG. 7A ) (S 100 ). A second gamma offset OFS 2  (refer to  FIGS. 4 and 6 ) corresponding to a second gamma reference voltage GRV 2  (refer to  FIG. 4 ) is determined by performing the MTP operation with respect to a second reference gray value RG 2  (refer to  FIG. 7A ) greater than the first reference gray value RG 1  (S 200 ). A base gamma offset OFSb (refer to  FIG. 6 ) is determined by performing the MTP operation with respect to a base reference gray value RGb (refer to  FIG. 7A ) smaller than the first reference gray value RG 1  (S 300 ). 
     Hereinafter, the first reference gray value RG 1  and the second reference gray value RG 2  associated with low gray voltages are mainly described, and the other reference gray values such as the third reference gray value, the fourth reference gray value, etc. may be described only when they are necessary. 
     In an exemplary embodiment, as illustrated in  FIGS. 6 and 7A , the first reference gray value RG 1  may be 11, the second reference gray value RG 2  may be 23 and the base reference gray value RGb may be 7, for example. The first reference gray value RG 1  and the second reference gray value RG 2  may be set to proper values for implementing a gamma curve of the electroluminescent display device. The base reference gray value RGb may be set to a gray value corresponding to a minimum brightness that may be sensed by a detecting device used in the manufacturing process of the electroluminescent display device. 
     Low gray voltages corresponding to low gray values smaller than the first reference gray value RG 1  may be generated based on the base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2  (S 400 ). In exemplary embodiments, as will be described below, a slope factor SF representing a trend of the low gray voltages may be determined based on the base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2 , and the low gray voltages may be generated based on the slope factor SF (refer to equation 2 below). 
     As will be described with reference to  FIGS. 10A and 10B , according to the conventional method, a gamma offset corresponding to a minimum reference gray value (e.g. a gray value of 3) near a gray value of zero may be estimated or presumed to generate a minimum gamma reference voltage, and the low gray voltages may be generated based on the estimated minimum gamma reference voltage. It is not easy to estimate the minimum gamma reference voltage exactly and the color distortion occurs with respect to the low gray values to degrade the image quality. The electroluminescent display device and the method of operating the electroluminescent display device according to exemplary embodiments may reduce color distortion of low gray values and enhance image quality of the electroluminescent display device by determining the slope factor representing trend of the low gray voltages based on the base gamma offset that is obtained through the MTP operation and by generating the low gray voltages based on the slope factor. 
       FIG. 2  is a block diagram illustrating an electroluminescent display device according to exemplary embodiments. 
     Referring to  FIG. 2 , an electroluminescent display device  100  may include a display panel  110 , a timing controller TMC  120 , a data driver DDRV  130 , a scan driver SDRV  140 , a power supply circuit  150  and a gamma circuit GMC  200 . Even though not illustrated in  FIG. 2 , the electroluminescent display  100  may further include a buffer for storing image data to be displayed, etc. 
     The display panel  110  includes a plurality of pixels PX or pixel circuits disposed in rows and columns. In an exemplary embodiment, the pixels PX may be arranged in a matrix form of n rows and m columns as illustrated in  FIG. 2 , for example. The display panel  110  is connected to the data driver  130  through data lines D 1  to Dm, and to the scan driver  140  through scan lines S 1  to Sn. The display panel  110  is connected between a first power node NP 1  and a second power node NP 2  to be powered by the power supply circuit  150 . 
     The power supply circuit  150  may operate based on control signals CTRL, and at least a portion of the control signals CTRL may be provided from the timing controller  120 . The power supply circuit  150  may include a first voltage converter VCON 1  and a second voltage converter VCON 2 . In an exemplary embodiment, an input voltage Vin provided to the power supply circuit  150  may be a direct current (“DC”) voltage such as a battery voltage, and the first and second voltage converters VCON 1  and VCON 2  may be DC-DC converters. The first voltage converter VCON 1  generates a first power supply voltage ELVDD having a positive voltage level based on the input voltage Vin to drive the first power node NP 1  with the first power supply voltage ELVDD. The second voltage converter VCON 2  generates a second power supply voltage ELVSS having a negative voltage level based on the input voltage Vin or generates a ground voltage Vg to drive the second power node NP 2  with the second power supply voltage ELVSS or the ground voltage Vg. 
     The gamma circuit  200  may generate a plurality of gamma reference voltages GRV based on a regulator voltage VREG. In an exemplary embodiment, the regulator voltage VREG may be the first power supply voltage ELVDD itself or another voltage that is generated based on the first power supply voltage ELVDD, for example. The gamma circuit  200  may store a plurality of gamma offsets OFS corresponding to a plurality of gamma reference voltages GRV where the gamma offsets OFS are determined by performing a multi-time programmable (“MTP”) operation with respect to a plurality of reference gray values. The gamma circuit  200  may generate the gamma reference voltages GRV based on the stored gamma offsets OFS. 
     In exemplary embodiments, the gamma circuit  200  may generate a minimum gamma reference voltage GRVc (refer to  FIG. 6 ) based on a first gamma offset OFS 1  (refer to  FIGS. 4 and 6 ) corresponding to a first reference gray value RG 1  (refer to  FIG. 7A ), a second gamma offset OFS 2  (refer to  FIGS. 4 and 6 ) corresponding to a second reference gray value RG 2  (refer to  FIG. 7A ) greater than the first reference gray value RG 1  and a base gamma offset OFSb corresponding to a base reference gray value RGb smaller than the first reference gray value RG 1 . As will be described with reference to  FIGS. 6 through 9 , the minimum gamma reference voltage GRVc may correspond to a gray value of 0 or a gray value of 1. 
     The data driver  130  may provide data signals to the display panel  110  through the data lines D 1  to Dm. The data driver  130  may generate a plurality of gray voltages based on the gamma reference voltages GRV, and may drive the data lines D 1  to Dm based on image data and the gray voltages. 
     As such, the gamma circuit  200  and the data driver  130  may generate the minimum gamma reference voltage GRVc based on the base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2 , thereby reducing the color distortion of the low gray values and enhancing the image quality of the electroluminescent display device  100 . 
     The scan driver  140  may provide row control signals to the display panel  110  through the scan lines S 1  to Sn. The pixels PX may be located where the data lines D 1  to Dm and the scan lines S 1  to Sn cross. The timing controller  120  may control overall operations of the electroluminescent display  100 . The timing controller  120  can provide control signals to control the display unit  110 , the data driver  130 , the scan driver  140 , the power supply circuit  150  and the gamma circuit  200 . 
     In some embodiments, the timing controller  120 , the data driver  130 , the scan driver  140 , the power supply circuit  150  and the gamma circuit  200  may be implemented as a single integrated circuit (“IC”). In other embodiments, the timing controller  120 , the data driver  130 , the scan driver  140 , the power supply circuit  150  and the gamma circuit  200  may be implemented as two or more ICs. 
       FIG. 3  is a circuit diagram illustrating an example of a pixel included in the electroluminescent display device of  FIG. 2 . 
     Referring to  FIG. 3 , each pixel PX may include a switching transistor ST, a storage capacitor CST, a driving transistor DT, and an organic light-emitting diode (“OLED”). Each of the red sub pixel R, the green sub pixel G and the green sub pixel B may have the configuration as illustrated in  FIG. 3 . 
     The switching transistor ST includes a first source/drain terminal connected to a data line, a second source/drain terminal connected to the storage capacitor CST, and a gate terminal connected to the scan line. The switching transistor ST transfers a data signal DATA received from the data driver  130  to the storage capacitor CST in response to a scan signal SCAN received from the scan driver (also referred to as “gate driver”)  140 . 
     The storage capacitor CST has a first electrode connected to a high power supply voltage ELVDD and a second electrode connected to a gate terminal of the driving transistor DT. The storage capacitor CST stores the data signal DATA transferred through the switching transistor ST. 
     The driving transistor DT has a first source/drain terminal connected to the high power supply voltage ELVDD, a second source/drain terminal connected to the OLED, and the gate terminal connected to the storage capacitor CST. The driving transistor DT is turned on or off according to the data signal DATA stored in the storage capacitor CST. 
     The OLED has an anode electrode connected to the driving transistor DT and a cathode electrode connected to a low power supply voltage ELVSS. The OLED emits light based on a current flowing from the high power supply voltage ELVDD to the low power supply voltage ELVSS while the driving transistor DT is turned on. 
       FIG. 4  is a block diagram illustrating an exemplary embodiment of a gamma circuit included in the electroluminescent display device of  FIG. 2 . 
     Referring to  FIG. 4 , a gamma circuit  200  may include an MTP processing unit MPU  220  and a voltage generation block VGB  250 . 
     The MTP processing unit  220  may store a base gamma offset OFSb and first through p-th gamma offsets OFS 1  to OFSp that are determined by performing the MTP operation, and may provide a minimum gamma offset OFSc and the first through p-th gamma offsets OFS 1  to OFSp based on the stored gamma offsets OFSb and OFS 1  to OFSp, where p is a positive integer. The voltage generation block  250  may generate a minimum gamma reference voltage GRVc and first through p-th gamma reference voltages GRV 1  to GRVp based on the minimum gamma offset OFSc and the first through p-th gamma offsets OFS 1  to OFSp. Exemplary embodiments of the gamma circuit  200  will be described below with reference to  FIGS. 6 through 9 . 
       FIG. 5  is a block diagram illustrating an exemplary embodiment of a data driver included in the electroluminescent display device of  FIG. 2 . 
     Referring to  FIG. 5 , a data driver  130  may include a shift register S/R  132 , a gray voltage generator GVG  134  and a digital-to-analog converter D/A  136 . 
     The gray voltage generator  134  may generate first through (q+1)-th gray voltages V 0  to Vq based on the gamma reference voltages GRVc and GRV 1  to GRVp from the gamma circuit  200 , where q is a positive integer. In an exemplary embodiment, the gray voltage generator  134  may include one or more resistor strings, each linearly dividing two gamma reference voltages, to generate the gray voltages V 0  to Vq, for example. In an exemplary embodiment, when the image data is comprised of eight bits, the number (q+1) of the gray values 0 to q and the gray voltages V 0  to Vq may be 256, for example. 
     The digital-to-analog converter  136  may include a plurality of conversion units D/A receiving the gray voltages V 0  to Vq. Each conversion unit D/A may select, among the gray voltages V 0  to Vq, the one gray voltage corresponding to the digital data bit received from the shift register  132  to driver the corresponding data line of the data lines D 1  to Dm. 
     The shift register  132  may receive the image data and control signal CONTROL from the timing controller  120  in  FIG. 2  and may output respective data bits of the image data to the conversion units D/A corresponding to the data lines D 1  to Dm, respectively. 
       FIG. 6  is a diagram illustrating a gamma circuit according to exemplary embodiments, and  FIGS. 7A and 7B  are diagrams for describing an operation of the gamma circuit of  FIG. 6 . 
     Referring to  FIG. 6 , a gamma circuit  200   a  may include an MTP processing unit and a voltage generation block  250   a . The MTP processing unit may include a storage unit  222   a  and a calculation unit MCU  224   a.    
       FIG. 6  illustrates a non-limiting example of eight reference gray values 11, 23, 35, 51, 87, 151, 203 and 255, eight gamma offsets OFS 1  to OFS 8  and eight gamma reference voltages GRV 1  to GRV 8 , but the number of them may be changed variously. 
     The storage unit  222   a  may store and provide a base gamma offset OFSb, and a plurality of gamma offsets OFS 1  to OFS 8 . The storage unit  222   a  may include a plurality of memory units Mb and M 1  to M 8  to store the respective gamma offsets. In an exemplary embodiment, as illustrated in  FIGS. 6, 7A and 7B , the base reference gray value RGb may be 7, the first reference gray value RG 1  may be 11 and the second reference gray value RG 2  may be 23. The reference gray values RGb, RG 1  and RG 2  may be changed depending on the gamma curve of the electroluminescent display device, the sensitivity of the detecting device for the MTP operation, etc. 
     The calculation unit  224   a  may determine a slope factor SF based on the base gamma offset OFSb corresponding to the base reference gray value RGb, the first gamma offset OFS 1  corresponding to the first reference gray value RG 1  and the second gamma offset OFS 2  corresponding to the second reference gray value RG 2 , where the slope factor SF represents a trend of the low gray voltages corresponding to the low gray values lower than the first reference gray value RG 1 . The calculation unit  224   a  may calculate a minimum gamma reference voltage GRVc corresponding to a minimum reference gray value RGc smaller than the base reference gray value RGb based on the slope factor SF, a first gamma reference voltage GRV 1  corresponding to the first gamma offset OFS 1  and a second gamma reference voltage GRV 2  corresponding to the second gamma offset OF S 2 . The calculation unit  224   a  may provide a minimum gamma offset OFSc corresponding to the calculated minimum gamma reference voltage GRVc. 
     The calculation unit  224   a  may include a lookup table LUT as illustrated in  FIG. 11 . The gamma offsets and the corresponding gamma reference voltages may be mapped to each other and stored in the lookup table LUT. The calculation unit  224   a  may refer to the lookup table LUT to extract the gamma reference voltage corresponding to the gamma offset or to extract the gamma offset corresponding to the gamma reference voltage. 
     The voltage generation block  250   a  may generate the minimum gamma reference voltage GRVc and the first through eighth gamma reference voltage GRV 1  to GRV 8  based on the minimum gamma offset OFSc and the first through eighth gamma offsets OFS 1  to OFS 8 . The voltage generation block  250   a  may include a plurality of voltage generation units VGc and VG 1  to VG 8  for generating the minimum gamma reference voltage GRVc and the first through eighth gamma reference voltage GRV 1  to GRV 8 , respectively. 
     In exemplary embodiments, as illustrated in  FIGS. 6, 7A and 7B , the minimum reference gray value RGc may correspond to a gray value of 1. In this case, a gray voltage V 0  corresponding to a gray value of 0 may have a fixed voltage regardless of the MTP operation. In an exemplary embodiment, the regulator voltage VREG, which is input to the gamma circuit  200   a , may be provided to the gray voltage generator  134  in  FIG. 5  and the regulator voltage VREG itself may be used as the gray voltage V 0  corresponding to the gray value of 0. 
     Referring to  FIGS. 7A and 7B , the low gray voltages V 1  to V 10  corresponding to the low gray values 1 to 10 lower than the first reference gray value RG 1 =11 may be determined finely by performing the MTP operation with respect to the base reference gray value RGb. 
     As illustrated in  FIG. 7 b   , the low gray voltages V 1  to V 10  may be determined as represented by Equation 1.
 
 V ( i )= V ( GR 1)+( V ( GR 1)− V ( GR 2))*( GR 2 −GR 1-1 −i )* K /( GR 2 −GR 1)  (Equation 1)
 
     In Equation 1, GR 1  is the first reference gray value (e.g., 11), GR 2  is the second reference gray value (e.g., 23), K is a proportional constant, i is the low gray values (e.g., 1 to 10), and V(i) is the gray value corresponding to the gray value of i. 
     Referring to Equation 1, the above-mentioned slope factor SF may be determined as represented by Equation 2.
 
 SF =−( V ( GR 1)− V ( GR 2))*( V 11 −V 23)* K/ 12  (Equation 2)
 
     The slope factor SF may represent the trend of the low gray voltages V 1  to V 10  corresponding to the low gray values 1 to 10. The slope factor SF may correspond to a changing amount of the low gray voltages when the low gray value increases by one. The slope factor SF may have a negative value as illustrated in  FIG. 7A . 
     The proportional constant K may be determined by performing the MTP operation with respect to the base reference gray value RGb. In an exemplary embodiment, the base gamma offset OFSb corresponding to the base gamma reference voltage GRVb=V 7  may be determined by performing the MTP operation with respect to the gray value of 7, the first gamma offset OFS 1  corresponding to the first gamma reference voltage GRV 1 =V 11  may be determined by performing the MTP operation with respect to the gray value of 11, and the second gamma offset OFS 2  corresponding to the second gamma reference voltage GRV 2 =V 23  may be determined by performing the MTP operation with respect to the gray value of 23, for example. The base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2  may be stored in the corresponding memory units Mb, M 1  and M 2  of the storage unit  222   a , respectively. The calculation unit  224   a  may refer to the lookup table LUT to extract the base gamma reference voltage GRVb, the first gamma reference voltage GRV 1  and the second gamma reference voltage GRV 2  corresponding to the base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2  and to calculate the proportional constant K. Once the proportional constant K is determined, the voltage levels of the low gray voltages V 1  to V 10  may be determined from Equation 1. 
     The red (R) pixel, the green pixel (G) and the blue (B) pixel included in the display panel  110  in  FIG. 2  have different gamma characteristics and thus independent gamma reference voltages and the gray voltages based thereon are required for the respective colors. The MTP operation may be performed per color and the gamma offset and the gamma reference voltages may be determined per color, that is, for the red (R), green (G) and blue (B) respectively as illustrated in  FIG. 11 . Accordingly the proportional constant K may be determined per color and the above-mentioned slope factor SF may include a red slope factor corresponding to the red pixels, a green slope factor corresponding to the green pixels and a blue slope factor corresponding to the blue pixels. 
       FIG. 8  is a diagram illustrating a gamma circuit according to exemplary embodiments, and  FIGS. 9A and 9B  are diagrams for describing an operation of the gamma circuit of  FIG. 8 . 
       FIG. 8  illustrates a non-limiting example of eight reference gray values 11, 23, 35, 51, 87, 151, 203 and 255, eight gamma offsets OFS 1  to OFS 8  and eight gamma reference voltages GRV 1  to GRV 8 , but the number of them may be changed variously. 
     The storage unit  222   b  may store and provide a base gamma offset OFSb, a plurality of gamma offsets OFS 1  to OFS 8 . The storage unit  222   b  may include a plurality of memory units Mb and M 1  to M 8  to store the respective gamma offsets. In an exemplary embodiment, as illustrated in  FIGS. 8, 9A and 9B , the base reference gray value RGb may be 7, the first reference gray value RG 1  may be 11 and the second reference gray value RG 2  may be 23, for example. The reference gray values RGb, RG 1  and RG 2  may be changed depending on the gamma curve of the electroluminescent display device, the sensitivity of the detecting device for the MTP operation, etc. 
     The calculation unit  224   b  may determine a slope factor SF based on the base gamma offset OFSb corresponding to the base reference gray value RGb, the first gamma offset OFS 1  corresponding to the first reference gray value RG 1  and the second gamma offset OFS 2  corresponding to the second reference gray value RG 2 , where the slope factor SF represents a trend of the low gray voltages corresponding to the low gray values lower than the first reference gray value RG 1 . The calculation unit  224   b  may calculate a minimum gamma reference voltage GRVc corresponding to a minimum reference gray value RGc smaller than the base reference gray value RGb based on the slope factor SF, a first gamma reference voltage GRV 1  corresponding to the first gamma offset OFS 1  and a second gamma reference voltage GRV 2  corresponding to the second gamma offset OF S 2 . The calculation unit  224   b  may provide a minimum gamma offset OFSc corresponding to the calculated minimum gamma reference voltage GRVc. 
     The calculation unit  224   b  may include a lookup table LUT as illustrated in  FIG. 11 . The gamma offsets and the corresponding gamma reference voltages may be mapped to each other and stored in the lookup table LUT. The calculation unit  224   b  may refer to the lookup table LUT to extract the gamma reference voltage corresponding to the gamma offset or to extract the gamma offset corresponding to the gamma reference voltage. 
     The voltage generation block  250   b  may generate the minimum gamma reference voltage GRVc and the first through eighth gamma reference voltage GRV 1  to GRV 8  based on the minimum gamma offset OFSc and the first through eighth gamma offsets OFS 1  to OFS 8 . The voltage generation block  250   b  may include a plurality of voltage generation units VGc and VG 1  to VG 8  for generating the minimum gamma reference voltage GRVc and the first through eighth gamma reference voltage GRV 1  to GRV 8 , respectively. 
     In exemplary embodiments, as illustrated in  FIGS. 8, 9A and 9B , the minimum reference gray value RGc may correspond to a gray value of 0. 
     Referring to  FIGS. 9A and 9B , the low gray voltages V 0  to V 10  corresponding to the low gray values 0 to 10 lower than the first reference gray value RG 1 =11 may be determined finely by performing the MTP operation with respect to the base reference gray value RGb. 
     As illustrated in  FIG. 9 b   , the low gray voltages V 0  to V 10  may be determined as represented by Equation 1. Here, i is the low gray values (e.g., 0 to 10), and V(i) is the gray value corresponding to the gray value of i. 
     The slope factor SF may represent the trend of the low gray voltages V 0  to V 10  corresponding to the low gray values 0 to 10. The slope factor SF may correspond to a changing amount of the low gray voltages when the low gray value increases by one. The slope factor SF may have a negative value as illustrated in  FIG. 9A . 
     The proportional constant K may be determined by performing the MTP operation with respect to the base reference gray value RGb. In an exemplary embodiment, the base gamma offset OFSb corresponding to the base gamma reference voltage GRVb=V 7  may be determined by performing the MTP operation with respect to the gray value of 7, the first gamma offset OFS 1  corresponding to the first gamma reference voltage GRV 1 =V 11  may be determined by performing the MTP operation with respect to the gray value of 11, and the second gamma offset OFS 2  corresponding to the second gamma reference voltage GRV 2 =V 23  may be determined by performing the MTP operation with respect to the gray value of 23. The base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2  may be stored in the corresponding memory units Mb, M 1  and M 2  of the storage unit  222   b , respectively. The calculation unit  224   b  may refer to the lookup table LUT to extract the base gamma reference voltage GRVb, the first gamma reference voltage GRV 1  and the second gamma reference voltage GRV 2  corresponding to the base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2  and to calculate the proportional constant K. Once the proportional constant K is determined, the voltage levels of the low gray voltages V 0  to V 10  may be determined from Equation 1. 
       FIGS. 10A and 10B  are diagrams for describing an effect of reducing color distortion of low gay values according to exemplary embodiments. 
       FIG. 10A  illustrates color index (Wx, Wy) of the gray voltages that are determined by performing an interpolation of the third and eleventh gray voltages V 3  and V 11  corresponding to the gray values of 3 and 11. The brightness corresponding to the gray value of 3 is about 0.020 nit (cd/m 2 ) and the detecting device cannot guarantee such low brightness. Therefore, when the third gray voltage V 3  is estimated as the gamma reference voltage and the low gray voltages V 4  to V 10  are generated based on the third gray voltage V 3 , there may occur the color distortion with respect to the low gray voltages V 4  to V 10  because the third gray voltage V 3  may be inexact. In addition, because the gray voltages are designed linearly whereas the OLED has non-linear characteristics, the color distortion may occur with respect to the intermediate gray values 4 to 10 as illustrated in  FIG. 10A , even though the third gray voltage V 3  may be estimated exactly. 
       FIG. 10B  illustrates color index (Wx, Wy) of the gray voltages that are determined by performing an extrapolation of the first gamma reference voltage GRV 1  and the second gamma reference voltage GRV 2 , e.g., the eleventh and twenty third gray voltages V 11  and V 11  corresponding to the gray values of 11 and 23, using the slope factor SF as a weight value. As illustrated in  FIG. 10B , the color index (Wx, Wy) is provided uniformly and the color distortion may be improved with respect to the intermediate gray voltage V 7 . 
       FIG. 11  is a diagram illustrating an example mapping relation between gamma offsets and gamma reference voltages. 
     Referring to a lookup table LUT of  FIG. 11  representing the mapping relation between the gamma offsets OFS and the gamma reference voltages GRV, the gamma offsets OFS and the gamma reference voltages GRV may be determined per color by performing the MTP operation with respect to red (R), green (G) and blue (B). Accordingly the above-mentioned proportional constant K may be determined per color, and the above-mentioned slope factor SF may include a red slope factor corresponding to red pixels, a green slope factor corresponding to green pixels and a blue slope factor corresponding to blue pixels. 
       FIG. 11  illustrates a plurality of mapping relations between the gamma offsets OFS and the gamma reference voltages GRV corresponding to a plurality of cases CASE 1  to CASEk. 
     In exemplary embodiments, the cases CASE 1  to CASEk may correspond to a plurality of temperature intervals. The pixels have operational characteristics changing according to the operational temperature, and thus the different gray voltages need to be provided according to the operational temperature. As such, the above-mentioned proportional constant K may be determined per temperature interval, and each of the red slope factor, the green slope factor and the blue slope factor may include a plurality of values corresponding to the temperature intervals. 
     In other exemplary embodiments, the cases CASE 1  to CASEk may correspond to a plurality of dimming brightness intervals. The dimming operation may be performed so as to reduce the brightness of the displayed image entirely. The brightness may be divided into the brightness intervals, for example, based on 80%, 60%, 40% of the maximum brightness and the entire brightness of the image may be reduced gradationally. As such, the above-mentioned proportional constant K may be determined per dimming brightness interval, and each of the red slope factor, the green slope factor and the blue slope factor may include a plurality of values corresponding to the dimming brightness intervals. 
       FIG. 12  is a block diagram illustrating an electroluminescent display device according to exemplary embodiments. 
     A display device  300  or display module illustrated in  FIG. 12  may be an electroluminescent display device including a light-emitting diode (“LED”) or an organic light-emitting diode (“OLED”) that emits light through recombination of electrons and holes. 
     The display device  300  may include a display panel  310  including a plurality of pixels PX, a scan driver SDRV  320 , a data driver DDRV  330 , an emission control driver EDRV  340 , a timing controller TMC  350 , a voltage providing circuit VPC  100  and a gamma circuit GWC  200 . 
     The scan driver  320  may provide row control signals GW, GI, and GB as illustrated in  FIG. 13  to the pixels PX by units of rows through row control lines SLO to SLn. The data driver  330  may provide data signals DATA as illustrated in  FIG. 13  to the pixels PX by units of columns through data lines D 1  to Dm. The emission control driver  340  may provide emission control signals EM as illustrated in  FIG. 13  to the pixels PX by units of rows through emission control lines EML 1  to EMLn. 
     The timing controller  350  may receive and convert image signals R, G, B from an external device and provide converted image data DR, DG, DB to the data driver  330 . Also the timing controller  350  may receive a vertical synchronization signal Vsync, a horizontal synchronization signal Hsync, and a clock signal MCLK from the external device and generate control signals for the scan driver  320 , the data driver  330 , and the emission control driver  340 . The timing controller  350  provides scan driving control signals SCS to the scan driver  320 , data driving control signals DCS to the data driver  330 , and emission driving control signals ECS to the emission control driver  340 , respectively. Each pixel PX emits light by a driving current flowing through the LED or the OLED based on the data signals provided through the data lines D 1  to Dm. 
     The data driver  330  generates the data signals based on the data voltage VDH. The display panel  310  receives the power supply voltage ELVDD and the pixels PX in the display panel  310  are driven based on the power supply voltage ELVSS and the data signals from the data driver  330 . The timing controller  350  generates the ready signal indicating the power supply timing. 
     The gamma circuit  200  may generate a plurality of gamma reference voltages GRV based on a regulator voltage VREG. In an exemplary embodiment, the regulator voltage VREG may be the first power supply voltage ELVDD itself or another voltage that is generated based on the first power supply voltage ELVDD. The gamma circuit  200  may store a plurality of gamma offsets OFS corresponding to a plurality of gamma reference voltages GRV where the gamma offsets OFS are determined by performing a multi-time programmable (“MTP”) operation with respect to a plurality of reference gray values. The gamma circuit  200  may generate the gamma reference voltages GRV based on the stored gamma offsets OFS. 
     The gamma circuit  200  may generate a minimum gamma reference voltage GRVc based on a first gamma offset OFS 1  corresponding to a first reference gray value RG 1 , a second gamma offset OFS 2  corresponding to a second reference gray value RG 2  greater than the first reference gray value RG 1  and a base gamma offset OFSb corresponding to a base reference gray value RGb smaller than the first reference gray value RG 1 . As described with reference to  FIGS. 6 through 9 , the minimum gamma reference voltage GRVc may correspond to a gray value of 0 or a gray value of 1. 
     The data driver  330  may provide data signals to the display panel  310  through the data lines D 1  to Dm. The data driver  330  may generate a plurality of gray voltages based on the gamma reference voltages GRV, and may drive the data lines D 1  to Dm based on image data and the gray voltages. 
     As such, the gamma circuit  200  and the data driver  130  may generate the minimum gamma reference voltage GRVc based on the base gamma offset OFSb, the first gamma offset OFS 1  and the second gamma offset OFS 2 , thereby reducing the color distortion of the low gray values and enhancing the image quality of the electroluminescent display device  100 . 
       FIG. 13  is a circuit diagram illustrating an example of a pixel included in the electroluminescent display device of  FIG. 12 . 
     Referring to  FIG. 13 , a pixel PX may include an OLED, a first transistor TR 1 , a second transistor TR 2 , a third transistor TR 3 , a storage capacitor CST, a fourth transistor TR 4 , a fifth transistor TR 5 , a sixth transistor TR 6 , and a seventh transistor TR 7 , which are connected through first through sixth nodes N 1  through N 6 . In an exemplary embodiment, the pixel PX may further include a diode parallel capacitor CEL. In another exemplary embodiment, the diode parallel capacitor CEL may be a capacitor provided by a parasitic capacitances. 
     The OLED may emit light based on a driving current ID. The anode of the OLED may be to a negative power voltage ELVSS or a ground voltage and the cathode of the OLED may be coupled to the fourth node N 4 . 
     The first transistor TR 1  may include a gate electrode connected to the fifth node N 5 , a source electrode coupled to the second node N 2 , and a drain electrode coupled to the third node N 3 . The first transistor TR 1  may generate the driving current ID. The digital driving may be performed such that the grayscale is represented by the sum of the times in each frame during which the driving current ID is provided to the OLED. 
     The second transistor TR 2  may include a gate electrode receiving a scan signal SW, a source electrode receiving the data signal DATA, and a drain electrode coupled to the second node N 2 . The second transistor TR 2  may transfer the data signal DATA to the source electrode of the first transistor TR 1  during the activation time interval of the scan signal SW. 
     The third transistor TR 3  may include a gate electrode receiving the scan signal SW, a source electrode coupled to the fifth node N 5 , and a drain electrode coupled to the third node N 3 . The third transistor TR 3  may electrically couple the gate electrode of the first transistor TR 1  and the drain electrode of the first transistor TR 1  during the activation time interval of the scan signal SW. In other words, the third transistor TR 3  may form a diode-connection of the first transistor TR 1  during the activation time interval of the scan signal SW. Through such diode-connection, the data signal DATA compensated with the respective threshold voltage of the first transistor TR 1  may be provided to the gate electrode of the first transistor TR 1 . Such threshold voltage compensation may prevent or reduce irregularity of the driving current ID due to deviations of the threshold voltage of the first transistor TR 1 . 
     The storage capacitor CST may be coupled between the first node N 1  and the fifth node N 5 . The storage capacitor CST maintains the voltage level on the gate electrode of the first transistor TR 1  during the deactivation time interval of the scan signal SW. The deactivation time interval of the scan signal SW may include the activation time interval of an emission control signal EM. The driving current ID generated by the first transistor TR 1  may be applied to the OLED during the activation time interval of the emission control signal EM. 
     The fourth transistor TR 4  may include a gate electrode receiving a data initialization signal GI, a source electrode connected to the fifth node N 5  and a drain electrode coupled to the sixth node N 6 . The fourth transistor TR 4  may provide an initialization voltage VINT to the gate electrode of the first transistor TR 1  during the activation time interval of the data initialization signal GI. In other words, the fourth transistor TR 4  may initialize the gate electrode of the first transistor TR 1  with the initialization voltage VINT during the activation time interval of the data initialization signal GI. 
     The fifth transistor TR 5  may include a gate electrode receiving the emission control signal EM, a source electrode coupled to the first node N 1 , and a drain electrode coupled to the second node N 2 . The fifth transistor TR 5  may provide the power supply voltage ELVDD to the second node N 2  during the activation time interval of the emission control signal EM. In contrast, the fifth transistor TR 5  may disconnect the second node N 2  from the power supply voltage ELVDD during the deactivation time interval of the emission control signal EM. The first transistor TR 1  may generate the driving current ID while the fifth transistor TR 5  provides the power supply voltage ELVDD to the second node N 2  during the activation time interval of the emission control signal EM. In addition, the data signal DATA compensated with the threshold voltage of the first transistor TR 1  may be provided to the gate electrode of the first transistor TR 1  while the fifth transistor TR 5  disconnects the second node N 2  from the power supply voltage ELVDD during the deactivation time interval of the emission control signal EM. 
     The sixth transistor TR 6  may include a gate electrode receiving the emission control signal EM, a source electrode coupled to the third node N 3 , and a drain electrode coupled to the fourth node N 4 . The sixth transistor TR 6  may provide the driving current ID generated by the first transistor TR 1  to the OLED during the activation time interval of the emission control signal EM. 
     The seventh transistor TR 7  may include a gate electrode receiving a diode initialization signal GB, a source electrode coupled to the sixth node N 6 , and a drain electrode coupled to the fourth node N 4 . The seventh transistor TR 7  may provide the initialization voltage VINT to the anode of the OLED during the activation time interval of the diode initialization signal GB. In other words, the seventh transistor TR 7  may initialize the anode of the OLED with the initialization voltage VINT during the activation time interval of the diode initialization signal GB. 
     In exemplary embodiments, the diode initialization signal GB may be the same as the data initialization signal GI. The initialization of the gate electrode of the first transistor TR 1  and the initialization of the anode of the OLED may not affect each other, that is, independent of each other. Thus the diode initialization signal GB and the data initialization signal GI may be combined as one signal. The initialization voltage VINT may depend on the characteristics of the diode parallel capacitor CEL and the initialization voltage VINT may be set to a sufficiently low voltage. In an exemplary embodiment, the initialization voltage VINT may be set to the negative power supply voltage ELVSS or the ground voltage. 
       FIG. 14  is a block diagram illustrating a mobile device according to exemplary embodiments. 
     Referring to  FIG. 14 , a mobile device  700  includes a system on chip (“SoC”)  710  and a plurality of functional modules  740 ,  750 ,  760  and  770 . The mobile device  700  may further include a memory device  720 , a storage device  730  and a power management device  780 . 
     The SoC  710  controls overall operations of the mobile device  700 . In an exemplary embodiment, the SoC  710  controls the memory device  720 , the storage device  730  and the plurality of functional modules  740 ,  750 ,  760  and  770 , for example. The SoC  710  may be an application processor (“AP”) that is included in the mobile device  700 . 
     The SoC  710  may include a CPU  712  and a power management system PM SYSTEM  714 . The memory device  720  and the storage device  730  may store data for operations of the mobile device  700 . In an exemplary embodiment, the memory device  720  may include a volatile memory device, such as a dynamic random access memory (“DRAM”), a static random access memory (“SRAM”), a mobile DRAM, etc. In an exemplary embodiment, the storage device  730  may include a nonvolatile memory device, such as an erasable programmable read-only memory (“EPROM”), an electrically EPROM (“EEPROM”), a flash memory, a phase change random access memory (“PRAM”), a resistance random access memory (“RRAM”), a nano floating gate memory (“NFGM”), a polymer random access memory (“PoRAM”), a magnetic random access memory (“MRAM”), a ferroelectric random access memory (“FRAM”), etc. In exemplary embodiments, the storage device  730  may further include a solid state drive (“SSD”), a hard disk drive (“HDD”), a CD-ROM, etc. 
     The functional modules  740 ,  750 ,  760  and  770  perform various functions of the mobile device  700 . In an exemplary embodiment, the mobile device  700  may include a communication module  740  that performs a communication function (e.g., a code division multiple access (“CDMA”) module, a long term evolution (“LTE”) module, a radio frequency (RF) module, an ultra-wideband (“UWB”) module, a wireless local area network (WLAN) module, a worldwide interoperability for a microwave access (“WIMAX”) module, etc.), a camera module  750  that performs a camera function, a display module  760  that performs a display function, a touch panel module  770  that performs a touch sensing function, etc., for example. In exemplary embodiments, the mobile device  700  may further include a global positioning system (“GPS”) module, a microphone (“MIC”) module, a speaker module, a gyroscope module, etc., for example. However, the functional modules  740 ,  750 ,  760 , and  770  in the mobile device  700  are not limited thereto. 
     The power management device  780  may provide an operating voltage to the SoC  710 , the memory device  720 , the storage device  730  and the functional modules  740 ,  750 ,  760  and  770 . 
     According to exemplary embodiments, the display module  760  includes the gamma circuit GMC  762  as described above. The gamma circuit  762  may reduce the color distortion of the low gray values and enhance the image quality by generating the minimum gamma reference voltage GRVc using the base gamma offset OFSb, the first gamma offset OFS 1  and the second offset OFS 2 . 
       FIG. 15  is a block diagram illustrating an interface included in a mobile device according to exemplary embodiments. 
     Referring to  FIG. 15 , a mobile device  800  includes a SoC  802  and a plurality of interfaces  811 ,  812 ,  813 ,  814 ,  815 ,  816 ,  817 ,  818 ,  819 ,  820 ,  821 ,  822  and  823 . According to exemplary embodiments, the mobile device  800  may be any mobile device, such as a mobile phone, a smart phone, a tablet computer, a laptop computer, a personal digital assistants (“PDA”), a portable multimedia player (“PMP”), a digital camera, a portable game console, a music player, a camcorder, a video player, a navigation system, etc. 
     The SoC  802  controls overall operations of the mobile device  800 . In an exemplary embodiment, the SoC  802  may be an application processor (“AP”) that is included in the mobile device  800 , for example. 
     The SoC  802  may communicate with each of a plurality of peripheral devices (not illustrated) via each of the plurality of interfaces  811  to  823 . In an exemplary embodiment, each of the interfaces  811  to  823  may transmit at least one control signal, which is output from a respective IP among a plurality of IPs implemented in each of power domains, to each of the plurality of peripheral devices, for example. 
     In an exemplary embodiment, the SoC  802  may control a power state and an operation state of each flat panel display device via each of display interfaces  811  and  812 , for example. The flat panel display device may include a liquid crystal display (“LCD”), a light emitting diode (“LED”) display, an organic light emitting diode (“OLED”) display or an active matrix organic light-emitting diode (“AMOLED”) display, etc., for example. 
     The SoC  802  may control a power state and an operation state of a camcorder via a camcorder interface  813 , may control a power state and an operation state of a TV module via a TV interface  814 , and may control a power state and an operation state of a camera module or an image sensor module via an image sensor interface  815 . 
     The SoC  802  may control a power state and an operation state of a GPS module via a GPS interface  816 , may control a power state and an operation state of a UWB module via a UWB interface  817 , and may control a power state and an operation state of an universal serial bus (“USB”) drive via a USB drive interface  818 . 
     The SoC  802  may control a power state and an operation state of a DRAM via a DRAM interface  819 , may control a power state and an operation state of a nonvolatile memory device (e.g., a flash memory) via a nonvolatile memory interface  820  (e.g., a flash memory interface), may control a power state and an operation state of an audio module through an audio interface  821 , may control a power state of a multi-format codec (“MFC”) through an MFC interface  822 , and may control a power state of an MP3 player through an MP3 player interface  823 . In an exemplary embodiment, a module or an interface may be implemented in hardware or software, for example. 
       FIG. 16  is a block diagram illustrating an electronic device including a display device according to exemplary embodiments. 
     Referring to  FIG. 16 , the electronic device  1000  may include a processor  1010 , a memory device  1020 , a storage device  1030 , an input/output (“I/O”) device  1040 , a power supply  1050 , and a display device  1060 . The electronic device  1000  may further include a plurality of ports for communicating a video card, a sound card, a memory card, a universal serial bus (“USB”) device, other electronic devices, etc. 
     The processor  1010  may perform various computing functions. The processor  1010  may be a micro-processor, a central processing unit (“CPU”), etc. In an exemplary embodiment, the processor  1010  may be coupled to other components via an address bus, a control bus, a data bus, etc. In an exemplary embodiment, the processor  1010  may be coupled to an extended bus, such as a peripheral component interconnection (“PCI”) bus. The memory device  1020  may store data for operations of the electronic device  1000 . In an exemplary embodiment, the memory device  1020  may include at least one non-volatile memory device, such as an EPROM device, an EEPROM device, a flash memory device, a 
     PRAM device, a RRAM device, a NFGM device, a PoRAM device, a MRAM device, a FRAM device, etc., and/or at least one volatile memory device, such as a DRAM device, a SRAM device, a mobile DRAM device, etc. The storage device  1030  may be a SSD device, a HDD device, a CD-ROM device, etc. 
     In an exemplary embodiment, the I/O device  1040  may be an input device such as a keyboard, a keypad, a mouse, a touchpad, a touch-screen, a remote controller, etc., and an output device such as a printer, a speaker, etc. The power supply  1050  may provide a power for operations of the electronic device  1000 . The display device  1060  may communicate with other components via the buses or other communication links. 
     According to exemplary embodiments, the display module  1060  includes the gamma circuit GMC  1062  as described above. The gamma circuit  1062  may reduce the color distortion of the low gray values and enhance the image quality by generating the minimum gamma reference voltage GRVc using the base gamma offset OFSb, the first gamma offset OFS 1  and the second offset OFS 2 . 
     The above described embodiments may be applied to various kinds of devices and systems such as a mobile phone, a smart phone, a tablet computer, a laptop computer, a personal digital assistant (“PDA”), a portable multimedia player (“PMP”), a digital television, a digital camera, a portable game console, a music player, a camcorder, a video player, a navigation system, etc. 
     The foregoing is illustrative of exemplary embodiments and is not to be construed as limiting thereof. Although a few exemplary embodiments have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of the invention. Accordingly, all such modifications are intended to be included within the scope of the invention as defined in the claims. Therefore, it is to be understood that the foregoing is illustrative of various exemplary embodiments and is not to be construed as limited to the specific exemplary embodiments disclosed, and that modifications to the disclosed exemplary embodiments, as well as other exemplary embodiments, are intended to be included within the scope of the appended claims.