Abstract:
General speaking, a resistor of high resistivity has a negative-temperature-coefficient and a resistor of low resistivity has a positive-temperature-coefficient. Utilizing this characteristic, an appropriate proportion between the above resistors can be found to make a combined resistor with an approximate zero-temperature-coefficient. The combined resistor can be used to design a circuit for generating voltage and current with approximate zero-temperature-coefficients.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a voltage or current generator, and more particularly, to a zero-temperature-coefficient voltage or current generator. 
     2. Description of the Prior Art 
     Generally speaking, an analog circuit often needs a reference voltage circuit not influenced by supply voltage and temperature variation for improving yield of the analog circuit, reliability, and accuracy. The reference voltage circuit is known as a “bandgap reference circuit”. The bandgap reference circuit provides a voltage level (bandgap reference voltage) for other function blocks, such as an output voltage level of a regulator, or turning-on or turning-off of a battery charger, and it is a widely used and important circuit. The bandgap reference voltage is generated by adding a proportional to absolute temperature (PTAT) voltage to a complementary to absolute temperature (CTAT) voltage. The CTAT voltage is generated through a base-emitter voltage of a forward-biased bipolar transistor, and the PTAT voltage is generated through using a voltage difference between base-emitter voltages of two bipolar transistors, wherein currents flowing through the two bipolar transistors are the same, but the base-emitter voltages of the two bipolar transistors are different. Thus, the bandgap reference circuit has a low correlation with the supply voltage and process parameters, and the bandgap reference circuit is independent of temperature. Thus, the bandgap reference circuit is widely used in the analog circuits. 
     Temperature may influence diodes, resistors, capacitors, and transistors to different degrees. However, design of a mixed-signal integrated circuit (IC) requires more complexity, lower voltage and higher speed on an uneven power-density chip, which increases temperature gradient of the chip. Therefore, an IC designer must consider influence of the temperature gradient on the whole chip, because the analog circuits may be very sensitive to the temperature difference, even only a few degrees Celsius. But, current zero temperature-coefficient voltage and current technologies may not consider temperature effect on resistors, so that the reference voltage still correlates with the temperature, and accuracy of the reference voltage is influenced. 
     SUMMARY OF THE INVENTION 
     An embodiment of the present invention provides a zero-temperature-coefficient (ZTC) voltage or current generator. The voltage or current generator includes a power amplifier, a first P type metal-oxide-semiconductor, a first PNP type bipolar transistor, a second P type metal-oxide-semiconductor, a group of second PNP type bipolar transistor, a negative-temperature-coefficient resistor, a positive-temperature-coefficient resistor, a first zero-temperature-coefficient combined resistor, a third P type metal-oxide-semiconductor transistor and a second zero-temperature-coefficient combined resistor. The first P type metal-oxide-semiconductor is coupled to an output terminal of the power amplifier. The first PNP type bipolar transistor has an emitter coupled to a negative input terminal of the power amplifier and a drain of the first P type metal-oxide-semiconductor. The second P type metal-oxide-semiconductor is coupled to the output terminal of the power amplifier. Each of the group of second PNP type bipolar transistors has an emitter coupled to a positive input terminal of the power amplifier and a drain of the second P type metal-oxide-semiconductor. The negative-temperature-coefficient resistor is coupled between the positive input terminal of the power amplifier and the emitter of the each second PNP type bipolar transistor. The first zero-temperature-coefficient combined resistor is coupled to the positive input terminal of the power amplifier. The third P type metal-oxide-semiconductor transistor is coupled to the output terminal of the power amplifier. And the second zero-temperature-coefficient combined resistor is coupled to a drain of the third P type metal-oxide-semiconductor transistor. 
     Another embodiment of the present invention provides a voltage or current generator with an approximately zero-temperature-coefficient. The voltage or current generator comprises a power amplifier, a first P type metal-oxide-semiconductor, a first NPN type bipolar transistor, a second P type metal-oxide-semiconductor, a group of second NPN type bipolar transistor, a negative-temperature-coefficient resistor, a first zero-temperature-coefficient combined resistor, a third P type metal-oxide-semiconductor transistor and a second zero-temperature-coefficient combined resistor. The first P type metal-oxide-semiconductor is coupled to an output terminal of the power amplifier. The first NPN type bipolar transistor comprises a collector coupled to a negative input terminal of the power amplifier and a drain of the first P type metal-oxide-semiconductor transistor. The second P type metal-oxide-semiconductor is coupled to the output terminal of the power amplifier. Each of the group of second NPN type bipolar transistors comprises a collector coupled to a positive input terminal of the power amplifier and a drain of the second P type metal-oxide-semiconductor transistor. The negative-temperature-coefficient resistor is coupled between the positive input terminal of the power amplifier and the collector of the each second NPN type bipolar transistor. The positive-temperature-coefficient resistor is coupled between the positive input terminal of the power amplifier and the collector of the each second NPN type bipolar transistor. The first zero-temperature-coefficient combined resistor is coupled to the positive input terminal of the power amplifier. The third P type metal-oxide-semiconductor transistor is coupled to the output terminal of the power amplifier. And the second zero-temperature-coefficient combined resistor is coupled to a drain of the third P type metal-oxide-semiconductor transistor. 
     These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating a voltage or current generator with a zero-temperature-coefficient according to an embodiment of the present invention. 
         FIG. 2  is a diagram illustrating a voltage or current generator with a zero-temperature-coefficient according to another embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Please refer to  FIG. 1 .  FIG. 1  is a diagram illustrating a voltage or current generator  10  with an approximately zero-temperature-coefficient according to an embodiment of the present invention. The voltage or current generator  10  comprises a first P type metal-oxide-semiconductor  101 , a second P type metal-oxide-semiconductor  102 , a third P type metal-oxide-semiconductor transistor  103 , a power amplifier  104 , a third zero-temperature-coefficient combined resistor  105 , a first zero-temperature-coefficient combined resistor  106 , a second zero-temperature-coefficient combined resistor  107 , a negative-temperature-coefficient resistor  108 , a positive-temperature-coefficient resistor  109 , a first PNP type bipolar transistor  110 , and a group of second PNP type bipolar transistors  111 . The first zero-temperature-coefficient combined resistor  106  comprises a positive-temperature-coefficient resistor  1062  and a negative-temperature-coefficient resistor  1061 ; the second zero-temperature-coefficient combined resistor  107  comprises a positive-temperature-coefficient resistor  1072  and a negative-temperature-coefficient resistor  1071 ; the third zero-temperature-coefficient combined resistor  105  comprises a positive-temperature-coefficient resistor  1052  and a negative-temperature-coefficient resistor  1051 . A value of the first zero-temperature-coefficient combined resistor  106  is L*R, a value of the second zero-temperature-coefficient combined resistor  107  is N*R, a value of the third zero-temperature-coefficient combined resistor  105  is L*R, and a value of a combination of the negative-temperature-coefficient resistor  108  and the positive-temperature-coefficient resistor  109  is R. The K first PNP type bipolar transistors  110  connect in parallel to form the group of second PNP type bipolar transistors  111 , where K≧1. 
     As shown in  FIG. 1 , voltages of two input terminals of the power amplifier  104  are the same when the power amplifier  104  operates normally. That is to say, the voltage of the positive input terminal V 1  is the same as the voltage of the negative input terminal V 2 , so a PTAT current I PTAT  is generated as follows: 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         
                           I 
                           PTAT 
                         
                         * 
                         R 
                       
                       + 
                       
                         V 
                         
                           EB 
                           ⁢ 
                           
                               
                           
                           , 
                           111 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       V 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     = 
                     
                       
                         
                           V 
                           
                             EB 
                             , 
                             110 
                           
                         
                         ⁢ 
                         
                           
 
                         
                         ∵ 
                         
                           V 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       = 
                       
                         
                           
                             V 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           ⁢ 
                           
                             
 
                           
                           ⇒ 
                           
                             I 
                             PTAT 
                           
                         
                         = 
                         
                           
                             
                               
                                 V 
                                 
                                   EB 
                                   , 
                                   110 
                                 
                               
                               - 
                               
                                 V 
                                 
                                   EB 
                                   , 
                                   111 
                                 
                               
                             
                             R 
                           
                           = 
                           
                             
                               
                                 
                                   
                                     V 
                                     T 
                                   
                                   * 
                                   ln 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   K 
                                 
                                 R 
                               
                               ⁢ 
                               
                                 
 
                               
                               ∵ 
                               
                                 V 
                                 T 
                               
                             
                             = 
                             
                               
                                 kT 
                                 q 
                               
                               ⁢ 
                               
                                 
 
                               
                               ⇒ 
                               
                                 
                                   I 
                                   PTAT 
                                 
                                 ∝ 
                                 T 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In addition, a CTAT current I CTAT  is generated as follows: 
     
       
         
           
             
               
                 
                   
                     I 
                     CTAT 
                   
                   = 
                   
                     
                       V 
                       
                         EB 
                         , 
                         110 
                       
                     
                     
                       L 
                       * 
                       R 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Because V EB,110  has a negative-temperature-coefficient and L*R has a zero-temperature-coefficient, I CTAT  is a CTAT current. Please refer to equations (1), (2), and (3). A current I with a zero-temperature-coefficient is generated through the equation (1) and the equation (2), then a parameter L is derived from the current I through the equation (3): 
     
       
         
           
             I 
             = 
             
               
                 
                   I 
                   PTAT 
                 
                 + 
                 
                   I 
                   CTAT 
                 
               
               = 
               
                 
                   
                     
                       V 
                       T 
                     
                     * 
                     ln 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     K 
                   
                   R 
                 
                 + 
                 
                   
                     V 
                     
                       EB 
                       , 
                       110 
                     
                   
                   
                     L 
                     * 
                     R 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 ∂ 
                 I 
               
               
                 ∂ 
                 T 
               
             
             = 
             
               
                 
                   
                     ln 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     k 
                   
                   R 
                 
                 * 
                 
                   
                     ∂ 
                     
                       V 
                       T 
                     
                   
                   
                     ∂ 
                     T 
                   
                 
               
               - 
               
                 
                   
                     
                       V 
                       T 
                     
                     * 
                     ln 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     K 
                   
                   
                     R 
                     2 
                   
                 
                 * 
                 
                   
                     ∂ 
                     R 
                   
                   
                     ∂ 
                     T 
                   
                 
               
               + 
               
                 
                   1 
                   
                     L 
                     * 
                     R 
                   
                 
                 * 
                 
                   
                     ∂ 
                     
                       V 
                       
                         EB 
                         , 
                         110 
                       
                     
                   
                   
                     ∂ 
                     T 
                   
                 
               
               - 
               
                 
                   
                     V 
                     
                       EB 
                       , 
                       110 
                     
                   
                   
                     L 
                     * 
                     
                       R 
                       2 
                     
                   
                 
                 * 
                 
                   
                     ∂ 
                     R 
                   
                   
                     ∂ 
                     T 
                   
                 
               
             
           
         
       
     
     The value R of the combination of the negative-temperature-coefficient resistor  108  and the positive-temperature-coefficient resistor  109  is independent of temperature, that is 
                 ∂   R       ∂   T       =   0.         
Therefore, the above equation can be simplified to the equation (3):
 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       I 
                     
                     
                       ∂ 
                       T 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               ln 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               K 
                             
                             R 
                           
                           * 
                           
                             
                               ∂ 
                               
                                 V 
                                 T 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                         
                         + 
                         
                           
                             1 
                             
                               L 
                               * 
                               R 
                             
                           
                           * 
                           
                             
                               ∂ 
                               
                                 V 
                                 
                                   EB 
                                   , 
                                   110 
                                 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                         
                       
                       ⁢ 
                       
                         
 
                       
                       ⇒ 
                       L 
                     
                     = 
                     
                       - 
                       
                         
                           
                             ∂ 
                             
                               V 
                               
                                 EB 
                                 , 
                                 110 
                               
                             
                           
                           
                             ∂ 
                             T 
                           
                         
                         
                           
                             
                               ∂ 
                               
                                 V 
                                 T 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                           ⁢ 
                           ln 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           K 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Therefore, when a ratio of the value of the first zero-temperature-coefficient combined resistor  106  to the value of the combination of the negative-temperature-coefficient resistor  108  and the positive-temperature-coefficient resistor  109  is L, the current I with a zero-temperature-coefficient is generated. 
     Before discussing a parameter N and a reference voltage V ref , please note that the third P type metal-oxide-semiconductor transistor  103  duplicates the current I with a zero-temperature-coefficient. Then, please refer to equation (4): 
     
       
         
           
             
               
                 
                   
                     V 
                     ref 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             I 
                             PTAT 
                           
                           + 
                           
                             I 
                             CTAT 
                           
                         
                         ) 
                       
                       * 
                       N 
                       * 
                       R 
                     
                     = 
                     
                       
                         
                           
                             
                               V 
                               T 
                             
                             * 
                             ln 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             K 
                             * 
                             N 
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   EB 
                                   , 
                                   110 
                                 
                               
                               L 
                             
                             * 
                             N 
                           
                         
                         ⁢ 
                         
                           
 
                         
                         ⇒ 
                         N 
                       
                       = 
                       
                         - 
                         
                           
                             V 
                             ref 
                           
                           
                             
                               
                                 V 
                                 T 
                               
                               * 
                               ln 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               K 
                             
                             + 
                             
                               
                                 V 
                                 
                                   EB 
                                   , 
                                   110 
                                 
                               
                               L 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Substituting the parameter L generated through equation (3) into equation (4) yields a relationship equation between the parameter N and the reference voltage V ref . Referring to equation (4), the reference voltage V ref  varies with the parameter N, and is not limited to 1.25V. 
     A function of the third zero-temperature-coefficient combined resistor  105  is making the circuits viewed from the positive input terminal and the negative input terminal of the power amplifier  104  more symmetrical. 
     Please refer to  FIG. 2 .  FIG. 2  is a diagram illustrating a voltage or current generator  20  with a zero-temperature-coefficient according to another embodiment of the present invention. The voltage or current generator  20  comprises a first P type metal-oxide-semiconductor  201 , a second P type metal-oxide-semiconductor  202 , a third P type metal-oxide-semiconductor transistor  203 , a power amplifier  204 , a third zero-temperature-coefficient combined resistor  205 , a first zero-temperature-coefficient combined resistor  206 , a second zero-temperature-coefficient combined resistor  207 , a negative-temperature-coefficient resistor  208 , a positive-temperature-coefficient resistor  209 , a first NPN type bipolar transistor  210 , and a group of second NPN type bipolar transistors  211 . The first zero-temperature-coefficient combined resistor  206  comprises a positive-temperature-coefficient resistor  2062  and a negative-temperature-coefficient resistor  2061 ; the second zero-temperature-coefficient combined resistor  207  comprises a positive-temperature-coefficient resistor  2072  and a negative-temperature-coefficient resistor  2071 ; the third zero-temperature-coefficient combined resistor  205  comprises a positive-temperature-coefficient resistor  2052  and a negative-temperature-coefficient resistor  2051 . A value of the first zero-temperature-coefficient combined resistor  206  is L*R, a value of the second zero-temperature-coefficient combined resistor  207  is N*R, a value of the third zero-temperature-coefficient combined resistor  205  is L*R, and a value of a combination of the negative-temperature-coefficient resistor  208  and the positive-temperature-coefficient resistor  209  is R. The K first NPN type bipolar transistors  210  connect in parallel to form the group of second NPN type bipolar transistors  211 , wherein K≧1. 
     As shown in  FIG. 2 , voltages of two input terminals of the power amplifier  204  are the same when the power amplifier  204  operates normally. That is to say, the voltage of the positive input terminal V 1  is the same as the voltage of the negative input terminal V 2 , so a PTAT current I PTAT  is generated as follows: 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         
                           I 
                           PTAT 
                         
                         * 
                         R 
                       
                       + 
                       
                         V 
                         
                           BE 
                           , 
                           211 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       V 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     = 
                     
                       
                         
                           V 
                           
                             BE 
                             , 
                             210 
                           
                         
                         ⁢ 
                         
                           
 
                         
                         ∵ 
                         
                           V 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       = 
                       
                         
                           
                             V 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           ⁢ 
                           
                             
 
                           
                           ⇒ 
                           
                             I 
                             PTAT 
                           
                         
                         = 
                         
                           
                             
                               
                                 V 
                                 
                                   BE 
                                   , 
                                   210 
                                 
                               
                               - 
                               
                                 V 
                                 
                                   BE 
                                   , 
                                   211 
                                 
                               
                             
                             R 
                           
                           = 
                           
                             
                               
                                 
                                   
                                     V 
                                     T 
                                   
                                   * 
                                   ln 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   K 
                                 
                                 R 
                               
                               ⁢ 
                               
                                 
 
                               
                               ∵ 
                               
                                 V 
                                 T 
                               
                             
                             = 
                             
                               
                                 kT 
                                 q 
                               
                               ⁢ 
                               
                                 
 
                               
                               ⇒ 
                               
                                 
                                   I 
                                   PTAT 
                                 
                                 ∝ 
                                 T 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In addition, a CTAT current I CTAT  is generated as follows: 
     
       
         
           
             
               
                 
                   
                     I 
                     CTAT 
                   
                   = 
                   
                     
                       V 
                       
                         BE 
                         , 
                         210 
                       
                     
                     
                       L 
                       * 
                       R 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Due to V BE,210  having a negative-temperature-coefficient and L*R having a zero-temperature-coefficient, I CTAT  is a CTAT current. Please refer to equations (5), (6), and (7). A current I with a zero-temperature-coefficient is generated through equation (5) and equation (6), then a parameter L is derived from the current I through equation (7): 
     
       
         
           
             I 
             = 
             
               
                 
                   I 
                   PTAT 
                 
                 + 
                 
                   I 
                   CTAT 
                 
               
               = 
               
                 
                   
                     
                       V 
                       T 
                     
                     * 
                     ln 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     K 
                   
                   R 
                 
                 + 
                 
                   
                     V 
                     
                       BE 
                       , 
                       210 
                     
                   
                   
                     L 
                     * 
                     R 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 ∂ 
                 I 
               
               
                 ∂ 
                 T 
               
             
             = 
             
               
                 
                   
                     ln 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     K 
                   
                   R 
                 
                 * 
                 
                   
                     ∂ 
                     
                       V 
                       T 
                     
                   
                   
                     ∂ 
                     T 
                   
                 
               
               - 
               
                 
                   
                     
                       V 
                       T 
                     
                     * 
                     ln 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     K 
                   
                   
                     R 
                     2 
                   
                 
                 * 
                 
                   
                     ∂ 
                     R 
                   
                   
                     ∂ 
                     T 
                   
                 
               
               + 
               
                 
                   1 
                   
                     L 
                     * 
                     R 
                   
                 
                 * 
                 
                   
                     ∂ 
                     
                       V 
                       
                         BE 
                         , 
                         210 
                       
                     
                   
                   
                     ∂ 
                     T 
                   
                 
               
               - 
               
                 
                   
                     V 
                     
                       BE 
                       , 
                       210 
                     
                   
                   
                     L 
                     * 
                     
                       R 
                       2 
                     
                   
                 
                 * 
                 
                   
                     ∂ 
                     R 
                   
                   
                     ∂ 
                     T 
                   
                 
               
             
           
         
       
     
     Because the value R of the combination of the negative-temperature-coefficient resistor  108  and the positive-temperature-coefficient resistor  109  is independent of temperature, that is 
                   ∂   R       ∂   T       =   0     ,         
the above equation can be simplified into the equation (7):
 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       I 
                     
                     
                       ∂ 
                       T 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               ln 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               K 
                             
                             R 
                           
                           * 
                           
                             
                               ∂ 
                               
                                 V 
                                 T 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                         
                         + 
                         
                           
                             1 
                             
                               L 
                               * 
                               R 
                             
                           
                           * 
                           
                             
                               ∂ 
                               
                                 V 
                                 
                                   BE 
                                   , 
                                   210 
                                 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                         
                       
                       ⁢ 
                       
                         
 
                       
                       ⇒ 
                       L 
                     
                     = 
                     
                       - 
                       
                         
                           
                             ∂ 
                             
                               V 
                               
                                 BE 
                                 , 
                                 210 
                               
                             
                           
                           
                             ∂ 
                             T 
                           
                         
                         
                           
                             
                               ∂ 
                               
                                 V 
                                 T 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                           ⁢ 
                           ln 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           K 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Therefore, when a ratio of the value of the first zero-temperature-coefficient combined resistor  106  to the value of the combination of the negative-temperature-coefficient resistor  108  and the positive-temperature-coefficient resistor  109  is L, the current I with a zero-temperature-coefficient is generated. 
     Before discussing a parameter N and a reference voltage V ref , please notice the third P type metal-oxide-semiconductor transistor  203  duplicating the current I with a zero-temperature-coefficient. Then please refer to equation (8): 
     
       
         
           
             
               
                 
                   
                     V 
                     ref 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             I 
                             PTAT 
                           
                           + 
                           
                             I 
                             CTAT 
                           
                         
                         ) 
                       
                       * 
                       N 
                       * 
                       R 
                     
                     = 
                     
                       
                         
                           
                             
                               V 
                               T 
                             
                             * 
                             ln 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             K 
                             * 
                             N 
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   BE 
                                   , 
                                   210 
                                 
                               
                               L 
                             
                             * 
                             N 
                           
                         
                         ⁢ 
                         
                           
 
                         
                         ⇒ 
                         N 
                       
                       = 
                       
                         - 
                         
                           
                             V 
                             ref 
                           
                           
                             
                               
                                 V 
                                 T 
                               
                               * 
                               ln 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               K 
                             
                             + 
                             
                               
                                 V 
                                 
                                   BE 
                                   , 
                                   210 
                                 
                               
                               L 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Substituting the parameter L generated through equation (7) into equation (8) yields an equation describing a relationship between the parameter N and the reference voltage V ref . Please refer to equation (8). The reference voltage V ref  varies with the parameter N, and is not limited to 1.25V. 
     A function of the third zero-temperature-coefficient combined resistor  20  makes the circuits seen by the positive input terminal and the negative input terminal of the power amplifier  204  more symmetrical. 
     To sum up, the bandgap reference circuit can generate a zero-temperature-coefficient reference voltage in theory. However, the bandgap reference circuit is still affected by the temperature when the temperature effect of the resistor is not taken into consideration. The present invention uses the negative-temperature-coefficient resistor and the positive-temperature-coefficient resistor to form the resistor having an approximately zero-temperature-coefficient, so as to reduce the temperature effect on the bandgap reference circuit, and generate a bandgap reference voltage at any voltage level, and a reference current with an approximately zero-temperature-coefficient. 
     Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention.