Patent Publication Number: US-7218059-B2

Title: Discharge-lamp control device

Description:
BACKGROUND OF THE INVENTION 
   1. Technical Field 
   This invention relates to a discharge-lamp control device for controlling a discharge lamp used, for example, as a backlight of a liquid crystal display. 
   2. Related Art 
   Liquid crystal displays are widely used as personal computer monitors and/or televisions as well as displays for portable personal computers and word-processors. Recently, as the liquid crystal displays have become larger in size, the number of devices for lighting a plurality of discharge-lamps connected in parallel has increased. 
   Japanese Patent Application Publication 2004-241136 discloses a discharge-lamp control device for a single discharge-lamp having two electrodes. The discharge-lamp control device includes a pair of inverters, each of which is electrically connected to each of two electrodes. In this apparatus, the lighting of the discharge-lamp is controlled by transmitting high-frequency alternating-current power from the inverter to the discharge-lamp. 
   However, when this apparatus is used to light a plurality of discharge-lamps connected in parallel, the pair of inverters are necessary for each discharge-lamp, which increases power consumption and manufacturing cost. In order to solve these problems, a new system for lighting the plurality of discharge-lamps has been developed and is commercially available which has two inverter circuits, and two driving circuits connected to each of the inverter circuits. In this system, one inverter is connected to one of the two electrodes of the plurality of discharge-lamps connected in parallel. 
   However, when the plurality of discharge-lamps connected in parallel is lighted in the above new system, the amount of electric power supplied from the driving circuits to the discharge-lamps may become unbalanced because of variation in the impedances of the discharge-lamps. The power balance may also lose by distributed capacities of the discharge-lamps induced by the alternating-current driving. When the power of the driving circuits is unbalanced, a variation in a current flowing in the discharge-lamp may arise, which may result in shortening the service lives of discharge-lamps. 
   As described above, variation in the impedances of driving circuits may result in a loss of the power balance and/or current balance of the driving circuits. Therefore, the above phenomenon may lead to variation in the brightness of the discharge-lamp along the longitudinal direction and/or shortening the service lives of the discharge-lamps. 
   One attempt to conform the impedances of the driving circuits is to mount another component for adjustment, such as a transformer and a ballast capacitor, in the driving circuit. However, it is still difficult to obtain power balance and current balance of the driving circuits because of initial variations in characteristics of these components. 
   Further, if the transformer and the capacitor are selected with more strict specifications, cost will increase for selecting the components, thereby increasing the manufacturing cost of the discharge-lamp control device. 
   SUMMARY 
   An object of the present invention is to provide a discharge-lamp control device which can readily and easily balance the amount of electric power and/or current supplied from driving circuits connected to a discharge-lamp. 
   The present invention provides a discharge-lamp control device for controlling a discharge-lamp having two electrodes. The discharge-lamp control device includes a first driving unit and a second driving unit. The first driving unit is configured to be connected to one of the two electrodes to supply electric power at an operating frequency to the discharge-lamp. The first driving unit includes a first transformer having a first primary coil and a first secondary coil, and a first capacitor connected in parallel to the first secondary coil. The first driving unit has impedance characteristics with a minimum impedance at a first frequency and a maximum impedance at a second frequency. The second frequency is lower than the first frequency. The second driving unit is configured to be connected to the other of the two electrodes to supply electric power at the operating frequency to the discharge-lamp. The second driving unit includes a second transformer having a second primary coil and a second secondary coil, and a second capacitor connected in parallel to the second secondary coil. The second driving unit has impedance characteristics with a minimum impedance at a third frequency and a maximum impedance at a fourth frequency. The fourth frequency is lower than the third frequency. The first frequency is set to be higher than the third frequency. The second frequency is set to be lower than the fourth frequency. The operating frequency is selected within a frequency bandwidth from the fourth frequency through the third frequency. 
   The present invention provides a discharge-lamp control device for controlling a plurality of discharge-lamps connected in parallel between a first line and a second line. Each of the plurality of discharge-lamps has two electrodes. Ones of the two electrodes are connected to the first line. The other ones of the two electrodes are connected to the second line. The discharge-lamp control device includes a first driving unit and a second driving unit. The first driving unit is configured to be connected to the first line to supply electric power at an operating frequency to the plurality of the discharge-lamps. The first driving unit includes a first transformer having a first primary coil and a first secondary coil, and a first capacitor connected in parallel to the first secondary coil. The first driving unit has impedance characteristics with a minimum impedance at a first frequency and a maximum impedance at a second frequency. The second frequency is lower than the first frequency. The second driving unit is configured to be connected to the second line to supply electric power at the operating frequency to the plurality of the discharge-lamp. The second driving unit includes a second transformer having a second primary coil and a second secondary coil, and a second capacitor connected in parallel to the second secondary coil. The second driving unit has impedance characteristics with a minimum impedance at a third frequency and a maximum impedance at a fourth frequency. The fourth frequency is lower than the third frequency. The first frequency is set to be higher than the third frequency. The second frequency is set to be lower than the fourth frequency. The operating frequency is selected within a frequency bandwidth from the fourth frequency through the third frequency. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The particular features and advantages of the invention as well as other objects will become apparent from the following description taken in connection with the accompanying drawings, in which: 
       FIG. 1  is a circuit diagram showing a discharge-lamp control device according to an embodiment of the present invention; 
       FIG. 2  is a graph showing impedance characteristics of a master driving circuit and a slave driving circuit in the discharge-lamp control device; 
       FIG. 3  is a graph showing another impedance characteristics of the master driving circuit and the slave driving circuit in the discharge-lamp control device; 
       FIG. 4  is a circuit diagram showing a discharge-lamp control device for lighting a plurality of discharge-lamps connected in parallel; 
       FIG. 5  is a graph showing impedance characteristics of the master driving circuit and the slave driving circuit for lighting the plurality of discharge-lamps connected in parallel; and 
       FIG. 6  is a circuit diagram searching for an alternating-current frequency at which an impedance of the master driving circuit matches an impedance of the slave driving circuit. 
   

   DESCRIPTION OF THE EMBODIMENT 
   Embodiments according to the present invention will be described while referring to  FIGS. 1 through 6 . 
     FIG. 1  shows a discharge-lamp control device  10  according to an embodiment of the present invention. The discharge-lamp control device  10  controls the lighting of a discharge-lamp L with power supplied from a power source. The discharge-lamp control device  10  includes a switching circuit  20 , a control circuit  30 , a master driving circuit  40 M, and a slave driving circuit  40 S. The discharge-lamp L is configured to include a cold-cathode tube having electrodes E 1 , E 2  at both ends thereof. It should be noted that the cold-cathode tube is one example of the discharge-lamp L, and the discharge-lamp control device  10  can control any type of discharge-lamp as well as the cold-cathode tube. 
   The switching circuit  20  is configured to include an inverter circuit having input terminals A and B and output terminals C and D. The switching circuit  20  is electrically connected to the power supply  22  through the input terminals A and B to receive electric power having a direct-current voltage V in  from the power supply  22 . The switching circuit  20  is electrically connected to the master driving circuit  40 M and the slave driving circuit  40 S through the output terminals C and D to supply electric power having a switching frequency to each driving circuit  40 M,  40 S. The switching circuit  20  is connected to the control circuit  30 . 
   The control circuit  30  produces a control signal to control switching of the switching circuit  20 . The control signal determines the switching frequency and the pulse width of the switching. The control circuit  30  performs a suitable electric power control over the switching circuit  20 , such as pulse-width modulation (PWM) and phase modulation by means of the control signal. 
   The master driving circuit  40 M has a transformer T M  and a resonant capacitor C 1M . The transformer T M  has a primary coil  41  and a secondary coil  42  which are wound to have the same polarities to each other. The transformer T M  has a mutual inductance M M , a primary-coil leak inductance L L1M , a secondary-coil leak inductance L L2M , an exciting impedance L 1M , and a secondary inductance L 2M . The primary coil  41  is electrically connected between the terminals C and D. The secondary coil  42  is electrically connected in parallel to the resonant capacitor C 1M . The resonant capacitor C 1M  has one end connected to a reference potential G M  and the other end connected to an output terminal F of the master driving circuit  40 M. A capacitor C 2M  is connected between one end of the primary coil  41  and the terminal D. The master driving circuit  40 M is electrically connected to the electrode E 1  of the discharge-lamp L through the terminal F and a ballast capacitor C BM . The ballast capacitor C BM  is connected between the master driving circuit  40 M and the discharge-lamp L. 
   The master driving circuit  40 M contains a parallel resonant circuit including the resonant capacitor C 1M  and the exciting inductance L 1M  which are connected in parallel. The master driving circuit  40 M further includes a serial resonant circuit including the resonant capacitor C 1M  and the secondary inductance L 2M  which are connected in series. Accordingly, prior to lighting the discharge-lamp L, the master driving circuit  40 M has impedance characteristics Z M  having a serial resonant frequency f 0sM  and a parallel resonant frequency f 0pM , given by the following equations. 
   
     
       
         
           
             
               
                 
                   f 
                   
                     0 
                     ⁢ 
                     pM 
                   
                 
                 = 
                 
                   
                     1 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       π 
                     
                   
                   ⁢ 
                   
                     
                       
                         L 
                         
                           1 
                           ⁢ 
                           M 
                         
                       
                       
                         
                           C 
                           
                             1 
                             ⁢ 
                             M 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 L 
                                 
                                   1 
                                   ⁢ 
                                   M 
                                 
                               
                               · 
                               
                                 L 
                                 
                                   2 
                                   ⁢ 
                                   M 
                                 
                               
                             
                             - 
                             
                               M 
                               M 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
           
             
               
                 
                   f 
                   
                     0 
                     ⁢ 
                     SM 
                   
                 
                 = 
                 
                   1 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     π 
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             
                               L 
                               
                                 2 
                                 ⁢ 
                                 M 
                               
                             
                             + 
                             
                               L 
                               L2M 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           C 
                           
                             1 
                             ⁢ 
                             M 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   where C 1M  is a capacitance of the resonant capacitor C 1M , and the serial resonant frequency f 0sM  is greater than the parallel resonant frequency f 0pM . 
   The serial resonant frequency f sM  and the parallel resonant frequency f pM  of the master driving circuit  40 M are changed after lighting the discharge-lamp L as follows; 
   
     
       
         
           
             
               
                 
                   f 
                   pM 
                 
                 = 
                 
                   
                     1 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       π 
                     
                   
                   ⁢ 
                   
                     
                       
                         L 
                         
                           1 
                           ⁢ 
                           M 
                         
                       
                       
                         
                           
                             
                               
                                 C 
                                 
                                   1 
                                   ⁢ 
                                   M 
                                 
                               
                               + 
                               
                                 Z 
                                 lamp 
                               
                             
                             // 
                             
                               C 
                               BM 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 L 
                                 
                                   1 
                                   ⁢ 
                                   M 
                                 
                               
                               · 
                               
                                 L 
                                 
                                   2 
                                   ⁢ 
                                   M 
                                 
                               
                             
                             - 
                             
                               M 
                               M 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 3 
                 ) 
               
             
           
           
             
               
                 
                   f 
                   SM 
                 
                 = 
                 
                   1 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     π 
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             
                               L 
                               
                                 2 
                                 ⁢ 
                                 M 
                               
                             
                             + 
                             
                               L 
                               L2M 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 C 
                                 
                                   1 
                                   ⁢ 
                                   M 
                                 
                               
                               + 
                               
                                 Z 
                                 lamp 
                               
                             
                             // 
                             
                               C 
                               BM 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   where C BM  is a capacitance of the ballast capacitor C BM , Z lamp  is an impedance of the discharge-lamp L, and the serial resonant frequency f sM  is greater than the parallel resonant frequency f pM . 
   As described above, it is apparent that the serial and parallel resonant frequencies f sM  and f pM  of the master driving circuit  40 M change as a function of the impedance of the discharge-lamp L which is connected to the driving circuits. 
   The slave driving circuit  40 S includes a transformer T S  and a resonant capacitor C 1S . The transformer T S  includes a primary coil  43  and a secondary coil  44  which are wound to have polarities that are reverse to each other. The transformer T S  has a mutual inductance M S , a primary-coil leak inductance L L1S , a secondary-coil leak inductance L L2S , an exciting inductance L 1S , and a secondary inductance L 2S . The primary coil  43  is electrically connected between the terminals C and D. The secondary coil  44  is connected in parallel to the resonant capacitor C 1S . The resonant capacitor C 1S  has one end connected to a reference potential G S  and the other end connected to an output terminal H of the slave driving circuit  40 S. A capacitor C 2S  is connected between one end of the primary coil  41  and the terminal D. The slave driving circuit  40 S is electrically connected to the electrode E 2  of the discharge-lamp L through the terminal H and a ballast capacitor C BS . The ballast capacitor C BS  is connected between the slave driving circuit  40 S and the discharge-lamp L. 
   The slave driving circuit  40 S includes a parallel resonant circuit having the resonant capacitor C 1S  and the exciting inductance L 1S  which are connected in parallel. The slave driving circuit  40 S further includes a serial resonant circuit having the resonant capacitor C 1S  and the secondary inductance L 2S  which are connected in series. 
   Therefore, the slave driving circuit  40 S has a serial resonant frequency f 0sS  and a parallel resonant frequency fops defined by equations (5) and (6) prior to lighting the discharge-lamp L, the same as the master driving circuit  40 M. The slave driving circuit  40 S has a serial resonant frequency f sS  and a parallel resonant frequency f pS  defined by the equations (7) and (8) after lighting the discharge-lamp L. 
   
     
       
         
           
             
               
                 
                   f 
                   
                     0 
                     ⁢ 
                     pS 
                   
                 
                 = 
                 
                   
                     1 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       π 
                     
                   
                   ⁢ 
                   
                     
                       
                         L 
                         
                           1 
                           ⁢ 
                           S 
                         
                       
                       
                         
                           C 
                           
                             1 
                             ⁢ 
                             S 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 L 
                                 
                                   1 
                                   ⁢ 
                                   S 
                                 
                               
                               · 
                               
                                 L 
                                 
                                   2 
                                   ⁢ 
                                   S 
                                 
                               
                             
                             - 
                             
                               M 
                               S 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 5 
                 ) 
               
             
           
           
             
               
                 
                   f 
                   
                     0 
                     ⁢ 
                     sS 
                   
                 
                 = 
                 
                   1 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     π 
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             
                               L 
                               
                                 2 
                                 ⁢ 
                                 S 
                               
                             
                             + 
                             
                               L 
                               L2S 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           C 
                           
                             1 
                             ⁢ 
                             S 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
           
             
               
                 
                   f 
                   pS 
                 
                 = 
                 
                   
                     1 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       π 
                     
                   
                   ⁢ 
                   
                     
                       1 
                       
                         
                           ( 
                           
                             
                               
                                 C 
                                 
                                   1 
                                   ⁢ 
                                   S 
                                 
                               
                               + 
                               
                                 Z 
                                 lamp 
                               
                             
                             // 
                             
                               C 
                               BS 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 L 
                                 
                                   1 
                                   ⁢ 
                                   S 
                                 
                               
                               · 
                               
                                 L 
                                 
                                   2 
                                   ⁢ 
                                   S 
                                 
                               
                             
                             - 
                             
                               M 
                               M 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
           
             
               
                 
                   f 
                   sS 
                 
                 = 
                 
                   1 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     π 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             
                               L 
                               
                                 2 
                                 ⁢ 
                                 S 
                               
                             
                             + 
                             
                               L 
                               L2S 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 C 
                                 
                                   1 
                                   ⁢ 
                                   S 
                                 
                               
                               + 
                               
                                 Z 
                                 lamp 
                               
                             
                             // 
                             
                               C 
                               BS 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
   In the slave driving circuit  40 S, the serial resonant frequency f 0sS  is greater than the parallel resonant frequency f 0pS , as in the case of the master driving circuit  40 M. Even after lighting the discharge-lamp L, the serial resonant frequency f sS  remains greater than the parallel resonant frequency f pS . The serial and parallel resonant frequencies f sS  and f ps  of the slave driving circuit  40 S change as a function of the impedance of the discharge-lamp L, as the master driving circuit  40 M. 
   The next description will be made for explaining characteristics of the master and slave driving circuits  40 M and  40 S. 
   The transformers T S  and T M  have the same structure and the same transformer voltage ratio except for the polarities of the primary and secondary coils. In this embodiment, the transformers T S  and T M  manufactured to have the same characteristics except for the polarities are adopted for the driving circuits  40 M and  40 S. The capacitors C 1M  and C 1S  have the same capacitance. In other words, The capacitors C 1M  and C 1S  manufactured to have the same characteristics including a capacitance are adopted for the driving circuits  40 M and  40 S. Accordingly, the slave driving circuit  40 S is basically expected to have the same impedance characteristics as the master driving circuit  40 M. 
   However, generally, impedance characteristics Z M  of the master driving circuit  40 M are often inconsistent with impedance characteristics Z S  of the slave driving circuit  40 S, due to manufacturing tolerances of the transformers T M , T S  and capacitors C 1M  C 1S , even if the corresponding components of the driving circuits  40 M and  40 S are manufactured to have the same characteristics. 
   Referring to  FIG. 2 , the master driving circuit  40 M and the slave driving circuit  40 S have a relationship in terms of the impedance characteristics Z M  and Z S  as follows:
 
f pM &lt;f pS , 10 kHz&lt;Δf p &lt;40 kHz  (9)
 
f sS &lt;f sM , 10 kHz&lt;Δf s &lt;20 kHz  (10)
 
   where Δf p =f pS −f pM , Δf s =f sM −f sS    
     FIG. 2  shows one example of the impedance characteristics of the master driving circuit  40 M and slave driving circuit  40 S which satisfy equations (9) and (10). If the impedance characteristics Z M  an Z S  have a relationship satisfying equations (9) and (10), the impedance characteristics Z M  an Z S  have an intersection point at a frequency f c  within the bandwidth from the parallel resonant frequency f pS  to the serial resonant frequency f sS . In other words, the impedance value Z M  of the master driving circuit  40 M is equal to the impedance value Z S  of the slave driving circuit  40 S at the frequency f c . 
   The next description will be made for explaining the operation of the discharge-lamp control device  10 . When the switching circuit  20  receives a control signal from the control circuit  30 , the switching circuit  20  converts input power of the power supply  22  to high frequency alternating-current power having a switching frequency f defined by the control signal. The switching circuit  20  then supplies the high frequency alternating-current power to both of the master driving circuit  40 M and the slave driving circuit  40 S. 
   The master driving circuit  40 M operates at an operating frequency corresponding to the switching frequency f. The master driving circuit  40 M converts an input voltage from the switching circuit  20  to an output voltage V outM  to apply the converted voltage  outM  to the electrode E 1  of the discharge-lamp L. 
   The slave driving circuit  40 S also operates at the same operating frequency as that of the master driving circuit  40 M. The slave driving circuit  40 S converts the input voltage from the switching circuit  20  into an output voltage V outS  to apply the output voltage V outS  to the electrode E 2  of the discharge-lamp L. A 180-degree phase shift is generated between the output voltages V outS  and V outM , because the transformer T M  of the master driving circuit  40 M has a polarity that is reverse to that of the transformer T S  of the slave driving circuit  40 S. Therefore, a voltage of |V outM +V outS | is applied between the electrodes E 1  and E 2  of the discharge-lamp L to control the lighting of the discharge-lamp L. 
   When driving the master driving circuit  40 M and the slave driving circuit  40 S at the operating frequency corresponding to the intersecting point shown in  FIG. 2 , the impedance of the master driving circuit  40 M becomes equal to that of the slave driving circuit  40 S. The electric power supplied from the master driving circuit  40 M becomes equal to the electric power supplied from the slave driving circuit  40 S, because the applied voltage from the switching circuit  20  to the master driving circuit  40 M is equal to the applied voltage from the switching circuit  20  to the slave driving circuit  40 S. Accordingly, the amount of current flow to the discharge-lamp L through the electrode E 1  is equal to the amount of current flow to the discharge-lamp L through the electrode E 2 , because the amount of electric power of the master driving circuit  40 M is balanced with the amount of electric power of the slave driving circuit  40 S. Therefore, a detrimental effect on the operating life of the discharge-lamp L can be avoided. For example, shortening of the operating life of the discharge-lamp is avoided. 
   The operating frequency of the driving circuits  40 M and  40 S is determined in order that the driving circuits  40 M and  40 S may have the same impedances, after the driving circuits  40 M and  40 S are assembled into the discharge-lamp control device  10 . Accordingly, criteria to select an electric component constituting the driving circuits  40 M and  40 S can be relaxed. Therefore, there is no need to strictly select each and every electric component constituting the driving circuits  40 M and  40 S in order to impose the same impedance on the driving circuits  40 M and  40 S in manufacturing the discharge-lamp control device  10 . Accordingly, the manufacturing cost of the discharge-lamp control device  10  can be reduced. 
   Further, the operating frequency of the driving circuits  40 M and  40 S is determined in order that the driving circuits  40 M and  40 S may have the same impedances, after a discharge-lamp L is connected to the discharge-lamp control device  10 . Accordingly, the amount of electric power from the master driving circuit  40 M can be balanced with the amount of electric power from the slave driving circuit  40 S, even if the impedance of the discharge-lamp L changes. 
   When the impedance characteristics Z M  and Z S  have the following relationship defined by equations (11) and (12), the discharge-lamp control device  10  has similar advantages of those of the driving circuits  40 M and  40 S satisfying equations (9) and (10).
 
f pM &lt;f pS , 10 kHz&lt;Δf p ′&lt;20 kHz  (11)
 
f sM &lt;f sS , 10 kHz&lt;Δf s ′&lt;20 kHz  (12)
 
   wherein Δf p ′=f pS −f pM , Δf s ′=f sS −f sM . 
     FIG. 3  shows another example of the impedance characteristics of the driving circuits  40 M and  40 S satisfying equations (11) and (12). If the impedance characteristics Z M  and Z S  satisfy equations (11) and (12), the impedance characteristics Z M  and Z S  have an intersecting point at a frequency fc′ within the bandwidth from the serial resonant frequency f sM  to the serial resonant frequency f sS . In other words, the impedance of the master driving circuit  40 M is equal to the impedance of the slave driving circuit  40 S at the frequency fc′. 
   Accordingly, if the switching circuit  20  is switching at the frequency f c ′, and the master and slave driving circuits  40 M and  40 S are driven at the frequency f c ′, the impedance of the master driving circuit  40 M becomes equal to the impedance of the slave driving circuit  40 S. Simultaneously, the amount of electric power of the driving circuit  40 M can be balanced with the amount of electric power of the driving circuit  40 S, because the same voltages are applied to both of the driving circuits  40 M and  40 S. 
   In this embodiment, the discharge-lamp control device  10  controls lighting of a single discharge-lamp L. Alternatively, the discharge-lamp control device  10  is capable of lighting a plurality of discharge-lamps L connected in parallel, as shown in  FIG. 4 . Referring to  FIG. 4 , n-number discharge-lamps L 1 –L n  are connected in parallel. Each discharge-lamp L i  has one electrode connected to the output terminal F of the master driving circuit  40 M through a capacitor C Mi  and the other electrode connected to the output terminal H of the slave driving circuit  40 S through a capacitor C si . It should be note that “n” is an integer equal to or greater than 2 and “i” is an integer between 1 through “n”. 
   When the plurality of discharge-lamps L is connected in parallel to be lighted, the impedance characteristics Z M  and Z S  of the master and slave driving circuits  40 M and  40 S do not have abrupt peak impedance values as the serial resonant frequency and the parallel resonant frequency. As shown in  FIG. 5 , the parallel resonant frequencies f pM  and f pS  appear as sloping maximum impedance values within the lower-frequency bandwidth. The serial maximum resonant frequencies f sM  and f sS  appear as minimum impedance values within the higher-frequency bandwidth which is higher than the lower-frequency bandwidth. After lighting the plurality of discharge-lamps L, the impedance characteristics of the driving circuit for controlling the plurality of discharge-lamps L is combined impedance characteristics of the driving circuit for a single discharge-lamp L, because each discharge-lamp L has a different impedance from each other. 
   In this case, the minimum and maximum values of each driving circuit  40 M,  40 S are regarded as the serial and parallel resonant frequencies, respectively, and then the driving circuits are configured in order that the impedance characteristics Z M  and Z S  may meet one of the conditions which satisfies equations (9) and (10) and the condition which satisfies equations (11) and (12), it is preferable that the impedance characteristics Z M  and Z S  satisfy equations (9) and (10). Therefore, the frequency fc at which the impedances Z M  and Z S  are equal to each other can be set as the operating frequency of the discharge-lamp control device  10 . Accordingly, when the driving circuits  40 M and  40 S light the plurality of discharge-lamps L connected in parallel, the amount of electric power of the master driving circuit  40 M is balanced with the amount of electric power of the slave driving circuit  40 S. 
   In this embodiment, a description is given for the driving circuits  40   M  and  40   S  having the impedance characteristics Z M , Z S  which intersect at the frequency f c  within a predetermined frequency bandwidth from f pS  to f sS . Unless the impedance characteristics Z M  and Z S  have an intersecting point frequency f c  within the predetermined frequency bandwidth, a frequency f at which the impedance Z M  is in proximity to the impedance Z S  is adopted as the switching frequency of the switching circuit  20 . In other words, the frequency at which the impedance Z M  is considered to be substantially the same as the impedance Z S  can be set as the switching frequency of the switching circuit  20 . 
   In this case, the electric power of the driving circuit  40 M is determined to be approximately balanced with the electric power of the driving circuit  40 S. As a result, the service lives of the discharge-lamps L are not shortened by the power imbalance of the driving circuits, and the discharge-lamp L can emit light uniformly along its longitudinal direction. 
   One way to search for the frequency at which the impedance Z M  is equal to the impedance Z S  is a simulation of the impedance characteristics Z M  and Z S  of the driving circuits  40 M and  40 S. With the simulation, an intersecting point of the two characteristics curves can be obtained and thus the intersecting frequency point can be set as the operating frequency f c . 
   Another way is an experiment to search for the frequency of the intersecting point of the impedance characteristics Z M  and Z S . Referring to  FIG. 6 , an alternating-current frequency at which the impedance Z M  matches the impedance Z S  can be searched for by a measurement. An ammeter A M  for measuring an amount of current I M  flowing through the primary coil  41  of the transformer T M  is provided in the master driving circuit  40 M. Another ammeter A S  for measuring an amount of current I S  flowing through the primary coil  43  of the transformer T S  is provided in the slave driving circuit  40 S. A comparator  50  receives detection signals from the ammeters A M  and A S  and compares one detection signal with the other signal. The control circuit  30  selects the switching frequency of the switching circuit  20  to meet the relationship of ΔI=I M −I S =0. 
   Even when the discharge-lamp control device  10  is used to light a single discharge-lamp L, a frequency fc at which the impedance Z M  is equal to the impedance Z S  can be searched for. 
   In this case, a phase matching of the detected currents I M  and I S  is one of the requirements for searching for the intersecting frequency fc. It is preferable that the phase of the current I M  matches the phase of the current I S  at a given frequency. However, if the phases of the currents I M  and I S  do not match but root-mean-square currents or effective currents of the currents I M  and I S  match at the given frequency, the impedances Z M  and Z S  are considered close to each other at the given frequency. The electric power of the driving circuit  40 M can be approximately balanced with the electric power of the driving circuit  40 S at the given frequency. Accordingly, the frequency to satisfy the condition: ΔI=I M −I S =0 can be determined by measuring the effective current value and/or effective power. The determined frequency can be set as the operating frequency of the driving circuits  40 M and  40 S. 
   As described above, after the master and slave driving circuits are assembled from electric components which have the same structure and characteristics, the frequency at which the impedance Z M  matches the impedance Z S  is determined by simulation or experimentation and set as the operating frequency for the both driving circuits. Accordingly, the electric power of the master driving circuit  40 M is balanced with the electric power of the slave driving circuit  40 S. Further, the current of the driving circuit  40 M is balanced with the current of the driving circuit  40 S. Therefore, the strict sorting of electric components for the discharge-lamp control device is not necessary when assembling the discharge-lamp control device. Accordingly, the manufacturing cost of the discharge-lamp control device can be reduced. 
   In the above embodiment, the transformers T M , T S  having the same transformer voltage ratio are used, and the capacitors C 1M , C 1S  having the same capacitors are used. However, if the driving circuits  40 M,  40 S obtain the same impedance at a given frequency, any electric components other than the above components T M , T S ; C 1M , C 1S  can be used for the driving circuits  40 M,  40 S. 
   Referring to the drawings, like elements in the drawings are identified by the same reference numerals. It is understood that the foregoing description and accompanying drawings set forth the embodiments of the invention. Various modifications, additions and alternative designs will, of course, become apparent to those skilled in the art in light of the foregoing teachings without departing from the spirit and scope of the disclosed invention. Thus, it should be appreciated that the invention is not limited to the disclosed embodiments but may be practiced within the full scope of the appended claims.