please refer to fig3 , which is a diagram of a bandgap voltage regulator 300 of a first embodiment according to the present invention . the bandgap voltage regulator 300 comprises a start - up circuit 310 , a bandgap voltage generating circuit 320 , and a voltage regulator 330 . the bandgap voltage generating circuit 320 is utilized to generate a bandgap voltage v bg , and the voltage regulator 330 is utilized to generate a regulated voltage according to the bandgap voltage v bg . in addition , in this embodiment , the function of the start - up circuit 310 is the same as that of the above - mentioned start - up circuit 110 . the start - up circuit 310 is also utilized to keep the bandgap voltage generating circuit 320 in a predetermined steady state such that the bandgap voltage generating circuit 320 can generate the bandgap voltage v bg accurately . in addition , the bandgap generating circuit 320 also comprises a zone 321 . the zone 321 is similar to the zone 121 ; therefore the voltages of the node a and the node b should also be the same . furthermore , in this embodiment , the resistances of the resistors r 2 and r 3 are the same . theoretically , the voltages of the node c and the node d are the same . the zone 322 is equivalent to the circuit diagram shown in fig2 . in other words , the current i 2 is generated due to the voltage differences v be1 − v be2 of the bjts q 1 and q 2 , and the resistor r 1 . the current i 2 can be represented by : i 2 = ( v be ⁢ ⁢ 1 - v be ⁢ ⁢ 2 ) / r 1 = v t ⁡ [ ln ⁡ ( n ) ] / r 1 equation ⁢ ⁢ ( 6 ) the current i 2 is the current having a positive temperature coefficient . in this embodiment , the current i 2 passes through the resistor r 2 to generate a voltage also having a positive temperature coefficient . the voltage v b of node b is the sum of the resistor ( r 1 + r 2 ), and the voltage difference v be2 between the base and the emitter of the bjt q 2 . it can be represented by the following equation . v b = v be ⁢ ⁢ 2 + v ( r ⁢ ⁢ 1 + r ⁢ ⁢ 2 ) = v be ⁢ ⁢ 2 + v r ⁢ ⁢ 1 + v r ⁢ ⁢ 2 = v be ⁢ ⁢ 2 + r 1 ⁡ ( v be ⁢ ⁢ 1 - v be ⁢ ⁢ 2 ) / r 1 + v t ⁡ [ ln ⁡ ( n ) ] ⁢ ( r 2 / r 1 ) = v be ⁢ ⁢ 1 + v t ⁡ [ ln ⁡ ( n ) ] ⁢ ( r 2 / r 1 ) equation ⁢ ⁢ ( 7 ) as the voltage difference between the base and the emitter is a voltage having a negative temperature coefficient , the above - mentioned equation ( 4 ) can be combined with equation ( 7 ) such that the following equation ( 8 ) can be obtained . v b = v bg − v t ( a * ln t − ln k )+ v t [ ln ( n )]( r 2 / r 1 ) equation ( 8 ) similarly , the circuit designer can appropriately adjust parameters of each device ( such as the transistors or the resistor ) such that a voltage at the node b , which is not dependent on temperature , can be generated . the present invention utilizes a resistor r 2 in series with the resistor r 1 , and utilizes another resistor r 3 to match the resistor r 2 in order to make the voltages of the node c and the node d equal . furthermore , the present invention utilizes the voltage of the resistor r 2 and the voltage difference between the base and the emitter of the transistor q 2 to generate the bandgap voltage v bg . in fig3 , the voltage level of the node b is the bandgap voltage v bg , and the voltage level v e of the node e is the sum of the bandgap voltage v bg and the voltage difference between the gate and the source of the transistor m 2 . v e can be represented by the following equation : moreover , the voltage level at the node e is the same as that of the node f . therefore , the voltage level v g of the node g is equal to that the voltage level v e of the node e minus the voltage difference between the gate and the source of the transistor m 9 . v g can be represented by the following equation : v g = v e - v gs ⁢ ⁢ 9 = v bg + v gs ⁢ ⁢ 2 - v gs ⁢ ⁢ 9 equation ⁢ ⁢ ( 10 ) the circuit designer can properly adjust the parameters of the transistors m 2 and m 9 to select the above - mentioned voltage differences v gs2 and v gs9 such that a required regulated voltage can be obtained . for example , if the voltage differences between the gate and the source of the transistors m 2 and m 9 are the same , the voltage level of the node g can substantially correspond to the bandgap voltage v bg . the circuit designer can also select different transistors such that the voltage level of the node g can correspond to difference voltage levels . this change also complies with the spirit of the present invention . the bandgap voltage generating circuit 320 of the present invention does not need the current i 4 shown in fig1 , thus reducing power consumption . furthermore , since the voltage regulator 330 does not include an operational amplifier , the current utilized by the voltage regulator 330 is also diminished . this makes the standby current much lower when the core circuit 340 is in standby mode . please refer to fig4 , which is a diagram of the bandgap voltage regulator 300 of a second embodiment according to the present invention . in the second embodiment , a single resistor r is utilized to replace the two resistors r 1 and r 2 of the first embodiment . obviously , if the resistance of the resistor r corresponds to the total resistance of the two resistors r 1 + r 2 , the second embodiment is equivalent to the first embodiment . as the circuit operation and function of the second embodiment are the same as those of the first embodiment , the details are omitted here . please refer to fig5 , which is a diagram of the bandgap regulator 300 of a third embodiment according to the present invention . in the third embodiment , the voltage regulator 530 utilizes the operational amplifier structure to generate a relatively accurate regulated voltage . in contrast to the circuit shown in fig1 , the circuit shown in fig5 also removes the current i 4 shown in fig1 . in the third embodiment , resistors r 1 and r 2 can be replaced by a single resistor r . those skilled in the art should understand the corresponding circuit structure and the function , and further illustration is thus omitted here . although the above - mentioned bandgap voltage regulator 300 consumes less power , meaning the standby current is lower when the core circuit 340 is in standby mode , the regulated voltage is relatively not so accurate due to the fact that the regulated voltage generated by the bandgap voltage regulator 300 utilizes an open loop at the transistor m 9 . in other words , the bandgap voltage regulator 300 using an open loop structure is not appropriate when used in a high - speed digital circuit , which requires an accurate input voltage . please refer to fig6 , which is a diagram of a bandgap voltage generating device 600 according to the present invention . as shown in fig6 , the bandgap voltage generating device 600 comprises a bandgap voltage regulator 300 , a conventional bandgap voltage regulator 100 , and a controller 610 . the controller 610 is respectively coupled to the conventional bandgap voltage regulator 100 , the bandgap voltage regulator 300 , and the core circuit 340 . the conventional bandgap voltage regulator 100 , the bandgap voltage regulator 300 , and the core circuit 340 are all coupled to the node a . the bandgap voltage generating device 600 provides the bandgap voltage continuously to the node a to keep the core circuit 340 running even during standby mode . however , during standby mode , the consumed current ( the standby current ) is preferably a low current . when the core circuit 340 is switched into active mode , the core circuit 340 should then be relatively accurate . therefore , in the following disclosure , a bandgap generating device having the advantages of accurate input voltage and low standby current is disclosed . the controller 610 shown in fig6 is utilized to switch the core circuit 340 into active mode or standby mode . for example , the controller 610 can output an enable signal to the core circuit 340 to switch the core circuit 340 from the original standby mode into active mode . alternatively , the controller 610 can output a disable signal to switch the core circuit from the original active mode to standby mode . when the core circuit 340 is in standby mode ( at this time , the core circuit 340 has not been activated yet ), the controller 610 turns off the conventional bandgap voltage regulator 100 , so at this time only the bandgap voltage regulator 300 works . as mentioned previously , the bandgap voltage regulator 300 consumes less power , which is however necessary for providing the bandgap voltage of node a and the operating voltage of the controller 610 in standby mode . the bandgap voltage generating device 600 therefore has a lower standby current during this time . the controller 610 controls the core circuit 340 to switch the core circuit 340 from standby mode into active mode . as the core circuit 340 requires an accurate regulated voltage to work , the bandgap voltage regulator 300 is no longer utilized at this time . instead , the controller 610 outputs the enable signal to the conventional bandgap voltage regulator 100 to turn on the bandgap voltage regulator 100 to generate an accurate regulated voltage . this enables the core circuit 340 to utilize the bandgap voltage generated by the bandgap voltage regulator 100 to perform a predetermined operation . as the conventional bandgap voltage regulator 100 and the bandgap voltage regulator 300 are both coupled to node a , when the core circuit 340 is in active mode , the bandgap voltage regulator 300 and the bandgap voltage regulator 100 simultaneously output voltages to the node a . in this embodiment , however , some techniques are utilized to make the output current of the bandgap voltage regulator 100 larger than that of the bandgap voltage regulator 300 . the voltage of node a will then be mainly determined by the bandgap voltage regulator 100 . in other words , the bandgap voltage regulator 100 is dominant when the bandgap voltage regulator 300 and the bandgap voltage regulator 100 both work . please note that the above - mentioned techniques are well known by those skilled in the art . for example , the source of the transistor m 9 of the bandgap voltage regulator 300 and the source of the transistor m 5 of the bandgap voltage regulator 100 correspond to the same voltage level . therefore , if the gate of the transistor m 5 corresponds to a higher voltage level , the output current of the bandgap voltage regulator 100 can be larger . please note that the input voltage required by the core circuit 340 in active mode can be different from that required by the core circuit 340 in standby mode . for example , because the core circuit 340 does not really work in standby mode , the core circuit 340 can utilize a lower voltage for ensuring that the core circuit 340 can be activated later . therefore , in this embodiment , the bandgap voltage regulator 100 and the bandgap voltage regulator 300 can output different voltage levels ( for instance , the bandgap voltage regulator 100 can generate a higher voltage level ). however , as mentioned previously , since the bandgap voltage regulator 100 provides a larger output current , the bandgap voltage regulator 100 can pull up the voltage level of the node a such that the bandgap voltage required can be generated when the core circuit 340 is in active mode . please refer to fig7 , which is a diagram of the bandgap voltage generating device 600 of a second embodiment according to the present invention . as shown in fig7 , the bandgap voltage generating device 600 also comprises the conventional bandgap voltage regulator 100 , the bandgap voltage regulator 300 , and a controller 610 . the controller 610 is coupled to the bandgap voltage regulator 100 , the bandgap voltage regulator 300 , and a core circuit 340 . the bandgap voltage generating device 600 of the second embodiment further comprises a switch 620 coupled between the bandgap voltage regulator 300 and the node a . the controller 610 is also coupled to the switch 620 . in this embodiment , the switch 620 breaks the electrical connection between the bandgap voltage regulator 300 and node a . in other words , when the controller 610 switches the core circuit 340 into active mode , the controller 620 simultaneously breaks the electrical connection between the bandgap voltage regulator 300 and node a , so that voltage output from the bandgap voltage regulator 300 to node a is interrupted . this means that the voltage level of node a is entirely determined by the bandgap voltage regulator 100 . please note that other operations of the second embodiment are the same as the first embodiment , and thus omitted here . 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 . accordingly , the above disclosure should be construed as limited only by the metes and bounds of the appended claims .