1.  Field of the Invention
The present invention relates to a voltage reference circuit with low sensitivity to temperature, and more specifically, to a low-voltage bandgap reference circuit. 
2.  Description of the Prior Art
Reference voltage generators are widely used in both analog and digital circuits such as DRAM and flash memories.  A bandgap reference (also termed BGR) is a circuit that provides a stable output voltage with low sensitivity to temperature and supply voltage. 
A conventional bandgap reference output is about 1.25 V, which is almost equal to the silicon energy gap measured in electron volts.  However, in modern deep-submicron technology, a voltage of around 1 V is preferred.  As such, the conventional bandgap reference is inadequate for current requirements. 
The 1 V minimum supply voltage is constrained by two factors.  First, the reference voltage of about 1.25 V exceeds 1 V. Second, low voltage design of proportional to-absolute-temperature (PTAT) current generation loops is limited by the input common-mode voltage of the amplifier.  The effects of these constraints can be reduced by resistive subdivision methods and by using low threshold voltage devices or BiCMOS processes.  However, both of these solutions require costly special process technology. 
Bandgap references can be divided into two groups: type-A and type-B. Type-A bandgap references sum voltages of two elements having opposite temperature components.  Type-B bandgap references combine the currents of two elements.  Both type A and type B bandgap references can be designed to function with a normal supply voltage of greater than 1 V and a sub-1-V supply voltage. 
FIG.  1 illustrates a conventional type-A bandgap reference circuit 10.  The bandgap reference circuit 10 includes an operational amplifier 12, two transistors M1 and M2, two resistors R1 and R2, and two diodes Q1 and Q2.  The sources of the transistors M1, M2 are connected to a supply voltage VDD.  The drain of the transistor M1 is connected to the emitter of the diode Q1 through the resistor R1 and to the positive input of the amplifier 12.  Similarly, the drain of the transistor M2 is connected to the emitter of the diode Q2 through the resistor R2 and to the negative input of the amplifier 12.  The gates of the transistors M1, M2 are connected to the output of the amplifier 12.  In CMOS applications, each diode Q1, Q2 is formed with a parasitic vertical bipolar transistor having a collector and base connected to ground. 
Neglecting base current, the emitter-base voltage of a forward active operation diode can be expressed as:                               V          EB                =                                            k              ⁢                                                          ⁢              T                        q                    ⁢                      ln            ⁡                          (                                                I                  C                                                  I                  S                                            )                                                          (        1        )            where:
k is Boltzmanns constant (1.38×10−23 J/K),
q is the electronic charge (1.6×10−19 C),
T is temperature,
IC is the collector current, and
IS is the saturation current. 
When the input voltages of the amplifier 12 are forced to be the same, and the size of the diode Q1 is N times that of the diode Q2, the emitter-base voltage difference between diodes Q1 and Q2, ΔVEB, becomes:                               Δ          ⁢                                          ⁢                      V            EB                          =                                            V              EB2                        -                          V              EB1                                =                                                    k                ⁢                                                                  ⁢                T                            q                        ⁢            ln            ⁢                                                  ⁢            N                                              (        2        )            where:
VEB1 is the emitter-base voltage of diode Q1, and
VEB2 is the emitter-base voltage of diode Q2. 
Finally, when the current through resistor R1 is equal to the current through resistor R2 and is set to be PTAT, an output reference voltage, VREF, can be obtained by:                               V          REF                =                                            V              EB2                        +                                                            R                  2                                                  R                  1                                            ⁢              Δ              ⁢                                                          ⁢                              V                EB                                              ≡                      V                          REF              ⁢                              -                            ⁢              CONV                                                          (        3        )            where:
R1 is the resistance of resistor R1,
R2 is the resistance of resistor R2, and
VREF-CONV is the reference voltage (conventional). 
The emitter-base voltage, VEB, has a negative temperature coefficient of −2 mV/° C., while the emitter-base voltage difference, ΔVEB, has a positive temperature coefficient of 0.085 mV/° C. Hence, if a proper ratio of resistances of resistors R1 and R2 is selected, the output reference voltage, VREF, will have low sensitivity to temperature.  In general, the supply voltage, VDD, is set to about 3–5 V and the output reference voltage, VREF, is about 1.25 V, as the conventional bandgap circuit 10 cannot be used at a lower voltage such as 1 V.
FIG.  2 illustrates a conventional type-B bandgap reference circuit 20.  Elements in FIG.  2 having the same reference numbers of those in FIG.  1 are the same.  The bandgap reference circuit 20 includes an operational amplifier 22; three transistors M1, M2, and M3; four resistors R1, R2, R3, and R4; and two diodes Q1 and Q2 interconnected as illustrated in FIG.  2. 
Compared with the type-A circuit 10, the type-B circuit 20 is more suitable for operating with a low supply voltage.  Instead of stacking two complementary voltages, the type-B bandgap reference 20 adds two currents with opposite temperature dependencies.  In the bandgap reference of FIG.  2, the current through the resistor R3 is PTAT.  If the resistances of the resistors R1 and R2 are equal, then the current through the MOS transistor M3 mirrored from transistors M1 and M2 can be expressed as:                               I          M3                =                              1                          R              1                                ⁢                      (                                          V                EB2                            +                                                                    R                    1                                                        R                    3                                                  ⁢                                                      k                    ⁢                                                                                  ⁢                    T                                    q                                ⁢                ln                ⁢                                                                  ⁢                N                                      )                                              (        4        )            with the reference voltage being expressed as:                               V          REF                =                                                            R                4                                            R                1                                      ⁢                          (                                                V                  EB2                                +                                                                            R                      1                                                              R                      3                                                        ⁢                                                            k                      ⁢                                                                                          ⁢                      T                                        q                                    ⁢                  ln                  ⁢                                                                          ⁢                  N                                            )                                =                                                    R                4                                            R                1                                      ·                          V                              REF                ⁢                                  -                                ⁢                CONV                                                                        (        5        )            
Thus, in the bandgap reference circuit 20 of FIG.  2, as ratios of resistances are key, the variations in individual resistances due to process conditions does not greatly affect the reference voltage.  In general, the supply voltage, VDD, is set to about 1.5 V and the output reference voltage, VREF, is about 1.2 V.
FIG.  3 illustrates a conventional type-B bandgap reference circuit 30 capable of sub-1-V operation.  Elements in FIG.  3 having the same reference numbers of those in FIG.  2 are the same.  The bandgap reference circuit 30 includes an operational amplifier 32; three transistors M1, M2, and M3; six resistors R1a, R1b, R2a, R2b, R3, and R4; and two diodes Q1 and Q2 interconnected as illustrated in FIG.  3.  The supply voltage is limited by the input common-mode voltage of the amplifier 32, which must be low enough to ensure that the input pair operate in the saturation region. 
The improvement of low supply voltage realized with the bandgap reference circuit 30 is based on the positions of the input pair of the operational amplifier 32.  The established feedback loop produces a PTAT voltage across the resistor R3.  The resistance ratio of the resistors R1a and R2a causes the voltage between the supply voltage and the input common voltage of the operational amplifier 32 to become increased.  This makes the p-channel input pair operate in the saturation region even when the supply voltage is under 1V. The sub-1-V reference voltage output by the circuit 30 can be expressed as:                               V                      REF            ⁢                          -                        ⁢            SUB1F                          =                                                            R                4                                            R                1                                      ⁢                          (                                                V                  EB2                                +                                                                            R                      1                                                              R                      3                                                        ⁢                                                            k                      ⁢                                                                                          ⁢                      T                                        q                                    ⁢                  ln                  ⁢                                                                          ⁢                  N                                            )                                =                                                    R                4                                            R                1                                      ·                          V                              REF                ⁢                                  -                                ⁢                CONV                                                                        (        6        )            which is similar to the circuit 20 of FIG.  2.  During operation of the circuit 30, the supply voltage, VDD, is set to about 1.0–1.9 V and the output reference voltage, VREF, is about 0.6 V.
Given the state-of-the-art bandgap reference circuits 10, 20, and 30 described above, it is clear that an improved and inexpensive low-voltage bandgap reference circuit is required.