Patent Publication Number: US-8536854-B2

Title: Supply invariant bandgap reference system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Application No. 61/306,638, filed Feb. 22, 2010. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates in general to the field of electronics, and more specifically to a supply invariant bandgap reference system. 
     2. Description of the Related Art 
     Electronic systems represent a wide range of systems including controllers for switching power converters, microprocessors, and memories. Electronic systems include digital, analog, and/or mixed digital and analog circuits. The circuits are often implemented using discrete, integrated, or a combination of discrete and integrated components. To properly operate, many electronic systems utilize one or more voltage and/or current reference generators. In many instances, particularly for analog circuits, more precise circuits utilize more precise reference signals. Thus, in many instances, the reference generators attempt to provide a stable reference signal over variations in supply voltage and temperatures. A bandgap reference represents an accepted choice to supply the reference signal. In general, bandgap references refer to the utilization of a voltage difference between two p-n-junctions operating at different current densities to generate the reference signal. 
       FIG. 1  depicts a bandgap reference  100 , which provides a bandgap reference voltage VBG. In general, the bandgap reference  100  develops the bandgap reference voltage VBG based on the inherent forward-biased voltages across diodes  102  and  104 . The bandgap reference  100  receives power from a voltage source having a voltage VCC referenced to a ground reference  101 . When forward biased, diodes  102  and  104  have respective forward biased voltages VBE 1  and VBE 2 . Voltage VBE 2  is a fraction of voltage VBE 1 . A desired ratio of voltages VBE 2  to VBE 1  can be achieved by increasing the size, and, thus, the current density, of diode  104  relative to diode  102  or placing multiple diodes in parallel to collectively from diode  104 . Operational amplifier  106  maintains the voltage V NN  equal to voltage V NP  by driving the gate of p-channel metal oxide semiconductor field effect transistor (PMOSFET)  112  in accordance with the difference voltage of V NN -V NP . For V NN &gt;V NP , current i C2  decreases, and for V NN &lt;V NP , current i C2  increases. The voltage V NP  is at the cathode of diode D 1 . Accordingly, the bandgap reference voltage VBG is derived as follows with “R” being the resistance value of resistors  110  and  111  and “R 1 ” representing the resistance value of resistor  108 :
 
 VBE 2+ i   C2   ·R 1 =VBE 1  [1];
 
 i   C2   ·R 1= VBE 1− VBE 2=Δ VBE   [2];
 
Since  V   NN   =V   NP   ,i   C1   =i   C2 ,then  i   C1   ·=ΔVBE/R 1  [3];
 
 i   C1   ·R=V   NN   −VBG =(Δ VBE·R )/ R 1  [4]; and
 
 VBG=VBE 1+(Δ VBE·R )/ R 1  [5].
 
     In at least one embodiment, bulk error currents develop in semiconductor bulk material, especially with changes and increases in the supply voltage VCC. Bulk error currents occur because of, for example, hot electron injection of current in a semiconductor device, such as a metal oxide semiconductor field effect transistor (MOSFET). The bulk error current occurs when, for example, “hot” electrons cross an energy barrier in a channel region of the MOSFET. In a stable environment with an approximately constant bulk error current i BULK     —     ERROR , bandgap reference  100  provides a relatively stable bandgap reference voltage VBG. However, in some environments the direct current (DC) component of supply voltage VCC varies by 100-200% or more, e.g. 6V&lt;VCC&lt;18V, and alternating current (AC) signals, such as transient voltages and ripples, in supply voltage VCC can cause high frequency variations in supply voltage VCC. Variations in the supply voltage VCC tend to vary and, thus, destabilize the bulk error current i BULK     —     ERROR . Variations in the bulk error current i BULK     —     ERROR  destabilize the currents i C1  and i C2  and, thus, cause the bandgap reference voltage VBG to vary. Variations of the bandgap reference voltage VBG can cause errors in circuits, such as analog-to-digital converters, that rely upon a stable bandgap reference voltage VBG to function properly and accurately. 
     SUMMARY OF THE INVENTION 
     In one embodiment of the present invention, an apparatus includes a bandgap reference circuit to generate one or more bandgap reference signals that are substantially invariant to at least changes in direct current values of a supply voltage of the bandgap reference circuit. The apparatus further includes a current mirror, coupled to the bandgap reference circuit, to receive and mirror a control signal. The control signal controls the one or more bandgap reference signals generated by the bandgap reference circuit. The apparatus further includes a proportional to absolute temperature reference signal generator coupled between the bandgap reference circuit and the current mirror to generate one or more proportional to absolute temperature currents from at least one of the bandgap reference signals. The one or more proportional to absolute temperature currents are substantially invariant to at least changes in direct current values of the supply voltage of the bandgap reference circuit. 
     In another embodiment of the present invention, a method includes generating one or more bandgap reference signals that are substantially invariant to at least changes in direct current values of a supply voltage of the bandgap reference circuit. The method further includes receiving a control signal and mirroring the control signal using a current mirror to control the one or more bandgap reference signals generated by the bandgap reference circuit. The method also includes generating one or more proportional to absolute temperature currents from at least one of the bandgap reference signals. The one or more proportional to absolute temperature currents are substantially invariant to at least changes in direct current values of the supply voltage of the bandgap reference circuit. 
     In a further embodiment of the present invention, a system includes a bandgap reference circuit to generate one or more bandgap reference signals that are substantially invariant to at least changes in direct current values of a supply voltage of the bandgap reference circuit. The bandgap reference circuit includes first and second parallel current paths, each current path includes one or more diodes, and the total diode forward voltage reduction during operation of the bandgap reference circuit is different for the two paths. The system further includes an operational amplifier having an inverting node coupled to the first parallel current path of the bandgap reference circuit and a non-inverting node coupled to the second parallel current path of the bandgap reference circuit. The operational amplifier is configured to generate a control signal to maintain equal currents through the first and second parallel current paths of the bandgap reference circuit. The system also includes a current mirror, coupled to the bandgap reference circuit, to receive and mirror the control signal. The system further includes a proportional to absolute temperature reference signal generator coupled between the bandgap reference circuit and the current mirror to generate one or more proportional to absolute temperature currents from at least one of the bandgap reference signals. The one or more proportional to absolute temperature currents are substantially invariant to at least changes in direct current values of the supply voltage of the bandgap reference circuit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention may be better understood, and its numerous objects, features and advantages made apparent to those skilled in the art by referencing the accompanying drawings. The use of the same reference number throughout the several figures designates a like or similar element. 
         FIG. 1  (labeled prior art) depicts a bandgap reference circuit. 
         FIG. 2  depicts an electronic reference-signal generation system that includes a supply invariant bandgap reference circuit. 
         FIG. 3  depicts an embodiment of the electronic reference-signal generation system of  FIG. 2 . 
         FIG. 4  depicts an exemplary design and arrangement of diodes in the electronic reference-signal generation system of  FIG. 3 . 
         FIG. 5  depicts a voltage-time graph of a time-varying supply voltage in the electronic reference-signal generation system of  FIG. 3 . 
         FIG. 6  depicts an exemplary resistor degeneration circuit. 
         FIG. 7  depicts an exemplary startup current generator. 
         FIG. 8  depicts an embodiment of an alternating current (AC) compensation circuit. 
         FIG. 9  depicts a supply invariant reference voltage generation circuit. 
     
    
    
     DETAILED DESCRIPTION 
     In at least one embodiment, an electronic reference-signal generation system includes a supply invariant bandgap reference system that generates one or more bandgap reference signals that are substantially unaffected by bulk error currents. In at least one embodiment, the bandgap reference generates a substantially invariant bandgap reference signals for a range of direct current (DC) supply voltages. Additionally, in at least one embodiment, the bandgap reference system provides substantially invariant bandgap reference signals when the supply voltage varies due alternating current (AC) voltages. In at least one embodiment, the bandgap reference system generates a bandgap reference voltage VBG, a “proportional to absolute temperature” (PTAT) current (“i PTAT ”) and a “zero dependency on absolute temperature” (ZTAT) current (“i ZTAT ”) that are substantially unaffected by variations in the supply voltage and unaffected by a bulk error current. Thus, in at least one embodiment, the electronic reference-signal generation system provides a stable output voltage, i PTAT  current, and i ZTAT  current as reference signals for any electronic circuit despite variations in supply voltage and bulk error current. 
       FIG. 2  depicts an electronic reference-signal generation system  200  that includes a supply invariant, bandgap reference circuit  202  to generate a bandgap reference voltage VBG. The electronic reference-signal generation system  200  also includes a proportional to absolute temperature signal generator  204  to generate a supply invariant current i PTAT . The electronic reference-signal generation system  200  also optionally (as indicated by dashed lines) includes a zero dependency on absolute temperature signal generator  206  to generate a supply invariant i ZTAT  current. The electronic reference-signal generation system  200  also includes a current mirror  208  to assist operational amplifier  210  in maintaining constant reference signals. 
     In at least one embodiment, the bandgap reference voltage VBG is referenced to the supply voltage VDDH+ rather than the ground reference voltage GNDH to assist in substantially reducing the effects of bulk currents on the values of bandgap reference voltage VBG and currents i PTAT  and i ZTAT . During operation of electronic reference-signal generation system  200 , the i PTAT  and i ZTAT  currents remain substantially invariant with respect to a range of DC voltage levels of supply voltage VDDH and, in at least one embodiment, and also with respect to AC variations of supply voltage VDDH. The term “substantially” is used because signals can have minor variations that do not affect the use of the bandgap reference voltage VBG or the i PTAT  or i ZTAT  currents as reference signals. For example, in at least one embodiment, for variations of supply voltage VDDH from 7.5V to 14.5V, the bandgap reference voltage VBG varies by approximately 1 mV. The term “invariant” means substantially no variation. AC variations of supply voltage VDDH are, for example, transient voltages such as a spike, ringing (such as a sin wave superimposed on a DC voltage), and any other periodic or non-periodic perturbations of supply voltage VDDH. 
     The electronic reference-signal generation system  200  includes an operational amplifier  210  to provide an input current i OP  to the current mirror  208 . The PTAT signal generator  204 , and current mirror  208  provide a feedback path between the operational amplifier  210  and the bandgap reference circuit  202 . The operational amplifier  210  drives current mirror  208  to compensate for variations in supply voltage VDDH+ and to compensate for error currents, such as bulk error currents. The current mirror  208  receives and responds to the current i OP  from the operational amplifier  210  and drives a current in the current mirror to control the bandgap reference signal current i PTAT  and the bandgap reference voltage VBG in the bandgap reference circuit  202 . Thus, the current i OP  from operational amplifier  210  functions to control the feedback loop through current mirror  208 , PTAT signal generator  204 , and bandgap reference circuit  202  to maintain the supply invariant bandgap reference voltage VBG and supply invariant current i PTAT . 
     The respective positive and negative voltage rails VDDH+ and VDDH− of operational amplifier  210  float with respect to supply voltage VDDH. In other words, voltage rails VDDH+ and VDDH− change values as supply voltage VDDH changes values so that the difference between VDDH+ and VDDH− is constant. Floating the voltage rails VDDH+ and VDDH− with respect to supply voltage VDDH provides a constant voltage supply for operational amplifier  210 , and allows operational amplifier  210  to be substantially unaffected by variations in supply voltage VDDH. In at least one embodiment, variations in supply voltage VDDH+ are the dominant source of bulk error currents. 
       FIG. 3  depicts an electronic reference-signal generation system  300 , which represents one embodiment of the electronic reference-signal generation system  200 . The electronic reference-signal generation system  300  includes a bandgap reference circuit  302 , which represents one embodiment of bandgap reference circuit  202 . The bandgap reference circuit  302  includes a voltage node  303  to receive the supply voltage VDDH+. The bandgap reference circuit  302  includes two, forward-biased diodes D 1  and D 2 . Diodes D 1  and D 2  have respective forward biased voltages VBE 1  and VBE 2 . Voltage VBE 2  is a fraction of voltage VBE 1 . As subsequently discussed in more detail, a desired ratio of voltages VBE 2  to VBE 1  can be achieved by increasing the size of diode D 2  relative to diode D 1  or placing multiple diodes D 2  in parallel. Operational amplifier  304  maintains voltage V NN  equal to voltage V NP . Thus, the voltage across resistor  306  is ΔVBE=VBE 1 -VBE 2 . The resistance value of resistor  306  is R 1 . The particular value R 1  of resistor  306  is a matter of design choice. As subsequently described in more detail, the resistance value R 1  sets the value of current i PTAT . The resistance value R 1  is indicated as adjustable because changing the value R 1  can change the current i PTAT . In at least one embodiment, the resistance value R 1  is set using a conventional resistor degeneration network (such as resistor degeneration circuit  600  ( FIG. 6 )). The bandgap reference circuit  302  also includes resistors  308  and  310 , which both have a resistance value R. Because of the symmetry of resistors  308  and  310 , current i PTAT  equals 2·i C1 =2·i C2 . Since current i C2 =ΔVBE/R 1 , current i PTAT =2·ΔVBE/R 1 . As subsequently discussed in more detail, the relationship between current i PTAT  and ΔVBE and R result in the current i PTAT  being supply voltage invariant. A “resistor” can be implemented using any number of series and/or parallel connected resistors. 
     In at least one embodiment, the voltage rails VDDH+ and VDDH− of operational amplifier  304  float with respect to supply voltage VDDH+ as described in conjunction with operational amplifier  210 . In at least one embodiment, operational amplifier  304  is fabricated using low voltage devices. Low voltage devices are generally less susceptible to hot electron injection and associated bulk error currents than high voltage devices. The design of operational amplifier  304  generally determines the DC offset voltage property of operational amplifier  304 . Generally, a higher DC voltage offset results in a change in the voltage ΔVBE across resistor R 1 . To minimize the percentage change of voltage ΔVBE due to the DC offset voltage, the value of voltage ΔVBE can be increased. As previously discussed, the value of voltage ΔVBE is set by the difference between voltages VBE 2  and VBE 1 . Thus, in at least one embodiment, the value of voltage ΔVBE can be increased by increasing the size of diode D 2  relative to the size of diode D 1 . 
     The particular design, arrangement, and size ratios of diodes D 2  and D 1  are matters of design choice. In at least one embodiment, diodes D 2  and D 1  are designed so that ΔVBE is sufficiently greater than an offset voltage of operational amplifier  304  to allow operational amplifier  304  to equalize the V NN  and V NP .  FIG. 4  depicts an exemplary design and arrangement of diodes D 2  and D 1  of  FIG. 3 . Referring to  FIGS. 3 and 4 , in at least one embodiment, diodes D 2  and D 1  are arranged as a diode group  402 . In diode group  402 , diode D 2  is actually eight, parallel connected diodes D 2   0 -D 2   7 , and diodes D 2   0 -D 2   7  are efficiently arranged in a rectangular pattern around central diode D 1 . Each of diodes D 2   0 -D 2   7  is the same size as diode D 1 . The particular area ratio of diodes D 2  and D 1  is a trade-off between an amount of area occupied by diodes D 2  and D 1  and accuracy current i PTAT . In at least one embodiment, an area ratio of 8:1 is used because the current i PTAT  is directly proportional to a natural logarithmic function of the reverse bias currents i S1  and i S2  of respective diodes D 1  and D 2 . Thus, increases in the size of diode D 2  have a subdued effect on the value of current i PTAT . 
     Referring to  FIG. 3 , as illustrated in the following derivation of current i PTAT  for electronic reference-signal generation system  300 , the value of current i PTAT  is supply voltage invariant: 
     
       
         
           
             
               
                 
                   
                     
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     “i C1 ” and “i C2 ” are the respective currents through diodes D 1  and D 2 , R 1  is the resistance value of resistor  306 , V t  is the diode thermal voltage of diodes D 1  and D 2 , “i S1 ” and “i S2 ” are the respective saturation currents of diodes D 1  and D 2 . The ratio i S2 /i S1  of reverse bias currents i S1  and i S2  is a constant and is proportional to VBE 1 -VBE 2 . Thus, the value of current i PTAT  is independent of the supply voltage VDDH+ and also independent of the bulk error current i BULK     —     ERROR . 
     The electronic reference-signal generation system  300  also optionally includes a supply invariant reference voltage generation circuit  336 . The supply invariant reference voltage generation circuit  336  generates a supply invariant reference V REF  using the currents i PTAT  and i ZTAT . An exemplary embodiment of the supply invariant reference voltage generation circuit  336  is subsequently described with reference to  FIG. 9 . 
       FIG. 5  depicts a voltage-time graph  500  of the supply voltage VDDH+ varying over time. The DC value of supply voltage VDDH+ can vary over time from VDDH+ MIN  to VDDH+ MAX . The particular values of VDDH+ MIN(DC)  and VDDH+ MAX(DC)  generally depend on factors external to electronic reference-signal generation system  300 , such as available supply voltage values from an external power source (not shown). In at least one embodiment, VDDH+ MIN(DC)  and VDDH+ MAX(DC)  are respectively 7V and 17.5V. In at least one embodiment, the supply voltage VDDH+ also experiences AC variations, such as high frequency transient voltages  502  and  504 , which have a frequency of, for example, 100 MHz. AC components of supply voltage VDDH+ can be caused by any number of factors, such as transient changes in power provided by an external power source (not shown) that supplies power to the electronic reference-signal generation system  300  and ripple voltages due to imperfect voltage rectification. Referring to  FIGS. 3 and 5 , in accordance with Equation [9], the current i PTAT  depends on the thermal voltage V t , resistance value R 1 , and the saturation currents ratio i S1 /i S2 . Since the thermal voltage V t , the resistance value R 1 , and the ratio of i S1 /i S2  are independent of the value of supply voltage VDDH+, current i PTAT  is invariant with respect to changes in the supply voltage VDDH+. 
     Additionally, in at least one embodiment, the current i PTAT  and bandgap reference voltage VBG are substantially unaffected by the bulk error current i BULK     —     ERROR . The PTAT signal generator  315  generates PTAT currents i PTAT0  through i PTATM  directly from the current i PTAT  through resistor  312 . “M” is an integer index ranging from 0 to the number of current i PTAT  copies. The value of M represents a number of copies of i PTAT  current to be supplied by the PTAT signal generator  315 . “R 2 ” is the resistance value of resistor  312 . To generate the PTAT currents i PTAT0  through i PTATM , the M+1 PMOSFETs  330 . 0  through  330 .M provide M+1 copies of i PTAT . MOSFETs  330 . 0 - 330 .M have common gates connected to the gate of PMOSFET  316 . The PMOSFETs  330 . 0 - 330 .M generate M+1 respective PTAT currents i PTAT0  through i PTATM . The sum of PTAT currents i PTAT0  through i PTATM  equals 2·ΔVBE/R 1 . The sum of the M+1 PTAT currents i PTAT0  through i PTATM  equals the value of current i PTAT , i.e. i PTAT0 +i PTAT1 + . . . i PTATM =i PTAT . Each of the M+1 currents i PTAT0  through i PTATM  is referred to as a copy of the current i PTAT . If M&gt;0, the currents i PTAT0  through i PTATM -are scaled copies of current i PTAT . The particular values of PTAT currents i PTAT0  through i PTATM  are also function of the size of respective PMOSFETs  330 . 0  through  330 .M. In at least one embodiment, because PMOSFETs are less susceptible to bulk error currents, using PMOSTFETs in PTAT signal generator  315  allows the currents i PTAT0  through i PTATM  to be substantially unaffected by bulk error currents. Additionally, in at least one embodiment, the connection of the gates of PMOSFETs  330 . 0 - 330 .M to the gate of PMOSFET  316  to form a current replicator allows all the PTAT currents i PTAT0  through i PTATM  to be substantially unaffected by bulk error currents. In at least one embodiment, PTAT signal generator  315  generates the M+1 copies of current i PTAT  for use by any other circuits, such as analog-to-digital converters, digital-to-analog converters, and comparators (not shown), that utilize a current that is “proportional to absolute temperature”. 
     The current mirror  314  includes a diode connected NMOSFET  326 , and a gate of the NMOSFET  326  connects to the gate of NMOSFET  318 . In at least one embodiment, the bulk current i BULK     —     ERROR  derives from differences between the drain voltages V D1  and V D2 , which are affected by variations in supply voltage VDDH+, of respective NMOSFETs  318  and  326 . The current mirror  314  represents one embodiment of current mirror  208 . NMOSFET  318  is configured as a source follower having a source terminal connected to the source of diode connected to PMOSFET  316  of PTAT signal generator  315 . The output current i OP  of operational amplifier  304  drives the gate of NMOSFET  318 . Any bulk error current i BULK     —     ERROR  will change the value of current i PTAT  and, thus, the values of currents i C1  and i C2 . When the value of current i C2  changes, voltage V NN  changes with respect to voltage V NP . Operational amplifier  304  includes transconductance circuitry to convert the difference between voltages V NN  and V NP  into current i OP . Current mirror  314  mirrors the current i OP  so that the current i OP  controls the current i PTAT  in the bandgap reference circuit  302 . The operational amplifier  304  generates current i OP  to modulate the value of current i PTAT  to equalize the voltages V NN  and V NP . Equalizing the voltages V NN  and V NP  ensures that current i PTAT  remains equal to 2·ΔVBE/R 1 , and, thus, current i PTAT  remains unaffected by bulk error current i BULK     —     ERROR . 
     The electronic reference-signal generation system  300  also generates a voltage supply invariant current i ZTAT . In at least one embodiment, to achieve a voltage supply invariant current i ZTAT , one or more circuit parameters of electronic reference-signal generation system  300  are adjusted so that d(VDDH+−V B )/dT=dR 3 /dT, i.e. the change of voltage VDDH+minus voltage V B  with respect to a change in temperature equals the change in resistance value R 3  with respect to temperature. In at least one embodiment, PMOSFETs  316 ,  320 ,  322 , and  324  and diode-connected NMOSFETs  316  and  326  are biased to operate in the saturation region. In at least one embodiment, PMOSFETs  316 ,  320 ,  322 , and  324  are biased to operate in the sub-threshold region. Because PMOSFETs  322  and  324  have a common gate, bulk current error correction circuit  314  maintains voltage V A  at the source of PMOSFET  322  equal to voltage V B  at the source of PMOSFET  324 . Accordingly, current i ZTAT  is referenced to the supply voltage VDDH+, and i ZTAT =(VDDH+−V B )/R 3 . “R 3 ” is the resistance value of resistor  328 . 
     The voltage V B  has a non-zero temperature coefficient with respect to the supply voltage VDDH+, i.e. VDDH+−V B  varies with temperature. A “temperature coefficient” is a factor by which a value changes as temperature changes. The “temperature coefficient” is generally represented herein as “dX/dT”, where dX is the value change of X over for a temperature change of dT. However, the temperature coefficient dR 3 /dT of resistor  328  is proportional to the temperature coefficient dV B /dT of voltage V A . In general, dR 3 /dT can be positive, negative, or zero. The temperature coefficient of voltage V A  is set so that d(VDDH+−V B )/dT equals dR 3 /dT. In at least one embodiment, the voltages V A  and V B  are generated so that di ZTAT /dT=0. 
     Voltage V A =VBE 1 +K·ΔVBE and, thus, dV A /dT=dVBE 1 /dT+K·dΔVBE/dT. In terms of temperature coefficients K·dΔVBE/dT is a positive temperature coefficient and dVBE 1 /dT is a negative temperature coefficient. In at least one embodiment, “K” is a ratio of resistance values and is, for example, K=(R 2 +2R)/R 1 . The value of dVBE 1 /dT and dΔVBE/dT are functions of the respective properties of diode D 1  and diodes D 1  and D 2  and are, thus, fixed. Accordingly, the resistance values R, R 1 , and R 2  can be set so that dV B /dT=dR 3 /dT and, thus, make current i ZTAT  temperature invariant. Accordingly, setting the values of R, R 1 , and R 2  so that: 
                         ⅆ   R     ⁢           ⁢   3       ⅆ   T       =         ⅆ     V   A         ⅆ   T       =           ⅆ   VBE     ⁢           ⁢   1       ⅆ   T       +           R   ⁢           ⁢   2     +     2   ⁢           ⁢   R         R   ⁢           ⁢   1       ·         ⅆ   Δ     ⁢           ⁢   VBE       ⅆ   T         +           ⅆ   Δ     ⁢           ⁢   Vgs       ⅆ   T       .                 [   10   ]               
“ΔVgs” represents the difference between the gate voltages Vgs 320  and Vgs 316  of respective PMOSFETs  320  and  316 , i.e. ΔVgs=Vgs 320 −Vgs 316 .
 
     In at least one embodiment, ZTAT signal generator  317  generates G+1 copies of currents i ZTAT  for use by any other circuits, such as analog-to-digital converters, digital-to-analog converters, and comparators (not shown), that utilize a current that has “zero dependency on absolute temperature” (i ZTAT ). “G” is an integer index ranging from 0 to the number plus one of current i ZTAT  copies. The G+1 PMOSFETs  332 . 0  through  332 .G provide G+1 copies of i ZTAT . MOSFETs  332 . 0 - 332 .G have common gates connected to the gate of PMOSFET  324 . The PMOSFETs  332 . 0 - 332 .G generate G+1 respective i ZTAT  currents: i ZTAT0  through i ZTATG . Because of the connection of the gates of PMOSFETs  332 . 0 - 332 .G to the gate of PMOSFET  324 , the currents i ZTAT0  through i ZTATG  are also substantially unaffected by bulk error currents. 
     In at least one embodiment, electronic reference-signal generation system  300  includes one or more of respective variable resistance circuits  338 ,  340 ,  342 ,  344 ,  346 . 0 - 346 .M, and  348 . 0 - 348 .M. In at least one embodiment, each included variable resistance circuits  338 ,  340 ,  342 ,  344 ,  346 . 0 - 346 .M, and  348 . 0 - 348 .G is connected to a respective source of PMOSFETs  316 ,  320 ,  322 ,  324 ,  330 . 0 - 330 .M, and  332 . 0 - 332 .G. In at least one embodiment, the resistance of each included variable resistance circuits  338 ,  340 ,  342 ,  344 ,  346 . 0 - 346 .M, and  348 . 0 - 348 .G is set to match the voltage and current characteristics of respective PMOSFETs  316 ,  320 ,  322 ,  324 ,  330 . 0 - 330 .M, and  332 . 0 - 332 .G. 
       FIG. 6  depicts an exemplary resistor degeneration circuit  600  and represents one embodiment of variable resistance circuits  338 ,  340 ,  342 ,  344 ,  346 . 0 - 346 .M, and  348 . 0 - 348 .G. Resistor degeneration can be used in electronic reference-signal generation system  300  to set resistance values and to improve effective matching of properties of MOSFETs. For example, resistor degeneration can be used to match the voltage and current characteristics of respective PMOSFETs  316 ,  320 ,  322 ,  324 ,  330 . 0 - 330 .M, and  332 . 0 - 332 .M, accurately set ΔVBE, set the resistance value R 1  of resistor  306 , and so on. Resistor degeneration circuit  600  includes N+1 resistors  602 . 0 - 602 .N, where “N” is an integer index greater than or equal to 1. In at least one embodiment, the value of N and, thus, the number N+1 of resistors  602 . 0 - 602 .N equals the number of PMOSFETs  330 . 0 - 330 .M and  332 . 0 - 332 .G. The tap  604  can be set at any point, such as point A, to set the resistance value of the resistor degeneration circuit  600 . In the exemplary embodiment of  FIG. 600 , the resistance value of resistor degeneration circuit  600  equals the sum of the resistance values of resistors  602 . 1  through  602 .N. The number of resistors and values of the resistors in resistor degeneration circuit  600  is a matter of design choice. In general, increasing the number of resistors provides a wider range of resistances and/or finer gradations in resistance. 
     Referring to  FIG. 3 , in at least one embodiment, a startup current i STARTUP  is used by electronic reference-signal generation system  300  to enter a predictable steady state operation where operational amplifier  304  maintains voltage V NN  equal to V NP  and current i PTAT  is not equal to zero. Because the startup current i STARTUP  can be affected by, for example, supply voltage VDDH+ and temperature changes, in at least one embodiment, the startup current i STARTUP  is a small percentage of the current i PTAT . For example, in at least one embodiment, i STARTUP ≦0.01·i PTAT . 
       FIG. 7  depicts an exemplary startup current generator  700  to generate the startup current i STARTUP . The startup current generator  700  utilizes a current mirror that includes diode-connected PMOSFET  702  having a common gate with PMOSFET  704 . DC voltage source  706  provides a reference voltage V 1 , and resistor  708 , having a resistance value of R BIAS1 , establishes a bias current. If PMOSFETs  702  and  704  are identical, the voltage V 2  across bias resistor  710  equals the reference voltage V 1 . Therefore, the startup current i STARTUP  equals V 2 /R BIAS1 . In at least one embodiment, the voltage V 1  is generated by a forward biased voltage drop across a diode or diode connected transistor. Because voltage V 1  is independent of supply voltage VDDH+ and V 2 /R BIAS1  equals V 1 , the current i STARTUP  is also independent of supply voltage VDDH+. 
       FIG. 8  depicts an embodiment of a transient compensation circuit  800  that responds to AC transients, such as transients  502  and  504  of supply voltage VDDH+ of  FIG. 5 , to maintain a supply invariant current i PTAT . Referring to  FIGS. 3 and 8 , in at least one embodiment, the transient compensation circuit  800  replaces NMOSFET  318  in bulk current error correction circuit  314 . The transient compensation circuit  800  includes a high frequency dominant path through NMOSFET  802  and capacitor  804 . Diode-connected NMOSFET  806  has a common gate with NMOSFET  802 , and the gate is driven by the output voltage V OP  of operational amplifier  304 . NMOSFET  806  biases NMOSFET  802  in the saturation region. When supply voltage VDDH+ experiences a high frequency transient, the voltage V A  and V B  ( FIG. 3 ) and current i PTAT  can also change in response to the transient. Capacitor  804  shunts the drain of NMOSFET  804  to ground GNDH and, thus, any high frequency components of current i PTAT  are also shunted to ground. NMOSFET  802  has a faster reaction time than NMOSFET  808  and NMOSFET  810 . Thus, bypassing NMOSFET  808  allows operational amplifier  304  to recover equality between voltages V A  and V B  more quickly. Thus, the current path established by NMOSFETs  802  and  806  is referred to as a “high frequency dominant path”. Diode-connected NMOSFET  810  biases NMOSFET  808  in the saturation region. For low frequency values of current i PTAT , NMOSFET  808  dominates the current path of current i PTAT . Thus, the current path established by NMOSFETs  808  and  810  is referred to as a “low frequency dominant path”. 
       FIG. 9  depicts a supply invariant reference voltage generation circuit  900 . As previously discussed, currents i PTAT  and i ZTAT  are supply invariant. The supply invariant bandgap reference voltage generation circuit  900  combines currents i PTAT  and i ZTAT  through a resistor divider network to generate a supply invariant reference voltage V REF . The resistor divider has two resistors  902  and  904  having respective resistance value of R 4  and R 5 . From Equations [11]-[17], the values of R 4  and R 5  can be set so that the reference voltage V REF  has a zero dependency on absolute temperature:
 
 V   REF =( R 4 +R 5)· i   ZTAT   +R 5· i   PTAT   [11];
 
 V   REF   =V   ZTAT   +J·V   PTAT   [12];
 
 dV   REF   /dT=dV   ZTAT   /dT+J·dV   PTAT   /dT   [13];
 
 dV   ZTAT   /dTαd ( R 4 +R 5)/ dT   [14];
 
 J·V   PTAT   =[d ( R 4 +R 5)/ dT]·i   ZTAT ;  [15]
 
 V   PTAT   =R 5 ·i   PTAT ; and  [16]; and
 
 J=[d ( R 4 +R 5)/ dT·i   ZTAT ]/( R 5 ·i   PTAT )  [17].
 
     “V ZTAT ” equals (R 4 +R 5 )·i ZTAT , “α” is a proportionality symbol, and “V PTAT ” equals R 5 ·i PTAT . The values of the temperature coefficients dV ZTAT /dT and dV PTAT /dT are a function of device parameters. In at least one embodiment, the values R 4  and R 5  are set so that dV REF  In at least one embodiment, dV ZTAT /dT equals−734 ppm/° C. and dV PTAT /dT equals (4129−724) ppm/° C. To set the reference voltage temperature coefficient equal to zero, dV REF /dT=dV ZTAT /dT+J·dV PTAT /dT=0, so J=0.216. Thus, in accordance with Equation [17], for a 1.216V reference voltage V REF , the resistance values R 4  and R 5  are set so that V ZTAT =1 V and V PTAT  equals 0.216 V. 
     Thus, an electronic reference-signal generation system generates a supply invariant bandgap reference voltage and currents i PTAT  and i ZTAT . Additionally, the electronic reference-signal generation system includes bulk current error correction to compensate for bulk error currents. 
     Although embodiments have been described in detail, it should be understood that various changes, substitutions, and alterations can be made hereto without departing from the spirit and scope of the invention as defined by the appended claims.