Trimmable bandgap voltage reference

[0001] This invention relates generally to bandgap voltage references, and more particularly to a trimmable bandgap voltage reference.

[0002] Bandgap voltage references provide a stable voltage reference by summing voltages that have opposing temperature dependencies. For example, the voltage across a forward-biased PN junction will decrease approximately 2 milli-volts per degree Celsius as the temperature of the PN junction is increased. Such a temperature dependency may be denoted as a complementary-to-absolute-temperature (CTAT) dependency. In contrast, the difference in base-to-emitter voltages (ΔV_BE) between matched transistors operating at different current densities shows a positive-to-absolute-temperature (PTAT) dependency that is proportional to the thermal voltage V_T. The thermal voltage equals kT/q, where k is the Boltzmann constant, T is the absolute temperature in degrees Kelvin, and q is the magnitude of electronic charge. Thus, the thermal voltage will increase about 0.085 milli-volts per degree Celsius, giving it a PTAT temperature dependency. By proper scaling of the PTAT and CTAT voltages, a thermally stable voltage reference may be obtained.

[0003] A conventional bandgap reference 10 is shown in FIG. 1. Current source 20 generates a current I proportional to the thermal voltage. Thus, because current I increases with temperature, passing current I through a resistor of resistance R will generate a PTAT voltage equaling I*R. A diode D, which may comprise a diode-connected transistor, is in series with resistor R and is forward biased in response to current I to provide a CTAT voltage V_BE. Taking the output voltage V_out from node A provides the sum of the CTAT and PTAT voltages. By choosing the value of R appropriately, V_out will be thermally stable. In other words, V_out may be made independent with respect to changes in temperature.

[0004] Although bandgap reference 10 may provide a thermally stable output voltage assuming a careful choice for resistance R, the reality is typically that some thermal variations will be observed in a certain percentage of devices during mass production. For example, the PTAT voltage depends upon the matching between two transistors, which may vary during production due to transistor dimension and doping variations. In addition, thermal variation may result from modeling inaccuracies. As a result, trimmable bandgap voltage references have been developed that include variable resistances. Through means such as switches, the resistances are varied to compensate for process inaccuracies so as to balance the PTAT and CTAT voltages. Although trimmable bandgap voltage references allow process inaccuracies to be addressed, these references often require an excessive number of adjustments and still suffer from mismatches.

[0005] Accordingly, there is a need in the art for improved trimmable bandgap voltage references that can provide an output voltage that is stable with respect to temperature changes without requiring an excessive number of adjustments or switches.

[0006] In accordance with one aspect of the invention, a bandgap reference is provided having a first current source configured to provide a current that is proportional to the sum of a first voltage having a positive-to-absolute-temperature (PTAT) temperature dependency and a second voltage having a complementary-to-absolute-temperature (CTAT) dependency. The bandgap reference further includes a variable resistor including a first resistor and a plurality of second resistors, wherein each of the second resistors is adapted to be selectively combined in parallel with the first resistor, and wherein the second voltage is inversely proportional to the resistance of the variable resistor. Advantageously, the variable resistor requires relatively few resistors in the plurality of second resistors to provide a relatively broad dynamic range over which the resistance of the variable resistor may be varied to achieve a balance between the first and second voltages. In this fashion, should process variations or other affects upset the expected balance between the first and second voltages, the bandgap reference may still provide an output voltage that is stable across an operating temperature range through an appropriate resistance variation in the variable resistor.

[0015] A bandgap reference 200 having an output voltage V_out that depends upon a voltage having a positive-to-absolute-temperature (PTAT) dependency and upon a voltage having a complementary-to-absolute-temperature (CTAT) dependency is shown in FIG. 2. A resistor having a variable resistance R₁ determines the balance between the PTAT and CTAT voltages as will be explained further herein. A differential amplifier 205 maintains the same voltage at nodes A and B and provides the same gate voltages to matched PMOS transistors M₁, M₂, and M₃ (transistors M₁ through M₃ may also be constructed as NMOS transistors). Because matched transistors M₁ through M₃ each receives the same gate voltage, currents I₁, I₂, and I₃ are equal. The currents through a pair of matched resistors having equal resistances R₂ and R₃ must also be equal since the voltages at nodes A and B are kept equal by differential amplifier 205. A diode D₁ couples in parallel with resistance R₂ to node A. Similarly, a series combination of the variable resistance R₁ and diode D₂ couples in parallel with resistance R₃ to node B.

[0016] Note that the feedback from differential amplifier 205 is both negative and positive in that differential amplifier 205 receives the voltage from node A at its positive input and the voltage from node B at its negative input. If the voltage at node A is too high with respect to a desired operating voltage, differential amplifier 205 increases its output voltage so that the current through transistors M1 through M3 is reduced, thereby reducing the voltage across resistor R₂ to bring the voltage at node A down. Similarly, if the voltage at node B is too low, differential amplifier decreases its output voltage so that the current in transistors M1 through M3 is increased, thereby increasing the voltage across resistor R₃ to bring the voltage at node B up. In this fashion, equilibrium is reached such that the voltages of nodes A and B are kept substantially equal.

[0017] The cross-sectional area of diode D₂ is n times larger than that of diode D₁, where n is an arbitrary value. Both diodes D₁ and D₂ may be implemented using diode-connected transistors. It follows from the equality of currents I₁ and I₂ and the equality of the currents through resistances R₂ and R₃ that the current through diode D₁ and the current through diode D₂ must also be equal. Both diodes D₁ and D₂ may each comprise a diode-connected PNP or NPN bipolar junction transistor having a base-to-emitter voltage of V_BE1 and V_BE2, respectively.

[0018] These two voltages V_BE1 and V_BE2 may be used to derive the value of I₁ (and hence I₂ and I₃) as follows. Current I₃ must equal the sum of the current through resistance R₂, which equals V_BE1/R₂, and the current through diode D₁. Because the diode currents are the same, the current through diode D₁ equals the current through variable resistance R₁. In turn, the current through variable resistance R₁ equals (V_BE1 −V_BE2k )/R₁. Thus, the currents I₁, I₂, and I₃ may be expressed as:
I₁=I₂=I₃=(1/R₂)*[V_BE1+ΔV_BE*R₂/R₁]  Eq.(1)
where ΔV_BE2 =V_BE1 −V_BE2. As discussed above, a voltage such as V_BE1 will have a CTAT dependency whereas a voltage such as ΔV_BE will have a PTAT dependency. In particular, the voltage ΔV_BE equals V_T In (n), which in turn equals (kT/q) * ln(n), where V_T is the thermal voltage, k is Boltzmann's constant, n is the cross sectional ratio (area of D₂)/(area of D₁), and q is the electronic charge. Thus, the bracketed component in equation (1) depends upon the summation of a PTAT voltage and a CTAT voltage. By proper compensation of these PTAT and CTAT components, currents I₁ through I₁ may be made stable with respect to changes in temperature. The output voltage V_out, which depends upon the product of a variable resistance R₄ and current I₃, becomes:
V_out=(R₄/R₂)*[V_BE1+ΔV_BE*R₂/R₁]  Eq. (2)
Thus, by varying the resistance R₁, the balance between the PTAT and CTAT voltage contributions may be changed to ensure that V_out is stable with respect to changes in temperature. Similarly, by varying the resistance R₄, the output voltage level for V_out may be changed. The variation of R1 will be discussed first.
Varying R₁ to Balance the PTAT and CTAT Voltage Contributions

[0019] From Equation (2), it may be seen that the contribution of the PTAT voltage ΔV_BE is proportional to the inverse of the variable R₁ resistance. Alternatively, given that the resistance R₂ is static, the contribution of the PTAT voltage may be viewed as proportional to the quantity R₂/R₁, a quantity which will be denoted as α. Although R₂ is static, it may not be arbitrarily chosen because it must be of a sufficient resistance to ensure that diode D₁ is forward-biased. A current I_D1 through diode D₁ is an exponential function of the voltage V_BE1 as given by
I_D1≅I_S exp(V_BE1/V_T)  Eq. (3)
where I_S is the saturation current and V_T is the thermal voltage. From equation (3), it can be shown that I_D1 is negligible until V_BE1 exceeds a cut-in voltage of approximately 0.5 to 0.7 volts. This apparent threshold results from the exponential relationship given in equation (3). Thus, R₂ must be of a sufficient value to raise V_BE1 to the cut-in voltage and will depend upon the value of the supply voltage VCC. Having determined a value for R₂, equation (2) may be used to determine a desired starting value for α. From equation (2), it may be shown that the bracketed quantity is expected to equal the bandgap voltage for silicon when the PTAT and CTAT components are balanced. The bandgap voltage for silicon at room temperature is approximately 1.24 volts. From this voltage and given the value of R₂, which sets the value of V_BE1, an appropriate value for α may be chosen for which the output voltage V_out is expected to be thermally stable as seen from equation (2).

[0020] But as discussed earlier, process variations and modeling inaccuracies make predicting a thermally stable output voltage problematic. To accommodate such uncertainty, variable resistor R₁ may be implemented as seen in FIG. 3. The resistance R₁ includes a fixed resistance R₁₀ and a plurality of resistances such as resistances R₁₁ through R₁₄ that may be selectively coupled in parallel with resistance R₁₀ depending upon the activation of a plurality of corresponding switches S₁₁ through S₁₄. Each resistor may be a discrete device or formed in an N-well or P-well of a semiconductor substrate as is known in the art. In addition, each switch may comprise a transistor such as a MOSFET. Alternatively, each switch may comprise a laser-fusible switch. The value of R₁₀ may be chosen as follows. As discussed above, bandgap reference 200 may be designed using an appropriate value for α for which a thermally stable output voltage is expected, a value which may be denoted as α₀. For example, in one embodiment, stable operation would be expected for α₀=10. Depending upon the margin of safety desired, R₁ may be varied across a certain dynamic range to give a corresponding dynamic range to α. Should a 20% safety margin be desired about α₀, the dynamic range for a would thus range from a minimum value of 8 to a maximum value of 12. Depending upon the number of resistances that may be selectively coupled in parallel with R₁₀, the dynamic range may be sampled more finely.

[0021] The sampling of the dynamic range for α depends upon the expected probability distribution for this value. It has been found that, in general, this distribution is reasonably evenly distributed. As such, a uniform spacing between sampling points of α would provide the most accurate matching of the sampled α to the actual value required to provide the best temperature compensation. Were the samples perfectly evenly spaced throughout the sampling space, they would define a linear slope from the minimum value of α to the maximum value. In turn, because the value of α is inversely proportional to the resistance of variable resistor R₁, the conductance of variable resistor R₁ should span linearly the corresponding range of conductances. With respect to the embodiment of R₁ shown in FIG. 3, there are four selectable resistances R₁₁ through R₁₄, thereby providing 2⁴=16 sample points in the conductance dynamic range. The minimum conductance value is determined by the conductance of resistor R₁₀. In this case, all switches S₁₁ through S₁₄ would be open. As additional resistors are coupled in parallel through operation of switches S₁₁ through S₁₄, the resulting conductance for the combination increases. By providing a binary progression to the resistances for resistors R₁₁ through R₁₄, the resulting conductance may be increased in equal increments.

[0022] The selection of values for resistances R₁₁ through R₁₄ may now be described where the sampling space for a extends from a minimum value of 8 to a maximum value of 12. In this example, all resistances are given as multiples of 3KΩ. Should R₂ be a 10 for such a scaling (actual value of 30KΩ), to achieve a minimum value for α of 8 requires R₁₀ be 1.25. With 16 sample points including both the maximum and minimum values, α should be selectively adjustable in 0.27 unit increments. A binary progression to approximate such a spacing gives R₁₁=4.5, R₁₂=9, R₁₃=18, and R₁₄=36. The following table 1 demonstrates the resulting switch positions (zero representing OFF, and 1 representing ON), the resistance of R₁, and α.

[0023]

	TABLE 1
	sw11	sw12	sw13	sw14	R1	α
	0	0	0	0	1.25	8
	0	0	0	1	1.208129	8.277264
	0	0	1	0	1.169111	8.553506
	0	0	1	1	1.132404	8.83077
	0	1	0	0	1.098546	9.102941
	0	1	0	1	1.066075	9.380206
	0	1	1	0	1.035578	9.656447
	0	1	1	1	1.006673	9.933711
	1	0	0	0	0.981375	10.18978
	1	0	0	1	0.955379	10.46705
	1	0	1	0	0.930814	10.74329
	1	0	1	1	0.907396	11.02055
	1	1	0	0	0.885526	11.29272
	1	1	0	1	0.864305	11.56999
	1	1	1	0	0.844151	11.84623
	1	1	1	1	0.824845	12.12349

[0024] FIG. 4 is a plot of the α values for the 16 switch positions. It will be appreciated that other sample spacing may be used depending upon the expected probability distribution for α.

[0025] Note that the variation of resistance R₁ will change the common-mode input voltage (voltages at nodes A and B) for differential amplifier 205. Thus, currents I₁ through I₃ will change as well. In turn, this affects the voltages V_BE1 and V_BE2 across diodes D₁ and D₂, respectively. However, because diode current is an exponential function of the diode voltage as discussed with respect to equation (3), the change in diode voltages is relatively very small with respect to the change in diode current. Thus, the operating points for diodes D₁ and D₂ are not effectively changed, despite the variation of R₁.

Varying R₄ to Vary the Output Voltage

[0026] As seen from equation (3), V_out is proportional to the resistance ratio R₄/R₂. It will be appreciated that variation of either R₄ or R₂ will affect the output voltage, V_out. But note that variation of R₂ will affect the PTAT/CTAT balance already discussed with respect to the variation of R₁. Thus, variation of R₄ alone avoids unnecessary complication. It will be appreciated, however, that variation of other resistors besides R₁ and R₄ is within the scope of the invention.

[0027] Because the output voltage is directly proportional to the variable resistance R₄ (rather than inversely proportional), a combination of a fixed resistor that may be selectively combined in series with additional resistors achieves the greatest dynamic range for V_out with the least amount of switches. For example, an embodiment of variable resistor R₄ as seen in FIG. 5a provides sixteen resistance values between a minimum value of R_fixed and a maximum value of R_fixed+15R through operation of switches S_W1 through S_W4 that couple in parallel with corresponding resistors R through 8R. If a given switch is open, the corresponding resistor will couple in series with a fixed resistor R_fixed. However, if a given switch is closed, the corresponding resistor will not couple in series with fixed resistor R_fixed. For example, if all switches S_W1 through S_W4 are closed, the resulting resistance of variable resistor R₄ is R_fixed. If switch S_W1 is opened and the remaining switches kept closed, the resulting resistance of variable resistor R₄ is R_fixed+R. If switch S_W2 is opened and the remaining switches kept closed, the resulting resistance of variable resistor R₄ is R_fixed+2R. Through analogous operation of switches S_W1 through S_W4, the resulting resistance may be selectively increased in increments of R until the maximum resistance of R_fixed+15R is achieved. Such a linear progression of resistances assumes, however, that the ON resistance of switches S_W1 through S_W4 is zero. In reality, the ON resistance is finite should, for example, switches S_W1 through S_W4 be implemented using MOSFETs. To maintain approximately equal resistance increments, the ON resistance of switches S_W1 through S_W4 should be at least 1/10^th that of R. However, if the switches are implemented as MOSFETS, an inordinate amount of silicon must then be dedicated to their construction.

[0028] Thus, an alternate embodiment for variable resistor R4 may be implemented as seen in FIG. 5b which does not require such a rigorous restriction on the ON resistances of the switches. As seen in FIG. 5b, variable resistance R₄ may comprise a series combination of two variable resistances. The first resistance is formed from a fixed resistor R₄₁₀ and a plurality of resistances such as resistances R₄₁₁ and R₄₁₂ that may be selectively coupled in parallel with resistance R₄₁₀ depending upon the activation of corresponding switches S₄₁₁ and S₄₁₂. Similarly, the second resistance is formed from a fixed resistor R₄₂₀ and a plurality of resistances such as resistances R₄₂₁ and R₄₂₂ that may be selectively coupled in parallel with resistance R₄₂₀ depending upon the activation of corresponding switches S₄₂₁ and S₄₂₂. Each resistor may be a discrete device or formed in an N-well or P-well of a semiconductor substrate as is known in the art. In addition, each switch may comprise a transistor such as a MOSFET. Alternatively, each switch may comprise a laser-fusible switch. It will be appreciated that the number of resistors that may be selectively combined in parallel is a design choice and, having formed the parallel combinations, the number of parallel combinations that may be serially coupled together depends upon the degree of precision needed for the output voltage variation and cost considerations. Clearly, keeping the number of resistor/switch combinations to a minimum achieves a simpler, less costly design.

[0029] As discussed earlier, the value of the bracketed quantity in equation (3) is substantially equal to the silicon bandgap voltage (1.24 volts) when the PTAT/CTAT components have been balanced. In turn, the output voltage will equal (R₄/R₂) times this bandgap voltage. The value of resistance R₂ is governed by the need to keep diode D₁ forward-biased during operation. For example, in one embodiment, a value of 30K ohms was found sufficient. Given a value for R₂ and the desired output voltage, the desired value for the R₄ resistance may be determined. This desired value for R₄ may be denoted as R₄₀. Because of process variations and other affects, the actual output voltage may not be what one designed for. Thus, the variability of R₄ should allow for some dynamic range about the value R₄₀, for example +/−20% of this value. As discussed previously with respect to α, the sampling of the dynamic range for R₄ depends upon the expected probability distribution for this value. Assuming a flat probability distribution, a uniform spacing between sampling points in this dynamic range would provide the most accurate matching of the sampled R₄ resistance to the value required to provide the precise output voltage desired. In other words, it would be desirable to have the resistance R₄ be variable between a minimum and maximum value in equal-sized increments such that a linear variation is achieved. Depending upon the switch settings, R₄ would then vary in a linear fashion between its minimum and maximum values.

[0030] With respect to the R₄ embodiment shown in FIG. 5b, a linear slope cannot be achieved, however, because of the parallel resistance combinations. A number of numerical techniques such as a least mean squares approach may be used to minimize the error between realizable values for the selectable resistances and the resulting spacing between sample points. For example, suppose it is desired to have V_out equal 300 millivolts for an embodiment wherein the resistance of R₂ is 30KΩ. The implementation of a least mean squares optimization with respect to resistances R₁₄₀ through R₄₂₂ of FIG. 5 may now be described. Because there are four switches, R₄ may be varied through sixteen different resistances. In this example, all resistances are given as multiples of 3KΩ, where R₄₁₁=5.75, R₄₁₂=18, R₄₂₁=4.5, and R₄₂₂=25. The following table 2 demonstrates the resulting switch positions (zero representing OFF, and 1 representing ON), the resistance for R₄, and the ratio R₄/R₂.

[0031]

	TABLE 2
	sw411	sw412	sw421	sw422	R4	R4/R2
	1	1	1	1	2.080	0.208
	1	0	1	1	2.132	0.213
	1	1	1	0	2.134	0.213
	1	0	1	0	2.186	0.219
	0	1	1	1	2.262	0.226
	0	1	1	0	2.316	0.232
	0	0	1	1	2.337	0.234
	0	0	1	0	2.391	0.239
	1	1	0	1	2.457	0.246
	1	0	0	1	2.509	0.251
	1	1	0	0	2.554	0.255
	1	0	0	0	2.606	0.261
	0	1	0	1	2.639	0.264
	0	0	0	1	2.714	0.271
	0	1	0	0	2.736	0.274
	0	0	0	0	2.811	0.281

[0032] FIG. 6 is a plot of the R₄/R₂ ratio for the 16 switch positions. It will be appreciated that other sample spacing may be used depending upon the expected probability distribution for R₄₀.

[0033] Note that by including just 4 switches each for variable resistors R₁ and R₄, both the PTAT/CTAT balance and the output voltage balance may be varied through substantially equal increments over a broad dynamic range. In this fashion, during manufacture of bandgap references 200 from the same silicon ingot, a certain number of samples may be tested to judge their temperature compensation across the expected operating temperature range. If necessary, the switch positions for R₁ may be adjusted to achieve a balance between the PTAT and CTAT voltage contributions. In addition, the switch positions for R₄ may be adjusted to bring the output voltage to a desired level for the median temperature in the operating range. The remaining devices may be assumed to have similar properties such that the switches for resistors R₁ and R₄ would be set accordingly.

[0034] This procedure may be summarized with respect to the flowchart shown in FIG. 7. At step 700, V_out is measured across the expected temperature operating range. At step 705, the voltage variation for V_out is examined to determine if the PTAT and CTAT voltage contributions are in balance. Because a perfect balance is unobtainable, such a test would determine whether V_out remained within an acceptable tolerance across the temperature range. Should the variation be greater than an acceptable tolerance, the determination of whether the variation is a PTAT or CTAT variation occurs in step 710. In other words, if the output voltage V_out increases with respect to temperature, a PTAT dependency is shown. Alternatively, if the output voltage V_out decreases with respect to temperature, a CTAT dependency is shown. The goal, of course, is that V_out possesses neither a PTAT nor a CTAT dependency through proper variation of R₁. Should the variation be PTAT, R₁ is decreased one increment in step 720. Otherwise, R₁ is increased one increment in step 730. Upon appropriate adjustment of R₁, V_out will be independent with respect to changes in temperature across the desired operating temperature range. Having achieved temperature compensation, the output voltage is tested at the middle of the temperature range in step 735. Alternatively, the output voltage may be tested at the most probable operating temperature in the range, should this differ from the middle temperature. If V_out is outside the acceptable operating tolerance, a determination is made whether it above this acceptable operating tolerance at step 740. If yes, variable resistance R₄ is decreased one increment at step 745. Otherwise, variable resistance R₄ is increased one increment at step 750. At this point, both R₁ and R₄ will have been configured for optimal performance. It will be appreciated that the configuration process described with respect to FIG. 7 is subject to many variations. For example, rather than increment the resistances in single increments, a more advanced approach could initially increment in multiple increments to achieve a faster convergence.

[0035] Although the invention has been described with respect to particular embodiments, this description is only an example of the invention's application and should not be taken as a limitation. Consequently, the scope of the invention is set forth in the following claims.