A Product Line of Diodes Incorporated AN58 Designing with References - Shunt regulation Peter Abiodun A. Bode, Snr. Applications Engineer, Diodes Incorporated Introduction This application note introduces shunt regulators, sometimes called "reference diodes", "3terminal voltage references", or "adjustable voltage references". Using worked examples we introduce some applications of adjustable (3-terminal) shunt regulators. Diodes' range of three-terminal adjustable shunt regulators offer temperature stabilised reference voltage values ranging from 0.6V to 2.5V with an initial tolerance of 0.5% or 1% and maximum current sinking capability from 18mA to 200mA. Maximum operating voltage ranges from 18V to 36V. Adjustable references can be used as replacements for zener diodes in many applications that require an improved regulation. Also they can also be used in conjunction with other types of voltage regulators to improve the initial accuracy and regulation. This is discussed elsewhere particularly in the references provided towards the end of this document. The information presented in this Applications Note shows typical basic use of references with calculated examples. What are they? A reference in its basic form is a two terminal device that functionally behaves like a zener diode. The same circuit symbol is used for both of them as shown in Figure 1. A reference is therefore a shunt regulator and is quite often referred to as such. Note the polarity and direction of current flow. The primary difference between a zener diode and a reference lies in the accuracy of the two devices. Relative to a zener diode, a reference is a precision component. It is more accurate with a wider dynamic range of operation and better figures of merit all round. A reference can, for example, work over a current range of 500µA to 50mA (a dynamic range of 100:1) with little or no practical change in its key properties. This can never be possible with a zener diode which may typically work with a dynamic range of 2:1 or less and still perform worse than a reference. The reference is able to do this because, internally, it is in fact an integrated circuit containing amplifiers and temperature/stability compensating elements. A zener on the other hand is simply a specially fabricated p-n junction diode. R I + V K S u p p ly V OUT A Figure 1 - Shunt Regulator using a zener diode or a 2-terminal reference diode Issue 1 - September 2008 © Diodes Incorporated, 2008 1 www.zetex.com www.diodes.com AN58 Adjustable or 3-terminal references Whereas the standard reference comes in a narrow range of fixed voltages with two terminals, the adjustable kind has a third terminal which allows the user to set any output voltage in a prescribed range. It is often referred to as a "three-terminal reference". The third pin is interchangeably labelled "Ref" (reference pin), "Adj" (adjustment pin) or "FB" (feedback pin). The usual circuit symbol for an adjustable reference is shown in Figure 2 below. K Ref A Figure 2 - Adjustable or 3-terminal reference Applications Basic Shunt Regulator Vin I IN IL R3 R1 ⎞ ⎛ VOUT = VREF ⎜1 + ⎟ ⎝ R2 ⎠ Vout IR IKA R1 REF/FB REF1 R3 = VREF C1 VIN − VOUT I IN ΔI L (max) ≤ (I KA(max) − I KA(min) ) R2 GND Figure 3 Basic shunt regulator The basic shunt regulator circuit using a 2-terminal device has been shown in Figure 1. The low dynamic resistance of the diode establishes a voltage across the resistor which determines the resistor current. The same circuit function using a 3-terminal reference is shown in Figure 3 above. In response to changes in Vin or the load current, IL, REF1 will adjust how much current it sinks or "shunts" to maintain a voltage equal to VREF across its feedback (FB) or reference (REF) pin. It will be noticed that the input current, IIN, is the sum of three components, IKA, IL and IR. Usually R1 and R2 are chosen such that IR is much less than IIN to maximise the current that is available to the load. REF1 has a minimum bias current requirement, IKA(min), below which it is not able to operate. This is analogous to the "knee" current of a zener diode. Also it has a maximum current sink capability, IKA(max), beyond which the device will become unreliable or it will fail. These two parameters define the limit of use of the reference regulator within its maximum programmable voltage such that, at all times, ΔI L (max) ≤ (I KA(max) − I KA(min) ) The equation above for VOUT is accurate for most practical purposes. However it does not include the effect of the input current at the REF pin of the reference device. A more accurate expression is: R1 ⎞ ⎛ VOUT = VREF ⎜1 + ⎟ + I REF R1 ⎝ R2 ⎠ Issue 1 - September 2008 © Diodes Incorporated, 2008 2 www.zetex.com www.diodes.com AN58 where IREF is the REF pin input current. IREF is typically 40nA or less for the TLV431. For example, if R1=100kohm, VOUT is 4mV greater than that given by the simple formula. For the TLV431, this resistor value is a good choice because it also gives very low power dissipation in the feedback network. Calculated Example 1 Requirement Supply Voltage: Output voltage: Load current: 15V to 20V 10V ±1% 5mA Assume the use of TLV431 . Discussion The device needs some overhead current whilst delivering 5mA. The TLV431 can work with as little as 100µA shunt current. Let's assume R1 will be approximately 100k as discussed above. The voltage divider ratio is 10V/1.24V or roughly 8 to 1. Then R2 will be of the order of 10 or 12k. Choosing R2 = 10k, this makes the current, IR, equal to 1.24V/10k = 124µA. The minimum current requirement of the TLV431 is IKA(min) = 100µA. Therefore, allowance for a minimum overhead current of 224µA (i.e. IKA(min) + IR) must be made. Allowing for a safety margin, this might be rounded up to 250µA. More margin could be allowed but this could result in unnecessary wasted power which would especially be expensive for battery powered applications. This means the circuit, or more specifically, R3, needs to supply 5.25mA under worst case input condition which is 15V. Solution Therefore, R3 = VIN (min) − VOUT I IN = 15 − 10 0.00525 R3 = 953 = 952.38 to the nearest E48 value. Check that the maximum current handling capability of the TLV431 is not exceeded: Maximum current I max = VIN (max) − VOUT R3 = 20 − 10 953 Imax = 10.5mA - This is less than 15mA as required. Lastly, although this could have been computed first, R1 is determined thus, R1 ⎞ ⎛ VOUT = VREF ⎜1 + ⎟ 2⎠ R ⎝ Re-arrange to obtain Equation 1 ⎛V ⎞ R1 = R 2⎜⎜ OUT − 1⎟⎟ ⎝ VREF ⎠ ⎞ ⎛ 10 = 10k ⎜ − 1⎟ ⎠ ⎝ 1.24 = 70.64k Or 1 to the nearest E192 value and within 0.057%. R1 = 70.6k The same principles apply for all of Diodes' shunt regulators. Issue 1 - September 2008 © Diodes Incorporated, 2008 3 www.zetex.com www.diodes.com AN58 Component Tolerances Given the expression in Equation 1, the accuracy, vout, of the output voltage can be expressed in the reduced form as, Equation 2 ⎛ ⎛ ⎝ R1 ⎞⎞ ⎠⎠ α VOUT = ± ⎜⎜α TLV 431 + 2 ⋅ α R ⎜ ⎟⎟ R1 + R 2 ⎟ ⎝ where (see Appendix for proof) α TLV 431 = Manufacturing tolerance of TLV431 α R = Manufacturing tolerance of resistors R1 and R2 (different values but equal fractional tolerance) This expression applies provided both R1 and R2 are exact values as calculated. If preferred values, other than calculated ones, have to be used the error is given by Equation 3 ⎡ ⎛ R1C ⎝ R1C + R 2 C α VOUT = ± ⎢α TLV 431 + α RD + 2 ⋅ α RP ⎜⎜ ⎣ where, as before, ⎞⎤ ⎟⎟⎥ ⎠⎦ (see Appendix for proof) α TLV 431 = Manufacturing tolerance of TLV431 α RP = Manufacturing tolerance of preferred resistors R1 and R2 (see Appendix for P P R1C, R2C are the Calculated values of R1 and R2 respectively. And the new term, more explanation) α RD = Weighted deviation of resistors R1 and R2 from their calculated values given by, ⎛ R1C α RD = ⎜⎜ ⎝ R1C + R2C ⎞ ⎟(α R1D − α R2D ) ⎟ ⎠ where α R1 and α R 2 are fractional deviations of R1 and R2 from their calculated values respectively. Both are sign critical. Equation 4 Since the problem requires an accuracy of ±1%, only the TLV431B (0.5% tolerance) can be used. This then leaves 0.5% to be shared by the two resistors and any deviation from their standard values. Also because the calculated R1 is not a preferred value, Equation 3 rather than Equation 2 has to be used. Hence from Equation 4 ⎛ 70.64k ⎞ α RD = ⎜ ⎟( −0.057 − 0) ⎝ 70.64k + 10k ⎠ α RD = −0.05% Transposing Equation 3 ⎡⎛ α VOUT − (α TLV 431 + α RD ) ⎞⎛ R1C + R 2C ⎟⎜⎜ 2 R1C ⎠⎝ ⎣⎝ α RP = ± ⎢⎜ ⎞⎤ ⎟⎟⎥ ⎠⎦ ⎡⎛ 1 − (0.5 − 0.05) ⎞⎛ 70.64 + 10 ⎞⎤ = ± ⎢⎜ ⎟⎜ ⎟⎥ 2 ⎠⎝ 70.64 ⎠⎦ ⎣⎝ α RP = ±0.31% Issue 1 - September 2008 © Diodes Incorporated, 2008 4 www.zetex.com www.diodes.com AN58 Summary Using a TLV431B, R1 = 70.6k, R2 = 10k (both 0.31% or better) and R3 = 953 will satisfy the requirement. Current-boosted Shunt Regulator R3 IL R4 I R4 IKA IB REF1 ZX T P 2039F I IN Vin Vout IS H IR Q1 R1 ⎞ ⎛ VOUT = VREF ⎜1 + ⎟ R2 ⎠ ⎝ R1 VREF R3 = I IN = I R 4 + I SH + I L + I R R2 C1 VIN − VOUT I IN GND Figure 4 - High current shunt regulator It may at times be required to shunt-regulate more current than a reference device is capable of providing. Figure 4 shows how this can be done using a transistor Q1 to provide current amplification. Calculated Example 2 Requirement Supply Voltage: Output voltage: Load current: 15V to 20V 10V ±1% 20mA Assume the use of TLV431. Discussion This problem is similar to Calculated Example 1 above except that more load current is required. The values calculated for R1 and R2 are still valid. However, R3 will need to be recalculated. IR remains the same but IKA now consists of two components (IR4 + IB) whilst there is a new term, ISH. The overhead current can remain the same at 0.25mA making the total current through R3 20.25mA. Q1 is under the control of the reference and it is important that the reference can turn it fully off if necessary. R4 is chosen to enable this. As a minimum requirement therefore, R4 will be chosen to ensure that the voltage drop across it at IKA(min) is insufficient to turn on Q1. This will be the case if VBE at IKA(min) is kept to no more than 0.2V. In reality it would make more sense to allow the reference to supply as much of the shunt current as possible before bringing Q1 into service as this will result in the least strain on Q1. It will also mean that the reference would not have problem turning Q1 off to maximise power delivery to load. Solution R3 = VIN (min) − VOUT I IN = 15 − 10 0.02025 = 246.9 R3 = 240 Issue 1 - September 2008 © Diodes Incorporated, 2008 5 to the nearest lower E24 value. www.zetex.com www.diodes.com AN58 To determine R4, we need to know at what nominal current Q1 will be brought into service. Let this nominal hand-over current be IHC. I B (max) < I HC < 20mA V R 4 = BE I HC Let IHC = 10mA. Therefore, = 0 .6 10mA = 60 Hence, At maximum voltage however, Maximum current R4 = 62 I IN (max) = VIN (max) − VOUT R3 to the nearest E24 value. = 20 − 10 240 = 41.67mA This figure shows the wisdom of allowing the TLV431 to supply as much of the load current as possible before bringing Q1 into service. Had R4 been selected so that REF1 only supplies enough current for its own bias (i.e. 100µA), Q1 would be required to carry 41.57mA. With an output voltage of 10V, this would result in a power dissipation of 415.7mW in Q1 which is too much for the specified device to handle. As it is, with REF1 carrying 10mA, Q1 only needs to carry the remaining 31.67A. This would result in a power dissipation of 316.7mW which is more within the capability of Q12. Determination of IB I B(max) = = I SH (max) (h FE (min) +1) 31.67mA 101 I B = 313.6 μA This represents a very small contribution to the 10mA flowing through R4 making the total current, IKA = 10.31mA. Accuracy The same accuracy considerations as in applies here. Neither R3, R4 nor Q1 have any bearing on accuracy. 2 The ZXTP2039F is a SOT23 transistor with a VCEO rating of -60V, an IC of -1A and can dissipate up to 350mW when suitably mounted. Refer to datasheet ZXTP2039F. Issue 1 - September 2008 © Diodes Incorporated, 2008 6 www.zetex.com www.diodes.com AN58 Conclusion The above examples show basic considerations for use of references and amply demonstrate how easy it is to design with these versatile components. Recommended further reading AN59 - Designing with Shunt Regulators – Series Regulation AN60 - Designing with Shunt Regulators – Fixed Regulators and Opto-Isolation AN61 - Designing with Shunt Regulators – Extending the operating voltage range AN62 - Designing with Shunt Regulators – Other Applications AN63 - Designing with Shunt Regulators – ZXRE060 Low Voltage Regulator Issue 1 - September 2008 © Diodes Incorporated, 2008 7 www.zetex.com www.diodes.com AN58 Appendix - Calculating output error due to components' preferred values and tolerances R1 ⎞ ⎛ VOUT = VREF ⎜1 + ⎟ R2 ⎠ ⎝ αVOUT = δVOUT = Transfer function δVOUT - definition of fractional tolerance VOUT ∂VOUT ∂V ∂V ⋅ δV REF + OUT ⋅ δR1 + OUT ⋅ δR 2 ∂V REF ∂R1 ∂R 2 ⎛ ⎝ δVOUT = δV REF ⎜1 + δVOUT Therefore, αVOUT = Or αVOUT = αVREF + ⎜ VOUT = R1 ⎞ R1 ⎛ δR1 δR 2 ⎞ − ⎟ + V REF ⋅ ⎜ ⎟ R2 ⎠ R 2 ⎝ R1 R 2 ⎠ δVREF VREF ⎛ R1 ⎞⎛ δR1 δR 2 ⎞ +⎜ − ⎟⎜ ⎟ ⎝ R1 + R 2 ⎠⎝ R1 R 2 ⎠ ⎛ R1 ⎞ ⎟(α R1 − α R 2 ) ⎝ R1 + R 2 ⎠ Equation 5 Equation 6 It can be observed that the result consists of two terms namely the fractional tolerance of the reference itself and the manufacturing fractional tolerance of the two resistors, R1 and R2. It is entirely logical that these resistors will be of identical types of equal tolerance. Therefore, their worst case would be obtained when one resistor's tolerance is to one extreme and the other to the opposite extreme. This would result in their tolerances being an integer multiple with the appropriate sign as the case may be Therefore, Equation 6 becomes ⎡ ⎛ R1 ⎞⎤ ⎟⎥ ⎝ R1 + R 2 ⎠⎦ αVOUT = ± ⎢αVREF + 2 ⋅ α R ⎜ ⎣ where α R = tolerance of resistors Equation 7 This represents the worst case error using the calculated resistor values. Very often, the calculated value would not be exactly the same as a preferred value, resulting in additional deviation error. This deviation of actual resistor from calculated value needs to be accounted for which means Equation 6 needs to be modified. This is done by defining another error term representing the combined deviation of both resistors from their calculated values such that the overall error would then be ⎡ ⎤ α VOUT = ± ⎢α VREF + αRD + αRPE ⎥ ⎣ ⎦ where α RD = error due to preferred value and Equation 8 α RPE = error due to tolerance of the preferred value resistor The task then is determining RD and RPE as follows. Issue 1 - September 2008 © Diodes Incorporated, 2008 8 www.zetex.com www.diodes.com AN58 Consider the second term in the RHS of Equation 5. Each R can be assumed to consist of two components namely, 1. An error due to choosing a preferred resistor value different from the calculated one, and 2. The basic tolerance of the preferred resistor itself. Let RnC = Calculated value of Rn, and RnP = Preferred value of Rn. Let α RnD = RnP − RnC δRnC = RnC RnC =Error due to changing from RnC to RnP, and α RnP = Tolerance of RnP. Thus, from Equation 5, Substituting Equation 10 into Equation 5 gives Re-arranging gives ⎛ δR1 δR 2 ⎞ ⎛ δR1C + α R1P ⋅ R1P − ⎜ ⎟≡⎜ R1C ⎝ R1 R 2 ⎠ ⎜⎝ ⎞ ⎛ δR 2 C + α R 2 P ⋅ R 2 P ⎟⎟ − ⎜ ⎜ R2 C ⎠ ⎝ ⎛ δR1 δR 2 ⎞ ⎛⎜ δR1C α R1P ⋅ R1P + − ⎟= ⎜ R1C ⎝ R1 R 2 ⎠ ⎜⎝ R1C ⎞ ⎛ δR 2 C α R 2 P ⋅ R 2 P ⎟⎟ − ⎜⎜ + R2C ⎠ ⎝ R2 C α VOUT = α VOUT = δV REF V REF δV REF V REF ⎛ R1C + ⎜⎜ R 1 ⎝ C + R2 C ⎞⎛ ⎛ δR1C α R1P ⋅ R1P ⎟⎟⎜ ⎜⎜ + ⎜ R1C ⎠⎝ ⎝ R1C ⎛ R1C + ⎜⎜ R 1 ⎝ C + R2 C ⎞⎛ δR1C δR 2 C ⎟⎟⎜⎜ − R2 C ⎠⎝ R1C ⎛ R1C R 1 ⎝ C + R2 C α VOUT = α VREF + ⎜⎜ Again assuming worst case conditions with Equation 9 ⎞ ⎟⎟ ⎠ Equation 10 ⎞ ⎛ δR 2 C α R 2 P ⋅ R 2 P ⎟⎟ − ⎜⎜ + R2 C ⎠ ⎝ R2 C ⎞ ⎛ R1C ⎟⎟ + ⎜⎜ R 1 ⎠ ⎝ C + R2 C ⎞ ⎛ R1C ⎟⎟(α R1D − α R 2 D ) + ⎜⎜ R 1 ⎠ ⎝ C + R2 C α R1P ⎞ ⎟ ⎟ ⎠ ⎞⎞ ⎟⎟ ⎟ ⎟ ⎠⎠ ⎞⎛ α R1P ⋅ R1P α R 2 P ⋅ R 2 P ⎟⎟⎜⎜ − R2 C ⎠⎝ R1C ⎞⎛ α R1P ⋅ R1P α R 2 P ⋅ R 2 P ⎟⎟⎜⎜ − R2 C ⎠⎝ R1C ⎞ ⎟⎟ ⎠ ⎞ ⎟⎟ ⎠ Equation 11 = α R 2P (= α RP ) but opposite in sign, ⎡ ⎛ α ⋅ R1C ⎞ ⎛ R1C ⎟⎟(α R1D − α R 2D ) + ⎜⎜ RP αVOUT = ± ⎢αVREF + ⎜⎜ R 1 R 2 + C ⎠ ⎝ R1C + R 2C ⎝ C ⎣ ⎞⎛ R1P R 2 P ⎟⎟⎜⎜ + ⎠⎝ R1C R 2C ⎞⎤ ⎟⎟⎥ ⎠⎦ Equation 12 Check: If both calculated R1 and R2 are the same as the preferred values, the expression reduces to ⎡ ⎛ R1C ⎝ R1C + R 2C α VOUT = ± ⎢α VREF + 2 ⋅ α RP ⎜⎜ ⎣ ⎞⎤ ⎟⎟⎥ ⎠⎦ Same as Equation 7Equation 7 Also, comparing Equation 12 and Equation 8, it can be seen that, ⎛ R1 ⎞ C ⎟⎟(α R1D − α R 2D ) α RD = ⎜⎜ ⎝ R1C + R 2C ⎠ and, ⎛ α ⋅ R1C α RPE = ⎜⎜ RP ⎝ R1C + R 2C Issue 1 - September 2008 © Diodes Incorporated, 2008 ⎞⎛ R1P R 2 P ⎟⎟⎜⎜ + ⎠⎝ R1C R 2C ⎞ ⎟⎟ ⎠ As required. 9 www.zetex.com www.diodes.com AN58 In practice, one resistor (usually R2) is chosen by the user, effectively making its RC = RP, whilst the other is calculated. Also, if the remaining resistor's RP is very close to its RC, as is more likely than not, then is a valid assumption. Applying these facts, Equation 12 becomes, ⎡ ⎛ R1C R 1 ⎝ C + R 2C α VOUT = ± ⎢α VREF + α RD + 2 ⋅ α RP ⎜⎜ ⎣ ⎞⎤ ⎟⎟⎥ ⎠⎦ Equation 13 As required. Summary The cumulative error caused by variation in values of the component parts is given by Equation 12 which holds true under all conditions. However, in the special but realistic conditions given preceding it, Equation 13 produces the same result as Equation 12 with negligible difference. The latter is simpler and easier to remember than the former and is the one used in Calculated Example 1. Issue 1 - September 2008 © Diodes Incorporated, 2008 10 www.zetex.com www.diodes.com AN58 Intentionally left blank Issue 1 - September 2008 © Diodes Incorporated, 2008 11 www.zetex.com www.diodes.com AN58 Definitions Product change Diodes Incorporated reserves the right to alter, without notice, specifications, design, price or conditions of supply of any product or service. Customers are solely responsible for obtaining the latest relevant information before placing orders. Applications disclaimer The circuits in this design/application note are offered as design ideas. It is the responsibility of the user to ensure that the circuit is fit for the user’s application and meets with the user’s requirements. No representation or warranty is given and no liability whatsoever is assumed by Diodes Inc. with respect to the accuracy or use of such information, or infringement of patents or other intellectual property rights arising from such use or otherwise. Diodes Inc. does not assume any legal responsibility or will not be held legally liable (whether in contract, tort (including negligence), breach of statutory duty, restriction or otherwise) for any damages, loss of profit, business, contract, opportunity or consequential loss in the use of these circuit applications, under any circumstances. Life support Diodes Zetex products are specifically not authorized for use as critical components in life support devices or systems without the express written approval of the Chief Executive Officer of Diodes Incorporated. As used herein: A. Life support devices or systems are devices or systems which: 1. are intended to implant into the body or 2. support or sustain life and whose failure to perform when properly used in accordance with instructions for use provided in the labeling can be reasonably expected to result in significant injury to the user. B. A critical component is any component in a life support device or system whose failure to perform can be reasonably expected to cause the failure of the life support device or to affect its safety or effectiveness. Reproduction The product specifications contained in this publication are issued to provide outline information only which (unless agreed by the company in writing) may not be used, applied or reproduced for any purpose or form part of any order or contract or be regarded as a representation relating to the products or services concerned. Terms and Conditions All products are sold subjects to Diodes Inc. terms and conditions of sale, and this disclaimer (save in the event of a conflict between the two when the terms of the contract shall prevail) according to region, supplied at the time of order acknowledgement. For the latest information on technology, delivery terms and conditions and prices, please contact your nearest Diodes Zetex sales office. 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Samples may be available “Active” Product status recommended for new designs “Last time buy (LTB)” Device will be discontinued and last time buy period and delivery is in effect “Not recommended for new designs” Device is still in production to support existing designs and production “Obsolete” Production has been discontinued Datasheet status key: “Draft version” This term denotes a very early datasheet version and contains highly provisional information, which may change in any manner without notice. “Provisional version” This term denotes a pre-release datasheet. It provides a clear indication of anticipated performance. However, changes to the test conditions and specifications may occur, at any time and without notice. “Issue” This term denotes an issued datasheet containing finalized specifications. However, changes to specifications may occur, at any time and without notice. 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