4.5 (A4.3) - TEMPERATURE INDEPENDENT BIASING (BANDGAP)

Transcription

1 emp. Indep. Biasing (7/14/00) Page (A4.3) - EMPERAURE INDEPENDEN BIASING (BANDGAP) INRODUCION Objective he objective of this presentation is: 1.) Introduce the concept of a bandgap reference 2.) Show circuits that implement the bandgap reference 3.) Show how to improve the performance of the bandgap reference Outline Introduction Development of the bandgap circuit Bandgap reference circuits Improved bandgap reference circuits Summary

2 emp. Indep. Biasing (7/14/00) Page 2 emperature Stable References he previous reference circuits failed to provide small values of temperature coefficient although sufficient power supply independence was achieved. his section introduces the bandgap voltage concept combined with power supply independence to create a very stable voltage reference in regard to both temperature and power supply variations. Bandgap Voltage Reference Principle he principle of the bandgap voltage reference is to balance the negative temperature coefficient of a pn junction with the positive temperature coefficient of the thermal voltage, V t = k/q. Concept: V DD I 1 V BE -2mV/ C -V BE V t 0.085mV/ C Σ V REF = V BE KV t V t = k q K KV t Fig Result: References with C F s approaching 10 ppm/ C.

3 emp. Indep. Biasing (7/14/00) Page 3 DEVELOPMEN OF HE BANDGAP REFERENCE CIRCUI Derivation of the emperature Coefficient of the Base-Emitter Voltage o achieve small C F 's we must know the C F of V BE more precisely than approximately -2mV/ C. 1.) Start with the collector current density, J C : qd n n po J C = W exp V BE B where, V t J C = I C /Area = collector current density D n = average diffusion constant for electrons W B = base width, V BE = base-emitter voltage V t = k q k = Boltzmann's constant (1.38x10-23J/ K), = Absolute temperature n po = n i 2/N A = equilibrium concentration of electrons in the base n i 2 = D 3 exp -V GO V t = intrinsic concentration of carriers D = temperature independent constant V GO = bandgap voltage of silicon (1.205V) N A = acceptor impurity concentration

4 emp. Indep. Biasing (7/14/00) Page 4 Derivation of the emperature Coefficient of the Base-Emitter Voltage - Continued 2.) Combine the above relationships into one: qd n J C = N A W D 3 exp V BE - V GO B V = A γ exp V BE - V GO t V t where, γ = 3 3.) he value of J C at a reference temperature of = 0 is γ J C0 = A q 0 exp k (V BE - V GO ) 0 while the value of J C at a general temperature,, is J C = A γ exp q k (V BE - V GO ) 4.) he ratio of J C /J C0 can be expressed as, J C J = C0 γ exp q V BE - V G0 0 k - V BE0 - V G0 0 or ln J C J = γ ln C0 q 0 k V BE - V GO - (V BE0 - V GO ) 0 where V BE0 is the value of V BE at = 0. 5.) Solving for V BE from the above results gives, V BE () = V GO 1 - V BE0 0 γk 0 q ln 0 J C J C0 k q ln

5 emp. Indep. Biasing (7/14/00) Page 5 Derivation of the emperature Coefficient of the Base-Emitter Voltage - Continued 6.) Next, assume J C Τ α and find V BE /. V BE = V GO 1- - V GO 0 0 V BE0 0 γk q ln( 0 /) ln 0 7.) Assume that = 0 which means J C = J C0. Since, V GO / = 0, V BE 8.) Note that, ln( 0 /) herefore, V BE = 0 = 0 = - V GO 0 = 0 ( 0 /) = - V GO 0 V BE0 0 γk q = = -1 and V BE0 - γk 0 q αk q ln( 0 /) or ln(j C /J C0 ) Τ (γk/q) k ln(j C /J C0 ) q Τ V BE = J C0 J C (J C /J C0 ) k ln(j C /J C0 ) q Τ = J C0 J C α J C J C0 = 0 = V BE0 - V GO (α - γ) k 0 q ypical values of α and γ are 1 and 3.2. herefore, if V BE0 = 0.6V, then at room temperature: k q ln J C J C0 = α V BE = 0 = (1-3.2) = = mV/ C Derivation of the emperature Coefficient of the hermal Voltage (k/q) 1.) Consider two identical pn junctions having different current densities,

6 emp. Indep. Biasing (7/14/00) Page 6 V DD V DD I C1 I C2 V BE - A E1 Q1 Q2 AE2 Fig ) Find ( V BE )/, V BE = V BE1 - V BE2 = k q ln ( V BE ) J C1 = V t ln J = k C2 q ln J C1 J C2 J C1 J C2

7 emp. Indep. Biasing (7/14/00) Page 7 Derivation of the Gain, K, for the Bandgap Voltage Reference 1.) In order to achieve a zero temperature coefficient at = 0, the following equation must be satisfied: V BE ( V BE ) 0 = = 0 K" Τ where K" is a constant that satisfies the equation. 2.) herefore, we get V t0 J C1 J C2 0 = K" ln 0 V BE0 - V GO 0 3.) Define K = K" ln J C1 J, therefore C2 (α - γ)v t0 0 0 = K V t0 0 V BE0 - V GO 0 (α - γ)v t0 0 4.) Solving for K gives K = V GO - V BE0 - V t0 (α-γ) V t0 Assuming that J C1 /J C2 = A E1 /A E2 = 10 and V BE0 = 0.6V gives, (2.2)(0.026) K = = ) he output voltage of the bandgap voltage reference is found as, V REF = V BE0 KV t0 = V BE0 V GO - V BE0 (γ-α)v t0 or V REF = V GO (γ-α)v t0 = 0 For the previous values, V REF = (2.2) = 1.262V.

8 emp. Indep. Biasing (7/14/00) Page 8 Variation of the Bandgap Reference Voltage with respect to emperature he previous derivation is only valid at a given temperature, 0. As the temperature changes away from 0, the value of V REF / is no longer zero. Illustration: V (V) REF V REF = 0 0 = 400 K V REF = 0 0 = 300 K V REF = = 200 K C Fig Bandgap Curvature Correction will be necessary for low ppm/c bandgap references.

9 emp. Indep. Biasing (7/14/00) Page 9 Classical Widlar Bandgap Voltage Reference BANDGAP REFERENCE CIRCUIS Operation: V BE1 = V BE2 I 2 R 3 gives V BE = V BE1 - V BE2 = I 2 R 3 But, V BE = V t ln I 1 I - V t ln I 2 s1 I = V t ln I 1I s2 s2 I 2 I s1 Assume V BE1 V BE3, we get I 1 R 1 = I 2 R 2 herefore, I 2 = V BE R = V t 3 R ln I 1I s2 3 I 2 I s1 Now we can express V REF as = V t R ln R 2I s2 3 R 1 I s1 V REF = I 2 R 2 V BE3 = R 2 R V t ln R 2I s2 3 R 1 I V BE3 = KV t V BE s1 Design R 1, R 2, I s1, and I s2 to get the desired K. Example: V CC I 1 R 1 R 2 I 2 Q1 R 3 Q4 Q2 Q3 I V ref - Fig Let K = 25 and I s2 = 10I s1 and design R 1, R 2, and R 3. Choose R 2 = 10R 1 = 10kΩ. ln(100) = herefore R 2 /R 3 = 25/4.602 or R 3 = R 2 / = 1.842kΩ. R.J. Widlar, New Developments in IC Voltage Regulators, IEEE J. of Solid-State Circuits, Vol. SC-6, pp. 2-7, February 1971.

10 emp. Indep. Biasing (7/14/00) Page 10 A CMOS Bandgap Reference using PNP Lateral BJs Bootstrapped Voltage Reference using PNP Laterals- R 3 V DD R 2 M3 V REF Q1 Q2 I REF R 4 - I 2 I 1 R 1 M1 M2 V SS Fig I 1 I 2 = V BE1 - V BE2 R = V t 2 R 2 ln I - ln s1 I = V t s2 R ln 2 I = V t s1 R ln 2 A E1 if I 1 = I 2 which is forced by the current mirror consisting of M1 and M2. R 1 V REF = V BE1 I 1 R 1 = V BE1 R ln 2 I 2 A E2 A E1 I s2 V t = V BE1 KV t While an op amp could be used to make I 1 = I 2 it suffers from offset and noise and leads to deterioration of the bandgap temperature performance. V REF is with respect to V DD and therefore is susceptible to changes on V DD. A E2

11 emp. Indep. Biasing (7/14/00) Page 11 A CMOS Bandgap Reference using Substrate PNP BJs M7 M8 Operation: M5 M6 M9 M10 he cascode mirror (M5-M8) keeps the currents in Q1, Q2, and Q3 identical. hus, V BE1 = I 2 R V BE2 or M3 M1 R M4 M2 kr Q1 Q2 Q3 1 n n V REF - I 2 = V t R ln( n ) herefore, V REF = V BE3 I 2 (kr) = V BE3 kv t ln(n) Use k and n to design the desired value of K (n is an integer greater than 1). V SS Fig

12 emp. Indep. Biasing (7/14/00) Page 12 Weak Inversion Bandgap Voltage Reference Circuit: M2 I D2 M1 M4 V R1 R 1 I D4 M3 - V DD V SS V R2 Analysis: For the p-channel transistors: I D = I DO (W/L) exp V BG where V t = k/q. nv t exp -V BS -V BD V t V t - exp V BG If V BD >> V t, then I D = I DO (W/L) exp nv - V BS t V. t he various transistor currents can be expressed as: I D1 = I D2 = I DO (W 2 /L 2 ) exp V BG2 nv and I D3 = I D4 = I DO (W 4 /L 4 ) exp V BG4 t nv - V BS4 t V t Note that V BG2 = V BG4 and V BS4 = V R1. herefore, I D1 I = W 2/L 2 D3 W 4 /L exp V R1 4 V t where V R1 = V t ln W 1W 4 L 2 L 3 L 1 L 4 W 2 W and I R1 = V R1 3 R 1 Q5 - R 2 M6 V ref - Fig

13 emp. Indep. Biasing (7/14/00) Page 13 Weak Inversion Bandgap Voltage Reference - Continued he reference voltage can be expressed as, V REF = R 2 I 6 V BE5 However, I 6 = W 6L 3 L 6 W I R1 = W 6L 3 V t 3 L 6 W 3 R ln W 1W 4 L 2 L 3 1 L 1 L 4 W 2 W. 3 Substituting I 6 and the previously derived expression for V BE () in V REF gives, V REF = W 6L 3 R 2 L 6 W 3 R V t ln W 1W 4 L 2 L 3 1 L 1 L 4 W 2 W V GO 1-3 V BE0 0 3V t ln 0 o achieve V REF / = 0 at = 0, we get 0 V REF k q = R 2 R 1 W 6L 3 L 6 W ln W 1W 4 L 2 L 3 3 L 1 L 4 W 2 W 3 - V GO 0 V BE0 0 3k q herefore, R 2 W 6 L 3 R 1 L 6 W ln W 1W 4 L 2 L 3 q 3 L 1 L 4 W 2 W = 3 k (V GO - V BE0 ) Under the above constraint, V REF has an approximate zero value of temperature coefficient at = 0 and has a value of V REF = V GO 3k q 1 ln 0 = V GO 3k q Practical values of V REF / for the weak inversion bandgap are less than 100 ppm/ C.

14 emp. Indep. Biasing (7/14/00) Page 14 IMPROVEMEN OF HE BANDGAP REFERENCE CIRCUI Curvature Correction echniques: Squared PA Correction: V BE V PA Voltage V PA 2 V BE loop emperature coefficient 1-20 ppm/ C V Ref = V BE V PA V PA 2 emperature Fig M. Gunaway, et. al., A Curvature-Corrected Low-Voltage Bandgap Reference, IEEE Journal of Solid- State Circuits, vol. 28, no. 6, pp , June ß compensation I. Lee et. al., Exponential Curvature-Compensated BiCMOS Bandgap References, IEEE Journal of Solid-State Circuits, vol. 29, no. 11, pp , Nov Nonlinear cancellation G.M. Meijer et. al., A New Curvature-Corrected Bandgap Reference, IEEE Journal of Solid-State Circuits, vol. 17, no. 6, pp , December 1982.

15 emp. Indep. Biasing (7/14/00) Page 15 V BE Loop Curvature Correction echnique Circuit: where V DD I VBE I NL V DD V DD I PA IPA Q n1 x1 V t = k/q I c1 and I c2 are the collector currents of Q n1 and Q n2, respectively R x = a resistor used to define I PA R 2 I VBE V BE R 2 V t VDD 3-Output Current Mirror (I VBE I NL ) R 3 I NL I Constant Q n2 x2 2I PA I PA V REF = R 3 ln I NL I I PA R 1 constant emperature coefficient 3 ppm/ C with a total quiescent current of 95µA. V REF R 1 Fig Operation: I NL = V BE1 -V BE2 R = V t I c1 A 2 3 R 3 ln A 1 I c2 = V t 2I PA R 3 ln I NL I Constant where I constant = I NL I PA I VBE I NL V t R V BE x R 2 (a quasi-temperature independent current subject to the temperature coefficient of the resistors)

16 emp. Indep. Biasing (7/14/00) Page 16 ß Compensation Curvature Correction echnique Circuit: Operation: V V REF = V BE B A (1ß) R V BE A B in ß where I=A I=B A and B are constant R B 1ß V REF Fig = temperature he temperature dependence of ß is ß() e -1/ ß() = Ce -1/ V REF = V BE () A Be1/ C Not good for small values of V in. V in V REF V sat. = V GO V sat. = 1.4V R

17 emp. Indep. Biasing (7/14/00) Page 17 Nonlinear Cancellation Curvature Correction echnique Objective: Eliminate nonlinear term from the base-emitter. Result: 0.5 ppm/ C from -25 C to 85 C. Operation: From above, V REF = V PA 4V BE (I PA ) - 3V BE (I Constant ) Note that, I PA I c Τ 1 α = 1 and I constant I c 0 α = 0, Previously we found, V BE () V GO - 0 [ ] so that V GO -V BE ( 0 ) -(γ -α)v t ln V BE (I PA ) =V GO - 0 [ ] and 0 V GO -V BE ( 0 ) -(γ -1)V t ln V BE (I Constant ) =V GO - 0 [ ] V GO -V BE ( 0 ) -γv t ln Combining the above relationships gives, 0 0 V REF () = V PA V GO - 0 [V GO - V BE ( 0 )] - [γ - 4] V t ln 0 R1 V CC I PA V BE V PA V REF Conventional Bandgap Reference I PA Q4 Q3 Q2 Q1 V CC Q8 V BE V PA R1 R 2 I Constant V = REF R2 Q7 Q6 Q5 V REF Curvature Corrected Bandgap Reference Fig If γ 4, then V REF () V PA V GO 1 - V BE ( 0 ) 0 0

18 emp. Indep. Biasing (7/14/00) Page 18 Other Characteristics of Bandgap Voltage References Noise Voltage references for high-resolution A/D converters are particularly sensitive to noise. Noise sources: Op amp, resistors, switches, etc. PSRR Maximize the PSRR of the op amp. Offset Voltages Becomes a problem when op amps are used. or V BE2 = V BE1 V R1 V OS i C2A E1 V BE = V BE2 - V BE1 = V R1 V OS = V t ln i C1 A E2 i C2 R 3 = i C1 R 2 - V OS i C2 i = R 2 C1 R - V OS 3 i C1 R = R 2 3 R 3 1 V OS i C1 R 2 herefore, V R1 = -V OS V t ln R 2A E1 R 3 A E2 1 V OS i C1 R 2 V REF = V BE2 - V OS i C1 R 2 = V BE2 - V OS R R 2 = V 1 BE2 - V OS R V 1 R1 V R1 V REF = V BE2 - V OS 1 R 2 R R 2 1 R V t ln R 2A E1 1 R 3 A E2 1 - V OS i C1 R 2 V CC Q2 Q1 R 1 V R1 V - OS i C2 i C1 R 3 R 2 BGR01 V EE R 2 V REF - -

19 emp. Indep. Biasing (7/14/00) Page 19 How do you get a Stable Reference Current from the Bandgap? Assume that a temperature stable reference voltage is available (i.e. bandgap reference) and use the zero C NMOS current sink. he problem is that V REF may not be equal to the value of V GS that gives zero C. V GS = I R2 R 2 = R 2 dv GS R 2 V REF V REF R 2 I R1 R = 1 R V REF 1 R 1 1:1 Current Mirror V DD 1:1 Current Mirror dv REF I R2 R 2 d = dv REF R 1 d V REF dr 2 R 1 d - R 2 dr 1 R 2 1 d = R 2 R 1 d dr 2 d - dr 1 d If the temperature coefficients of R 1 and R 2 are equal dr 1 d = dr 2 d, then dv GS d = R 2 dv REF R 1 d V GS - I REF Fig and V GS is proportional to the temperature dependence of V REF. If the MOSFE is biased at the zero C point, then the current should have the same dependence on temperature as V REF.

20 emp. Indep. Biasing (7/14/00) Page 20 Practical Aspects of emperature-independent and Supply-Independent Biasing A temperature-independent and supply-independent current source and its distribution: V DD M7 M5 M8 M6 R 3 R 4 M9 M10 Bandgap Voltage, V BG M3 M4 - M11 M13 M15 M17 M19 M1 M2 M12 M14 M16 M18 M20 Constant current: Q1 I PA R1 R 2 Q2 xn Q3 I REF R ext o Slave Bias Ckt. I REF = V BG R ext where V BG = V BE3 I PA R 2 = V BE3 V R 1 ln(n) R 2 o Slave Bias Ckt. Fig

21 emp. Indep. Biasing (7/14/00) Page 21 Practical Aspects of Bias Distribution Circuits - Continued Distribution of the current avoids change in bias voltage due to IR drop in bias lines. Slave bias circuit: V DD VPBias1 From Master Bias I b I b V PBias2 V NBias2 V NBias1 Fig

22 emp. Indep. Biasing (7/14/00) Page 22 SUMMARY OF BANDGAP REFERENCES Summary Bandgap voltage references can achieve temperature dependence less than 50 ppm/ C Bandgap voltage references are also independent of power supply Correction of second-order effects in the bandgap voltage reference can achieve very stable (1 ppm/ C) voltage references. Watch out for second-order effects such as noise when using the bandgap voltage reference in sensitive applications.

23 emp. Indep. Biasing (7/14/00) Page 23