1. REFERENCE CIRCUITS A reference circuit is an independent voltage or current source which has a high degree of precision and stability. Output voltage/current should be independent of power supply. Output voltage/current should be independent of temperature. Output voltage/current should be independent of processing variations.

2. I-V curves of ideal references

3. Concept of Sensitivity Let Then: is called the sensitivity of y with respect to x i

4. Total percentage change in y = Sensitivity w.r.t. x 1 * percentage change in x 1 + Sensitivity w.r.t. x 2 * percentage change in x 2 + …… Goal: Design reference circuits so that the reference’s sensitivities w.r.t. various variations are minimized.

5. Types of commonly used references Voltage dividers - passive and active. MOS diode reference. PN junction diode reference. Gate-source threshold reference circuit. Base-emitter reference circuit. Thermo voltage reference circuit Bandgap reference circuit

6. Typical variations affecting the references Power supply variation (main concern here) Load variation (r o =∞ for I-ref, r o =0 for V- ref) Temperature variation (main concern also) Processes variation (good process and layout) Interferences and noise (not considered here)

7. For temperature variation, typically use fractional temperature coefficient: TC F = =

8. Voltage references Passive Divider Limited accuracy, ~6-bit, or 2% Large static power for small r o Large area Power sensitivity =1 Temp coeff depends on material

9. Active Dividers These can be used as “start up” circuits.

10. PN Junction Voltage References = If V CC = 10V, R = 10 k , and I S = 10 -15 A, then = 0.0362.

11. For a diode: Taking ∂/∂T and using: V CC − V REF + kT/q ≈ V CC − V REF : = where V GO = 1.205 V is the bandgap voltage of silicon. If V REF = V BE = 0.6V, TC F of R = 1500 ppm, then TC F of V REF = -3500 ppm/ o C TC F ≈

12. HW: Calculate Calculate TC F

13. MOS equivalent of VBE reference:

14. The sensitivity w.r.t. V DD : If V DD = 10V, W/L = 10, R = 100k ,and using parameters from Table3.1-2, then V REF = 1.97V and This is not nearly as good as the V BE reference. = 0.29

15.  o = KT -1.5 ; V T = V T0 -  T or V T (T) = V T (T o ) -  (T-T o ) For temperature coefficient

16. Solving for ∂V REF /∂T and computer TC: The book has one example of using this.

17. V GS based Current reference MOS version: use V GS to generate a current and then use negative feed back stabilize i in MOS Current mirror Start up V GS

18. Why the start up circuit? There are two possible operating points:  The desired one and  The one that gives I 1 = I 2 = 0. At power up, I 1 = I 2 = 0 without the start up. R B bias M 6 to be on, which turns M 2 and M 1 on.

19. Considering the -effect, (1) is more like: Then: Differentiating wrt V DD and assuming constant V DS1 and V GS4 gives the sensitivity of I OUT wrt V DD.

20. HW: Verify the following sensitivity expression: HW: Show that approximately:

22. V EB based current reference V EB =V R Start up

23. A cascoded version to increase r o and reduce sensitivity: V EB reference Requires start up Not shown here

24. Come up with a start up circuit for the circuit on the previous slide, using only active resisters without R B. Note that you need to make sure that at the desired operating point, the connection from the start up circuit should be turned off. HW: Analyze the sensitivity of the output I with respect to V DD and temperature.

25. A thermal voltage based current reference I 1 = I 2,  J 1 = KJ 2, but J = J s exp(V EB /V t )  J 1 /J 2 = K = exp((V EB1 ─ V EB2 )/V t )  V EB1 ─ V EB2 = V t ln(K)  I = (V EB1 ─ V EB2 )/R = V t ln(K)/R  V t = kT/q

26. A band gap voltage reference V out = V EB3 + I*L*R = V EB3 + (kT/q)*Lln(K)  V out /  T =  V EB3 /  T + (k/q)*Lln(K) At room temperature,  V EB3 /  T = ─2.2 mV/ o C, k/q = +0.085 mV/ o C. Hence, choosing appropriate L and K can make  V out /  T=0 When this happens, V out = 1.26 V

27. General principle of bandgap reference Generate a negatively PTAT (Proportional To Absolute Temperature) and a positively PTAT voltages and sum them appropriately.

28. A Common way of bandgap reference

29. V BE is negatively PTAT at roughly -2.2 mV/°C at room temperature V t (V t = kT/q) is PTAT that has a temperature coefficient of +0.085 mV/°C at room temperature. Multiply V t by a constant K and sum it with the V BE to get V REF = V BE + KV t If K is right, temperature coefficient can be zero.

30. In general, use V BE + V PTAT

31. How to get Bipolar in CMOS?

33. A conventional CMOS bandgap reference for a n-well process

34. V OS represents input offset voltage of the amplifier. Transistors Q 1 and Q 2 are assumed to have emitter- base areas of A E1 and A E2, respectively. If V OS is zero, then the voltage across R 1 is given as

35. Bandgap reference still varies a little with temp

36. Converting a bandgap voltage reference to a current reference

38. Vref=I 3 *R 3 =

44. Curvature corrected bandgap circuit V ref R 3 = R 4 Q2Q2 Q1Q1 R2R2 R1R1

45. V BE T V ref T

46. R 4 = R 5 D2D2 D1D1 R1R1 R2R2 Solution: V ref I PTAT ↓ R3R3 I PTAT 2

47. V ref T V PTAT V PTAT 2 V BE

48. Ex: 1.Suppose you have an I PTAT 2 source characterized by I PTAT 2 =  T 2, derive the conditions so that both first order and second order partial derivative of V ref with respect to T are canceled at a given temperature T 0. 2.Suggest a circuit schematic that can be used to generated I PTAT 2 current. You can use some of the circuit elements that we talked about earlier together with current mirrors/amplifiers to construct your circuit. Explain how your circuit work. If you found something in the literature, you can use/modify it but you should state so, give credit, and explain how the circuit works.