REFERENCE CIRCUITS

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 xi

4. Total percentage change in y = Sensitivity w.r.t. x1 * percentage change in x1 + Sensitivity w.r.t. x2 * percentage change in x2 + …… 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 (ro=∞ for I-ref, ro=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: TCF = =

8. Voltage references Passive Divider Limited accuracy, ~6-bit, or 2% Large static power for small ro 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 VCC = 10V, R = 10 kW, and IS = 10-15A, then = 0.0362.

11. For a diode: Taking ∂/∂T and using: VCC − VREF + kT/q ≈ VCC − VREF: TCF≈ = where VGO = 1.205 V is the bandgap voltage of silicon. If VREF = VBE = 0.6V, TCF of R = 1500 ppm, then TCF of VREF = -3500 ppm/oC

12. HW: Calculate Calculate TCF

13. MOS equivalent of VBE reference:

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

15. For temperature coefficient mo = KT-1.5 ; VT = VT0 - aT or VT(T) = VT(To) - a(T-To)

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

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

18. Why the start up circuit? • There are two possible operating points: • The desired one and • The one that gives I1 = I2 = 0. • At power up, I1 = I2 = 0 without the start up. • RB bias M6 to be on, which turns M2 and M1 on.

19. Considering the l-effect, (1) is more like: Then: Differentiating wrt VDD and assuming constant VDS1 and VGS4 gives the sensitivity of IOUT wrt VDD.

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

22. VEB based current reference Start up VEB=VR

23. A cascoded version to increase ro and reduce sensitivity: Requires start up Not shown here VEB reference

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

25. A thermal voltage based current reference I1 = I2,  J1 = KJ2, but J = Jsexp(VEB/Vt)  J1/J2 = K = exp((VEB1─ VEB2)/Vt)  VEB1─ VEB2 = Vt ln(K) I = (VEB1─ VEB2)/R = Vt ln(K)/R  Vt = kT/q

26. A band gap voltage reference Vout = VEB3 + I*L*R = VEB3 + (kT/q)*Lln(K) Vout/T = VEB3/T + (k/q)*Lln(K) At room temperature, VEB3/T = ─2.2 mV/oC, k/q = +0.085 mV/oC. Hence, choosing appropriate L and K can make Vout/T=0 When this happens, Vout = 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. VBEis negatively PTAT at roughly -2.2 mV/°C at room temperature Vt(Vt = kT/q) is PTAT that has a temperature coefficient of +0.085 mV/°C at room temperature. Multiply Vtby a constant K and sum it with the VBEto get VREF = VBE+ KVt If K is right, temperature coefficient can be zero.

30. In general, use VBE + VPTAT

31. How to get Bipolar in CMOS?

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

34. VOSrepresents input offset voltage of the amplifier. Transistors Q1 and Q2 are assumed to have emitter-base areas of AE1 and AE2, respectively. If VOSis zero, then the voltage across R1 is given as

35. Bandgap reference still varies a little with temp

36. Converting a bandgap voltage reference to a current reference

38. Vref=I3*R3=

44. Curvature corrected bandgap circuit R3= R4 Vref Q2 Q1 R2 R1

45. VBE T Vref T

46. Solution: R4= R5 Vref IPTAT↓ D2 D1 R1 R2 IPTAT2 R3

47. Vref VBE VPTAT VPTAT2 T

48. Ex: • Suppose you have an IPTAT2 source characterized by IPTAT2 = aT2, derive the conditions so that both first order and second order partial derivative of Vref with respect to T are canceled at a given temperature T0. • Suggest a circuit schematic that can be used to generated IPTAT2 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.