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Bandgap Reference Circuits: Second Order Compensation

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Bandgap Reference Circuits: Second Order Compensation

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    1. Bandgap Reference Circuits: Second Order Compensation Presentation By:- Nikhil Bhattar

    2. Basic Bandgap Voltage Reference

    3. Governing Equations Vref = Veb3 + ß *((Vth ln(n1) )/R1) *R2 = Veb3 + Kß *((Vth ln(n1) ) Temperature coefficient: ?Vref/?T = ?Veb3/?T + ?(Kß Vth ln(n1))/?T =?Veb3/?T + Kß ln(n1) *k/q ?Veb3/?? is negative. So, we can obtain a temperature compensated reference voltage by choosing proper value of the Kß parameter.

    4. Current Reference

    5. Governing Equations Iref = Vref/R3 = (Veb3 + Kß Vth ln(n1))/ R3 R3 = R0 (1+ a? + a2?2) Then, Temperature Coefficient is given by:- ?Iref/?? = 1/R3 (?Vref/ ?T) - Vref/R32 (?R3/??) =1/R3 (?Veb3/?T + Kß Vth/T ln(n1) ) - (1/R32) (Veb3 + Kß Vth ln(n1) * (R0 a)

    6. Problem with the Architecture So far so good. But if we substitute some practical values, we would see that this is not feasible: Ex: ?Veb3/?? = -1.5 mv/0C, n1 = 25 ,T= 300 K Vth ( T= 300 K) = 25.9 mv, a = 3.0 m 0C-1 Veb = 0.7v (approx.) Using the above values, we obtain Kß =128, which is a prohibitively large value for this design. If this value is used, we will get a very high Vref (~ 10 V)

    7. Analysis of the Design The problem arises because of the high temperature coefficient of the resistor. We need to either reduce the T.C. of the resistor ( a really cumbersome approach, since we would need to use both positive and negative T.C. resistors) or opt for alternate architectures. Also note that, the previous architecture ( for both Voltage and Current reference) gives a first order compensated reference; i.e. the T.C. is zero only at a single temperature, giving rise to a curvature in the reference quantity Vs temperature plot.

    8. First Order Compensation

    9. TCF Instead of Theoretical T.C. Theoretically, we can achieve a zero T.C. (for all temperatures) by substituting proper values; but the same does not occur in practice. Therefore, we need a new quantifying metric for measuring sensitivity to temperature. This new metric is known as Fractional Temperature Coefficient (TCF) and is defined as: TCF = ?I (or V) I (or V) *?T Where ?T is the temperature range of interest.

    10. Proposed Architecture

    11. Governing Equations Iref = (1/R3) *(Vref - Veb4) = (1/R3) *(Veb3 + Kß Vth ln(n1) - Veb4) = (1/R3) *(Veb3 - Veb4 + Kß Vth ln(n1)) Assuming that current through the two branches containing Q3 and Q4 are equal, Veb3 - Veb4 = Vth ln(n2) Temperature Coefficient:- ?Iref/?T = 1/R3 Vth [1/T - aR0 /R3] [ ln(n2) + Kß ln(n1)]

    12. Second Order Compensation Temperature Coefficient:- ?Iref/?T = 1/R3 Vth [1/T - aR0 /R3] [ ln(n2) + Kß ln(n1)] The equation for T.C. reveals two interesting characteristics: (a) The circuit is always temperature compensated and will have a zero T.C. for T= R3/(R0*a) (b) The circuit will have a second compensation point if we make the term in the second parenthesis zero. Thus, we can obtain a doubly compensated reference current (Second Order Compensation)

    13. Intuitive Analysis The voltage-to-current conversion circuit operates as follows: The reference voltage obtained from the bandgap reference generator circuit establishes a current through the resistor R3. Now, if temperature increases, increase in resistance of R3 will try to decrease the current. At the same time, the emitter-base voltage of BJT Q4 will decrease due to the increase in temperature. This decrease means a larger potential drop across the resistor and hence a larger current. The two effects are opposite in nature and tend to cancel each other. By proper cancellation, we can get a temperature independent current.

    14. Complete Circuit for the New Proposed Architecture

    15. Performance Obtained

    16. Temperature Sweep

    17. Other Considerations for the Reference Ckt… A good reference circuit should be resistant to variations in Process, Voltage (Power Supply) and Temperature ( P V T). For the Circuit under consideration: Temperature ( We have already seen) Voltage ( Op-amps and transistor lengths decide the PSRR) Process : The Circuit is also resistant ( to some extent) to variations in process. How???

    18. Process Variations Consider the following scenario:

    19. THANK YOU

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