Bandgap Reference Circuits: Second Order Compensation

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Bandgap Reference CircuitsSecond Order
Compensation

• Presentation By-
• Nikhil Bhattar

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Basic Bandgap Voltage Reference
Vref
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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.

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Current Reference
V-to-I Converter
Vref
Iref
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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)

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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)

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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.

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First Order Compensation
Reference I or V
Temperature ?
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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.

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Proposed Architecture
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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)

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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/(R0a)
• (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)

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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.

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Complete Circuit for the New Proposed Architecture
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Performance Obtained
The Performance achieved by the circuit is as
follows
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Temperature Sweep
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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???

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Process Variations

• Consider the following scenario

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