A Low Voltage Bandgap Reference Circuit with Current Feedback

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					EECS 413 Project                                                                                                                   1

       A Low Voltage Bandgap Reference Circuit with
                    Current Feedback
                                            Tao Li, Bhaskar Mitra, and Kabir Udeshi

   Abstract—This paper describes the design of a bandgap                                 II. CIRCUIT DESCRIPTION
reference, implemented in 0.25µm CMOS technology. The circuit
                                                                        A reference voltage is generated by adding two voltages
generates a reference voltage of 1.157V and has a temperature
coefficient of 0.03mV/K at 27C. It can operate with supply           that have temperature coefficients of opposite sign with
voltages between 2.25V and 2.75V and between 0C and 85C. It          suitable multiplication constants. The resulting voltage
has a PSRR of 59dB under normal operating conditions. This           obtained is independent of temperature. The diode voltage
circuit works in a current feedback mode, and it generates its       drop across the base-emitter junction, VBE, of a Bipolar
own reference current, resulting in a stable operation. A startup    Junction Transistor (BJT) changes Complementary to
circuit is required for successful operation of the system.
                                                                     Absolute Temperature (CTAT) [1]. Whereas if two BJTs
                                                                     operate with unequal current densities, then the difference in
                       I. INTRODUCTION
                                                                     the base emitter voltages, ∆VBE, of the transistors is found to

O     NE of the essential building blocks of many analog
      circuits is a voltage reference, which should exhibit little
dependence on supply and process parameters and a well
                                                                     be Proportional to Absolute Temperature (PTAT). The PTAT
                                                                     relationship is given by [2],
                                                                                   ∆ V BE = VT ln m ; VT = kT / q                (1)
defined dependence on temperature. For example, accurate
biasing voltages are critical for many circuit schemes; in              where, k is Boltzmann’s constant, T is the absolute
ADC, a reference voltage is required to quantify an input,           temperature, q is the electron charge and m is the ratio of the
while in DAC, it is required to define the output full-scale         current densities of the two BJTs. The PTAT voltage may be
range.                                                               added to the CTAT voltage with suitable weighting constants
   As a well-established reference generator technique,              to obtain a constant reference voltage.
bandgap reference is most popular for both Bipolar and                  Figure 1 shows the block diagram of the badgap reference
CMOS technologies. The principle of the bandgap circuits             circuit designed. By using a supply independent current
relies on two groups of diode-connected BJT transistors              source, a current ISS is passed through BJT A. The same
running at different emitter current densities. By canceling the     current ISS flows through m transistors connected in parallel,
negative temperature dependence of the PN junctions in one           identical to A. Thus the current density of A is m times the
group of transistors with the positive temperature dependence        current density of the m BJTs identical to A, connected in
from a PTAT (proportional-to-absolute-temperature) circuit           parallel. The voltages at node X and Y are maintained at the
which includes the other group of transistors, a fixed DC            same value, VBE using a feedback network through a
voltage which doesn’t change with temperature is generated.          differential amplifier. This results in a voltage of ∆VBE,
This voltage is typically 1.26 volts, which is approximately         across the resistor R. The voltages VBE and ∆VBE are added to
the band gap of silicon. [3][4]
                                                                            Startup                 Supply Independant
   There are many different implementation reported, while                  Circuit                 Current Source
essentially a bandgap reference circuit consists of a supply-
independent biasing circuit, a diode connected BJT transistor
generating a voltage with negative temperature coefficient, a                                 Iss                Iss
PTAT circuit and some kind of feedback mechanism to                                                  X                  Y
improve the performance. In this work, a measurement and
addition circuit is implemented to output the reference                                                  R1
                                                                                      Delta VBE
voltage. Current mirrors with current feedback mechanism are
used to minimize supply dependence. Feedback mechanism is                                                                    VBE
implemented by simple 2-stage single-ended differential                 Measure &                        mA            A
amplifier. The circuit has been optimized for minimum                   Add Voltages
temperature and supply dependence with simplest
                                                                       Fig. 1: Block diagram of Bandgap Reference Circuit.
EECS 413 Project                                                                                                                                 2

          C                       E                     B                      arrangement to generate the reference voltage while
                                                                               conserving voltage headroom.
                                                                                  The circuit has a stable operating point at which no current
              p+                   p+                       n+                 to flows through it. An arrangement must be made to force
                                                                               the saturation when the supply is turned on. This function is
                                                        n-well                 carried out by the startup circuit.
                                                                                                       III. CIRCUIT ANALYSIS
  Fig. 2: pnp BJT using CMOS process..
obtain the reference voltage. The circuit also requires a                        A. Bandgap Core
startup circuit since there exists a stable state at which no                     The bandgap reference voltage is generated by adding the
current flows through the circuit. The startup circuit forces                  base emitter voltage, VBE, of a BJT to the difference in base
the transistors to turn on and the circuit to operate at its other             emitter voltage, ∆VBE, of BJTs with a ratio of current density
stable state to generate the reference voltage.                                m. In order to generate a stable circuit, it is necessary to keep
   It should be noted that an ideal BJT is not available in                    the BJT in the exponential region. By simulating the
CMOS technology. A pnp BJT is made using the n-well                            transistor characteristics it was found that the minimum value
normally associated with a PFET [1] (Figure 2), the p-                         of collector current that could be used is 10 µA (Figure 4). By
substrate behaving as the collector.                                           selecting a current density ratio of 8, and a minimum collector
                                                                               current of 12.5 µA, we obtain a ∆ VBE of 52 mV using
   In order to generate supply independent current and carry                   Equation 1. The total collector current is 100 µA, which
out an addition of the CTAT and PTAT voltages, the circuit in                  allows the resistor R1 to be in the order of hundreds of ohms.
Figure 3 is used. The OPAMP provides the base voltage to                       It would be difficult to implement a smaller value of resistance
the transistors which are connected as current mirrors. By                     using the 0.25 µm IBM process.
selecting the value of R1 and current ISS, the circuit may be                     The value of the resistor R1 is calculated buy dividing the
designed to operate at the desired operating point. The value
                                                                               voltage by the current and turns out to be a value of 465 Ω
of R1 is given by,
                                                                               (Equation 2). By setting R2 we determine the multiplication
                     R1 = ∆ V BE / I SS                   (2)
                                                                               constant of the circuit. R2 is calculated using Equation 3 and
   Since the same current ISS flows through R2, the voltage at                 turns out to be 4.65 KΩ.
the output reference voltage nodes is given by,                                   The transistors in the circuit are sized to operate with a
                                        R1                (3)                  VDSAT of 0.4 V. We use the current equation [1] to determine
                 Vref = V BE + ∆ V BE .
                                        R2                                     the size of the current source transistors, TP1 and TP2.
   Thus by selecting the value of R2 the weighting constant                                            1        W                            (4)
                                                                                                 I D = µ C OX
                                                                                                                   V DSAT
may be set.         This arrangement provided an elegant                                               2        L

           Startup              Add CTAT and                     Bandgap Core with supply                                  OPAMP
           Circuit              PTAT Voltages                    independant current source

         TN2        TP4                       TP3                     TP2               TP1                      TP5                      TP6

                                                  Iss                  Iss                 Iss           TP7                     TP8
         TN3                                                                                                                              TN7
                       ∆ VBE.R2/R1
                   TN1 + VBE
                                               R2           ∆ VBE      R1
                                                                                                        TN4              TN5              TN6
                                              A                       mA               A

            Fig. 3: Schematic of Bandgap Reference Circuit showing the supply independent current source and generation of reference voltage..
EECS 413 Project                                                                                                                                          3

                                                                                                                  TABLE I
                                                                                                                 DEVICE SIZES

                                                                                                 Component                           Value (µm)

                                                                                    TP1,TP2, TP3, TP5, TP6                  52/2
                                                                                    TP7, TP8                                26/2
                                                                                    TP4                                     2/5
                                                                                    TN1, TN3                                20/1
                                                                                    TN2                                     2/5
                                                                                    TN4, TN5                                6.6/2
                                                                                    TN6, TN7                                13/2
                                                                                    R1                                      464 Ω
                                                                                    R2                                      4.13 KΩ

                                                                                  mirror circuit with a PMOS driver was selected.
                                                                                     The output common mode voltage corresponds to the gate
                                                                                  voltage of the current mirror transistors. In order to have a
                                                                                  VDSAT of 0.4 V for these transistors the output common mode
Fig. 4: The relation between the base-emitter voltage and the collector current   should be ideally about 1.5 V. A second stage was added to
of the BJT ceases to be logarithmic below about 10 µA of collector current.       the OPAMP to increase gain and shift the common mode
                                                                                  voltage up by using an NMOS driver. The NMOS driver only
   Where, ID is the drain current, µ is the mobility of the                       provided an output common mode of about 0.4 V. By adding
carriers, COX is the oxide capacitance per unit area, W is the                    a diode-connected transistor, TN7, to the second stage, the
width, and L the length of the transistors.                                       output voltage was pushed up to about 1.3 V without any
   The value of the W/L is 26. A length of 2 µm was used to                       effect on the gain of the stage. The voltage drop accress the
reduce the effect of channel length modulation.               The                 diode connected transistor is about 1.2 V corresponding to
dependence on the OPMAP gain may be reduced if channel                            VTH + VDSAT. The gain of each of the stages of the OPAMP is
length modulation is minimized. A longer channel also                             given by
improves circuit symmetry making it less sensitive to process                                            Av = gm .R O                       (7)
variation and giving it the ability to generate stable currents.
   In order to have the VBE of a BJT vary linearly with                              where, Av is the gain, gm is the transconductance of the
temperature, the collector current of the BJT must be constant.                   driving transistor and RO is the effective output resistance at
However, in the circuit used the collector current changes with                   the output node. The gain of each stage is about 42; the
temperature. The variation of VBE with temperature can be                         differential pair with a non-inverting gain and the single stage
expressed using the relation [1],                                                 with an inverting gain
            ∂ V BE V BE − ( 3 + m )VT − Eg / q                 (5)
             ∂T                   T
   Where, Eg is the bandgap voltage of the semiconductor
material, q is the electron charge and T is the temperature in
K. This relationship can be solved only numerically and is
plotted in Figure 4. By using the analytical estimation we see
that VBE does not change linearly with temperature. Using
this relationship the estimation of change of the reference
voltage with temperature is estimated to be 0.011 V over the
temperature range from 300 to 385 K.                                                                                  Temperature (K)
                      ⎡ ∂V      ∂ V BE          ⎤              (6)
          ∆ Vref = ∫ ⎢ BE −                     ⎥ dT
                      ⎣ ∂T        ∂ T T → 300 K ⎦                                  Fig. 5: Analytical estimation of nonlinearity of rate of change of VBE with
   The OPAMP was used to maintain equal node voltages and                          C. STARTUP CIRCUIT
provide a feedback to maintain the drain currents constant and                     Transistors TN1, TN2, TN3 and TP4 constitute the startup
insensitive to supply variations. A high gain of the OPAMP                         circuit. Initially all the transistors start off in off state. The
would result in better voltage tracking of nodes X and Y                           voltage at the gate of TN1 is low and so it remains in off
(Figure 1). The common mode voltages play an important                             state. TP4 being diode connected is always on and so the
role in determining the OPAMP topology. The input common                           transistor TN2 turns on forcing the drain to a low value. The
mode was determined by the base emitter voltage of the BJT,                        current mirror stack turns on and the gate voltage of TN1
which is 0.8 V at 100 µA of collector current. In order to                         rises and it starts to conduct. At this point there is a
meet the input common mode condition an active current                             competieion between the output of the amplifier TP6, and
EECS 413 Project                                                                                                                                  4

  TN2 for the current source load. TN2 is designed to be a
  weak transistor with W/L of 1/5 so the amplifier takes
  control of the current mirror gate.
         When the bandgap voltage is high enough ( ~1V) the
  transistor TN1 turns on. TN1 in linear region has to compete
  with TN2 in saturation so it is designed to be a big
  transistor. It draws all the current from TP2 and the base
  voltage of TN2 falls till it turns off. In this state the gate
  voltage at TN2 is about 0.6 V. This is high enough for the
  transistor TN1 to be conduct slightly. A diode connected
  transistor TN3 is added to increase the threshold voltage at
  the gate of TN3 to turn off.
  The transistor TP4 is designed to be a weak device so that
  low current flows through the parasitic path when the circuit
  is in full operation.                                                 Figure 7: Variation of the reference voltage with supply voltage at 27C

                             IV. RESULTS
The bandgap reference voltage gives a voltage of 1.1570V                Figure 8 shows the a.c response. A PSRR of 59dB is obtained
when adjusted to have a zero temperature coefficient at 27C.            at d.c at the high frequency corner of 10Mhz, the PSRR starts
Figure 1, shows the result of the simulation. It can be adjusted        to degrade ans is about 10dB for a frequency of abou 20Mhz.
to give a voltage of 1.26V, by sacrificing the zero temperature         This problem can be solved by putting a 100pF capacitor
coefficient at 27C, but this leads to a much more degraded              between Vdd and ground to suppress the noise in Vdd. This
response. Figure 5, shows the result of the simulation. As can          would probably be done external to the chip as it is not
be seen an overall temperature coefficient of 0.1mV/K is                feasible to put the supply bypass capacitor on-chip.
obtained between 0C and 85C, which corresponds to about
0.5% variation. The response it worse for temperatures from
65-85C with a temperature coefficient of 0.2mV/K. Below
these temperatures the temperature coefficient is 0.03mV/K.

                                                                                             Figure 8: PSRR of the circuit at 27C

                                                                        The D.C characteristics at 85degrees are shown in figure 9.
                                                                        The variation with Vdd is much worse in this case. The
                                                                        nominal value at 2.5V is still 1.1570V but at low Vdd it
                                                                        degrades to 1.100V, a 6%variation in voltage.

Figure 6: Variation of bandgap reference with temperature at Vdd=2.5V   Figure 10, shows the PSRR of the circuit at 85C. It comes
                                                                        down from 60dB at 27C to about 30dB in this case. This
Figure 7 shows the variation when the supply voltage is varied          degradation in characteristics is probably due to degradation
from 2.5V to 2.75V. The relative variation is 0.32%. at 27C.            in the gain of the amplifier, which increases the error voltage
Even here the response shows a two fold characteristic. The             that needs to be sustained to drive the circuit.
response is much better in the high voltage range 2.2-2.75
than in the low voltage range (2.25V-2.4V). So the worst case
operation of the device is at 85C and a supply voltage of
EECS 413 Project                                                                                                                                          5

                                                                                                           VI. CONCLUSION
                                                                                   A bandgap reference with a current feedback mode has
                                                                                been designed. The circuit uses no external current sources
                                                                                and is designed to have a zero temperature coefficient at 27C.
                                                                                The design is implemented with 0.25µm CMOS process and
                                                                                consumes very little headroom. The output voltage is 1.1570V
                                                                                at the nominal operating condition of 27C temperature and
                                                                                2.5V supply voltage. It has a temperature coefficient of
                                                                                0.03mV/K from 0-60C. It has a PSRR of 59dB and a large
                                                                                signal variation of 0.32% with Vdd under nominal operating
                                                                                conditions. The circuit performance degrades at higher
    Figure 9: Variation with Supply Voltage at 85C (absolute worst case)        temperatures and lower voltages. In the worst case corner of
                                                                                high temperature (85C) and low supply voltage (2.25V) the
                                                                                circuit puts out 1.100 volt, a 5% variation from the nominal
                                                                                TABLE 2: REFERENCE VOLTAGE OBTAINED UNDER DIFFERENT
                                                                                SUPPLY VOLTAGES AND TEMPERATURES

                                                                                                2.5V           2.25V           2.75V
                                                                                27C             1.157V         1.1555V         1.1573V
                                                                                85C             1.156V         1.100V          1.157V

                          Figure 10: PSRR at 85C                                [1]   B. Razavi, Design of Analog CMOS Integrated Circuits. New york, NY:
                                                                                      2001, ch 11.
                                                                                [2]   D. Hilbiber, “A New Semicondictor Voltage Standard,” IEEE J. of
                                                                                      Solid-State Circuits, vol. 8, pp. 222-226, June 1973.
                              V. LAYOUT                                         [3]   Robert A. Pease, “The Design of Band-Gap Reference Circuits: Trials
                                                                                      and Tribulations,” IEEE Proc. of the 1990 Bipolar Circuits and
Figure 9 shows the layout. The chip occupies a total area of .                        Technology Meeting, Minneapolis, Minnesota , Sept. 1990
The chip has been optimized by combining all the FETs. Most                     [4]   K. Lasanen, V. Koorkala, etc., “Design of A 1-V Low Power CMOS
of the area is taken up by the pnp transistors, so it cannot be                       Bandgap Reference Based on Resistive Subdivision,” IEEE 2002
optimized too much                                                              [5]   T. Brooks and A.C Westwisk, “ A low power differential CMOS
                                                                                      bandgap Reference”, ISSCC Dig. Of Tech. Papers, pp 248-249, Feb
                                                                                [6]   K. Lasanen, et. Al, “ Design of a 1-V low power bandgap reference
                                                                                      based on Resistive Subdivision”, Proceedings of the 45th IEEE Midwest
                                                                                      Symposium on Circuits and Systems, Tulsa, Oklahoma, USA, August

             Figure 7: Layout of the bandgap reference circuit

The simulation files are in /afs/engine.umich.edu/class/f03/eecs413/group3/bandgap/bandgap/concept_low_volt_test_sim

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