Analogue and Mixed Signal Integrated Circuit Design
Unit 3: Voltage Reference Design
Unit Contents
3.1 Historical Overview
Whether there is a need to generate a supply voltage of a known level or maybe to quantify an input to an analogue to digital converter, the need for temperature-stable voltage references pervades all analogue electronics. This section is intended to briefly summarise some of the earlier methods for voltage reference implementation.
3.1.1 Zener Diodes
Figure 1: Zener diode
A Zener diode is a specially engineered diode that operates in reverse breakdown mode and provides a reasonably sharp knee. They have almost disappeared from modern design practice for two reasons:
- Zener diodes tend to have relatively high reference (breakdown voltages). When analogue systems were based on +/- 15 Volt supplies this was not a problem but such big operating voltages are not really compatible with new designs operating from 5 volts or less.
- Although the temperature coefficient varies with the breakdown voltage, it is generally positive. This can be compensated for by placing a conventional (forward-biased) diode in series with the Zener diode but this only exacerbates the high operating voltage problem referred to above.
3.1.2 Reverse base-emitter junction
Figure 2: Emitter-base Breakdown
Zener diodes are traditionally discrete components and in an integrated circuit context, a similar function has been obtained by breaking down a base-emitter junction. The voltage obtained depends on the process used and is typically 6.5 Volts. Again this is slightly higher than would be wished. The reverse breakdown is a destructive process - the transistor could not be used again as a normal transistor because the current gain would have been seriously degraded. In addition, certain processes could be subject to serious long-term drift in the stability of the reverse breakdown voltage that was obtained.
3.2 Diode references
3.2.1 Base-emitter Junction as a Diode
In BJT circuits, conventional diodes are obtained by using the base-emitter junction as shown in Figure 3.
Figure 3: Base-emitter junction resulting in a conventional diode
Base resistance can be relatively high but this is overcome by connecting
the otherwise unused collector to the base. The dynamic slope resistance of
the diode is thus greatly reduced, while the current handling capacity is similarly
increased.
You should note that the collector base junction is almost never used to form
a diode. The reason is that, in a junction isolated bipolar process, the collector-base
forms a parasitic substrate PNP structure when the collector base diode is forward
biased: current is injected into the substrate. This is undesirable because it
can cause local increases in the substrate voltage leading to loss of isolation
between adjacent structures. There is an even more serious drawback when using
a collector base diode. Current flows into the anode (p-type base region) and
some of it 'vanishes' into the substrate - the current that emerges from the
cathode (n-type collector region) may only be two thirds of the current entering
the diode. If you stick to base-emitter diodes, you will avoid all these problems
and be very glad that you did.
3.2.2 BJT Diode Characteristics
Because such diodes are operating as transistors - most of the current flows through the collector - BJT diodes follow the law described by Equation 3 of Unit 1 of this module. The forward-biased voltage depends on Is, Ic and diode area but is usually in a range from 0.6 to 0.8 volts. The temperature coefficient of the voltage is approximately -1.8mV per degree Kelvin.
3.2.3 Diode Based References
As can be seen from Figure 4, diodes can be stacked in multiples or even multiplied up by using a potential divider on the base.
Figure 4: Diode stacking and multiplying
The idea of obtaining a scalable reference voltage from such easily understood and simple circuits may seem very seductive but 'multi-diode' references are best avoided for two reasons. The initial absolute voltage is very hit and miss - you simply can't rely on it being a convenient 0.700 Volts. Even worse is the temperature coefficient: for example, if there are four diodes in series a -7.2 mV T.C. results. A temperature change between 0 and 70 °C will cause the reference voltage to fall by half a volt!
Diode-based voltage references do come into their own, however, and are the ideal choice for diode-based circuits. For example, consider the cascode current source from unit 1 where Q3 acts as a diode reference to bias Q4. Both base-emitter voltages fall together with increasing temperature.
3.3 Band-gap References
3.3.1 Introduction
The first of the band-gap references is shown in Figure 5.
Figure 5: Widlar Bandgap reference
Areas: Q2 = 10; Q1, Q3 = 1; R1 = R3
Reference 7 in Gray and Meyer, Unit 4, refers to the original 1971 paper by Robert Widler. The circuit can be biased by a current source, but for simplicity I have shown it biased by a resistor dropped from a supply such as +5 volts. The reference voltage, Vref, is given by VBE of Q3 plus the voltage across R1.
The collector voltages of Q1 and Q2 are at a VBE level and the collector resistors are the same value (R1=R3) so the Q1, Q2 collector currents are the same. Q2 has ten times the area of Q1 which causes a VBE difference (D VBE ) to appear across R2. From unit 1, we know that this difference is VTln[(IC1/A1)/(IC2/A2)] which in this case is equal to VTln(10) = 2.3VT. The emitter current of Q2 is thus (2.3VT)/R2.
Ignoring base currents, the collector and emitter currents of Q2 are the same.
The voltage across R1 is therefore (2.3VTR1)/R2
= (2.3kTR1)/(qR2).
Differentiating this with respect to T shows that the temperature coefficient
of VR1 is
2.3(k/q)(R1/R2) volts/°K. We would now have to go leaping for our physics
encyclopaedia to find the values of 'k' and 'q' but luckily we know that kT/q=26mV
at 300°K, hence k/q is 26mV/300 or 87µV/°K.
We can now see that the voltage across R1 has a positive temperature coefficient given by +2.3 x 87 x (R1/R2) or +200(R1/R2) µV/°K. This appears in series with the negative temperature coefficient of Q3 (approximately -1.8mV/°K). If we add the two, to obtain zero T.C. we can write:
200(R1/R2) µV/°K - 1800 µV/°K = 0, therefore R1/R2 = 9 for zero T.C.
Finally we can return to the voltage across R1 which appears in series with VBE(Q3) to produce the reference voltage:
Vref = 2.3VT(R1/R2) + 0.7 (assumed) = (2.3 x 9 x VT) + 0.7 = 1.238V
This is only an approximate value, it obviously depends on the VBE value that we have assumed for Q3 but it is very much the sort of value that would be obtained in practice and is closely related to the band-gap voltage of silicon (1.205V) - hence the term "bandgap reference". Note that in the above analysis, the area ratio of Q1 and Q2 is not critical. For example, a ratio of eight to one could be used. In that case, a different ratio for R1:R2 would be obtained but the absolute output voltage would be the same.
Note: You should be aware that the simple first order analysis presented above is not the whole story by any means. In fact the Vref versus temperature response is curved but by adjusting the R1:R2 ratio it is possible to place the flat part of the curve at any temperature we wish. For example for a 0 to 70°C temperature range it is best that the flat portion of the curve lies at 35°C. See G&M Figure 4.48.
The Widlar reference, or "Widlar diode" as it is sometimes known, represented a major breakthrough because for the first time it offered the prospect of a reference voltage with two very desirable features:
- An absolute voltage source.
- Zero (or very small) temperature drift.
Drawbacks of the basic three-transistor circuit include the fact that the voltage (conveniently low though it is) cannot be changed. Also the performance of the circuit depends heavily on the current density in Q3 which will change if the circuit is loaded. One way round this is to drive Q3 from a constant current source and then to use an amplifier to buffer and scale the raw Vref output. The next section presents a modified band-gap reference, which combines the band-gap element and the amplifier into a single circuit.
Interactive Spice Simulation Exercise
Schematically capture and simulate the circuit of Figure 5 from 0 to 70°C.
Adjust the ratio R1:R2 until the temperature coefficient is nominally zero in the vicinity of 35°C and confirm that the absolute voltage output obtained is similar to that derived in section 3.1.1.
Hints:
- Q2 must have its area parameter set to 10.
- Use 5 Volts for Vcc and adjust Rbias so that Q1 and Q3 operate at similar currents.
Reference Texts
See Figure 6 and Reference 9 of G&M Unit 4.
Further Study
Gray and Meyer Appendix 4.3.2
Supplementary Information
For further information on bandgap reference design visit the home page of Bob Pease at the National Semiconductors site: http://www.national.com/rap
His excellent bandgap page is at: http://www.national.com/rap/Application/0,1570,24,00.html