Handout #20: EE214 Fall 2001 Voltage References and Biasing  1993 Thomas H. Lee; rev. November 19, 2001; All rights reserved Page 1 of 15 Voltage References and Biasing 1.0 Introduction In this set of notes, we take up the study of an important topic: How to generate voltages and currents that are relatively independent of supply voltage and/or temperature. Because CMOS offers relatively limited options for realizing bias circuits, we’ll see that some of the most useful biasing idioms are actually those based on bipolar circuits. A parasitic bipolar device exists in every CMOS technology, and may be used in a bandgap voltage reference, for example. Even though the characteristics of parasitic transistors are far from ideal, the performance of bias circuits made with such devices is frequently vastly superior to that of “pure” CMOS bias circuits.In what follows, it is worthwhile to keep in mind that any voltage we produce must depend on some collection of parameters that ultimately have the dimensions of a voltage (such as kT / q , for example). Similarly, any current we produce must depend on parameters that ultimately have the dimensions of current (such as V / R ). Although seemingly obvious and trivial statements, we’ll see that they are extremely useful guides for the design of sta-ble references. 2.0 Review of Behavior of Diodes While the voltage across a forward-biased diode is relatively insensitive to current because of the logarithmic dependence of diode current on diode voltage, its variation with temperature is significant. To understand the precise nature of the temperature depen-dence, recall that the diode voltage may be expressed as: (1) where V T is the thermal voltage, kT / q , and n , the ideality factor, is typically between 1 and 1.5 in diodes. Transistor V BE ’s conform more closely to the “ideal diode law” than do ordi-nary diodes, so we will assign n a unity value in all that follows.It is frequently inferred incorrectly from Eqn. 1 that V D has a positive temperature coeffi-cient (TC) because of its proportionality to V T . The fly in the ointment is that I D itself has an exponential temperature dependence, and this alters the situation considerably. To clar-ify matters, consider the following quasi-empirical expression for I S : (2)VDnVTlnIDIS=ISI0expVG0VT−=Handout #20: EE214 Fall 2001 Voltage References and Biasing  1993 Thomas H. Lee; rev. November 19, 2001; All rights reserved Page 2 of 15 where I O is some process- and geometry-dependent current 1 ( I 0 is typically around 20 orders of magnitude larger than I S at room temperature, so I 0 is much larger than typical values of I D ), and V G0 is the bandgap voltage (about 1.2 volts) extrapolated to absolute zero.Using this detailed expression for I S , we can expand the equation for V D as follows: 2(3) Thus, we see that the junction voltage decreases linearly from a value of V G0 , as seen in the following plot of V D vs . temperature at constant diode current: FIGURE 1. Approximate behavior of V D vs . temperature Note that this equation tells us that V D always equals V G0 at absolute zero. 3 Furthermore it’s easy to see that the temperature coefficient at any temperature is simply (4) With the assumption of constant I 0 , the temperature coefficient is independent of tempera-ture and equal to about –2mV/K. This linearly decreasing behavior is known as CTAT, for 1. It also depends weakly on temperature, but we’ll defer a detailed discussion about the behavior of I 0 until the section on bandgap voltage references.2. The minus sign is not an error. Just remember that the argument of the log here is typically much larger than unity.3. Again, this value is an extrapolated one. It must be stressed that the behavior of real junctions at both extremes of temperature will differ from that shown; the equations presented lose validity at extremely cold temperatures (say, <100K) because of carrier freeze-out (i.e., failure of dopants to ionize) and because of bandgap variation with temperature, and at high temperatures (>450-500K) because the silicon goes intrin-sic.VDVGOVT− lnI0ID=T (kelvins)VD600K, typ.higher IDlower IDVG0 ≈ 1.2about –2mV/KTddVDVG0VD−T−=Handout #20: EE214 Fall 2001 Voltage References and Biasing  1993 Thomas H. Lee; rev. November 19, 2001; All rights reserved Page 3 of 15 “complementary to absolute temperature.” Note that the voltage does depend (logarithmi-cally) on diode current, so the temperature coefficient also depends somewhat on the diode current, with lower currents associated with higher temperature coefficients.Although a V D -based reference can provide an output that depends very little on supply voltage, the CTAT behavior may or may not be acceptable, depending on the application. However, we shall see that the CTAT behavior of a V D is particularly valuable for use in a class of references based on the bandgap voltage V G0 . We’ll take up the detailed study of bandgap references in Section 5.0. 3.0 Diodes and Bipolar Transistors in CMOS Technology The most flexible option for realizing diodes and bipolar transistors in standard CMOS technology derives from the parasitic substrate pnp transistor available in n-well pro-cesses. The p+ source/drain diffusions serve as the emitter, the n-well as the base, and the substrate as the collector: FIGURE 2. Parasitic substrate PNP in n-well CMOS (not drawn to scale) In applications where it is important to reduce series base resistance, it is advisable to sur-round completely the emitter with n+ diffusions placed as close to the emitter as the design rules allow, as suggested by Fig. 2.Just as its counterpart in inexpensive bipolar processes, the substrate pnp in CMOS tech-nology can only be used in circuits that allow the collector to be at substrate potential. For-tunately, there are numerous circuits that satisfy this condition. For example, a simple voltage “reference” can be constructed with this device connected as a grounded diode, in which the emitter is the anode, and the cathode is the base and collector (substrate) tied together.p-substraten-wellp+n+ n+emitter basecollectorHandout #20: EE214 Fall 2001 Voltage References and Biasing  1993 Thomas H. Lee; rev. November 19, 2001; All rights reserved Page 4 of 15 4.0 Supply-Independent Bias Circuits To minimize sensitivity to power