Dr. T (Tamara Schmitz): Hey, Dave, how's the new job in design?

Dave (Dave Ritter): Hi Dr. T: ! It's going pretty well, but I'm still an apps guy at heart. I miss soldering irons and scope probes.

Dr. T: Ahh yes, the smell of burning tantalum. . . .Yeah, I'll always be an apps girl.

Dave: So what's your latest adventure?

Dr. T: It's a teaching gig—I'm so excited!

Dave: I'll bet you miss those days at Stanford and San Jose State with all your adoring fans, your students.

Dr. T: I sure do.

Dave: But people still want you to teach.

Dr. T: Yes they do! And I'm grateful.

Dave: What did they ask for?

Dr. T: This request was for a refresher course in op amps. It's a wonderful opportunity for me and the group is really attentive and responsive. It's a happy surprise that 50 people will give up their lunch breaks once a week for a month to hear me babble about circuits.

Dave: Babbling? I don't think you ever babble, Dr. T.

Dr. T: No, I'm teaching. . . .just from a more practical angle than I would have academically. I like breaking down complex ideas down into manageable, bite sized pieces.

Dave: Like a food processor?

Dr. T: Very funny. . . .

Dave: Okay, sorry about that. Are you teaching bipolar or MOS circuits? Or both?

Dr. T: I like to teach them side-by-side. There are a lot of similarities: they both amplify input signals and deliver output current. The difference is that the bipolar transistor is controlled by an input current while the MOS transistor is controlled by an input voltage.

Dave: Hmmm. . . I think that's the key to understanding more detailed ideas like noise contributors, why the bipolar would be susceptible to input current noise, while the MOS transistor wouldn't.

Dr. T: It's a great way to teach more general circuits, too. I find it completely understandable that the first analog MOS circuits were put together in configurations identical to their bipolar counterparts.

Dave: And the first bipolar circuits were put together like their vacuum tube ancestors. That doesn't work for everything, though. There are circuits like the bandgap that absolutely need a bipolar device to work.

Dr. T: Bandgap is really a magic word for most people in electronics. Let me tell you what I understand and you can fill in the blanks, OK?

Dave: Wow! I get to teach something to Dr. T, cool!

Dr. T: I know that the base-emitter voltage of a bipolar transistor changes by 2 mV/°C. I also know that the thermal voltage, V_T, will rise with temperature (= kT/q), Figure 1. Of course, we should be able to sum the two together in some way to get a stable reference versus temperature.

Figure 1: V_BE and V_T variation with temperature
(Click on image to enlarge)

Dave: That's the gist of it. The two curves above show the V_BE falling with temp, and V_T rising with temperature. The problem is that V_BE is something we can directly measure with a voltmeter, and V_T is something that shows up in equations but doesn't seem to appear explicitly in our circuits.

Dr. T: Then how do we get V_T?

Dave: Sounds like a question for Dr. Brokaw [Editor's note: Paul Brokaw, legendary IC designer and bandgap design expert], but I'll do my best. We need to talk about the math a bit. Here's the basic diode equation:

(Click on equation to enlarge)

The equations tell us that the voltage across a diode, V_D, is a function of the diode current, I_D, the reverse saturation current, I_s, the thermal voltage, V_T, and a simple constant, n. We can measure V_D and I_D in the lab. V_T is what we are trying to compute in our circuit and n is a constant, which leaves I_s. Now, I_s is messy because it has a very complex temperature characteristic. So, here's the trick: we write the equations for V_D for two diodes operating at different currents but with everything else the same:

(Click on equation to enlarge)

and then we subtract them:

(Click on equation to enlarge)

Dr. T: You just got rid of the dependence on I_s! I wonder if someone knew the math or the physics better when they figured that out.

Dave: I don't know. What I do know is ΔV_BE is proportional to V_T if we keep the ratio of the currents constant. I_s is gone, thankfully. One way to keep the ratio of currents constant is to run the same current through a single diode and, let's say, four diodes in parallel. We do that in the next set of curves, Figure 2, which shows two sets of V-I curves. One set (dashed) is a diode with four junctions in parallel. So the ratio of currents is exactly 4.

Figure 2: ΔV_BE variation with temperature
(Click on image to enlarge)

Dr. T: We get all that from the simple diode equation we learned in basic electronics.

Dave: Sure thing. A lot of seemingly complex stuff makes a lot more sense if you remember the basics.

Dr. T: The curves are interesting. They get softer, more curved as the temperature rises, and they also separate more. Looks like you might need at least 200 μA in the diodes to get reliable and scalable results. As you instructed, the voltage difference is larger at higher temperatures and goes to zero at very low temperatures.

Dave: Exactly. So the answer is this: to get V_T we arrange a circuit with junctions (usually transistor base-emitter junctions) operating at different currents and amplify the result to get V_T. A clever circuit called the 'Brokaw' cell creates a current proportional to V_T (and therefore proportional to absolute temperature, PTAT). If the PTAT current is forced through a diode and a resistor in series, the total voltage drop is the sum of a V_BE and a multiplied version of V_T, (Figure 3).

Figure 3: Simple experimental bandgap design
(Click on image to enlarge)

If we get the resistor value correct, the result is the bandgap voltage, about 1.23 V for silicon. Here's a simple circuit that uses a pack of transistors and an op amp that our readers could easily assemble. V_be1X is the voltage of one junction, V_be4X is the voltage of four junctions. (Equivalent to one diode operating at ¼ of the current.) The op amp creates a feedback loop that keeps the current the same in both paths. The output is the sum of V_beX1 and a multiplied version of (V_be1X – V_be4X), adjusted to give the bandgap voltage.

Dr. T: That's great for bipolar, but what do we do for CMOS?

Dave: Traditionally, we use parasitic bipolars to make bandgaps in a CMOS process. Parasitic transistors are bipolars that "accidentally" exist because of the structures inherent in CMOS devices, so we get them for free. They aren't great transistors in terms of bandwidth and gain, but clever circuits can balance out their weaknesses, and make a pretty respectable voltage reference.

Dr. T: Very nice. You learn something new in this business every day!

Previous "dialogues" in this series:

• Avoiding op amp "motor boating" (also known as "inadvertent positive feedback")
• A bypass-capacitor dialogue peels back the layers, Part 1
• A bypass-capacitor dialogue peels back the layers, Part 2: The theory of ground relativity
• A bypass-capacitor dialogue peels back the layers, Part 3: Continuing the discussion on layout considerations

Other related articles by Dave Ritter:

• Desert Island Design: Bridging the (filter) gap without software
• Desert Island Design: Bridging the (band) gap without software

About the authors
Dave. Ritter grew up outside of Philadelphia in a house that was constantly being embellished with various antennas and random wiring. By the age of 12, his parents refused to enter the basement anymore, for fear of lethal electric shock. He attended Drexel University back when programming required intimate knowledge of keypunch machines. His checkered career wandered through NASA where he developed video-effects machines and real-time disk drives. Finally seeing the light, he entered the semiconductor industry in the early 90's. Dave. has about 20 patents, some of which are actually useful. He has found a home at Intersil Corporation as a principal applications engineer. Eternally youthful and bright of spirit, Dave. feels privileged to commit his ideas to paper for the entertainment and education of his soon to be massive readership.

Tamara Schmitz grew up in the Midwest, finding her way west with an acceptance letter to Stanford University. After collecting three EE degrees (BS, MS, and PhD), she taught analog circuits and test-development engineering as an assistant professor at San Jose State University. With 8 years of part-time experience in applications engineering, she joined industry full-time at Intersil Corporation as a principal applications engineer. In twenty years, she hopes to be as eternally youthful as Dave. .