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

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**The Setup **

Can anyone design anything without touching a keyboard and invoking a software tool? There was a time when design involved paper, pencil, mathematics and slide rules. Now we have Spice, Matlab, Mathcad, Simulink, Altium, Excel, ad infinitum. The modern knee-jerk reaction to a new engineering problem is a request for new engineering software.

But can we manage without it? How far can we go with just our human gray matter and snapping synapses? Let's find out!

**The Premise **

You are enjoying the salt air and sea breezes aboard a small touring boat, on a short three hour cruise. Suddenly, the weather turns and you find yourself beached on an uncharted island. Your companions are depending on you to save them, so you need to fix the radio beacon which has a broken voltage reference. You have a collection of electronic odds and ends that you always keep with you, including: a five-transistor array, an op amp, a bag of resistors and a prototyping board (protoboard). For the sake of argument, we'll assume your spare parts are all through-hole devices, with real leads, and can be easily manipulated by a human being. Can you do it?

**The Motivation **

This is a bit farfetched, but it is important: it's the "Apollo 13" problem: fix it, build it, and twiddle it into working order with nothing but what you find lying around. IC and PC-board designers find themselves in this predicament every day. It is costly and time-consuming to make large changes in chips and boards that have minor production problems.

If an IC designer can 'fix it in metal' or a PC-board designer can cure it with 'a flying diode', he is a hero, and rightly so. So our exercise here is of great practical import. Now, how do we build a voltage reference from a few parts and the few notions we have in our heads?

**Thinking It **

We need something that gives us a known voltage. V_{be} comes to mind. It is about 0.65 volts for modest current densities, but it varies with temperature, dropping by 2 mV for every 1° C rise at room temperature. We need something better versus temperature (lower temperature coefficient). Have to think harder.

Remember "delta V_{be}" (ΔV_{be})? Bipolar junctions have a curious property: the voltage decreases with temperature but the voltage between two junctions with different currents (ΔV_{be}) rises with temperature. In fact, the difference is directly proportional to absolute temperature.

At room temperature (300 K), ΔV_{be} changes by 1/300 for a change of 1 degree C. It turns out that ΔV_{be}'s are relatively small, so we have to amplify them. If we boost the ΔV_{be} to 600 mV, then the 1/300 change turns into 2 mV/°C! (That's equal in magnitude and opposite in direction V_{be}'s temperature effect.)

Add the two together and we get 650 mV + 600 mV (at room temperature), which is 1.25 volts. Since both change in opposite directions with temperature, the sum remains constant. Therefore, 1.25 volts happens to be the 'magic voltage' for bandgap references.

**Deep Theory **

To understand why this is called a bandgap voltage, imagine that the temperature drops to absolute zero. ΔV_{be} would also drop to zero (**Figure 1**). For the output to remain constant, V_{be} would have to rise to 1.25 volts.

*Figure 1:Junction characteristics*

*(Click on image to enlarge)*

What exactly does that imply? The temperature dependence of V_{be} comes from the nature of silicon semiconductors. To get a current going. you have to increase voltage until the electrons are ripped out of the crystal lattice. When the silicon is very cold, the electrons have little energy and stay firmly attached to their atoms.

If we slowly raise the voltage (across the junction) the current will suddenly jump up at a very particular voltage. This is the voltage required to give an electron enough energy to move freely through the crystal; it is the bandgap voltage. As the silicon gets hotter, the curves become gentler and the voltages get lower. Figure 1 also shows how the curves move with temperature and illustrates how the ΔV_{be} increases with temperature. The dotted lines are the V-I curves of a junction operating at 1× current and the solid lines are a junction at 4× current.

When we add the right portion of ΔV_{be} to V_{be}, we get the bandgap voltage, which is independent of temperature. How important is this? Almost every chip ever made has a bandgap reference in it, to establish bias voltages and currents for widely varying supply voltages.

**Building It **

Electronic circuits are always more accurate if based on ratios rather than absolute values, so ΔV_{b} should be ratiometric. The easiest approach is to create two branches, one with a few devices in parallel and one with a single device. We then arrange a feedback loop to maintain the same current in both branches.

**Figure 2** shows a simple circuit to accomplish this.

*Figure 2: Simple experimental bandgap circuit*

*(Click on image to enlarge)*

The op amp closes the loop and keeps the collector voltages the same. The single NPN has its emitter grounded. The 4× NPN has a resistor (R3) in series. The difference in voltage between the 1× and 4× appears across R3 and generates a current proportional to V_{t}, which is Proportional To Absolute Temperature.

Designers call this a 'PTAT' current. The same current flows in the feedback resistor making a (larger) voltage proportional to V_{t}. The output of the op amp is V_{be}_{1×} plus a multiple of (V_{be1×} - V_{be}_{4×}). Adjust the resistors for an output of 1.25 volts and we're done. **Figure 3** shows the component voltages and the output of our Desert Island Reference versus temperature.

*Figure 3: Temperature characteristics of bandgap circuit*

*(Click on image to enlarge)*

**Back to the Real World **

Of course, we don't usually design on a desert island, but the exercise tells us how much we know about a subject in a practical sense. Real designs often need references that are more accurate than our little experiment. We have ignored secondary issues like bulk resistance in the devices and deviations from ideal that cause our reference to curve with temperature.

Well-designed references, such as the X600008A, use 'curvature correction' circuits to flatten the curve to within 1 mV over the operating temperatures of interest (-40 °C to 85 °C),. Modern references, (for example, the ISL21009), may even use advanced CMOS circuits that are calibrated with floating gate technology, and give a variety of reference levels.

**About the author**

** 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.