ASSIGNMENT #3

(Due Wednesday, April 9th - problem session asap thereafter, last problem April 16th.)

This assignment is intended to offer you partial relief from typical text-book problems and excercise your design thinking. (Given the varying scope, I also indicated the % weight of each problem in this set.)
Also note that there is a problem (4) below the problem (3) figures.

(1) (25%) I'd like you to revisit the power-meter circuit we discussed earlier (see class Web page and your notes). We left a few details unfinished. The meter is 100µA full scale and has an internal resistance of 1kohm.

(a) Calculate the emitter bias resistor RE so that meter full scale corresponds to 1kW load power.

(b) Design, with two resistors, a diode and a capacitor, a half-wave rectifier to give a +10V collector supply voltage for the differential pair. Give your chosen values for these components, and in the case of the resistors, their needed power dissipation rating. Indicate the meter polarity.

(c) Explain again how using a Cu current sensing shunt RS compensates the diff. pair's dgm/dT. How good is this compensation? (Look up some data for Cu, e.g. in the Handbook for Physics and Chemistry.).

(2) (50%) We did something useful with a matched pair of transistors when we built the above power meter with them. Now something different. Consider two matched base-emitter junctions at the same unknown temperature, biased at significantly different emitter currents, the current ratio precisely known. Consider the opportunity this represents for making a thermometer based on very fundamental physical proportionality constants.

Using ideas from Sedra & Smith and class discussion so far,

• arrange two junctions appropriately biased,
• amplify the difference between their Vbe drops with a differential amplifier,
• indicate temperature on a meter (could be a 100µA full-scale meter movement, as in our power meter). Calculate the scale factor of the meter reading.
• Having the meter indicate absolute temperature is easy but not very useful. I want you to introduce an offset so that the meter reads zero for 0°C and full scale for 100°C. Consider carefully the circuit functions you are performing, and where/how to introduce that offset so as to not compromise the linearity of operation of your differential amplifier.

Use ±15V supplies, or a single +15V supply if you can (worth 15% extra credit).

This is largely meant to be a "pre-op amp" problem where I intend you to use a few matched transistors. You can use the CA3096 transistor array (3 npn, 2 pnp, matched) as a source of a matched pair for temperature sensing, or you can use the LM394 "super-matched" pair which is indeed splendidly matched but more expensive.

If you use the LM394 as temperature sensor, you can use the CA3096 transistors for the rest of your circuit. If you use the CA3096 as sensor, use a second one to supply the transistors for the rest of the circuit.

Hard, but worthwhile to try (for up to another 30% extra credit): It is possible to use the CA3096 both as sensor and amplifier, both on the same chip. But now the amplifier is exposed to the same temperature changes as your sensor pair and you have to allow for that. This time you can use an (ideal) op amp in conjunction with the transistor array. On the level of such extra design, there are thermometer project possibilities here for those still struggling with a choice. One even more evolved version that would make a fine project, is the use of a single junction as thermometer, with its current switched between two values. The junction voltage change is amplified and becomes the basis of the measurement, just as above, but this time using a single transistor, avoiding the need for a matched pair.

(3) (25%) (a) In line with our discussion of Gilbert’s "translinear" circuits, derive the output current for these two circuits (over), again assuming perfect matching and neglecting base currents. Note that A is the junction transistor area, i.e. 2A is twice the area. In (a) consider the summation of the Vbe terms around the two loops, Q2-Q3 and Q1-Q4-Q5-Q2. (The initial publication of Barrie Gilbert's methodology is in two papers in the IEEE Journal of Solid State Circuits, vol.SC-3, no.4, pp.353-365 and pp.365-372.)

(4) This problem is not due on April 9th (though you can hand it in then if you want to ;-). Rather you have an extra week until April 16th to complete it.
It is worth 40% (i.e. when you have done it, this homework will have a total weight of 1.4, exclusive of the possibility of the extra credit in problem (2) above.)

Since I raised the issue of capacitance sensing in my summary of initial project choices, find and print out for me two papers involving capacitance measurement in the IEEE literature, most likely in the IEEE Journal of Solid State Circuits, the IEEE Transactions on Circuits and Systems, the IEEE Transactions on Instrumentation and Measurement, or the IEEE Transactions on Consumer Electronics. The likeliest contexts are MEMS, or external capacitor sensors used as position, pressure, or proximity transducers.

Search the IEEE literature using either INSPEC or COMPENDEX, starting with our Becton Library as the gateway (i.e. I want you to demonstrate that you know how to use those databases). Most IEEE publications should be available as a .pdf file directly using IEEE Xplore.

For each paper write me a short summary of the principle used in the capacitance measurement (please don't just copy the paper's abstract), and relate it, if at all possible, to an idea discussed in class or in S&S. I want you to look for two papers you can understand enough to grasp what is going on, not just any two that involve capacitance measurement.