This project is intended to introduce the student to design procedures and, particularly, the effect of component variations in the behavior of a simple circuit.

The circuit used in the project is an interval timer based on the 555 timer IC chip. The circuits behavior is as follows: When a pushbutton is pressed, an LED lights for a certain time interval. This interval depends on the value of a resistor and of a capacitor in the circuit. The theoretical relation is:

1. Building a 3-Second Timer

Each student builds the circuit on a protoboard using a 120k resistor and a 22 uf capacitor for the timing elements. This produces a time interval of about 3 seconds.

2. Preliminary Experimental Work

In the laboratory, the time interval of each student's circuit is measured using a counter instrument (HP DC509 Universal Counter/Timer). Also the resistance, R, and capacitance, C, are measured with a digital multimeter (Fluke 45 Digital Multimeter) and an LCR meter (HP 4261A LCR Meter) respectively.

This produces a set of data which is analyzed statistically. Two effects are studied:

First, the time predicted by the above equation is doesn't agree exactly with tthe measured time. The time measured is about a factor of 1.06 greater than the time predicted by the equation. (This systematic error is explained to the students by noting that the model used to derive the equation is only approximate; the circuit is more complicated than the series circuit used in the derivation.)

Second, the measured times have a variation. This variation is studied by generating a probability density function by sorting the measured samples into "bins". The average and standard deviations of the samples are also calculated and compared to the probability density function. (Probability density functions are also introduced generally to the students through a simple computer study.)

3. Nominal Design Procedures

A design graph is prepared on 4 cycle loglog paper whose ordinate is interval times and abscissa is resistance values. Lines of constant capacitance values are plotted for a set of specified capacitances. (They turn out to be straight lines with a slope of 1 time-decade/resistance-decade.)

The student is also introduced to a computer program which select combinations of a resistor and a capacitor from files of available resistors and capacitors, such that a specified time interval and tolerance are met.

4. Additional Experimental Work

The students are given a set of 3 resistors (10K, 100K, and 1M) and 3 capacitors (22uf, 100uf, and 470 uf) which they use in the prototype circuit. The interval times for the 9 possible combinations (measured with a watch) are plotted on the nominal design graph produced above.

5. The 1-Minute Interval Timer Contest

Finally each students is given a 100k potentiometer which is connected in series with a fixed resistor (that the student selects) to produce a time of 1 minute.

The project concludes with a contest in which the 1-minute timers are measure (with the HP Universal/Counter). Prizes are awarded to the 3 students with times closest to 1 minute.