Of Software Sweatshops, Electronics Engineering Education, Compound Interest Rate Equation and Resistor Values

Software Sweatshops and Electronics Engineering Education

This year, for the first time ever, I have decided to teach an introductory course in electronics (EC-201 in local parlance. Electronics 101 would be the American equivalent). Even though it is an introductory course, it is a very significant course and one that has the potential to make or break the interest and involvement of the students in more advanced electronics courses and electronics hardware in general. As things stand now, the common grouse is that students enroll in electronics (including various flavors of electronics) engineering courses largely because they did not get admission in Computer Engineering or even Information Technology. These two courses are considered lucrative because they offer better chances of employment at the end of the undergraduate degree course and to a majority of incoming students that is all that matters.

For someone like me (an electronics teacher), the implications are that you are surrounded by a bunch of students who want to get done with the degree and seek better opportunities through further courses in management or getting employment in one of the many software sweatshops that abound in India (Infosys, Wipro, TCS etc.) and if they are lucky, they might end up getting a break in more (software) product oriented companies such as Facebook, Google etc. The seemingly lucrative job opportunities for Computer Engineering and Information Technology students come, primarily from these (software) product companies but only for the top achievers in top colleges and for others, other software sweatshops mentioned above mop up the rest. Notice that there is not a single Indian software product company. But then, there is not a single electronics hardware company either. The common refrain for the lack of local electronics hardware companies is the lack of suitably trained electronics hardware workforce!

So, this is a catch-22 situation. My observation is that our syllabi does very little to relate real life problems and their solutions to engineering education and that too, if at all, very late in the curriculum. Speaking for electronics engineering courses, we teach our students the basics of electronics building blocks (semiconductor devices) followed by circuit design analysis and synthesis principles and eventually (if at all) applications that they are supposed to create. By the time, the applications of electronics are discussed, the student has lost all interest in electronics. This is bizarre because all through the growing up years, the student is actually surrounded by gadgetry made up by use of electronics hardware (and no doubt programming), be it the ubiquitous mobile phone, a microwave oven or a washing machine and so on.

Could it be, that if we reverse the flow of teaching, certainly not entirely, but at least to a small extent and bring in application areas and then relate them to circuit and system design and eventually to basic electronic components, that we could get the students to fall in love with electronics? As an educator, if I can make my students fall in love with electronics, half my job is done! I am not alone in thinking this way. Professor KRK Rao (former head of the electrical engineering department, IIT Madras) has quite succinctly described this problem and possible solution through this blog “Analog curriculum: A shift towards analog system design”. I am copying a great picture from the blog to highlight the present approach and juxtapose it with the proposed approach below

 

As a nation, we are on the threshold of electronics hardware revolution and perhaps, currently we are not ready for it. It is estimated that the demand for electronics gadgets (phones, tablets etc) fueled by the mobile revolution and aided and abetted by the Internet Of Things paradigm, is set to exceed 500 billion USD by the year 2020. At the current rate of local manufacturing, it is said that we can only meet 80 billion USD worth of the demand. How would the rest be managed? Of course, by import from China amongst others. But it need not be this way. Electronics hardware is not a natural resource. With a proper application of our collective minds, governmental intervention beyond sloganeering ‘Make In India’ and most importantly, by us, the teachers, it is possible to energize and enthuse next wave of students to take to hardware design. If the trends towards local design, invention and manufacturing change positively, I can predict that the fad of incoming students towards computer engineering and information technology undergraduate courses would undergo a course correction towards electronics undergraduate courses.

Resistor Values and Compound Interest Rates

Well anyway, I have digressed a lot from the original title. Let me come back to the syllabus for EC-201. Our syllabus for this course was laid down way back in 1991. Nothing wrong with that, considering that this is an introductory course in electronics and that since 1991, not many disruptive, groundbreaking inventions in electronics have happened to alter the syllabus for an introductory electronics course in any fundamental way. This observation is further substantiated by the fact that a very popular book amongst hobbyists and professionals alike, The Art Of Electronics only underwent an edition change in 2015. The earlier edition is 1989 vintage and between these two editions, the material related to basic electronics, circuit design etc., hasn’t changed much.

EC-201 starts with PN junction characteristics and then goes on to other semiconductor devices, circuit design with BJT in various configurations and so on. A corresponding laboratory course (EC-206) is supposed to offer suitable lab exercises in keeping with the coursework of EC-201, which means, the lab is open to incorporating insightful lab exercises that could capture student interest.

But, this is where things could appear to be perplexing. Most lab exercises would start off with experiments involving diodes of various kinds. But you cannot perform any experiment with a diode alone. What about resistors? When I started using resistors myself, as a student, I was surprised at the seemingly odd values of resistors. 1K, 1.2K, 2.2K, 3.3K, 3.9K and so on! I always wondered at the reason behind these numbers. Why not have 1K, 1.5K, 2K, 2.5K, 3K and so on? And I am not alone. Almost every new student perhaps has the same query. Without suitable explanation, they take a ‘chill pill’ and take it in their stride as yet another ‘ways on the world’ thing.  This must be addressed.

When you search available text and popular literature you are presented with this list of resistors in a decade. Depending upon the tolerance, you have E6, E12, E24, E48, E96 series and so on. The E series numbers are applicable not only to resistors but also capacitor and Zener diode values.

Common 5% tolerance resistors in lab are part of the E24 series. Resistors with tolerances of 20%, 10%, 5%, 2%, 1% and even 0.5% are available. Why do resistors have tolerances? Because of the imperfections in manufacturing processes, variations in material quality at the source and so on. If 0.5% tolerance resistors can be made then why have 5% tolerance resistors? Because, it requires lesser quality control for a 5% tolerance resistors than for 0.5% and that makes the 5% resistors cheaper. Also, not every electronic circuit design requires tighter tolerances. The values available for the E12 series, which are 10% tolerance, are:

10  12  15  18  22  27  33  39  47  56  68  82

Note, that a 10% tolerance resistor is actually +/-10%. The actual variation between the minimum and maximum values is 20%. The questions still remain: How does one decide how many values in a series and the actual values?

For a decade (1 to 10 or 10 to 100 and so on) each subsequent value is decided such that there is no overlap between the two values considering the tolerances. R+tolerance and R(next)-tolerance should just overlap. This is where the formula used to calculate value of a principal amount after ‘n’ years and ‘r’ rate of interest comes in and has a strong relationship with the E series. The compound interest rate equation is: 

S = P(1 + r/100)^n

If we apply this equation to calculate the number of values required to cover a decade of resistance values, say from 10 to 100 ohms, we could find out exactly how many would be required such that each value with the tolerance, stacks up nicely to the next value it it’s own tolerance.  The compound interest rate equation would tell us the maximum required numbers but in reality, the E series has numbers equal to or less than the values suggested by the compound rate equation.

For example: 100=10(1 +t/100)^n. Considering the 10-100 ohm decade, t is the resistor tolerance and n, the number of values in the series from 10 to 100 ohms. For 10% tolerance resistors, t is actually 20% (because it is +/-10%).

Thus: n = 1/ log(1.2)= 12.63. This is why there are 12 values of resistors for 10% tolerance resistors. The incremental values are calculated by multiplying a previous value with a constant k = nth root of(10) . Thus, for E12 series, K = 12th root of (10) = 1.21 which explains the values (which are rounded off) in E12 series:

10  12  15  18  22  27  33  39  47  56  68  82

The following image shows the E12 series values from 1 to 10 Ohms and the colored band around each value shows tolerance values.

Similarly, the E24 series, the constant k = 24th root of (10) = 1.1 and the resultant values, with suitable adjustment, are:

10 11 12 13 15 16 18 20 22 24 27 30 33 36 39 43 47 51 56 62 68 75 82 91

The table below lists the number of elements in each E series and also the number from the compound interest rate equation, which serves as an upper limit. The number of elements in the higher E series (E48 onwards) is less than this upper limit purely due to manageability issues. The E series is not restricted to resistors alone and is used for other electronic components such as capacitors and zeners.

S. No.	E Series	Tolerance %	Number of elements in E series	Number according to compound interest rate eqn.
1.	E6	20%	6	6
2.	E12	10%	12	12
3.	E24	5%	24	24
4.	E48	2%	48	58
5	E96	1%	96	116
6.	E192	0.5%	192	231

I hope to share this with my students in EC-201 and then hopefully, they can appreciate the principle behind these ‘preferred numbers’! However, what if the value you require is not available in the list? Well, two options are available: use a series or parallel combination of resistors from the list of available values to get the desired value or use a ‘trim’ potentiometer to achieve the required value. Also, often times, the resistors in, say, the 5% tolerance series can well qualify to be 1% tolerance resistors! Another insight is, if you want a value slightly higher than what you have, take an abrasive file and file the surface of the cylindrical resistor. This changes the cross section area of the resistor and hence the resistance value. We have tried this on carbon film resistors (the common 5% resistors) and it works well.

References:

1.    The Art of Electronics, 3rd Edition

2.   Prof. Rao's Blog

3.    Preferred Numbers

4.    Resistor Values