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:
posted by Dhananjay Gadre at 8:23 AM
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