A philosophy of circuits and systems in biomedical engineering

A final lecture delivered to the students of BIOMEDE 211, Winter 2018

I was hoping to deliver this speech on a day whose morning did not begin with snow falling. The gods on that front have not obliged. But if you will, I would like to give a short speech on what I believe my philosophy has been through this course. I believe such guiding principles – such a philosophy – are necessary for the doing of anything well. As I intend to do this job well for many years yet to come, I have decided, even at this early stage in my career, that every class, every semester, I would like to write out what I believe each class was and why I think it was important.

Today marks the final lecture of the final class I will give for my second semester in my first year teaching. Today’s speech (this thing) is the third such speech I have prepared to end a course. While there is something tempting in making the third of something bigger, grander, with headier themes, loftier heights, and on and on, I have resisted this temptation. My philosophy, as I hold it today, regarding circuits and systems in biomedical engineering is simple: the universe has an unequal distribution charges, we may exploit such distributions for our personal gain, and we ought to do so with a mind towards the betterment of our fellow conscious creatures. Boiled down, that’s where I stand.

If that’s all you needed to hear, then I thank you for your time in this class, there is the door, you are free to leave whenever you’d like, and I will see you at the Final Exam. However, if you’d like a little bit more, today I’m going to ramble on from these prepared remarks regarding my “philosophy” of this class. If that interests you, then please lend me your attention for about another hour. If it does not, there again is the door.

To those that stay, let me posit the following.

Our bodies comprise many circuits. Many routes, channels, networks, systems, signals sent and received, interpreted, fedback upon. Our bodies – the very same we lug to this class most every Tuesday and Thursday from 12:30 to 2:30 unless we’re on a particularly good lunch date, have a job interview, it is sunny out, we just don’t feel like, or plain forgot – are describable in rigorous mathematical details, a subset
of which
you have
I hope
learned in this class. This subset of mathematical detail and old engineer’s tricks, when seen from an electrical engineering perspective, include but are not limited to the following: potential, current, energy, the conservations thereof; what resistors, capacitors, and inductors are, and their real and complex formulations; the conservation of mass and its relation to Kirchhoff’s current law; Kirchhoff’s current law and nodal analysis; supernodes; the conservation of energy and its relation to Kirchhoff’s voltage law; Kirchhoff’s voltage law and mesh analysis; supermeshes; circuit theorems, with particular emphasis given to Thevenin and Norton equivalents [Because Thevenin and Norton are often the first really hard/funky thing circuits classes get to and because they invariably come right before a quiz or exam, students get it into their heads that this is what their mean old teachers are going to put on said quiz or exam. Perhaps I should have been more clear in this class that I am not out to be vindictive in my educational capacities. I want each and every one of you to learn this material not to be put off by this material. I digress. Continuing on.]; operational amplifiers and their ideal properties; operational amplifiers and that one weird lecture where the professor made us read the whole damn datasheet; a review of the material; a first set of examination problems and solutions; the Laplace transform and how you can use it to solve differential equations; an example using a simple RCL circuit; circuits as ordinary differential equations, first order (with a large section reviewing first examination questions); circuits as ordinary differential equations, second-order; the response of systems, convolution, transfer functions (a lesson taught by Adithya Reddy) for both mechanical and electrical systems; the evaluation of basic electric circuits including both passive and active variants (which, I emphasize here, you ought to remember once you get to BIOMEDE 458: Biomedical instrumentation and design); how filters can be used to tune output to tune input to tune output to tune input and on and on and fedback and forth; we took a glimpse at what it means to control such systems (though not nearly even a fraction of what you ought to learn in a proper feedback-controls class) via proportional, integral, and derivative means; we briefly saw the Fourier transform and how it is helpful to those of us looking into the frequency responses of systems; and we took an ever too brief survey of digital electronics with special reference to basic digital logic (manifest in this class by knights and knaves), transistors, and a couple of communication protocols thanks to a pair of our colleagues. We have learned a lot.

But sometimes, some days, you’re so tired. The weight of the world, the weight of the coming day, the weight of the come down too late to get around to that comfortable place we visit less and less often: peaceful contentment. Because that’s the thing you don’t have when you’re tired. When your eyes look back at you and say, You look like you’ve seen a few.

Back in my day, back in my day, they used to tell war stories. Well, generally not stories about war which we were all sickened and wrenched every day with as a result of confronting American foreign policy at the time, but rather those shrugs of Atlas, tears of Christ symbolic stories where more was meant than merely conveyed. And these massive, missive war stories would center around how little sleep you got the night or nights before. I hear them still, even within these walls. We carry as something of a badge of honor. ‘I got up at four in the morning to finish this.’ ‘I didn’t go to bed until four in the morning, then I had an exam at eight am that next day.’ ‘I had that exam, that Calc one yesterday, Physics the day before, and a quiz in my Thermo class. I haven’t slept in three days.’ If I didn’t quite get the phrasing right, I’m pretty sure you all will still recognize what it is I’m after here.

These the-night(s)-of-sleep-that-got-away stories are all too common in what it is we do here. We work hard, we fray at nerves, pull out our hair, and try to catch a date or a movie or both every now and then. And because we are looking for this life towards which we aspire and trying to make it happen and have it all and do it all, we cut back on sleep.

[Perhaps you have never tried it before now, but you can put a rank to what bodily functions of yours you’d like control over. I encourage you to try it now. My list, so far as I’ve thought it through to any great extent, is as follows:

  1. Breathing. We are, by and large, aerobic creatures. While I’m sure there’s some gut bacteria out there who might otherwise be fine, most of who and what we are requires oxygen. The way our collection of cells functions is that each and just about every single one of them spend their entire lives (that trajectory from creation to void, from 1 to 0) specializing to become some itty bitty billionth billionth part of you. From the skin on the inner portion of your pinky toe to that strange smooth muscle that beats with the selective, stochastic influx of ions, they all do just a few things really well, forgoing their own ability to maintain certain functions, such as the production and transportation of metabolic products, instead relying on a larger system to provide it, much as there is a whole apparatus to deal with your waste of which you (and I) are largely ignorant. The number one currency in this specializing exchange program seen from a macrophysiological/organismal perspective: oxygen. We get that from breathing, therefore, breathing is first on my list of bodily functions.
  2. Motion. Once I can provide oxygen to all my cells, I want all of those cells to be able to coordinate at least some gross motor functions. Moving limbs, manipulating environment, interacting with environment, all big in my book.
  3. Seeing. Being able to identify the world around me is a great tool to have at the ready.
  4. Eating food, drinking.
  5. Disposal of waste (urination, defecation). We spend most of our first two years mastering these abilities. And we’re still learning. How to dispose of our waste, to recycle. Hell, some of us are still learning to eat (I spill on myself every other day) and from some of the eyes I saw after spring break, some of us are still learning to drink.
  6. Autonomy over many functions. (I want to breathe whenever I want, I want to move whenever I want, I want to see, eat, do anything I want. In fact, I note here for the first time, that I suppose my system of greatest injustice also generally follows the same trend: I can’t breathe, I can’t move, I can’t see, I can’t eat, I can’t do…)
  7. Taste. I’d like to be subjective about the world every now and then.
  8. Clarity of forethought. I’d like to know what I’m going to do in a given situation. I, often, do not want my future to come as any great surprise. Call me old fashioned but I’d rather just work for it if I know it’s what I want. I don’t like betting on the longshot as anything but a laugh. And only then because I know it’s what I’m doing to do.
  9. Sleeping whenever I want.

And 10, well, I couldn’t think of ten. I really just got to nine. And even by nine I was thinking I ought to just scale back, I was already grasping at straws for some of them: taste, clarity of forethought? Are these bodily functions? Maybe. I had space to fill and thoughts to fill it with and so I only got a list of nine. And the last one, the very last one, the one I was just saying does not get enough attention from us when we’re in the thick of it – namely, sleeping whenever I want – was number nine.

Still, I bet nine was more than you had at the start of this. Continuing on.]

We do all these things because we like them in our lives, we like them in our lives because they propel in favored directions. Out with friends, good grades in hard classes, time doing what we want. (Sometimes.) And but so as our waking hours grow, our resting hours dwindle, and you find yourself lulled to sleep by what the guy at the front of the room is saying, snapping to only now and again, coming back to the life you’re living. (Those just snapping to, weird right? Like weren’t we just talking about bodily functions or something?) We’re trying to get somewhere in all of this, but sometimes we’re just so tired. The weight of the world, the weight of the coming day, the weight of the come down too late to get around to that comfortable place we visit less and less often: peaceful contentment.

Because that’s the thing you haven’t yet. 

And unfortunately, I cannot give it to you. It is, in a sense, my job, to take up as much of your brain as I can in the time you allow me. I’ve got to get in there, restructure things so you know what you’re talking about when you get out there in the world. And the way that I’m going about this teaching thing, or trying to at least, is to be in your every waking thought. I want, when you’re brushing your teeth in the morning waking up from the night before, that one blissful moment of peaceful contentment you may have the whole rest of the day, right then, right at on the positive side of t equals zero, I want you to be thinking about circuits, signals, and systems in biomedical engineering.

In doing so, I largely disturb the peace.

Would you believe me if I told you it was for what I mostly thought were mostly good reasons most of the time? Am I knight, am I knave? I contend, I am engineer. I am someone trained in the arts and sciences of the arts and sciences and I have tried my best to tell you why you should care in this class. I am proud of my own achievements on this matter, though I have a list of specific changes that I intend to implement and specific goals I hope to achieve next time.

I am also proud of each and every one of you for having made it through this rather difficult class. Some take to calling such classes “weed out” classes as they’re meant to separate the engineering wheat from the well, not-engineering chaff. I do like nor abide by such titles. Each and every one of you can be a fully capable somebody doing something. All that needs be done by me is give you a little knowledge, a little nudging, and a little nurturing. I can unequivocally say that each and every one of you now understand circuits and systems better than about 99% of your fellow human beings on this planet. Given what you know of circuits and what more you know there is to know, such a fact might be worrying to some. To me it is heartening. You are all well on your way to being competent and capable engineers.

As such I would like to spend the next twenty or so minutes listing some of the things about you all that have made me proud. I have listed you in order of your initial enrollment into one of my classes.

16. Number sixteen. A. You were my first student to try me twice and I take that as quite a compliment. While it somewhat pains me to hear that you are likely going down that electrical engineering pathway, I suppose I can take some solace that I must not have put you off the material too much here. Thank you for spending ~150 hours of your first academic year here with me. Hope you got something out of it.

104. One-hundred four. B. Someone who sits in the front seat in the front row is going somewhere in the world. This is true of just about every room you walk in. Those that matter, those that count, those that want to be in it to win it, sit in the middle, sit in the front. It is perhaps cliche to point out that some large chunk of success in something is merely showing up. And B. you have shown up again and again. I look forward to each and every one of your future successes.

105. One-hundred five. M. Your consistent and demonstrated performance of our dark electronic arts has been commendable and I hope you pursue your education in it further. While I suspect you have an intuition for electronics, we likely still have to work somewhat against it to fully round out your expertise in these matters. However, rumor has it that you might be more on the “medical” side than the “engineering” side of our enterprise here and might one day end up in med school, be a doctor, serve patients. To that end, you know most the circuits you’ll need and the rest you can pick up along the away. That’s all the rest of this is folks, experience. May you practice these and all the dark arts well.

106. One-hundred six. C. Thank you for your constant participation in many of the aspects of this class from the asking and answering of questions to the performance and refinement of our mathematical techniques, I could always count on you to help when you could. May people continue to count on you in such ways.

107. One-hundred seven. K. There are a few people whose names you learn quickly in a class. As you might suspect, M. back there was one such person. C. was another. You are another. There are many ways to be known in life, many ways to be remembered. In this class, at least to me, you will be remembered as a voice of the people, a man whose question represents a dozen others. You were not afraid to press for clarification or question my explanation. Such will serve you well in every honest pursuit of actual truth. May your pursuits be honest.

108. One-hundred eight. C. I thank you for putting together that presentation regarding wifi last Thursday. It is a topic modern engineers ought to know something about and we in this room now know something about because of you. I hope even in the transmission of that small subset of All Possible Knowledge that you got a sense for why some folks want to do this every day. And while perhaps teaching circuits may not be your calling, I hope you get to where you’re going and are happy on the journey and the arrival. May you go far.

109. One-hundred nine. S. You have been a helpful fellow traveler in this class always at the ready with a question, an answer, a statement, or a furtive glance that I could generally leverage into hearing someone’s voice in the class other than my own. For that I thank you and for that I am sure your fellow student travelers her thank you too. May you continue onward in your travels.

110. One-hundred ten. G. You quietly sit in back and just dominate this class on the page. You are a well-qualified engineer, at the very least in basic circuits and systems, to that I can attest. I hope your confidence grows with time and with it, I hope your voice becomes a larger part of any conversation.

111. One-hundred eleven. J. If we’ve made it through this class without breaking your arms and/or wrist than we will have done better here than when before you got here. May you get through the rest of life with few broken bones, fewer broken hearts, and fewer still broken promises.

112. One-hundred twelve. L. I am sorry to have heard, as I did on the very first day of class, that you missed meeting Barack Obama by 3 minutes. And again, I really do feel that should be thought of as his missing his opportunity to meet you. Well speaking as a fellow bearer of the name Barry, as was our forty-fourth President for a time, may I say it has been lovely to make your acquaintance. Unfortunately, making the acquaintance of this Barry does not confer onto you any sort of political favor or powers. Still, I hope it’s something.

113. One-hundred thirteen. A. You seem to be a remarkable woman. From the mere bits about you this class has allowed me to learn I know the following: you are from the Boston area, you have sat for chickens, you are active in extracurriculars (M-HEAL?), you know something about a mid-eighties American postmodernist novel for some reason. Such are not the facets of unremarkable people. May you continue to draw remarks, most of them good, most of them in your favor, as you make your way through life.

114. One-hundred fourteen. K. Thank you for bringing in a portion of our community’s larger political discussions. While many of us in this room, and indeed many like us in many similar rooms, are not usually the political sort – engineer by and large are typically professionally apolitical creatures – we would all do well here and always to remember the communities we serve and which in turn serve us. Let us make of this world what we will. Or barring that, let us make of it what we can. Or barring that, let us at least vote on who they let us. Or barring that, let us at least get close to winning sometimes. Or barring that, let us at least sit around and play with some circuits. Life, liberty, and the pursuit of happiness.

115. One-hundred fifteen. M. On the first day of class you were the first to take me up listing your spirit animal. In your case, if I’ve got it right, I believe yours was a fox, due at least in part to the one that comes to your parent’s backyard when you’re around. As far as I can tell, you have used your spirit animal quite well in this class, answering questions with cunning and guile. May you continue to apply such cunning and guile to your life and it entails.

116. One-hundred sixteen. R. You are among the most adept practitioners of our art in this classroom. You seem to “get” electronics in a way that I suspect many envy and if I but speak for myself, that I envy. I’d have not done half as well then as you do now in this class and I’m not sure I know double what I knew then. Students like you help prompt me to learn more, to be better, to think fuller. For that I thank you. May you continue to inspire those around you with your adeptness.

117. One-hundred. Seventeen. E. Having been a longtime fan of the Detroit Lions, I, of course, need not tell you of the soaring euphoria of triumph and the stinging pains of loss. Hopefully here in this class you’ve gotten to experience more of the former than the latter. May that be true of all your days.

118. One-hundred eighteen. H. Thank you for your recent presentation on Bluetooth communication. I know and I hope most of the class found it informative. A couple of weeks back when you originally reached out to me, I was taken by your initiative and was happy to reward it. May life continue to reward the initiatives you take to meet and transform it. This is the most we may ever ask of it.

119. One-hundred nineteen. K. C. Perhaps no one has ever told you, but you keep quite the poker face. Most times, when an instructor scans the room, students’ eyes will dart, immediately become fixated on the newly fascinating hyperlocal phenomenon that is best embodied by the Not Going To Be Getting Called On Today pose. But you’ve gone to some other extreme, you never break eye contact and keep the same generally chipper demeanor about you. It’s enigmatic. Hard to pick up on. We’ve spent over one-hundred days knowing one another and I don’t know too much about you. Other than, as you mentioned on the first day of class, that you binged Gossip Girl at the start of the semester. Hope you’re all caught up on the life of Serena van der Woodsen and ready to make of yours what you will.

120. One-hundred twenty. T. From our initial meeting during that lunch last semester to our upcoming laboratory class next semester, I have enjoyed getting to know you. Though I wish I learned a little bit more about the life of P., your pet bearded dragon, of what I know about your life, you seem to be living it pretty well. That’s more than can be said for many of us. At times the struggle will be much too much, but you’ve got to grapple with it. From what I’ve seen of your character in class, you will grapple just fine.

121. One-hundred twenty-one. K. G. I really am quite sorry for making you stand up at the front of the room the other day for what must have felt like forever. All the same, I respect that you stood up there all the while without one ill-word to say and had a rapid response to Tyrone’s salvation and doom parable. At times, this class’s material has obviously not been your favorite. Just as obvious is the work you put in. May you keep up your efforts and not have to put up with a lot else.

122. One-hundred twenty-two. T. Thank you for putting together our second crowd-sourced set of notes for the final exam. In the short term, I am sure many in this room will benefit from your work. In the long term, I am equally as sure that many more will yet benefit. While I must admit that the extent to which I know you is the sum total number of times I’ve seen you sit approximately there in this class and for half a lab in that Incubator module class – which is about true of your colleague G. back there – you have nevertheless proven yourself both knowledge about capable. Keep at it.

123. One-hundred twenty-three. R. Though you have mostly been the quiet type in this class, if I’ve gotten to know anything about you via your work product it’s that you understand the subject very well. You are able to spot some of the nuances that escape some of our coarser glances. If you don’t already have an interest in the subject, I would encourage you to maybe take a second look at it outside of this class. And talk more in my next class!

124. One-hundred twenty-four. R. I am glad to see that your bilateral hip surgery – which cruelly took away your ability to sit criss-cross apple sauce – has not hindered your ability to sit and analyze circuits. You and at times members of your family have sat in this room and worked well. May that be true of all rooms you enter in life.

125. One-hundred twenty-five. A. Due to some strange sequence of events, I don’t believe A. can join us today, all the same, we speak in her memory. A. was a good student to teach and from what I gather she has been a good student to work / study with. She’s involved in multiple extracurriculars and seems to find ways of occupying her time. While I wish she once occupied some portion of that time at the Engineering Student Government Movie Night, what can you do? C’est la vie. May A. continue to do good at what she tries.

126. One-hundred twenty-six. T. T? I prefer T. to give you my frank and unsolicited remarks on the matter. I figure if the people naming you went to all the trouble to give you the fully thing I may as well go to the trouble of saying it all. But I suppose it is in a sense equally arbitrary to say any arbitrary portion of one’s name, after all, it’s not like saying more of the name says more of the person. Moreover, we are already so foreshortening who you are and what you embody in even trying to “name” you that in a pinch any garble of sounds will do as well as any other. However, T., you have risen above your garble of sounds to become one of the better students of our art. May you continue onward.

127. One-hundred twenty-seven. A. I’m sorry if my explanation of the Laplace transform of zero never failed to properly satisfy. Even to my own ears. We may get it one day yet. All the same, every day you were here I saw you working hard, participating, helping your friends, and then periodically video recording some of them. You were a force in this class it was the better for it.

128. One-hundred twenty-eight. E. You have the single nicest looking homeworks I’ve seen all year. Every single one of them, uploaded to Canvas, each of them, a PDF. They’re handwritten, but computerized, everything is neat and orderly, but it doesn’t look like a technical manual, they’ve even got a color code to them. Such good work consistently demonstrated, even for things as simple as homework, demonstrates consistently good abilities. May you remain ever in possession of such faculties.

129. One-hundred twenty-nine. D. I hope you have had at least some moderate success bringing the fanny pack back.

130. One-hundred thirty. J. You once paid me what I consider to be among the better compliments one can receive in life in saying after having attended one of our bioethical discussions, “this is the kind of thing I always thought college would be.” Perhaps said in the afterglow, still, it meant something to me then. If I can but return the compliment and say that making such experiences possible are why I got into this line of work. I wish you well in your future endeavors.

131. One-hundred thirty-one. B. You have been a constant force in this class: adding your voice to the discussions as they go on and asking questions as they arrive. Everything from puns to jokes to anecdotes to answers to profounder thoughts on the world, you have added much to this class. I can only hope that it has added something to you in return.

132. One-hundred thirty-two. C. I consider you among my most reliable students in class, sitting right against that wall, turning in good assignments on time and without comment, asking a solid question every now and again. I suspect I am not the only one in your life and/or general environment who finds you to be quite reliable. On behalf of those for whom your stability has been a boon (especially in this ever tumultuous times) and of those who know not yet: thank you. And keep it up.

133. One-hundred thirty-three. N. You once said of this class that your favorite material had been mesh analysis given its relative straightforwardness and disliked superposition for its lack of straightforwardness. I can respect an engineer who can appreciate the virtues of simplicity and rue the need for their complication. Throughout this course I have hoped to show the power of said virtues and cultivate the resilience of said engineers. May you be so virtuous and resourceful.

134. One-hundred thirty-four. A. Sometimes the good are forgotten. Many have said plenty on this, let me say this more: sometimes students sit there quietly, do their work well, know what they’re talking about, like the aforementioned C. over there. Your performance in this class has, I’m sorry to say, had the somewhat unfortunate effect of making you “forgettable” in the sense that as I go to grade your work, I’m making so few lines and comments, so few instances I have to point out stumbles – you do such good work, that I hardly have to do any. You get answers right and right answers are often boring, unglamorous affairs. And boring, unglamorous affairs are best forgotten. And while I had originally hoped to turn that phrase around and say something to the effect of “And you, A. are best remembered” I realized that indeed you are better known, talked to, conversed with, than remembered. While I may not have as many opportunities to know, talk to, or converse with you and your colleagues here, we would all do seize those chances we can and to remember those moments we had.

135. One-hundred thirty-five. H. I have appreciated your candid feedback and your thoughtful counsel throughout this semester. You have helped me see better from a student’s perspective, both with respect to the narrow confines of the particular subject matter of this specific class and with respect to the larger world you all are placed in. I can only hope to have returned the favor by teaching you at least a thing or two with respect to circuits and systems.

136. One-hundred thirty-six. E. I’m glad you got whatever overrides you needed to get into this class. You had whatever technical skills or wherewithal necessary to learn and apply this subject matter. In a word, you showed the fortitude necessary to get somewhere in life. I hope you continue to forge ahead with such fortitude.

That’s it, that’s all of you. That was our class.

As for me, all of this is just an act, you know? I get up here, with a short script in hand, and try to perform the educative arts to your benefit. These are dark arts and I am but a novice in their mechanisms. But I do have machinations.

I am here putting up an act that I think will train you sufficiently to do electronics in the workplace at a minimum. We still do not, after a single class, know enough to know everything. We spent nearly a third of the year together, thinking about the same topic for awhile, and it’s still not enough to know enough.

If you were to but get that out of this class – that there is more – I would be confident in having satisfied my professional obligation to you as my students. I do, however, hope you get a little more than that.

It’s an act, don’t you see? We need to perform the science, play with the mathematics, try on the intellectual garb of electrical engineers. This can be a challenge for some of us who maybe feel a little more comfortable on the softer, wetter, more biological portions of our fields. In this class, we learned, bit by bit, how to interpret these mathematical puzzles, these technical maps.

What’s this? You might have some sense of its use. Let us merely squint our eyes whose focus we have honed here in our class. Those right there are voltage followers. What do they do? They allow voltage to be conveyed without current. High, high, high impedance. When might high input be beneficial? Well, we saw earlier in the semester that it might be useful when interfacing an electrode with the body.

That there is an inverting amplifier. That there is a bandpass filter, we know the frequency responses of those. We know how to analyze those. Could probably even think to design one ourselves. Okay, I need to collect between 0.05 Hz and 150 Hz to capture my signal of interest, what values should my resistors and capacitors be? Why? Okay, let’s try and make it.

I talk a little fast up here, you may have noticed. I take little jumps, somewhat at random, I’ve got an odd mathematical flow to what we’re doing. Part of that is nervousness, it really is sometimes hard to show your work up at the board in front of people, and sometimes you’ll make mistakes, try not to. You’ll get frustrated, try not to. You’ll get worried, try not to. We will all make mistakes and so long as you have a forgiving audience (starting with yourself), we need not feel their burden.

It’s an act. It’s an art. It’s a profession. It is what I profess and why I profess. Or so I think.

With that, I thank you for the opportunity to dismiss this class one final time. May each of you rise to meet everyday regardless of what the gods oblige. I hope you all do well on your fast-approaching exams and on your ever-to-the-horizon journeys. I’ve done what I’ve can for you here and I trust that you can do more. Good luck.