Advanced Math in Electronics Engineering - Page 1
Forum section: electronics / beginners

author: Legion
author_rank: Frequent Contributor
timestamp: March 16, 2014, 06:44:38 pm
content: General question for the engineers out there. How often do you directly use advanced math (differential equations, fourier analysis, etc.) in your job?By "directly use" I mean if you were put in a differential equations for engineers course, for example, would it be trivially easy cause you do this stuff everyday, or would you need to go back and leaf through the textbook for a while to remember?

author: IanB
author_rank: Super Contributor
timestamp: March 16, 2014, 06:52:33 pm
content: Not an EE, but quite a lot. That's because I work in the area of simulation/computation where mathematics is both important and necessary.

author: Legion
author_rank: Frequent Contributor
timestamp: March 16, 2014, 06:55:17 pm
content: Quote from: IanB on March 16, 2014, 06:52:33 pmDo you use software tools like Matlab and/or Maple to help?

author: IanB
author_rank: Super Contributor
timestamp: March 16, 2014, 07:03:25 pm
content: Quote from: Legion on March 16, 2014, 06:55:17 pmGenerally not. I either use Excel or I write code in C++ or C#. I'm in the software business so code is the end product of what we do (we create commercial tools that allow engineers to do simulation).

author: mtdoc
author_rank: Super Contributor
timestamp: March 16, 2014, 10:47:41 pm
content: I believe Dave said in a recent video (or AmpHour podcast?) that he has never needed to use calculus or other higher level math in his career as an EE.

author: EEVblog
author_rank: Unknown
timestamp: March 16, 2014, 10:55:36 pm
content: Quote from: Legion on March 16, 2014, 06:44:38 pmNever used advances math like that once in 20+ years in the electronics design industry. But YMMV, some people use it daily.Yes, I'd have to look up the textbooks to remember any of it.

author: Fsck
author_rank: Super Contributor
timestamp: March 16, 2014, 11:38:01 pm
content: fractal antennae come as an easy example for using math in electronics design.

author: EEVblog
author_rank: Unknown
timestamp: March 16, 2014, 11:57:44 pm
content: Quote from: Fsck on March 16, 2014, 11:38:01 pmHow many design engineers would have to design their own fractal antenna?IME the majority of electronics design engineers will rarely, if ever have to use advances math. It's usually statistics, or concepts like integration are needed, rather than actually solving integrals or whatever.

author: Fsck
author_rank: Super Contributor
timestamp: March 17, 2014, 12:20:06 am
content: Quote from: EEVblog on March 16, 2014, 11:57:44 pmindustry, no clue. I guess I forgot to type out my longer answer:for most people in "electronics engineering", as typically defined (industry & selftaught/Bachelors level stuff [which is most], excluding theoretical research [yes, there are theoretical researchers in ElecE!]), >90% of people will not use advanced math. you can probably forget how to do anything manually above first year univ math. any higher level stuff, you'll probably just have a computer to do it for you, if it needs to be done at all.

author: IanB
author_rank: Super Contributor
timestamp: March 17, 2014, 01:13:08 am
content: I think it is hard to answer this question properly without defining what "advanced math" is. It will surely mean different things to different people?For instance, if you are in Grade 10, then first year college math will seem like "advanced math" to you. If you are in the first year of college, then the subjects covered by graduate students will seem advanced. It's all relative.But as to fundamental areas of applied mathematics like ordinary and partial derivatives, differential equations, integration, vectors, matrices, complex numbers and so forth, then I think most engineers should expect that to be part of their world at least some of the time.One way to answer this question is to look at the mathematical content of the American EIT/FE (Engineer in Training/Fundamentals of Engineering) exam. The material in the FE exam is considered by the exam admininstrators to be foundation knowledge for engineers of all specializations.

author: Rick Law
author_rank: Super Contributor
timestamp: March 17, 2014, 01:35:13 am
content: Quote from: Legion on March 16, 2014, 06:44:38 pmLet me add some fruit for thought - or random thoughts if you will.I am not an EE person. I am trained in Physics (Master Degree). I have never worked a day in Physics after graduate school, but I use the skills I learned in Physics in every job. The problem solving skills I learned, the analytical skills I learned... In the 30+ years I have worked, I have taken on many roles, from junior to executive level. The skills I learned as a Physics student are skills I used everyday.Mathematics is a language on its own. It is a form of expressions and thus a form of communication. The more mathematics you learn, the more ways of approaching (thinking about) a problem you got.There is no such thing as too much knowledge. Eat it up. It will only help.Rick

author: EEVblog
author_rank: Unknown
timestamp: March 17, 2014, 01:38:52 am
content: Quote from: IanB on March 17, 2014, 01:13:08 amIME of practical PCB and system level electronics, I've found that not to be the case, and am struggling to think of any colleagues who have needed to do so either (and I've asked them over the years too, as I've often wondered this myself). I'm also struggling to think of any instances where I have seen it documented in any company engineering documents, and being from a big military background, that's all we did, document stuff, including all calculations and equations etc. Granted, I'm just one case having only worked at a half dozen companies.I do know of some that have used such advanced math is basic research and the like with in the company. But that's pretty rare. Usually it's done once and then you spend 5 years design engineering the actual product and into production.Of course I've had to understand the concepts behind it all and know when such things apply etc, but the actual calculations I've left up to pre-written routines that do the advanced number crunching or simulation packages etc.

author: ablacon64
author_rank: Frequent Contributor
timestamp: March 17, 2014, 01:44:00 am
content: 7h15 15 7h3 m057 4dv4n<3d m47h 1'd 3v3r h4d 70 u53 1n my 3n71r3 l1f3. h3h3h3h3...Sorry, very good topic but I couldn't help myself!

author: vk6zgo
author_rank: Super Contributor
timestamp: March 17, 2014, 01:56:04 am
content: Quote from: Fsck on March 16, 2014, 11:38:01 pmAmong RF folk,fractal antennas are largely regarded as a "gimmick" offering no advantage over conventional designs.Of course,they do contain that magical word "fractal" in their name!The real antenna "gurus" do extensively use high level maths,but most of us lesser folk rely uponwell established design rules for antennas.

author: Fsck
author_rank: Super Contributor
timestamp: March 17, 2014, 01:58:31 am
content: Quote from: vk6zgo on March 17, 2014, 01:56:04 amthe problem is when you're trying to save every mm^2 in your design, or when compressing your circuit into the smallest area possible you've left a very oddly shaped space available for antennae.

author: nuhamind2
author_rank: Regular Contributor
timestamp: March 17, 2014, 02:22:53 am
content: I'm sure things like making robot require a hell lot of control theory.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 17, 2014, 02:59:44 am
content: If you're content to just "look it up" on everything, yes, damn near everything has been derived at one point or another, and all you really need is a search engine, or a good solid data book.But if you're the kind of person who needs to understand things, and wants to see theorems proven in class, and wants to derive things yourself, you will need it.Personally, I use arithmetic daily; algebra frequently, during design (most often playing with resistor dividers, AC steady state filters, diodes and transistors, etc.); and calculus and diff eq occasionally (more at complicated coupling networks, time-domain stuff, certain models of reality).I use Fourier and E&M (except for special cases for transformers) extremely rarely, however they are always intuitively present in my mind. Two cases where manual calculation is almost useless, but knowledge and intuition with their properties is invaluable. Practical calculations are almost exclusively computed, for example DFT on time series data, or FEA on E&M.The most recent diff eq I looked at was this problem:Suppose you have a heat source in the center of a round metal plate. The heat source has a radius r1 and the plate, r2. Thickness and conductivity do not matter directly, but the product, the heat spreading coefficient rho, does. The surface has a thermal conductivity to the surroundings defined as p = T(r) * k, where p is power density (W/m^2 or whatever), T(r) is the temperature at radius r (0 <= r <= r2) and k is the heat transfer coefficient. (This is at best a poor approximation of radiation -- which goes as Tabs^4, and a poor approximation of convection, which is nonlinear in the T^2 range or so, depending on airflow and awful stuff like that.) So, a transistor bolted to the chassis and how it heats up, simplified.Setting up the equations is fairly straightforward, the trouble comes when trying to solve it... it turns out to be of the form of the Bessel function. So you kind of have to compute it, or pick it out of a table or whatever, to do much with it.Another thermal conductivity problem I've done is uniform power (W/m^2) into the face of a conductor, which sinks the heat laterally (no surface dissipation or crap like that to deal with). It's a differential equation again, but easy to solve this time; it's a parabola, with the vertex at the hot end. The temperature at the end is simply the sum of all temp rises along the conductor (which, at a given point, is the sum of all power dissipated by that point, which is linearly cumulative).Tim

author: Legion
author_rank: Frequent Contributor
timestamp: March 17, 2014, 12:06:41 pm
content: Thanks for the responses. I enjoy math but I find if I don't use it, it's quickly forgotten. As my time gets more limited I have to prioritize the things I study.

author: tszaboo
author_rank: Super Contributor
timestamp: March 17, 2014, 12:56:02 pm
content: I daily use advanced math, like multiplying stuff... Jokes aside, the worst mathematical problems came for me from error analysis, and filter design, thermal design. None of which requires integration, or any kind of university math.Avoiding complex mathematical problems is part of the engineers job. If you can simplify an integration to multiplication with 10% accuracy, you will do it, because usually it doesn't matter. To say one example, you calculate an oddly shaped waveform dissipation on a resistor, to say if you need 63mW 125mW or 250mW one. There is no point, just point at the average of the signal, calculate the dissipation, add like 50% (which you need anyway) choose resistor.

author: TheRuler8510
author_rank: Regular Contributor
timestamp: March 17, 2014, 01:36:37 pm
content: Quote from: Legion on March 16, 2014, 06:44:38 pmThe strongest advise I can give you is to remember to actively manage your career as you progress through it, or else it will manage you. You can easily manage it in such a way that you never see advanced math, or never see an electronic component for that matter. Having the math background can give you insights into some problems you may not otherwise have had--even if you never actually use the math.Whatever you do, you should gravitate toward what you enjoy doing the most--but also use foresight into where that will lead you. Don't get pigeon-holed doing something that will cause you to be unemployable in ten years--I have seen that happen to people.Good Luck,

author: t3chiman
author_rank: Contributor
timestamp: March 17, 2014, 02:51:04 pm
content: Quote from: Legion on March 16, 2014, 06:44:38 pmI concur with the consensus: the daily grind of a workaday EE involves scant reference to the higher-order math so beloved by academics.But, say you find yourself putting CPUs into your circuits, and writing software to control interprocessor communications. Then, the situation changes. Personally, I found the switch from circuits to networked processors jarring. Even after pursuing (and getting) an MSCS, still I felt an intellectual void when weighing design alternatives. It took years to dispel my worries, and reach a conclusion.I had to crack open the old discrete structures book. After some reflection, I realized that relational algebra, finite state automata, regular expressions, parsers--all are merely different aspects of algebraic semigroups. Following such an insight led to high-confidence forays into areas that working programmers tend to avoid: formal specification, automated testing, even metaprogramming (very dramatic when it's used judiciously).Think that algebraic semigroups will never affect your daily work? Think again. Last week, I happened uponwww.systemsafetylist.org. One topic: the Toyota firmware lawsuit. The expert witness for the class action plaintiff had posted his direct examination. It went something like this:Q: How many global variables did the Toyota firmware exhibit?A: Over 10,000.Q: How many would good software engineering practice dictate?A: Zero.Etc., etc. Went on for days.Toyota had to settle, cost them millions.Thing is, control logic is modelled completely by a Reactor/Proactor pattern. And the sparse decision trees typical of real-time control programs are straightforward to generate with logic programs (After all, EEs don't really use the karnaugh mapping techniques shown in their circuit texts; it's all automated.). As for the thousands of global variables, who knows? I am skeptical. But I did not see any online cross examination of the expert.So, if you are an EE, and find yourself writing software that describes occasionally communicating finite state machines (sound familiar?), it would behoove you to get smart on your relational algebra, regular expressions, first order predicate calculus, and parser/generator logic. You will then be well prepared when the boss asks for formal specifications--you will have been there long before. As for metaprogramming, you can put it off for a while. But it is absolutely shocking to see an expert write a program that writes your program, I can tell you.Hope this helps.

author: Rick Law
author_rank: Super Contributor
timestamp: March 17, 2014, 05:34:34 pm
content: Quote from: Legion on March 17, 2014, 12:06:41 pmMr. / Ms. Legion,I am glad to see your response here "I enjoy math..." Good for you!My earlier response "eat it up, there is no such thing as too much knowledge..." was in part mistakenly thinking the original post may be a case of "looking for an excuse to avoid doing it".I place a lot of weight on "thinking". Math helps one think different and that alone is a lot of value.If you enjoy doing it, eat it up, do it. Knowledge in and of itself is valuable.RickSidebar 1 : It may be of interest to know: During WWII, one of USA's 5-star general was Omar N. Bradley. Omar Bradley did integral calculus for relaxation. This is according to his aide Chet Hansen in one of those History Channel shows about WWII.Sidebar 2 : An education series call TED Talk (The 2011 series on Inexplicable Connections), one episode is "Dan Cobley: What Physics Taught Me About Marketing" This is not a great episode per se, butit really high lights how knowledge in one field can be applied to solve problems in something totally unrelated. Dan Cobley is the current UK/Europe Google Marketing boss.http://www.ted.com/talks/dan_cobley_what_physics_taught_me_about_marketing

author: Neilm
author_rank: Super Contributor
timestamp: March 17, 2014, 08:46:26 pm
content: The only application I have had for advanced maths was measuring an unknown capacitance. The capacitor was discharged through a resistance - a voltage was tapped off this resistance (using the resistor as a divider) to charge up another capacitor (which of course began to discharge when the voltage on the load capacitor was low enough). We had to work out the algorithm to workout what the original capacitance was.

author: Kohanbash
author_rank: Regular Contributor
timestamp: March 17, 2014, 10:58:44 pm
content: Quote from: nuhamind2 on March 17, 2014, 02:22:53 amIn robotics there is a fair amount of math when getting into things like autonomy, machine learning, and data analysis. A lot of it comes down to implementing a mathematical idea. A lot of times the math (equations) look tough, but the ideas are easier to understand.For example to go back and forth from position, velocity, and acceleration you need to know the ideas of differentiation and integration.Some common uses of math are:Advanced Statistics - For machine learning stuff such as classification algorithmsApproximation/Interpolation - Working with sensor data and motion planningLinear Algebra - computer vision, building mapsedit: The TI-89 calculator is great for higher level math classes (and for those of us who forgot calculus and need to use it)

author: Phaedrus
author_rank: Frequent Contributor
timestamp: March 17, 2014, 11:38:19 pm
content: Quote from: T3sl4co1l on March 17, 2014, 02:59:44 amIn that case I would say, "Ok, what's the peak and average power output? 10W and 6W respectively? And we need four of 'em? Ok, I need an aluminum heatsink aboooouuuut this mass, and since we're doing mass production the stamped one is ok. Add a thermal pad and we'll tweak the fan speed curve once we build the EVT sample.It's a lot easier. There are times when you need to use higher math, but in 90% of cases, unless you're working on the bleeding edge or doing extreme optimization, rule of thumb works fine.

author: IanB
author_rank: Super Contributor
timestamp: March 18, 2014, 12:32:42 am
content: Quote from: Phaedrus on March 17, 2014, 11:38:19 pmRules of thumb are OK, but you do need to use the right thumb when picking the rule. In the example above, mass is not a direct factor affecting heat sink effectiveness, while surface area and/or quoted thermal resistance are. (It is an indirect factor, of course, since higher mass is likely to correlate with more area and lower thermal resistance.)I only make this seemingly pedantic comment since it is easy for the inexperienced to make incorrect assumptions about how things work, and therefore apply the wrong kind of rules in their analysis. Although you may know that size and weight of a commercial heat sink is a suitable proxy for thermal performance it doesn't stop the occasional person thinking that a big solid lump of aluminum would make a good heat sink.This is an area where studying applied mathematics will help with understanding the right physical rules governing the behavior of systems, even if detailed calculations are not performed.

author: Phaedrus
author_rank: Frequent Contributor
timestamp: March 18, 2014, 12:46:23 am
content: Mass comes into it as well. Mass, surface area, airflow. The actual math itself can get quite complicated. Generally though, mass adds thermal inertia, which can be as important as heat dissipation, especially when dealing with a pulsating load, like a power transistor in an SMPS. As for surface area, we only use about 5 stock heatsink designs with increasing surface area and cost, so it's just a matter of balancing mass (that is, heatsink length), surface area, cost, and the needs of the layout.The exception being in some of our really, really high-end PSUs, in which case yes the engineers use extensive math to optimize to get the most surface area in the smallest space with the lowest necessary airflow at an acceptable cost. But that's done as much or more by simulation tools than by hand-calculus.

author: mathsquid
author_rank: Frequent Contributor
timestamp: March 18, 2014, 03:24:54 am
content: Quote from: Kohanbash on March 17, 2014, 10:58:44 pmA good bit of algebra/linear algebra (by way of inverse kinematics) goes into calculating robot movement as well. Determining or optimizing how to position the end of a robot arm by moving the joints is a nontrivial problem, especially if there are obstacles that must be avoided.Granted, I know this example because I've seen it in books on algorithmic algebra. I'm sure that it is used in robotics, but I have no idea how much one solves these types of problems when doing usual work with robots.

author: KJDS
author_rank: Super Contributor
timestamp: March 18, 2014, 08:50:09 am
content: Quote from: Phaedrus on March 18, 2014, 12:46:23 amSomeone has to write the simulation tools, presumably an engineer.

author: JuKu
author_rank: Frequent Contributor
timestamp: March 18, 2014, 11:28:39 am
content: Quote from: EEVblog on March 17, 2014, 01:38:52 am+1. I use Fourier daily, but I've never done the calculations myself, except in school. I do discrete integrations every now and then. That is just summing, but I need to understand that by doing the sums, I'm really doing discrete integration - and why. Once every five years or so, I do multidimensional differentials: Because I know what those are and recongnized the situation to apply them, I was able to build the particular equations the first time, solve them, implement the solution to a computer, build the device and get the patent.

author: diyaudio
author_rank: Frequent Contributor
timestamp: March 18, 2014, 11:52:01 am
content: No math = No precision.Most projects wont make it off the bench without it, its for critical thinking and rational reasoning.I love math, just wish I was better at it.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 18, 2014, 04:58:00 pm
content: Quote from: Phaedrus on March 17, 2014, 11:38:19 pmThe case was more like "200 and 500W respectively".Down at 6 or 10W -- and the same equation provides quantitative proof to this -- it turns out it's reasonable to sink heat a long distance, laterally. A 1/8" aluminum plate might have a 40C temp rise across a PCB, but if that's okay, it's okay. Up at a few hundred watts, it would take a solid copper heatsink over half an inch thick to stay within tighter margins -- so the conclusion was clear, thanks to differential equations.It's much easier to do a little analysis -- plus it makes you look smart -- and show what will and won't work, instead of accidentally putting in too-small of a heatsink, bunging up the mechanical design for weeks and looking dumb for not researching it.Tim

author: free_electron
author_rank: Super Contributor
timestamp: March 18, 2014, 05:30:21 pm
content: anything beyond the functions found on a 1$ calculator (+ - / * sqrt and power-of. maybe throw in a log or ln for db calcs) are not worth spending time on. throw it in a simulator.nobody pulls the equation for a schematic by hand. there are tools for that. if you want to develop such tools, by all means become a math wizard.I don't make tools. i use them.

author: Dave Turner
author_rank: Frequent Contributor
timestamp: March 18, 2014, 10:27:39 pm
content: In the not too dim mists of time one might have said that mathematicians derive, discover and simplify equations whereas engineers find a way of using said equations practically, and not necessarily in the way originally envisaged.

author: Zero999
author_rank: Super Contributor
timestamp: March 18, 2014, 11:04:58 pm
content: I occasionally use complex numbers and some of the more basic calculus but I've forgotten most of the realy high level maths such as second order differential equations Fourier and Laplace.