Electronics and Mathematics - Page 1
Forum section: electronics / beginners

author: vinlove
author_rank: Frequent Contributor
timestamp: September 17, 2016, 10:10:09 am
content: Hi AllRecently I bought a few old and new Electronic Beginners books, and now I have about 10 of them in my bookshelf.One of them is the new 4th Edition of popular "Practical Electronics for Inventors" - a huge heavy tome of over 1000 pages,and the 1st Edition of "The Art of Electronics" from 1980s for a fiver.Yesterday I had a good look at them scanning the pages, and there were fair bit of high level maths - Trigonometry and Calculus stuff.I studied them briefly in high school days years and years ago, but used to hate them.Now the question, do we need the mathematical knowledge and understanding in order to get into Electronics?Or is it possible to ignore them, and still able to be good at Electronics? If we do, how much, high or what level?I suppose it depends what we wanna do, but in general, I would invite your opinions, thoughts and experiences regarding this issue.cheers.

author: tatus1969
author_rank: Super Contributor
timestamp: September 17, 2016, 10:29:38 am
content: it depends on the area of electronics that you want to go into. All digital microcontrollers and logic, fine. Analog or RF, definitely not. Hard to say, but I would say 90% electronics disciplines involve higher level math. Studying it you face it as the very first big hurdle to take. And understanding math is the same as understanding electronics: logic thinking.

author: Tandy
author_rank: Frequent Contributor
timestamp: September 17, 2016, 11:51:56 am
content: You can enjoy electronics with any level of mathematical skill, are you planning on a hobby or a career?Electronics is all about 'models', depending on the complexity and application for your circuit depends on what model you can use.Take for example you want to build an amplifier...You don't really care about the efficiency or the frequency response, you just want something that makes your voice louder. You can build such a thing just by making assumptions that the components are 'ideal'. You could cobble together a circuit with nothing more than basic addition and multiplication, or none at all if you use an on-line calculator that calculates the values for you.Once you start to care about things like frequency response you will need to use a little more maths to work out for example what maximum frequency your amplifier can achieve while still making a reasonable gain. You then need to consider some of the non-ideal characteristics of your components but it is still not complex algebra etc. You can always start with the ideal model and then begin to learn why the circuit has limitations by gaining understanding of the other aspects.If you are building something that you care about distortion, induced noise, linearity etc because you want a hifi experience then you will need to learn some more complicated maths as you have several interdependent values that when you reduce one, another will increase. To find the ideal balance you have a more complicated model that needs more complicated mathematics.I would say don't be put off by academic books, if you are a practical sort of person just get making and learn as you go along. You will probably find that building something and then trying to learn how to improve something is easier than trying to learn all the theory first.

author: tatus1969
author_rank: Super Contributor
timestamp: September 17, 2016, 02:00:00 pm
content: to see how quickly it gets into math, have a look here:https://www.eevblog.com/forum/beginners/help-with-very-basic-reaction-confusion/

author: R005T3r
author_rank: Frequent Contributor
timestamp: September 17, 2016, 02:25:12 pm
content: Mathematics is fundamental to understand the stuff involved in electronics. Math is a tool you need to learn how to use in order to understand how things works.The problem with maths is that's just complicated, but if you stick to the concepts, you shouldn't have any problem in learning electronics with it, and yes: you need maths, but the real gateway to electronics is physics. Everything starts with it.

author: rstofer
author_rank: Super Contributor
timestamp: September 17, 2016, 02:33:49 pm
content: You can do a lot of things with electronics without having to know any more than first semester algebra which would be used to calculate series and parallel resistances. Transistor bias circuits, used for designing amplifiers, take very little math beyond algebra UNTIL you want to worry about frequency response.Next up: DC circuits where we deal with charging and discharging capacitors and inductors. At a minimum, you need to be able to sling exponential equations around v(t)=v0(1-e-t/RC). There will also be some first semester calculus when working through i(t) = c dv/dtIf you are going to do anything with AC circuits, you will need complex numbers.All of this stuff can come along when it is necessary. After all, we took the next math class in parallel with the theory class so we were, at best, one semester ahead in math.Get started, learn what you need when you need it and, by all means, get very familiar with LTspice (a circuit simulator).These days, EE school assumes the student has already had precalculus and maybe even calculus in high school. If not, there may be a slight lag while those topics are covered before getting into circuits.I'm ambivalent: Sure, I had the math, did the program and made a pretty good career (electrical, not electronics). Most of the stuff on my bench involves microcontrollers and FPGAs and math just doesn't come up all that often. I never did much with analog circuits but I really wish I had. Some of the most fun I have been having of late involves a small analog computer I built and solving differential equations that were a real PITA to solve with a sliderule.

author: rstofer
author_rank: Super Contributor
timestamp: September 17, 2016, 02:42:27 pm
content: Whatever you do, don't let math put you off! There are a lot of fun things you can build simply by following along with a published project. Get started, let the math sort itself out.This is supposed to be fun hobby! Not something where we stay up all night studying equations. Right along side that charging equation there will be a graph. Understand the graph and don't worry so much about the exponential equation until you need it. Or, better yet, model it on a breadboard and study it with a scope. That's why we had lab classes. Just to show that electronics isn't just a heap of numbers.Resources (ie money) permitting, "Learning The Art Of Electronics" is the lab course for "The Art Of Electronics". Scale down what they are doing to keep the price within reason and see what you can pick up. There's a lot of electronics in that lab course.

author: AG6QR
author_rank: Frequent Contributor
timestamp: September 17, 2016, 05:21:31 pm
content: A tinkerer without a solid math background looks at an oscilloscope and sees squiggly lines.An electrical engineer with a solid math background looks at an oscilloscope and sees sine waves, exponentials, and combinations of sines and exponentials. And in the case when they're not obviously sines and exponentials, he pictures the combinations of sines and exponentials that will make up whatever shape he sees on the screen.Sines and exponentials are the solutions to second- and first-order ordinary differential equations that describe the voltages and currents through circuits made of inductors, capacitors, and resistors.There's a lot of things you can do without an understanding of higher math, but if you have a basic understanding, it will open up a lot more options, especially in dealing with analog electronics (and even digital electronic signals travel along analog wires through analog components).

author: tggzzz
author_rank: Super Contributor
timestamp: September 17, 2016, 05:30:37 pm
content: Quote from: vinlove on September 17, 2016, 10:10:09 amIf you want to be able to connect a few pre-existing "library" components together, and bodge them until it (appears to) work, then you may be able to get away without knowing much maths.If you want to understandwhythings workreliably and repeatably, and to be able to makepredictionsabout new circuitsandsystems that you are creating, then you need the maths.Exactly which maths you need will depend on which electronics topics you are/aren't interested in. Software people can get away with being particularly ignorant of the maths, digital people less so, whereas analogue and RF people absolutely require it.

author: DmitryL
author_rank: Regular Contributor
timestamp: September 17, 2016, 06:39:01 pm
content: Quote from: vinlove on September 17, 2016, 10:10:09 amYes, if you want to be just an electritian doing nothing but connecting wires together without understanding what it really means, then you don't need math, it's your choice.Painters don't care about geometry, brick layers don't need to know physics

author: rstofer
author_rank: Super Contributor
timestamp: September 17, 2016, 06:56:22 pm
content: Part of the answer lies in what interests you. That's not an easy question because interests evolve.Five things you will need are: A breadboard, a multimeter (or 2), a power supply (or 3), a scope and a signal generator. Plus parts, of course. Digital adds some input/output gadgets but maybe the signal generator isn't required. After all, I can generate a barn full of signals with an Arduino.I'm going to deviate from the standard recommendation to just buy a Rigol DS1054Z scope (although it is a great scope!) and suggest a Digilent Analog Discovery. First of all, it's cheaper but, more important to the beginner, it has two power supplies (very limited voltage and current), two signal generators, a dual channel scope of moderate bandwidth, 16 digital bits for use as a pattern generator or logic analyzer and, best of all, it uses my 27" monitor! This is an important feature when you get older!There is a pretty nice analog parts kit that is available at a discounted price at time of purchase and there is an entire online curriculum for budding engineers.http://store.digilentinc.com/analog-discovery-2-100msps-usb-oscilloscope-logic-analyzer-and-variable-power-supply/I'm of the opinion that you can do an entire undergraduate degree with this one tool assuming you can scale signals to fit. It's a great piece of equipment.Think about what you might be interested in and refine your question. It may turn out to be pretty easy. There are tens of thousands of hobbyists messing around with electronics who are not math majors.

author: vinlove
author_rank: Frequent Contributor
timestamp: September 17, 2016, 07:20:31 pm
content: Great points. Very interesting.I was trying to build some theoretical and practical knowledge on Electronics, rather than blindly tinkering about with the gadgets - in the past, me being a radio ham, I used to make antennas for hf and vhf transmitting and receiving, and building some kit radios. But these activities were comfortably possible without much theoretical Electronic knowledge. I used to get the length of the one element of hf or vhf antenna by simple formula from the ARRL Handbook, cut the elements to the lengths, made up antennas, and they used to work well. And by just following the kit instruction, and keep soldering on the components into the pcb, they worked ok.Now I am trying to get into more general electronics, and wanted to build the knowledge from the foundation. I bought some of the popular Electronics books, but they are full of mathematics, and without the Mathematical knowledge, it seems a bit daunting to understand the books. I was wondering if I, then should start with the Mathematical books prior to trying to read these Electronics books.

author: rstofer
author_rank: Super Contributor
timestamp: September 17, 2016, 08:03:56 pm
content: I don't think so! Math is boring! Well, not boring, exactly, but not a worthwhile subject in and of itself.Learn as you go along. While I have been fooling around with differential equations on my analog computer, I haven't used my college math for much of anything in my hobby. That's because my interests lie in digital, not analog.But even in the analog world of op amps, there is a lot of stuff that can be built with simple algebra. Amplifiers, integrators (and analog computers) and other circuits with no more math than just algebra and not much of that. Watch the eevBlog video on op amps:Watch how easy it can be to analyze op amp circuits. There's no high level math involved. There is a little magic but I don't want to let the black cat out of the bag. A four function calculator is all it takes!Get a copy of the free Microsoft Mathematics and learn how to graph functions like that capacitor charge function. Then change the values and see how the graph changes. DO NOT try to solve for several points on the curve of several graphs with your handy calculator. A graphing calculator is nice but, let's face it, the screen is too small to be useful. Learn what it means to be out 6 time constants and you pretty much know all you need to know about capacitor charging.Maybe get the hobby version of Matlab - I bought the extra Simulink pack so I can model analog computation. Pretty cool software.But for real circuit analysis, LTspice (also free) is the way to go. Let the computer worry about the math! Find a circuit you want to consider? Run it through LTspice and see what it will do. BTW, there's a bit of a learning curve to circuit simulation and I highly recommend the LTspice group on Yahoo Groups. A few of the contributors are VERY knowledgeable. And, yes, I built up some analog computing blocks so I could do computing on LTspice. Very cool!Wander around the Internet looking for explanations. There is an easy way to get through most everything when it is explained in a suitable manner. Heck, we get through relativity by waving our hands and messing around with a flashlight. We certainly don't have to solve Einstein's equations to get a handle on time/space/gravity.Yes, you will eventually need sin, cos, tan, along with the inverse functions as well as exand ln(x) but until they come up, don't worry about them. Then take them one at a time.I have been working with my grandson on math (just started college and thinking about the EE program). I find that the Khan Academy covers a lot of the topics and does it very well. Not necessarily from an EE perspective but more of the pure math approach. Still, very useful lectures.When they are on sale, the calculus and differential equations courses from Great Courses.com are excellent as are the lower division classes like algebra. Most programs come with a workbook so you can basically learn all the math you will ever need by watching videos. The programs are too expensive when they are sold for regular price but every once in awhile, they offer them up for around $100 and that's not bad for a 30 session class.If you want to crank up the heat, take the math classes at a community college (or regular college). I have often thought of going back to school just to see what a 70 year old man can do against the kids. I know, they're smarter and have more stamina but I have no outside commitments and unlimited resources (relatively). Old age and treachery will overcome youth and skill every single time!

author: vinlove
author_rank: Frequent Contributor
timestamp: September 17, 2016, 09:22:10 pm
content: wow cool rstofer.I feel that age doesnt really matter in learning. When I was younger, OK I used to have better memories and sharper minds than the now in thinking I recall. But now in my 50s, I feel I can focus a lot better, and can understand better on topics requiring deeper thoughts than in my teens or 20s.The Philosophical and Literature books I had no ideas what they were about in my late teens and early 20s, now I could understand when I read them again.As you say, when we go back to the basics and learn about these fundamentals of Electronics .i.e Mathematics, maybe the Electronics subjects will become more fun, and richer subject rendering us into position where we feel easier to grasp the more complex theories and ideas of the subject.Today I went to the local library and took out very basic Calculus and Trigonometry subjects, and they look fun already. They are,Pre-Calculus for DummiesTeach Yourself CalculusTeach Yourself TrigonometryAnd I am sure there are a lot of great sites online too, as you mentioned. cheers.

author: rstofer
author_rank: Super Contributor
timestamp: September 17, 2016, 09:44:43 pm
content: Make sure you go back far enough to work with matrices. You need to be able to solve 3x3 and sometimes 4x4 in order to work with Kirchoff's Laws. When it gets beyond 4x4, let a computer do it.Kirchoff, Norton and Thevinin are fundamental to working with circuits. I suspect Google will provide a lot of sites.It may be a stretch to see what is going on but here is a video of the Gauss Jordan approach to solving linear equations (like Kirchoff equations):The nice thing about video presentations, as compared to classroom lectures, is that you can watch the video as many times as it takes. Don't understand something? Rewind! Or Pause and go track it down on the Internet. There are so many alternatives compared to the EE program of the early '70s.The thing is, you may have to watch it a few times to see what he is doing. But the first time you analyze a DC circuit with a bunch of resistors, you will know exactly how to solve the system of equations.Here is a pretty nice lecture series. By lecture 4, you will need Gauss Jordan! No big deal, it's covered in the lecture but it's nice to be ahead of the game:https://learn.digilentinc.com/classroom/realanalog/

author: tggzzz
author_rank: Super Contributor
timestamp: September 17, 2016, 10:14:19 pm
content: Quote from: rstofer on September 17, 2016, 08:03:56 pmEven for that you need a solid understanding of complex numbers. If you don't have that then filters and phase response are, um, tricky.Simple misapplication/misunderstanding/mismanipulation of complex numbers is a great way to prove -1=1, without involving a "hidden" 0; everybody can see which step is faulty, but most can's saywhyit is faulty.QuoteThere is avastdifference between analysis and synthesis. Simulators are based on arithmetic, not mathematics. Synthesis (i.e. creating novel circuits) is based on mathematics.QuoteA simulation is only as useful as the models being simulated. All models mustby definitionomit some aspects of real-world behaviour.Trivial example: please show me where I can buy a capacitor (or resistor or even a wire!) corresponding to the spice components. The last time I did a spice model of a (small) circuit, each physical resistor was modelled by 5 spice components. Then move onto considering, say, opamp models that explicitly omit behaviour that is vitally important in many circuits.An extreme example: I was once approached to create some device models, with no acceptance tests nor acceptance critera The customerreallyreally didn't care whether or not they were correct. The customer only wanted models they could present to their client, so that their client would purchase our customer's product. I declined to tender.

author: rstofer
author_rank: Super Contributor
timestamp: September 17, 2016, 10:56:15 pm
content: All of the above is true but I'm not convinced it matters. Yes, you don't get to phase and frequency response without complex numbers and you don't do control theory without Laplace transforms but those are subjects for a later time.Complex numbers are trivial, it's just a little vector algebra. Probably takes a day or two to learn. I don't recall losing sleep over it in college. Even Excel can do complex arithmetic:http://mysite.avemaria.edu/jcdaly/Tutorials/ComplexExcel/ComplexNos.htmlLaplace? Sure, that required a lot of coffee. But complex numbers aren't a big deal. In fact, modern FORTRAN can handle them directly. That's cool because GFORTRAN runs under the new Ubuntu on Win 10. Just drop down to a BASH shell, write a little code and watch complex numbers work!Microsoft Mathematics also works with complex numbers as do all of the advanced calculators. Same with all the trig functions and their inverses. This stuff is so much easier with modern tools!Sure, if you screw up the phase response, your amplifier oscillates or your oscillator doesn't. That's the time to worry about the details.We're talking hobby level, not designing for hire. Simulations need to be 'close enough' and implementations will certainly vary from the simulation. True, you can't buy a capacitor without series resistance and series inductance. Whether it matters is a different issue. You can get close enough, for hobby purposes, without worrying about issues at the margins. Mostly...If you want to design very precise circuits, everything matters. But if it is being built on a breadboard, almost nothing matters. Every parameter is swamped by the breadboard and dangling wires.In early days, I think it is sufficient to consider ideal components. The realities can wait! The only thing that happens is the matrix gets bigger. Then we write a FORTRAN program to do Gauss Jordan elimination (which has already been written thousands of times).LTspice allows for lumped parameters like series resistance. The model can be as accurate as the designer chooses. He can include lumped capacitance, resistance or inductance. I'm not sure how it would deal with a transmission line and we certainly see those in digital design - much much later on. Distributed parameters are the topic of an entire course in transmissions lines. Again, much later on. Last year of school? I forget...

author: tggzzz
author_rank: Super Contributor
timestamp: September 17, 2016, 11:29:05 pm
content: Quote from: rstofer on September 17, 2016, 10:56:15 pmComplex numbers are not difficult, but theyarenecessary and they are more than "simple" algebra.Apart from that, you seem fixated on arithmetic rather than mathematics; all the languages and environments you mention do arithmetic, not maths.In addition, you seem fixated on analysis of an existing circuit rather than synthesis of a new circuit.When considering analysis, concentration on arithmetic simulation obfuscates intuition and obfuscates doing sensitivity analyses - anddefinitelyenables the GIGO phenomenon.BTW the resistors I modelled contained 3 ideal capacitors and one ideal inductor - and even then they were only a small-signal approximation. I haven't yet seen a spice model of the modern ceramic and electrolytic capacitors that include the non-linear C-vs-V relationships, nor dielectric absorbtion a.k.a. soakage. The former are important for low distortion analogue circuits, the latter for all sorts of reasons. but haven't actively looked for

author: rstofer
author_rank: Super Contributor
timestamp: September 18, 2016, 12:09:48 am
content: Quote from: wilfred on September 17, 2016, 11:02:40 pmBut I wouldn't major in math. I don't know what mathematicians do for a living. Other than teach... I went to school to get a job!For me, math was 'applied'. I learned what I needed to know to advance through the program at hand. I didn't spend any time on side issues. Somehow I managed to pull off 140 units in 4 years plus another 31 units of grad school in another year. There was no time for side issues. Head down, move forward...I agree, math describes everything around us. But it isn't necessary to know a lot about theoretical math to get through EE school.For the average hobbyist, math isn't going to be a stumbling block. Sure, they can't 'invent' new stuff but neither can I. But I can copy and paste quite well and much of hobby electronics really comes down to copy and paste. Everything I could possibly want has already been invented and I can find it on the Internet!There's no reason for us to discourage an interest in electronics by blowing the math side completely out of proportion. There's a lot of fun in the hobby without having to get a graduate degree in math.Furthermore, knowing the math doesn't provide an ounce of intuition. All of that comes from lab work. Build something, see how it works. Change some values and see how that works. Rinse and repeat. That's why I mentioned "Learning The Art Of Electronics". At some point it is necessary to put parts together. Equations are interesting but parts bring circuits to life.All of my references to number crunchers (FORTRAN, Excel, Microsoft Mathematics, calculators) are just simple tools to handle the arithmetic. Clearly they don't solve a 'problem', they just handle the boring details. They produce a number that we would have gotten with a sliderule back in the early '70s. No more, no less. Except, of course, that they can produce graphs that we had to plot by iterative solutions on that sliderule. What a PITA!The real math comes from knowing what to plug in to the cruncher. It seems to me that knowing what to plug in is a lot easier, and less tedious, than crunching the numbers. And a lot more important.We didn't start out taking 40+ units of math classes before starting DC circuits. It all just came along as it was necessary. The same will happen here.

author: R005T3r
author_rank: Frequent Contributor
timestamp: September 18, 2016, 07:15:42 am
content: mathematicians are well requested around the world, and, their applications may vary from analytics to system modeling. Not to mention that there are serious connection with economy and math.Getting a degree in math -> you will found work in no time, especially because is way more difficult than engineering, and there are few people who are willing to study it and in these few, even fewer succeed in getting the degree.

author: tggzzz
author_rank: Super Contributor
timestamp: September 18, 2016, 07:29:58 am
content: Quote from: rstofer on September 18, 2016, 12:09:48 amAgreed. But some people (not in this thread) on this forum have a decidely "anti-intellectual" stance, frequently manifested in terms of "theory/degrees are useless, practice is everything". That attitude needs challenging.QuoteThere I strongly disagree. A lot of my intuition comes from understanding the maths, how it applies in very simple examples, and how those examples are visible as part of the complex real-world situations I encounter. Without the maths it is monkey-see-monkey-do.QuoteThere I strongly disagree. You are describing blind fumbling, which, given the proverbial million monkeys might evolve a solution (i.e. think of genetic algorithms for problem solving).But I do agree that building things is fun and necessary - but not sufficient. Neither is the maths sufficient - but it is necessary.QuoteAgreed - and that last paragraph is the key point!

author: tatus1969
author_rank: Super Contributor
timestamp: September 18, 2016, 08:13:20 am
content: Quote from: rstofer on September 18, 2016, 12:09:48 amMathematics is one of the primary tools for natural Science. Without that many brilliant people having them developed over centuries all this would definitely not have been possible.And natural Science in turn is the foundation of everything that we have lying on our lab desk. We would again be left with nothing without math in the first place.I'm not saying that we now all have to climb the heights of math that were needed to develop such complex systems like GPS, but parts of this thread makes me think of another thread here about the meaningfulness of the LHC, where people call natural Science in question in general.I wonder why people are doing that. Today we have an awful lot of possibilities we can draw on, but we should appreciate that is was a long way and hard work to get there.

author: b_force
author_rank: Super Contributor
timestamp: September 18, 2016, 10:06:46 am
content: To answer the question if it's usefull, I think it all depends how you work, and what your way of working is. Some people think very planned, strict & theoretical. Others are more visual and practical.If you like it or not, electronics is still an applied form of science and engineering.This means that things need to work in a practical world, with very practical compromises, limitations and specifications.Therefore the question how it's done is sometimes a little less important. Also it is sometimes to difficult and time consuming to do all the math.So you work more with ballpark formulas and solves the left overs with experiments.From my own experience and the experience I have with interns I worked with, my opinion is that they have to change the scholing system. Mostly the emphisys for what is important is on the wrong things and not very efficient and equal.They don't have any practical skills anymore. With that goes having an open and creative mind for finding solutions.One of the things to my opinion, is that I think they can cut a lot of math. By that I don't mean the basics. But solving semeters long weird never excisting math problems is just a waste of time and energy to me. After a while people get the point, no need to repeat it a billion times.I can make a big list with things which are far more important than math if you work in a company or things that are heavily underrated at schools.In another EEVblog video Dave interviewed another EE guy (forgot his name, guy from USA). And both (dave and the other guy) agreed with this as well.I think people must admid that you don't ever use, need or needed (as a sence of knowledge/know how/engineering feeling) more than 50% of the math you had at school. Although math is important, at schools it's highly overrated. Which is to bad because it demotivates a lot of people. I actually know people who quit their study because of it. I can ensure you, they were clever enough to be a very good electronics engineer, but they just had more visual and practical way of thinking.I personnaly find the school system compared to what people really need and use, very conservative and inefficient. Mismatch with skills that are needed and asked for is high (sometimes close to useless even).

author: tggzzz
author_rank: Super Contributor
timestamp: September 18, 2016, 12:26:25 pm
content: Quote from: rstofer on September 18, 2016, 12:09:48 amMost of them apply the maths they learned, the problem identification and the problem solving techniques/disciplines they learned to... real world problems.They went to university to do something they enjoyed and to get jobs.

author: chris_leyson
author_rank: Super Contributor
timestamp: September 18, 2016, 02:16:23 pm
content: QuoteAs an electronics engineer dealing with digital signal processing you need the maths background, say you wanted to do an odd ball sized FFT that isn't radix 2 or radix 4 in VHDL, you've got to work it out from first principles because the FPGA vendors don't have the tools to do it for you, they just have a few IP libraries based on radix 2 or 4 and some newer pipelined algorithms.What do mathematicians do for a living ? DSP algorithms, image processing, pattern matching and recognition, software defined radio, OFDM modulators and demodulators, carrier aquisition, GPS etc etc. DSP is one branch of electronics where I would say you need the maths background.

author: rstofer
author_rank: Super Contributor
timestamp: September 18, 2016, 03:19:09 pm
content: Quote from: tggzzz on September 18, 2016, 12:26:25 pmYes, the math is important. But it needs to be taken in the context of the OPs situation.Starting a hobby!Can a new hobbyist get anywhere without years of math? Of course! Can an engineer? Nope!Nowhere did I ever want to get into the stupid argument of 'degrees are worthless'; they're not. Yes, there are talented technicians who can do some clever engineering. But when it gets down to it, on average, the degreed engineer makes more money. One company I worked for, one of the largest in the world, didn't think much of BS degrees. Sure, they were required, as a minimum, but to really get anywhere you had to have at least an MS. Oddly, the major wasn't as important.So, let's take this back on track. Can ahobbyistget anywhere in electronics without years of math? In my view, YES! There are tools to take the drudgery out of crunching numbers and the equations are pretty well known. But it's also true that some amount of math will be required.And by experimentation, I wasn't talking about 'random walk' or 'Mozart's Monkeys'. I was thinking about the simple RC low pass filter I was playing with the other day. From the equation fc=1/(2*PI*R*C), I can predict the corner frequency and I know the roll-off of a simple RC filter. I can model the filter in LTspice using ideal components, I can measure it's response using real components with my Analog Discovery (using the neat Network Analyzer Tool) and I can work out the math by hand.Now, from the equations, I can surmise that changing the value of R or C will move the corner frequency and I can predict how far. But it's just as useful to change the resistor and measure the results.Experimentation, not random walk. Knowledge gained from both sides: the math and the experiment. Fortunately, it will work out (at modest frequencies).The very type of experimentation we did in lab classes. Calculate, build, measure and explain the differences.

author: rstofer
author_rank: Super Contributor
timestamp: September 18, 2016, 04:01:14 pm
content: Quote from: chris_leyson on September 18, 2016, 02:16:23 pmYup, the math guys come up with all the algorithms. But they don't build the gadgets! That's left to engineers and technicians. Scientists figured out how to get to the Moon but engineers made it happen! Six times!I like math and science but I really like to build stuff.When I was a kid and my folks were promoting the idea that I should study math (as a field), I asked "What do mathematicians do?". They said mathematicians sat in a room and solved math problems. I came up with the image of an old man with thick glasses and a visor sitting at a desk with one of those old fashioned desk lamps writing in a ledger and decided right then and there that I wasn't going down that path.

author: IanB
author_rank: Super Contributor
timestamp: September 18, 2016, 04:49:08 pm
content: Quote from: rstofer on September 18, 2016, 04:01:14 pmHere are some mathematicians (sitting at their desk, with glasses even) describing some mathematical concepts:These examples are obviously presented for a non-mathematical audience, but you can imagine perhaps that similar levels of conceptual thinking are required to solve real world problems in engineering. If you cannot imagine, visualize and conceptualize, you will find it very difficult to succeed as an engineer.

author: rstofer
author_rank: Super Contributor
timestamp: September 18, 2016, 06:42:58 pm
content: Quote from: IanB on September 18, 2016, 04:49:08 pmBut we're not talking about engineering. We're talking about a hobby! Just a hobby! Not a profession...Yes, I took physics and we spent some time on waves. Light, sound, water, whatever. Actually, physics is my favorite subject.As to Numberphile - I really like their series. I also like their proof that 0.999... (repeating an infinite number of times) is EXACTLY 1.000... (repeating an infinite number of times). Turns out the matter came up last semester in my grandson's Precalc course when dealing with rational numbers. Given the decimal representation (with some repeating sequence), find the fractional representation. Having seen the proof made it a lot easier to explain what was going on.The proof is trivial BTW;10 times 0.9999... is 9.9999... then subtract1 times 0.9999... is 0.9999...-----------------------------------9 times 0.9999.... is 9.0000... then divide both sides by 91 times 0.9999... is 1.0000... EXACTLYOf course it only works with an infinite number of digits but, still, it's clever.

author: tatus1969
author_rank: Super Contributor
timestamp: September 18, 2016, 08:35:14 pm
content: Quote from: rstofer on September 18, 2016, 06:42:58 pmI get 8.9999 here?

author: rstofer
author_rank: Super Contributor
timestamp: September 18, 2016, 11:34:44 pm
content: Quote from: tatus1969 on September 18, 2016, 08:35:14 pmCarry the repeating decimals out to infinity and after subtraction all you have left is 9.000... That's the interesting part of the proof. If there are an infinite number of decimal digits and you multiply by 10, you still have an infinite number of decimal digits. So, after you subtract, they're all gone!It's fair to say there is some debate about this as there is with many topics.

author: rstofer
author_rank: Super Contributor
timestamp: September 19, 2016, 12:25:08 am
content: Whether you go for the 0.999... = 1 or not, here's how the idea works for finding fractions:Say you have the repeating decimal 3.45454545... and call it x100 x = 345.454545...-1 x = -3.454545...-------------------------99 x = 342x= 342/99 which, when you use a calculator is 3.454545...You can extend the idea for the case of n repeating digits, just multiply by 10n3.456456... multiply by 1000 and solve for 999 x

author: IanB
author_rank: Super Contributor
timestamp: September 19, 2016, 01:02:40 am
content: Quote from: rstofer on September 19, 2016, 12:25:08 amOne final step: fractions are usually expressed in their simplest form. Divide top and bottom by 9 to give 38/11, or 3 and 5/11.

author: b_force
author_rank: Super Contributor
timestamp: September 19, 2016, 08:27:37 am
content: From a physics point of view, fractions are non existing numbers, because it gives you infinite amount of accuracy/tolerance.Which is by definition impossible.For the same reason, a number is only as good as the accuracy which it is calculated from.So if you multiply two 2 digit numbers, you don't get a 4 digit result, but only a two or even one digit result.I see a lot of people doing that wrong.

author: JacquesBBB
author_rank: Frequent Contributor
timestamp: September 19, 2016, 08:44:39 am
content: Quote from: b_force on September 19, 2016, 08:27:37 amThis is certainly not true in quantum physics where you have spin 1/2 everywhere.It is also not true because of resonances. Motions are locked in exact ratio of frequencies. Like for example thespin/orbit resonance of Mercury around the Sun where Mercury rotates exactly 3 times during 2 revolutions around the Sun.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: September 19, 2016, 02:26:08 pm
content: A lot depends on what you mean by beginning and what you mean by hobby.Playing with microcontrollers, PA amplifiers and the such requires little math, and can't actually be improved a lot by applying complex math.On the other end I had a friend who got involved with sonar as a hobby. The first step was replicating the original Raytheon consumer depth finder (a spinning disk with a light on the periphery that was triggered by the return pulse). Little math required at that step. But very shortly he was trying to implement a 3D imaging sonar. Something at the very bleeding edge of sonar technology. Lots of very complex math involved in all steps of the system, from transmitter array through the display. Some folks just bite off an awful lot right from the start.Hobbyists have led the way in many areas of technology, and those hobbyists often need very advanced math on a daily basis.