Author Topic: Why little math required for electronics?  (Read 4273 times)

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Offline Kyl8145

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Why little math required for electronics?
« on: April 28, 2019, 02:18:04 am »
So one thing I have been curious about as a beginner, but I have read in The Art of Electronics and in Practical Electronics for Inventors that you don't need to know high-level math to design good circuits, just algebra basically. Now The Art of Electronics is considered a major reference in electronic design, but it doesn't seem to get into things like advanced calculus-based math. My question then, is why does acquiring an electrical engineering degree require so much math? Is it just to understand the underlying theory regarding WHY circuits work the way that they do, but otherwise isn't actually needed to create the circuits, or is it really needed for high-level circuit design? Or is it that the kind of circuit design performed by electrical engineers is different somehow...? :-//
 
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Offline jeremy

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Re: Why little math required for electronics?
« Reply #1 on: April 28, 2019, 02:52:16 am »
Math is a tool in your toolbox, just like a multimeter. You need different tools for different things (in fact, sometimes you don’t even need a multimeter). You can do a lot of circuit design simply without using maths because there is a lot of empirical data used (data sheet specs, look up tables, rules of thumb) which exists in part to avoid this complicated maths. Simulators like LTSpice also hide the complex maths from you, so things can look simpler than they really are.

Complicated maths is taught (I assume) because university is supposed to give you a broad base of knowledge, not job specific knowledge. Someone who designs digital circuits their whole life might think the maths is pointless, but someone who designs laser diodes would use it every day (or a simulator that uses it)

 

Online hamster_nz

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Re: Why little math required for electronics?
« Reply #2 on: April 28, 2019, 02:58:09 am »
In my shallow experience, simple math is used to design circuits, but hard math is used to work out why they don't work.

Things like stability analysis and filters design use transforms that I am only just starting to be able to grock.

Then there is also the issues that real world components don't behave like their ideal models, so theory and practice never match unless you design with lots of margin for real world tollorances, making near enough good enough in a lot of cases.

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Online NiHaoMike

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Re: Why little math required for electronics?
« Reply #3 on: April 28, 2019, 03:20:28 am »
I think they should cover more about the intricacies of digital math, e.g. fixed point arithmetic. It's really useful to know when dealing with microcontrollers.
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Offline schmitt trigger

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Re: Why little math required for electronics?
« Reply #4 on: April 28, 2019, 03:51:30 am »
Math is strength-training your brain.

Similar to a football player will do laps and pushups even before touching a ball, math will strengthen your mental agility to solve engineering problems.
« Last Edit: April 28, 2019, 03:53:29 am by schmitt trigger »
 

Offline basinstreetdesign

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Re: Why little math required for electronics?
« Reply #5 on: April 28, 2019, 04:00:16 am »
why does acquiring an electrical engineering degree require so much math?
All of the math taught at university is to demonstrate the validity of the principles they want you to learn.  You need to know how to manipulate Maxwell's equations to understand why clamp-on ammeters work, why transformers, motors and generators work like they do and why antennas work at all.  You need to do the calculus involved in the physics of semiconductor materials before you see the validity of the simpler algebra involved in biasing a transistor.  You have to do the calculus involved in Fourier transforms to know what different effects come from signal modulation and  Laplace transforms to know that you can avoid all that messy calculus in circuit analysis and replace it with much easier algebra.
The main effect of all this is to reduce the level of abstraction involved in all of this so that intelligent approximations can be used with resorting to any of that godawfull stuff.

I did all that in school but in my career I never used anything more sophisticated than a 4 banger calculator.  I got through half of my undergrad years with only a slide rule.
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Offline coppercone2

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Re: Why little math required for electronics?
« Reply #6 on: April 28, 2019, 04:05:53 am »
the main reason is because the real world does not really work well with theory, so you end up significantly adding to your already rough calculations to make something reliable.

Even if you do advanced mathematical analysis on electrical circuits, once you include mechanical and thermal effects on a circuit, and the effects they have on the electronics, and the effects those effects have on the thermal and electrical effects and so on (to get something exactly) it becomes extremely unweidly to build something more then a single resistor standard (and thats just a resistor). Then factor in a HUMAN and you find out the biggest problem is the buttons are too weak because someone is slamming on it like balboa

So 1) you simply the math by getting rid of all the 'non-affects (they really effect things but its just sub PPM and there is so many variables it essentially looks like its random, another factor is dominating, etc.. its basically hunting a fart in a tornado. and its all time consuming and expensive to measure. oh yea and simulators go out the window, you will need to make your own simulator algorithm that might link like 3 different simulation programs together to form a experimental guideline, that you need to test, that there wont be cheap equipment or trustworthy equipment or equipment with bandwidth required or stability required etc)
2) you make the circuit tougher then it needs to be to circumvent a potential defect

3) you know 1) and 2) so you save yourself the time and just aim high with a guess, if it fails you use some math to aim a bit higher.

4) worry if pursuing this relentlessly will make you feel accomplished in life, if it will help anyone, etc. is it just a psychotic obsession at this point? is this what you want? did you play any videogames, smell some flowers, watch some TV, bake a cake recently?

If you do high-order analysis of circuits and parts and stuff you will get insight but for many things that are being sold, its not difficult to figure out how to make it better (but it wont fit a PRICE or development time model that's considered realistic). perhaps you over heard the board room talk about baseball going on for 4 hours and you realized... i should take it easy rather then crush my brain for these guys... lets take it easy on youtube for a while.. is my hair turning grey??

Even with the art of electronics, if you studied something like Sedra Smith in school, then you read AOE after (since its not part of corriculums) you will likely want to go back to the 'classic hard' literature to follow up on something, then that might make you go back to the AOE and back and forth and back and forth... you kind of just get interesting ideas you want to follow up on
« Last Edit: April 28, 2019, 04:18:58 am by coppercone2 »
 

Online CatalinaWOW

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Re: Why little math required for electronics?
« Reply #7 on: April 28, 2019, 04:15:48 am »
All of the above answers are correct.  Another analogy may help. 

Basketball is now a worldwide sport and many, many people play.  You can learn and play basketball at a hoop in your backyard and may well develop the ability to shoot well and dribble well.  And those skills may serve you well in the local pickup game.  At that pickup game you may learn of the need to play defense and learn to keep your center of gravity low watch your opponents center of gravity.  Later you may get into organized basketball and learn elements of team play such as the pick and roll, zone defense and others.

At each level of play there is a higher and higher level of sophistication, requiring additional skills to succeed.  If you are playing in the local city league you may do quite well without employing any of the more sophisticated tools.  If you are playing in the Olympics in the medal rounds you will have to be versed in all that is known about basketball (and physically gifted as well).

Same general idea applies in engineering.  On the biggest stages you need all the tools there are to succeed.  Not just math.  Not just the basics taught in the Art of Electronics.  But both and many more.

 

Offline golden_labels

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Re: Why little math required for electronics?
« Reply #8 on: April 28, 2019, 04:26:34 am »
You need maths to understand details of how things work. But not to use those things in a useful manner.

If you would try to precisely model any real-world circuits of complexity equivalent to more than a few elements, you would soon face the need to symbolically solve arbitrary integrals. Good luck with that — there is no known general way to deal with integrals. Most probably you would also encounter problems equivalent to SAT for hundreds of parameters. Solve that efficiently for just 60 inputs and you will become the legend of comp-sci :D. Oh, did I mentioned 100-dimensional shapes representing probabilistic distributions of the solutions? ;)

It is much more efficient to divide the problem to easily digestible bits, which are approximated with simple (but good enough) models. And then adjust them, if something is not exactly as it should be. And that requires very little maths beyond arithmetic and a few other tools.

If you wish to see the problem yourself, try modeling the most basic thing in electronics: a voltage divider consisting of two resistors. But for real-world elements, not theoretical, simplified ones. Compare that to doing the same for the usual way and consider, if the effort was worth it for a typical scenario.
« Last Edit: April 28, 2019, 04:30:26 am by golden_labels »
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Offline Kyl8145

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Re: Why little math required for electronics?
« Reply #9 on: April 28, 2019, 04:28:29 am »
What I was finding confusing was that in some forums when asked, a lot of engineers were saying that they haven't used calculus since college. And it was just making me wonder if, other than in certain applications, you technically could have a person who didn't know any calculus or physics work in the same position as the engineer who had to learn all that stuff and yet design circuits just as well.

BTW, this question is out of curiosity, I have no issue with math or physics or any of that, I actually love calculus and calculus-based math in fact.
 

Offline Kyl8145

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Re: Why little math required for electronics?
« Reply #10 on: April 28, 2019, 04:31:40 am »
You need maths to understand details of how things work. But not to use those things in a useful manner.

If you would try to precisely model any real-world circuits of complexity equivalent to more than a few elements, you would soon face the need to symbolically solve arbitrary integrals. Good luck with that — there is no known general way to deal with integrals. Most probably you would also encounter problems equivalent to SAT for hundreds of parameters. Solve that efficiently for just 60 inputs and you will become the legend of comp-sci :D. Oh, did I mentioned 100-dimensional shapes representing probabilistic distributions of the solutions? ;)

It is much more efficient to divide the problem to easily digestible bits, which are approximated with simple (but good enough) models. And then adjust them, if something is not exactly as it should be. And that requires very little maths beyond arithmetic and a few other tools.

I see; well all of that is way over my head right now, but I'll get there :D But I see your point, that is what I figured, that they want you to know the underlying theory and also for applications where such knowledge is needed. However, what happens if there is a situation where the knowledge is needed, but the engineer has forgotten it because it's been awhile?
 

Offline coppercone2

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Re: Why little math required for electronics?
« Reply #11 on: April 28, 2019, 04:34:25 am »
consultant, team member, complain to boss, post on forum, send letter to lead company/designer, publish research in a journal and hope someone else decides to research it (playing the 20 year game), etc

you don't need to be a one man army

if something is such a complete dog then why are you building it? do you even know what solution you want?

oh yea, but if you want to misuse something, to save money, thats always what you get.  :-DD
« Last Edit: April 28, 2019, 04:36:45 am by coppercone2 »
 

Offline jeremy

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Re: Why little math required for electronics?
« Reply #12 on: April 28, 2019, 06:21:27 am »
And it was just making me wonder if, other than in certain applications, you technically could have a person who didn't know any calculus or physics work in the same position as the engineer who had to learn all that stuff and yet design circuits just as well.

Yes, you can. I think the point everyone is trying to make is that “electrical engineering” or “circuit design” do not refer to niche areas of knowledge; they are enormous, and many people who have jobs in these area will be doing completely different things (and possibly not even realise that others exist). For example: an “LED lighting engineer” may be someone who installs lots of LED lights with off the shelf drivers (minimal maths), designs LED drivers (moderate maths) or designs the LED die itself (knee deep in it).
 

Offline soldar

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Re: Why little math required for electronics?
« Reply #13 on: April 28, 2019, 07:38:22 am »
you don't need to know high-level math to design good circuits, just algebra basically.


Depending on what you are designing you might need Fourier analysis, Nyquist polar plot analysis, ...

Heck, how about the classic "how fast does a capacitor charge through a resistor". You can't get much simpler than that and you are already looking at an exponential. 

Designing transformers isn't even "electronics" and you will be dealing with harmonics.

Calculus is a useful tool which a good engineer has in his toolbox. He might use it more or less but it is a tool he should have.

Like any other engineer or scientist some tools get used more than others depending on what you are doing. 

Calculus, transforms and other tools help analyze mathematical models of physical things.

Higher math is everywhere. Just to give an example, MP3, MPG, NTSC, are all developed with much math analysis... not to mention all modern forms of cell phone, tv etc modulations and transmissions.

It gets to be annoying and frustrating when you hear someone with no preparation analyze or describe a circuit in terms which are not really engineering but just woo.

Why is a linear power supply oscillating? Why is an audio amp oscillating?  Why is my oscillator NOT oscillating?  You can do a good model analysis or you can fumble in the dark all day and get nowhere.
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Offline Benta

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Re: Why little math required for electronics?
« Reply #14 on: April 28, 2019, 11:02:23 am »
Another place where you'll really need higher maths and physics is at the edge of the electronic realm:
Real-life interfacing, more specifically sensors and transducers.

 

Online dmills

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Re: Why little math required for electronics?
« Reply #15 on: April 28, 2019, 01:22:14 pm »
It is somewhat rare to have to really get your math on, but knowing the mathematics helps to warn you when you are approaching one of those areas.

You have to know enough to know when the simplified models have reached their limits, and to know how to handle it when that is the case.

It is possible to go quite a long way just gluing datasheet and app note circuits together, but that hardly counts as engineering, sensor interfacing, design of oscillators and PLLs, Filters, Stability, the whole world of control theory really, electromagnetism, all of the fun stuff needs you to get your maths on.

Sure, you can usually buy a chip that does something complex for you that you could have done more cheaply if you fully grokked the theory, and sometimes that is a valid choice, but uni should teach the theory (Otherwise, where will the designers of chips that make the hard stuff go away come from?). 

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Offline GopherT

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Re: Why little math required for electronics?
« Reply #16 on: April 28, 2019, 01:24:23 pm »
There is a growing push to teach statistics or more linear algebra instead of calculus to engineers.



« Last Edit: April 28, 2019, 01:25:58 pm by GopherT »
 

Offline hans

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Re: Why little math required for electronics?
« Reply #17 on: April 28, 2019, 02:04:49 pm »
Stochastic research is getting more important in modern technologies. Think machine learning, but also high-level dependable networks such as car-to-car communication or other opportunistic networks.

Nevertheless, I think the main calculus in bachelor/master is still essential to be able to dive deep if you need to. Maths are useful to prove a problem. If you are trained well in modeling your problem and let loose some calculus on it, it's potentially far easier to demonstrate an issue.

For example: consider the problem of L+C inrush (in particular for low ESR situations, e.g. ceramic caps), where hotplugging may create an upsweep of the input voltage and potentially exceed absolute max specs of some components.

A measurement could show the problem, but since this may be a destructive test could be expensive and time consuming.
A numerical analysis (simulation) of this circuit can also showcase the problem, and is not destructive.
Finally, an analytical model (circuit theory) could show the real upper bound of the voltage upswing, i.e. Vpeak = 2 * Vdc, and use that result to dimension the input protection, component specification or realistically constrain your product specifications.

In the other cases, you would either perform a manual search of the problem, learn to avoid problems from experience or try to be on the too cautious side (overkill engineering).
 

Offline tggzzz

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Re: Why little math required for electronics?
« Reply #18 on: April 28, 2019, 02:28:41 pm »
My question then, is why does acquiring an electrical engineering degree require so much math? Is it just to understand the underlying theory regarding WHY circuits work the way that they do, but otherwise isn't actually needed to create the circuits, or is it really needed for high-level circuit design?

It is needed to create circuits that work predictably and reliably.

It is needed to understand where circuits won't work, could fail.

If you don't care about reliabilty or predictability, or you don't care about whether failure might occur and what the consequences might be, then you can just throw things together, cross your fingers, and hope. Hillbilly "engineering" at its "finest".

Far too much software falls into the latter camp.

The other point is that "the best result of maths is that you don't have to use it". That can happen because understanding the maths allows you to create simple models that are sufficient in some circumstances. But you need to know the preconditions necessary for validity, so that you can understand when you are breaking them.

Simple example: please go and buy me a resistor that can be used at 10GHz (or even 1GHz). You can't, because any real resistor also has associated inductance (unless it is zero length) and capacitance (unless the terminals are infinitely far apart). Those "added components" are critical at microwave frequencies.

Simple example: define and understand what you see on a medium speed scope (i.e. >100MHz) if you probe a digital signal with a standard *10 "high" impedance scope probe with a 6" ground lead.

Simple example: you have built a circuit and are looking at its output. It isn't behaving as you expect. Is that because of a faulty design, faulty components, or faulty measurement technique? Maths helps you eliminate possibilities.
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Offline free_electron

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Re: Why little math required for electronics?
« Reply #19 on: April 28, 2019, 02:53:15 pm »
why does acquiring an electrical engineering degree require so much math?
All of the math taught at university is to demonstrate the validity of the principles they want you to learn.  You need to know how to manipulate Maxwell's equations to understand why clamp-on ammeters work, why transformers, motors and generators work like they do and why antennas work at all.  You need to do the calculus involved in the physics of semiconductor materials before you see the validity of the simpler algebra involved in biasing a transistor.  You have to do the calculus involved in Fourier transforms to know what different effects come from signal modulation and  Laplace transforms to know that you can avoid all that messy calculus in circuit analysis and replace it with much easier algebra.
The main effect of all this is to reduce the level of abstraction involved in all of this so that intelligent approximations can be used with resorting to any of that godawfull stuff.

I did all that in school but in my career I never used anything more sophisticated than a 4 banger calculator.  I got through half of my undergrad years with only a slide rule.

you can also simply accept the stuff that has already been proven over and over and move on ...

Every year millions of students get questions on their finals to prove this or that theorem. Why ? Do math teachers really have no imagination ? Those theorems are sometimes thousands of years old and have been proven by billions of students through the ages. Do they really think there is need to prove it once again ? are they still unsure about them ?
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Offline apis

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Re: Why little math required for electronics?
« Reply #20 on: April 28, 2019, 03:36:09 pm »
You can build a bridge or a house without knowing any maths, but if you want to be sure it will be safe and long lasting while at the same time not using more materials than you need to meet the specs, then you need the math and theory to calculate strength and resonance modes, etc.

Still, you can get pretty far without any maths, consider medieval cathedrals and castles for example (or even older structures like the Pantheon). But many cathedrals collapsed shortly after completion, those that still stand today were the ones that got it right through trial and error, and a bit of luck.
« Last Edit: April 28, 2019, 03:53:41 pm by apis »
 

Offline GopherT

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Re: Why little math required for electronics?
« Reply #21 on: April 28, 2019, 05:53:16 pm »

Still, you can get pretty far without any maths, consider medieval cathedrals and castles for example (or even older structures like the Pantheon). But many cathedrals collapsed shortly after completion, those that still stand today were the ones that got it right through trial and error, and a bit of luck.

Or, like many of the cathedrals that are still standing, they are significantly over engineered and, therefore, so expensive that it took a century or more to fund to completion.
 

Offline Dave

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Re: Why little math required for electronics?
« Reply #22 on: April 28, 2019, 06:37:47 pm »
Being familiar with somewhat advanced maths topics (fourier/laplace transforms, differential equations, etc.) can only be beneficial. It's another tool in your arsenal that you take out when you need to tackle slightly more complex problems.

From personal experience, the people that speak loudest against "wasting time" to learn them either:
a) never learned them themselves, or
b) took a class and memorized procedures without ever fully grasping them, therefore never applying the knowledge on real life problems.

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Online 2N3055

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Re: Why little math required for electronics?
« Reply #23 on: April 28, 2019, 07:48:56 pm »
At the risk of starting the riot, I will postulate that many here are confusing mathematics with physics.
You absolutely need to thoroughly understand both physics behind your circuit and that of outside world your circuit is connected to (robot, vehicle, printer, sensor).
To do so you will need to calculate things according to models, and you do that using math. But nowadays, there are many computer tools that can do arduous math for you. But you still need to understand enough to be able to set up calculations correctly.
Today, you probably don't need to be really proficient in calculating something by hand over 20 pages.. But you need to understand concepts and logic behind it.
 

Offline coppercone2

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Re: Why little math required for electronics?
« Reply #24 on: April 28, 2019, 08:04:49 pm »
I actually think calculus education is useful. It does not even get hard until you get to multivariable equations.

If you want to make engineering boring then sure, skip the DE and MV and just teach linear algebra. :barf: I hated it.
 


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