Getting into electronics - which mathematics topics should I focus on?

Thread Starter

Yami

Joined Jan 18, 2016
282
Hi, I was wondering if you guys could direct me to which mathematics topics I should focus on. I would like to get into analyzing op amps, transistor circuits etc. Rather than trying to go through my math textbooks from cover to cover - I'd like to start with the important topics.
Thanks in advance
 

WBahn

Joined Mar 31, 2012
25,785
Hi, I was wondering if you guys could direct me to which mathematics topics I should focus on. I would like to get into analyzing op amps, transistor circuits etc. Rather than trying to go through my math textbooks from cover to cover - I'd like to start with the important topics.
Thanks in advance
What level of math are you at now?

A lot of it depends on how deep you want to get into things. Some people go their whole lives involved with electronics and never go beyond high school algebra, while other aspects require years of additional math background to do effectively.

But I can pretty confidently say that, no matter what you want to do, the value of a very strong proficiency in algebra can't be understated -- it is the foundation for whatever other math skills you eventually develop.
 

Thread Starter

Yami

Joined Jan 18, 2016
282
Learn everything.

We would be at a loss giving advice since we do not know what is your current level at school.
Oh yes true(hehehe)! I've completed A'level Mathematics 8 years ago. I have recently done a foundation level EE course - it focused more on the practical side rather than the theory, it sparked an interest in me to go further and self-study.
I noticed that I lack some basic mathematics background when I am going thorough EE lecture videos, text etc. Its not that I haven't learned those topics before but rather forgotten them due to not having to use them much in the past years.
 

MrChips

Joined Oct 2, 2009
21,161
For 99% of practical electricity and electronics, all you need to know is Ohm's Law.

However, if you wish to develop a deeper understanding of the behaviour of AC and RF circuits, here are some basics that you should learn.

Algebra
Geometry
Trigonometry
Cartesian and polar coordinate geometry
Bode diagrams
Complex numbers
Phasor and vector geometry
Lapace Transform
Fourier Series
Fourier Transform
Fast Fourier Transform
 

ebp

Joined Feb 8, 2018
2,332
A lot of what is required is not much more than what I call arithmetic - but that does include simultaneous equations, roots, exponents, logarithms & the like.

Algebra, including that for complex numbers (i.e. with real & imaginary components, not "complicated") is useful, as is familiarity with basic calculus.

Probably the most important thing is a willingness to apply math. Lots of people seem to balk at this and it is a real barrier to being able to analyze and design even simple circuits. Lots of it is drudgery - things like calculating resistor values, converting the ideal values to available real parts, checking the errors due to conversion, verifying what temperature coefficients do, and so on.

I'm terrible at algebra for complex numbers. I'm forever forgetting to carry the π or squaring j and forgetting the minus sign. There are many math software packages that are helpful for the likes of me, however, it is still necessary to be adequately versed in what is required to use them. "Solver" functions can be a great time saver. The same applies with spreadsheets, which I find extremely useful (partly because it makes the "damn, I need to change this value so I have to recalculate 6 others in consequence" a lot less annoying - but you have to be able to do the arithmetic "manually" to verify that the formulas you use are correct.

If you are doing programming or digital design, you need to be good at Boolean algebra. Again, I'm surprised by how many people involved in these things, especially programmers, are bad at Boolean algebra. De Morgan's theorem seems elusive.

===
Siphonaptera by Augustus De Morgan

Big fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so, ad infinitum.
And the great fleas, themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.
 

MrChips

Joined Oct 2, 2009
21,161
With input from other members, here is the amended list:

Algebra
Geometry
Trigonometry
Cartesian and polar coordinate geometry
Bode diagrams
Complex numbers
Phasor and vector geometry
Boolean Algebra
Calculus
Lapace Transform
Fourier Series
Fourier Transform
Fast Fourier Transform
 

bogosort

Joined Sep 24, 2011
459
I have recently done a foundation level EE course - it focused more on the practical side rather than the theory, it sparked an interest in me to go further and self-study.
Kudos! Theory is a deep rabbit-hole, but well worth the effort to explore. Assuming your goal is deeper understanding rather than computational proficiency, I'd recommend starting with differential equations (you can review any algebra/calculus you've forgotten along the way). Unfortunately, most introductory DE courses focus on memorizing the various techniques for solving DEs, but you really only need to have two in your pocket: separation of variables and Laplace transformations. The most important take-away is that you understand how we use DEs to model dynamic systems. Once you've done a few RLC circuit analyses, the connection will start becoming clear.

Next, I'd recommend a patient study of linear algebra, which is the foundation of practically every mathematical tool you'll use. I'd say the most difficult thing about learning linear algebra is that, at first, it seems so abstract that you'll wonder why you're bothering. But once you have a handle on linear spaces and transformations between linear spaces, you'll intuitively understand how and why your mathematical toolkit works. Linear algebra is the glue that ties everything conceptually together.

For example, the reason we use to DEs to model dynamic systems is that natural phenomena can generally be described as something that changes while some other thing changes. If we represent the changing things mathematically as functions, and the rates at which they change as derivatives, we can express the relationship between them as a differential equation. Solving the DE gives us a new function that tells us the direct relationship between the changing things themselves, allowing us to, e.g., know the voltage across a resistor or the position of an asteroid at some specified time. That it all just "works" is amazing and mystifying. But with an understanding of linear algebra, you'd see that the solution space of a homogeneous DE is a vector space of functions, and solving for the general solution is equivalent to choosing a basis. A Fourier transform is then just a change of basis.

The rabbit-hole goes far deeper, but at least the first few meters will become illuminated.
 

Thread Starter

Yami

Joined Jan 18, 2016
282
Kudos! Theory is a deep rabbit-hole, but well worth the effort to explore. Assuming your goal is deeper understanding rather than computational proficiency, I'd recommend starting with differential equations (you can review any algebra/calculus you've forgotten along the way). Unfortunately, most introductory DE courses focus on memorizing the various techniques for solving DEs, but you really only need to have two in your pocket: separation of variables and Laplace transformations. The most important take-away is that you understand how we use DEs to model dynamic systems. Once you've done a few RLC circuit analyses, the connection will start becoming clear.

Next, I'd recommend a patient study of linear algebra, which is the foundation of practically every mathematical tool you'll use. I'd say the most difficult thing about learning linear algebra is that, at first, it seems so abstract that you'll wonder why you're bothering. But once you have a handle on linear spaces and transformations between linear spaces, you'll intuitively understand how and why your mathematical toolkit works. Linear algebra is the glue that ties everything conceptually together.

For example, the reason we use to DEs to model dynamic systems is that natural phenomena can generally be described as something that changes while some other thing changes. If we represent the changing things mathematically as functions, and the rates at which they change as derivatives, we can express the relationship between them as a differential equation. Solving the DE gives us a new function that tells us the direct relationship between the changing things themselves, allowing us to, e.g., know the voltage across a resistor or the position of an asteroid at some specified time. That it all just "works" is amazing and mystifying. But with an understanding of linear algebra, you'd see that the solution space of a homogeneous DE is a vector space of functions, and solving for the general solution is equivalent to choosing a basis. A Fourier transform is then just a change of basis.

The rabbit-hole goes far deeper, but at least the first few meters will become illuminated.
Hehehehe thanks, it surely is a rabbit hole! - thinking about this has also opened a can of worms. A question often asked by some of my class mates and me is that why do we really need to learn all this mathematics and when is it really useful in a practical world? Is it so that we can make some what of a sense of all the abstract ideas? Like for instance when we have to fix a power supply do we really think about KVL and KCL or use certain theorems like the thevenin or norton, at most we might use good old ohms law but that's about it.
I guess it very much to do with how we are taught - we really don't get to understand the context in which we are learning this concepts.
 

MrChips

Joined Oct 2, 2009
21,161
Math is a package. You don't have to learn the whole thing and yet you cannot pick and choose which ones you want to learn. That may sound contradictory.

As an example, how many times in life would you need to know Pythagoras theorem or that the sin/cos = tan?
Yet, these are essential parts of learning about trigonometry.

And yes, what does learning geometry and trigonometry have to do with electronics?
 

Thread Starter

Yami

Joined Jan 18, 2016
282
Math is a package. You don't have to learn the whole thing and yet you cannot pick and choose which ones you want to learn. That may sound contradictory.

As an example, how many times in life would you need to know Pythagoras theorem or that the sin/cos = tan?
Yet, these are essential parts of learning about trigonometry.

And yes, what does learning geometry and trigonometry have to do with electronics?
True true :)
 

bogosort

Joined Sep 24, 2011
459
A question often asked by some of my class mates and me is that why do we really need to learn all this mathematics and when is it really useful in a practical world?
This is a common and perfectly valid question. From a practical standpoint, knowing math opens up doors to areas that would otherwise be inaccessible. Basic algebra gets you through the dc circuits door, but what if you want to work on simple ac circuits? You'll need to learn about impedance, and that requires understanding complex numbers and some trigonometry. Sure, there are tons of software tools that will do the math for you, but you won't have access to any of them during your job interviews. Companies want to know that you can reason about circuits in your head. Flip the script and imagine that you're part of a team trying to troubleshoot a difficult circuit issue. You're in a meeting standing around a whiteboard, drawing schematics and bouncing ideas around. Would you rather be the person who sits in quiet amazement as the rest of the team members attack the problem, or would you rather be in on the action?

As ac circuits get more interesting, they also get harder to analyze. What is the voltage doing across that inductor, or the current through that capacitor? This is where calculus and differential equations start to become important. The more mathematical tools you have, the more doors will open. The good news is that, like power-ups in video games, math tools stack. Want to understand filters? Better learn some Fourier analysis. But that won't be hard if you've already learned calculus and DEs. Once you've learned Fourier analysis, learning DSP is suddenly in your wheelhouse. The math "buffs" keep stacking, more doors open, and you keep leveling up as an engineer or tech. :)

Is it so that we can make some what of a sense of all the abstract ideas? Like for instance when we have to fix a power supply do we really think about KVL and KCL or use certain theorems like the thevenin or norton, at most we might use good old ohms law but that's about it.
Anyone can open a broken power supply, see that one of the big caps has exploded, and fix it by ordering a replacement part and soldering it in. You don't need to go to school to learn that. But what if you open it and there's nothing obviously wrong? Someone with basic dc skills can use Ohm's law to check that the dc output fails only under load. They may even be able to trace out where the problem exactly lies. But what if this is the 5th power supply that has come back with the same problem? How do you diagnose the cause?

Engineering/tech students have a tendency to underestimate the kinds of problems they'll run into in the real world. Unlike textbook problems, which are neat and orderly and always have a single clear, correct answer, the problems we get in the real world are rarely so nice. Solving them typically requires lots of creative thinking and hard analysis. You won't always use KVL or Thevenin's theorem, but you'll be glad you have them in your pocket.

I guess it very much to do with how we are taught - we really don't get to understand the context in which we are learning this concepts.
This is probably my biggest complaint about the way engineering is usually taught. They throw a bunch of finely detailed, complicated stuff at us and hope it sticks. But they don't show us the big picture, which is really the only way to make sense of it all. So, students naturally end up cramming the material to pass a test without actually absorbing the material. I've talked to so many engineers who've said something to the effect of, "If I had known in school what I know now, I would have paid more attention in DSP class." Invariably, the difference between "then" and "now" is that now the big picture is in view.

So I feel for you and your classmates, I really do. The best advice I can offer is to try to balance the finely detailed stuff you learn in class with some broader perspectives. Understandably, students tend to look up videos that show how to solve specific types of problems, because this is what they need to pass the tests. But try to mix in some videos on more general concepts that relate to the thing you're studying. Most importantly, try to develop the habit of connecting new stuff you're learning to old things you've already learned. These associations are the surest way to get your brain to integrate the new information.
 

OBW0549

Joined Mar 2, 2015
3,411
A question often asked by some of my class mates and me is that why do we really need to learn all this mathematics and when is it really useful in a practical world? Is it so that we can make some what of a sense of all the abstract ideas? Like for instance when we have to fix a power supply...
Mathematics will make the difference between being able to actually design power supplies (and other electronic things) and only being able to repair them.
 

Thread Starter

Yami

Joined Jan 18, 2016
282
This is a common and perfectly valid question. From a practical standpoint, knowing math opens up doors to areas that would otherwise be inaccessible. Basic algebra gets you through the dc circuits door, but what if you want to work on simple ac circuits? You'll need to learn about impedance, and that requires understanding complex numbers and some trigonometry. Sure, there are tons of software tools that will do the math for you, but you won't have access to any of them during your job interviews. Companies want to know that you can reason about circuits in your head. Flip the script and imagine that you're part of a team trying to troubleshoot a difficult circuit issue. You're in a meeting standing around a whiteboard, drawing schematics and bouncing ideas around. Would you rather be the person who sits in quiet amazement as the rest of the team members attack the problem, or would you rather be in on the action?

As ac circuits get more interesting, they also get harder to analyze. What is the voltage doing across that inductor, or the current through that capacitor? This is where calculus and differential equations start to become important. The more mathematical tools you have, the more doors will open. The good news is that, like power-ups in video games, math tools stack. Want to understand filters? Better learn some Fourier analysis. But that won't be hard if you've already learned calculus and DEs. Once you've learned Fourier analysis, learning DSP is suddenly in your wheelhouse. The math "buffs" keep stacking, more doors open, and you keep leveling up as an engineer or tech. :)


Anyone can open a broken power supply, see that one of the big caps has exploded, and fix it by ordering a replacement part and soldering it in. You don't need to go to school to learn that. But what if you open it and there's nothing obviously wrong? Someone with basic dc skills can use Ohm's law to check that the dc output fails only under load. They may even be able to trace out where the problem exactly lies. But what if this is the 5th power supply that has come back with the same problem? How do you diagnose the cause?

Engineering/tech students have a tendency to underestimate the kinds of problems they'll run into in the real world. Unlike textbook problems, which are neat and orderly and always have a single clear, correct answer, the problems we get in the real world are rarely so nice. Solving them typically requires lots of creative thinking and hard analysis. You won't always use KVL or Thevenin's theorem, but you'll be glad you have them in your pocket.


This is probably my biggest complaint about the way engineering is usually taught. They throw a bunch of finely detailed, complicated stuff at us and hope it sticks. But they don't show us the big picture, which is really the only way to make sense of it all. So, students naturally end up cramming the material to pass a test without actually absorbing the material. I've talked to so many engineers who've said something to the effect of, "If I had known in school what I know now, I would have paid more attention in DSP class." Invariably, the difference between "then" and "now" is that now the big picture is in view.

So I feel for you and your classmates, I really do. The best advice I can offer is to try to balance the finely detailed stuff you learn in class with some broader perspectives. Understandably, students tend to look up videos that show how to solve specific types of problems, because this is what they need to pass the tests. But try to mix in some videos on more general concepts that relate to the thing you're studying. Most importantly, try to develop the habit of connecting new stuff you're learning to old things you've already learned. These associations are the surest way to get your brain to integrate the new information.
Wow, thanks so much for the detailed answer and information/advice. Very insightful. :D
 

Thread Starter

Yami

Joined Jan 18, 2016
282
Once again thanks everyone, thanks very much for your time. It has given me the boost that I needed so much!
 
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