Hello. Since I started trying to learn about diy audio, my learning has been constantly restrained by my ignorance of math. Many of the texts I try to read through presuppose knowledge that I just don't possess, and inevitably, I get confused. So, I have decided to take a step back for the time being and try to develop some foundational knowledge. I just ordered the book Basic Mathematics by Serge Lang. It seems like it focuses mostly on algebra, although apparently it also gets slightly into trig, and even has some stuff on proofs. Does anyone have any other recommendations for books that I should read so that I may more meaningfully engage with this community? Maybe a book specifically about electronics? Or would such books also presuppose knowledge a layman might not possess? Thank you.
See if you can find some high school math texts. The math in electronic circuit design doesn't have to be super involved. The most complicated equation I use on a regular basis is: f0 = 1/(2*pi*sqrt(L*C)). It is handy to be able to take that and rearrange it to C = ....
It's also handy to have some level of understanding of what a derivative is and what an integral is. Maybe expose yourself to complex numbers. That's all A-level high school math. Some of it is covered in the first year of college in the US.
Unfortunately I don't have a reference for you but hopefully this can get you moving in the right direction.
It would be a bit easier to provide specific help if you elaborate a bit on what you're trying to accomplish. Are you trying to build a basic tube amp or are you trying to design your own FIR filter for an oversampling DAC?
Tom
It's also handy to have some level of understanding of what a derivative is and what an integral is. Maybe expose yourself to complex numbers. That's all A-level high school math. Some of it is covered in the first year of college in the US.
Unfortunately I don't have a reference for you but hopefully this can get you moving in the right direction.
It would be a bit easier to provide specific help if you elaborate a bit on what you're trying to accomplish. Are you trying to build a basic tube amp or are you trying to design your own FIR filter for an oversampling DAC?
Tom
For a basic tube amp I'd definitely recommend Morgan Jones, "Valve Amplifiers". He gives you the design equations and uses them. But if equations are strange beings for you or you need help rearranging/resolving them then an actual math text would be a good addition.
Oh... And for the love of Gawd get a calculator that supports scientific notation. It doesn't have to be a fancy graphing calculator, but it does need scientific notation. I started with a TI-30. It is much easier to type 10 [EE] 12 [+/-] than it is to type 0.00000000001 when you're punching in 10 pF for example. You'll notice that MS Excel supports scientific notation as well. You can type 10e-12 as a value. Help yourself by formatting the output to engineering notation so you get exponents in multiples of 3.
Ohm's Law: E = I * R
Power: P = E * I
Cutoff frequency for RC filter: fc = 1/(2*pi*R*C)
Resonance frequency: f0 = 1/(2*pi*sqrt(L*C))
Noise voltage spectral density: en^2 = 4*k*T*R
Noise power: En^2 = 4*k*T*R*BW
Thermal voltage: VT = k*T/q
Capacitance: C = Q/V
Charge: Q = I*t
I use the last two to find the charging time of a capacitor (assuming constant current): C = (I*t)/V <-> t = (C*V)/I
Inverting gain: Av = -Rf/Rg
Non-inverting gain: Av = 1+Rf/Rg
I have occasionally used the Ebers-Moll equation for a diode drop or to calculate Vbe, but don't have it committed to memory. Same for the exponential rise/decay of an RC. It's pretty rare that I work in the time domain. Working in the frequency domain is more intuitive for me 99% of the time.
Constants (also memorized):
Bolzmann's constant: k = 1.38*10^-23 J/K
Elementary charge: q = 1.602*10^-19 C
That's not a lot. I'm not good at memorizing but things do tend to stick if I use them a lot, which is how above equations stuck in my head. Definitely memorize the top 3-4 of them. Having to look up Ohm's Law every time I use it would make me a very inefficient circuit designer.
Get good at rearranging equations. For example, let's say you want to know the power dissipated in a resistor but you only know the resistance and the voltage. You could use Ohm's Law: E = I * R <-> I = E/R. Then insert that into P = E * I, which then becomes P = E * E/R = E^2/R. If you can do this in your head or quickly on a piece of scrap paper there's no need to memorize P = E^2/R separately.
Anyway. My $0.02 CAD worth. 🙂
Tom
Oh... And for the love of Gawd get a calculator that supports scientific notation. It doesn't have to be a fancy graphing calculator, but it does need scientific notation. I started with a TI-30. It is much easier to type 10 [EE] 12 [+/-] than it is to type 0.00000000001 when you're punching in 10 pF for example. You'll notice that MS Excel supports scientific notation as well. You can type 10e-12 as a value. Help yourself by formatting the output to engineering notation so you get exponents in multiples of 3.
Mine too.
I have the equations I use the most memorized. The rest are in textbooks that I've kept from college/university. It's really not many equations. These spring to mind:
Ohm's Law: E = I * R
Power: P = E * I
Cutoff frequency for RC filter: fc = 1/(2*pi*R*C)
Resonance frequency: f0 = 1/(2*pi*sqrt(L*C))
Noise voltage spectral density: en^2 = 4*k*T*R
Noise power: En^2 = 4*k*T*R*BW
Thermal voltage: VT = k*T/q
Capacitance: C = Q/V
Charge: Q = I*t
I use the last two to find the charging time of a capacitor (assuming constant current): C = (I*t)/V <-> t = (C*V)/I
Inverting gain: Av = -Rf/Rg
Non-inverting gain: Av = 1+Rf/Rg
I have occasionally used the Ebers-Moll equation for a diode drop or to calculate Vbe, but don't have it committed to memory. Same for the exponential rise/decay of an RC. It's pretty rare that I work in the time domain. Working in the frequency domain is more intuitive for me 99% of the time.
Constants (also memorized):
Bolzmann's constant: k = 1.38*10^-23 J/K
Elementary charge: q = 1.602*10^-19 C
That's not a lot. I'm not good at memorizing but things do tend to stick if I use them a lot, which is how above equations stuck in my head. Definitely memorize the top 3-4 of them. Having to look up Ohm's Law every time I use it would make me a very inefficient circuit designer.
Get good at rearranging equations. For example, let's say you want to know the power dissipated in a resistor but you only know the resistance and the voltage. You could use Ohm's Law: E = I * R <-> I = E/R. Then insert that into P = E * I, which then becomes P = E * E/R = E^2/R. If you can do this in your head or quickly on a piece of scrap paper there's no need to memorize P = E^2/R separately.
Anyway. My $0.02 CAD worth. 🙂
Tom
From back when books were useful and not just yet another way to extract money from students.
I seem to recall that the US Navy had a bunch of electronics tech training manuals. I've seen bits and pieces online. Maybe that could be worth a look.
Tom
First, I would say that reading math books is not enough for most people. Learning math best usually takes working lots of problems so you can be sure you really understand it and that you can do calculations reliably.
The above having been said, there is an old book I have seen called, "Handbook of Electronics Calculations." There may have been more than one book with that name, however.
Could have been this one: https://www.amazon.com/Handbook-Electronics-Calculations-Engineers-Technicians/dp/0070333920
It might be a useful reference.
Anyway, the main thing to know is most of what we need most of time is as others have already said: Its what you could have learned in high school. At least try to master that first and then see if you feel the desire to learn more. Its all good, but it takes time is all.
If you can find a tutor that might help get you going faster too. For some people its very helpful to have someone who can answer questions and or explain any sticking points that may come up along the way.
Also, at some point in engineering type math it can get to be a problem where the math isn't hard, but undefined symbols and or symbols re-used for different purposes in different contexts can get to be a problem. There are ways to help deal with ambiguity of nomenclature too, but probably won't be an issue for you at first. If it is, you can always ask here.
The above having been said, there is an old book I have seen called, "Handbook of Electronics Calculations." There may have been more than one book with that name, however.
Could have been this one: https://www.amazon.com/Handbook-Electronics-Calculations-Engineers-Technicians/dp/0070333920
It might be a useful reference.
Anyway, the main thing to know is most of what we need most of time is as others have already said: Its what you could have learned in high school. At least try to master that first and then see if you feel the desire to learn more. Its all good, but it takes time is all.
If you can find a tutor that might help get you going faster too. For some people its very helpful to have someone who can answer questions and or explain any sticking points that may come up along the way.
Also, at some point in engineering type math it can get to be a problem where the math isn't hard, but undefined symbols and or symbols re-used for different purposes in different contexts can get to be a problem. There are ways to help deal with ambiguity of nomenclature too, but probably won't be an issue for you at first. If it is, you can always ask here.
All the math won't usually be in one book.
I would start with reviewing algebra basics and going forward from there,
(you can skip statistics for now) here: https://www.khanacademy.org/math
I would start with reviewing algebra basics and going forward from there,
(you can skip statistics for now) here: https://www.khanacademy.org/math
Kahn Academy is good to mention, thank you.
Also IIRC they have a later lecture on 'slope fields,' which I thought might be of some intuitive value for students at the point of getting into differential calculus.
Also IIRC they have a later lecture on 'slope fields,' which I thought might be of some intuitive value for students at the point of getting into differential calculus.
I personally also wouldn't go to town with it.
Just get a good sense of general algebra and some standard things like complex numbers, phase relationships etc etc.
But keep it on a somewhat higher level.
Back in the day we had to do all these things at my university by hand (no reason why that was necessary) till you were so bored with it you wanted to quit everything in your life.
Total waste of time and effort.
I would personally just focus on a specific goal, see what you will bump into along the journey and than see what's needed. In that case you also have direct practical examples you can work with.
I find that a lot more useful than just brute force these things on a very dry and boring way.
Just get a good sense of general algebra and some standard things like complex numbers, phase relationships etc etc.
But keep it on a somewhat higher level.
Back in the day we had to do all these things at my university by hand (no reason why that was necessary) till you were so bored with it you wanted to quit everything in your life.
Total waste of time and effort.
I would personally just focus on a specific goal, see what you will bump into along the journey and than see what's needed. In that case you also have direct practical examples you can work with.
I find that a lot more useful than just brute force these things on a very dry and boring way.
In north America, especially the older generation uses E instead.
And yes that is confusing as hell 😀 : D
No, its "V" for Voltage here, not "V" for Volts. This is the IEEE standard, afaik.
"U" is common in german language.
This is a cute little book I remember reading many years ago. (I still have a dog eared copy somewhere...) https://www.zpag.net/Electroniques/Kit/Getting_Started_in_Electronics_-_3ed_-_[Forrest_M.Mims].pdf
I didn't know about Lang's book so I looked it up. It looks quite neat and seems to cover a pretty decent amount of high school core math without calculus. I suspect going through it will give a pretty solid background, even though it's not geared towards electronics.
BTW, Lang would make a pretty wicked eggnog at Christmas parties...
I didn't know about Lang's book so I looked it up. It looks quite neat and seems to cover a pretty decent amount of high school core math without calculus. I suspect going through it will give a pretty solid background, even though it's not geared towards electronics.
BTW, Lang would make a pretty wicked eggnog at Christmas parties...
E was short for EMF, in units of Volts
Capital E was for DC or Steady State AC values
Lower case e was for instantaneous values
Capital E was for DC or Steady State AC values
Lower case e was for instantaneous values
In addition to a book, get a graphing calculator. I bought a Casio FX-9750GIII not long ago. It can do complex arithmetic, numerical integration, and solve equations. Computer software can also do that.
Ed
Ed
In the end it doesn't matter wat letters we are using, as long as they are defined at the beginning of a book, paper or read.
(which often also seems to be very difficult for some writers 🙁 )
Just for giggles, I once handed in an exam were I wrote at the beginning something like;
Voltage = Rabbit (V)
Current = Carrots (A)
Power = Yummy (W)
And calculated accordingly, with Yummy = Rabbit * Carrots etc.
The professor found it quite funny 😀 😀
(which often also seems to be very difficult for some writers 🙁 )
Just for giggles, I once handed in an exam were I wrote at the beginning something like;
Voltage = Rabbit (V)
Current = Carrots (A)
Power = Yummy (W)
And calculated accordingly, with Yummy = Rabbit * Carrots etc.
The professor found it quite funny 😀 😀