[sdiy] SDIY MATH GOALS--need real help!

[Richard Wentk]

On 27 Feb 2009, at 02:00, Dan Snazelle wrote:

> AND i am wondering what else should i read, or study?
> AND WHAT MUST I KNOW?  is calc important? I know trig is.

Basic algebra will get you through DC circuit design, and some of the  
basics of op-amps - especially inverting and non-inverting amps and  
summers.

For digital you'll need basic programming, basics of logic design,  
and Boolean algebra.

You can do AC theory to three levels.

The first is learning some simple equations by rote. This will get  
you an intuitive idea about the relationships between (e.g.) blocking  
capacitor size and frequency.

The second is learning bode plots by rote without understanding why  
they work. You can design some simple filters like this.

The third is learning full AC theory, which will tell you the  
difference between filter types (e.g. Chebyshev vs Butterworth) and  
why they do what they do.

You don't actually need calculus for this, because the calc usually  
gets reduced to Laplace Transforms, which are a useful trick for  
turning calculus into much simpler algebra. Anything with lots of 's'  
or 'H(s)' is usually a Laplace equation. But as a foundation, it  
helps to understand the relationship between frequency and phase and  
what a filter actually does, and complex number theory will get you  
started there.

Half a level up from there you'll be able to do Fourier Transforms  
using both calculus and digital approximations, and understand a  
matrix approach to circuit design, among other things. You won't need  
to go that far.

There's a fourth level where you're completely fluent in the  
underlying maths, but that's PhD and upwards. Even fewer people get  
that far.

But - you can do a lot by rote, just by remembering useful equations,  
having a vague idea about what resistors, capacitors, transistors,  
diodes and op-amps do, and plugging numbers into formulae.

Most analog synth design uses the same old basic few circuits and  
ideas, which mostly haven't changed much since the 70s and 80s. The  
digital control element has changed, and some of the older hardware  
is no longer available and has been updated. (Hardly anyone uses 741  
op-amps for anything any more, ever.)

But the theory is a very tiny subset of the rest of electronics, and  
you can learn it fairly successfully without being too bothered by  
the rest, especially if you're using Electronotes as a reference.

Richard