Quote:
Originally Posted by mole42uk
it's only the square-to-sine section that's making me learn things I've avoided for 40 years. In school maths I was completely flummoxed by differential calculus and could never find anyone to explain. My maths tutor just said that I could never be an electronics engineer because my maths wasn’t good enough.
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Don't worry. It's not actually difficult. It's just weird and involves a few alien concepts. There is a threshold effect where once you get up to a certain level, you suddenly see how a number of things fit together and all of a sudden everything becomes simpler.
Calculus is rarely taught particularly well. They don't spend much time at the beginning telling you what it is, and then launch into lots of the detailed stuff. You don't see its applicability at the time, so you don't take as much interest as you could. You've also heard that it's difficult and a scary monster.
You're not alone. Some people get out of this trap by teaching themselves when they find they need it.
Calculus is all about things which are changing. Differentiation tells you how quickly something is changing, integration tells you how far something has changed. The bit worst-explained are limits... if you're working out how much change has occurred, then you need to say over what period of change you're talking about.
We live in a world of volts amps and ohms. These are all nice instantaneous things, firmly rooted in the here and now.
Then along came capacitors and inductors. They upset the applecart.
The voltage on a capacitor is directly related to the amount of charge stored in it. This is easy. But the amount of charge has history. To know it, you need to look at the profile of current versus time you've fed into it/out of it since you last knew its voltage. You could keep records, measuring the current very frequently and then doing a book-keeping exercise on it. This is called numerical integration. It won't be exactly right, but it can be right enough if you measure the current frequently enough. But if you go more and more frequent, the answer tends to settle on some value.
If you knew the current versus time fitted some equation, calculus is just a set of rules and some pre-calculated examples you can build together which will tell you what value the numerical integration would converge on.
So calculus does book-keeping at the equation level, not just the data file level.
It's actually a very neat trick.
In a world of sinusoidal and pulse signals, our signals are defined by equations. We have equations for the behaviours of resistors capacitors and inductors, so calculus is EXACTLY the right tool for the job, and inevitably a lot of what we do gets explained in calculus-speak.
There is a level above throwing straight-forward calculus at electronic circuits that involves a stunning new level of weirdness that actually makes things simpler. It involves a ridiculous concept that only a true vandal could have done
.... what would happen if we put in imaginary and complex values for frequency? Thinking how that might relate to the real world is mind-blowing, but it simplifies a lot of things into patterns and the human brain is a pattern recognition engine par excellence. We can use those patterns. This is where words like poles and zeroes crop up. They are a neat way of sneaking past differential equations.
So from the point of view of electronics, calculus isn't some scary beast you have to fight past, it's a very useful tool to add to your workshop. You don't need all of it at once, you can just pick up a bit at a time as you need it.
David