Advanced Math in Electronics Engineering

[IanB]

Ok, I need an aluminum heatsink aboooouuuut this mass

Rules of thumb are OK, but you do need to use the right thumb when picking the rule. In the example above, mass is not a direct factor affecting heat sink effectiveness, while surface area and/or quoted thermal resistance are. (It is an indirect factor, of course, since higher mass is likely to correlate with more area and lower thermal resistance.)

I only make this seemingly pedantic comment since it is easy for the inexperienced to make incorrect assumptions about how things work, and therefore apply the wrong kind of rules in their analysis. Although you may know that size and weight of a commercial heat sink is a suitable proxy for thermal performance it doesn't stop the occasional person thinking that a big solid lump of aluminum would make a good heat sink.

This is an area where studying applied mathematics will help with understanding the right physical rules governing the behavior of systems, even if detailed calculations are not performed.

[Phaedrus]

Mass comes into it as well. Mass, surface area, airflow. The actual math itself can get quite complicated. Generally though, mass adds thermal inertia, which can be as important as heat dissipation, especially when dealing with a pulsating load, like a power transistor in an SMPS. As for surface area, we only use about 5 stock heatsink designs with increasing surface area and cost, so it's just a matter of balancing mass (that is, heatsink length), surface area, cost, and the needs of the layout.

The exception being in some of our really, really high-end PSUs, in which case yes the engineers use extensive math to optimize to get the most surface area in the smallest space with the lowest necessary airflow at an acceptable cost. But that's done as much or more by simulation tools than by hand-calculus.

[mathsquid]

For example to go back and forth from position, velocity, and acceleration you need to know the ideas of differentiation and integration.

A good bit of algebra/linear algebra (by way of inverse kinematics) goes into calculating robot movement as well.  Determining or optimizing how to position the end of a robot arm by moving the joints is a nontrivial problem, especially if there are obstacles that must be avoided.

Granted, I know this example because I've seen it in books on algorithmic algebra.  I'm sure that it is used in robotics, but I have no idea how much one solves these types of problems when doing usual work with robots.

[KJDS]

Mass comes into it as well. Mass, surface area, airflow. The actual math itself can get quite complicated. Generally though, mass adds thermal inertia, which can be as important as heat dissipation, especially when dealing with a pulsating load, like a power transistor in an SMPS. As for surface area, we only use about 5 stock heatsink designs with increasing surface area and cost, so it's just a matter of balancing mass (that is, heatsink length), surface area, cost, and the needs of the layout.

The exception being in some of our really, really high-end PSUs, in which case yes the engineers use extensive math to optimize to get the most surface area in the smallest space with the lowest necessary airflow at an acceptable cost. But that's done as much or more by simulation tools than by hand-calculus.

Someone has to write the simulation tools, presumably an engineer.

[JuKu]

Of course I've had to understand the concepts behind it all and know when such things apply etc

+1. I use Fourier daily, but I've never done the calculations myself, except in school. I do discrete integrations every now and then. That is just summing, but I need to understand that by doing the sums, I'm really doing discrete integration - and why. Once every five years or so, I do multidimensional differentials: Because I know what those are and recongnized the situation to apply them, I was able to build the particular equations the first time, solve them, implement the solution to a computer, build the device and get the patent.

[diyaudio]

No math = No precision.

Most projects wont make it off the bench without it, its for critical thinking and rational reasoning.

I love math, just wish I was better at it.

[T3sl4co1l]

In that case I would say, "Ok, what's the peak and average power output? 10W and 6W respectively? And we need four of 'em? Ok, I need an aluminum heatsink aboooouuuut this mass, and since we're doing mass production the stamped one is ok. Add a thermal pad and we'll tweak the fan speed curve once we build the EVT sample.

It's a lot easier. There are times when you need to use higher math, but in 90% of cases, unless you're working on the bleeding edge or doing extreme optimization, rule of thumb works fine.

The case was more like "200 and 500W respectively".

Down at 6 or 10W -- and the same equation provides quantitative proof to this -- it turns out it's reasonable to sink heat a long distance, laterally.  A 1/8" aluminum plate might have a 40C temp rise across a PCB, but if that's okay, it's okay.  Up at a few hundred watts, it would take a solid copper heatsink over half an inch thick to stay within tighter margins -- so the conclusion was clear, thanks to differential equations.

It's much easier to do a little analysis -- plus it makes you look smart -- and show what will and won't work, instead of accidentally putting in too-small of a heatsink, bunging up the mechanical design for weeks and looking dumb for not researching it.

Tim

[free_electron]

anything beyond the functions found on a 1$ calculator (+ - / * sqrt and power-of. maybe throw in a log or ln for db calcs) are not worth spending time on. throw it in a simulator.
nobody pulls the equation for a schematic by hand. there are tools for that. if you want to develop such tools, by all means become a math wizard.
I don't make tools. i use them.

[Dave Turner]

In the not too dim mists of time one might have said that mathematicians derive, discover and simplify equations whereas engineers find a way of using said equations practically, and not necessarily in the way originally envisaged.

[Zero999]

I occasionally use complex numbers and some of the more basic calculus but I've forgotten most of the realy high level maths such as second order differential equations Fourier and Laplace.