Mathematical Model for a project

[shehry]

Hi,

i've been hearing a lot about the importance and the necessity of
developing a mathematical model before starting an electronics project.
could anyone guide me as to

1) how a mathematical model is developed?

2) how would i incorporate that model into my project or any project
for that matter

 

[Tim Wescott]

Hi,

i've been hearing a lot about the importance and the necessity of
developing a mathematical model before starting an electronics project.
could anyone guide me as to

1) how a mathematical model is developed?

2) how would i incorporate that model into my project or any project
for that matter

I'm not sure where you're hearing that. A more general statement is
that you should know what you're doing before starting an electronics
project, and unless you know exactly how they're going to behave any
analog circuits in your project should be modeled mathematically. You
shouldn't automatically make a mathematical model of a circuit -- making
a complete and detailed mathematical model of a microprocessor circuit
would be a waste of time unless you were the chip manufacturer trying to
make sure that a new chip will function correctly. On the other hand,
if it's a very fast microprocessor it would be a good idea to do some
form of preliminary validation that you are going to achieve the speeds
you want on your various buses, and know what you need to do to get there.

A mathematical model of a circuit (or anything else) is a description,
using math, of that circuit which is sufficient for predicting its
behavior. Sometimes you'll be interested in different aspects of a
circuit's behavior and you'll develop a model for each -- for example a
power amplifier may have a behavioral model that tells you what it does
assuming the finals don't get too hot, and a thermal model that tells
you how hot the finals do get.

So you develop a mathematical model by asking questions about your
circuit that you need answers to, then figuring out how to model the
circuit to answer those questions.

The model itself doesn't end up being incorporated into the actual
product, but any good engineering project should be accompanied with
good documentation; your models should be implemented in some manner
where they can stand or their own, or they should be incorporated into a
circuit description that anyone who works on your circuit in the future
will be able to read so they understand what the heck you were trying to do.

 

[roy]

well Mr. Wescott have give a link to its web page after checking that
link i could tell u that i have studied these stuff at the 3 rd yr of
my engineering degree ( i just want to say that these things are
complicated if ur not used to them...)
u could start by something like the RLC circuit modeling whish could
give u a much more easier differential equation....
Best Regards,
Eng. Roy.

 

[Ken Smith]

Hi,

i've been hearing a lot about the importance and the necessity of
developing a mathematical model before starting an electronics project.
could anyone guide me as to

No, that is one of the steps in doing an electronics project not something
you do before it. The steps in doing a project are:

(1)
Determine if this is a really stupid idea that can be rejected before we
even start. This step involves checking that the spec. doesn't suggest
that you know the future or produce more energy than you start with.

(2)
Guess at a few ways that the problem can be solved. If its audio guess
that it will be good op-amps if it is image processing guess that it will
involve a CPU of some sort. .. etc .. Either on paper or in your head
make a list of methods.

(3)
Now you make a very simple model in a form that works well for thinking
about how you are going to solve this problem. This model may well show
that you picked the wrong way to attack the problem. If it does, change
your mind[1]. The sooner you get rid of the dumb ideas, the less time
you'll spend going down the "garden path".

[1] When I change my mind, I always ask "will this new one work better".

 

[Ken Smith]

circuit description that anyone who works on your circuit in the future
will be able to read so they understand what the heck you were trying to do.

Stop one step short of "anyone who". There are some real morons out there
that won't get it if you spoon feed them. Assume the other guy isn't as
smart as you but that he does know how to tie his shoes.

A couple do and don'ts to demonstrate the point:

If you are writing software make your comments state why you do something:

Don't:
ADD A,#209 ; Add 209

Do:
ADD A,#209 ; (0-backslash) for compare


If you are writing about op-amp circuits:

Don't:
U1 is an op-amp that makes a gain of 7 and inverts the signal

Do:
U1's offset current forced me to use a low value resistor for R17

 

[[email protected]]

1) how a mathematical model is developed?

1) You use differential equations and algebra, and knowledge of the
behavior of the components of the system. Your project's requirements
and specifications should be able to be used to mathematically describe
how the circuit or system should behave, and how it needs to interface
with the rest of the world. And with a BSEE degree or equivalent
knowledge you should be able to create rudimentary mathematical models
of most electronic circuits, and the parts of the rest of the world to
which your circuits will be interfaced. You should be able to end up
with a set of equations, either in the time domain or the frequency
domain, that behave almost (within the limits of your modeling
techniques and knowledge) as your system behaves. i.e. If you solve
the set of time-domain differential equations that represent your
circuit, then, the algebraic equations that result, when plotted,
should show all of the various voltages or currents, at every point in
your circuit, as functions of time. Similarly, if you use an
equivalent set of equations, but in the frequency domain, the solution
should show the voltages or currents as functions of frequency.

2) how would i incorporate that model into my project or any project

for that matter

2) A mathematical model is one tool that can be used to help analyze
or synthesize a system. Other helpful tools might include imagination,
reasoning, logic, cleverness, research, and experience. Mathematical
models can be used in several ways. Two typical ways might be: a) put
pencil to paper, or, b) simulate on a computer. In both cases, you
should be able to learn how the properties of the components of a
system affect its internal and external behaviors. And you should also
be able to solve the equations, to arrive at the needed properties
(values) of components, in order to produce the desired responses of
the system.

All of the above can range from (at least) almost trivial to almost
impossible, depending on your project's requirements and complexity.

After you know how to theoretically do most of the modeling and solving
with pencil and paper, you can probably then safely use computer
simulation software, such as the freely-downloadable LT-SPICE, from
http://www.linear.com . If you need more component models, one of the
many places to look, for help with finding them, is:
http://homepages.which.net/~paul.hills/Circuits/Spice/ModelIndex.html .
For help with using the LT-SPICE software and the models, go to the
LT-SPICE discussion group, at http://www.yahoogroups.com .

Good luck!

Tom Gootee

http://www.fullnet.com/u/tomg

 

[John Larkin]

Hi,

i've been hearing a lot about the importance and the necessity of
developing a mathematical model before starting an electronics project.
could anyone guide me as to

1) how a mathematical model is developed?

2) how would i incorporate that model into my project or any project
for that matter

Entire projects/products are seldom modeled. Sometimes one will model
parts of a project, like one specific circuit, usually using Spice but
occasionally other tools, including specifically coded programs.

The first thing I do for a new project is write the manual.

John