Math question and electronics design?

[curry87]

Hi,

What math skills would you say are required to get you a long way in analog and digital circuit design ? is one easier than the other (ie less math required)?


What sorts of things in electronic circuit design are differential equations,laplace transform,fourier analysis and other advanced calculus topics used for please give some examples ?


What sort of math do you use the most when designing/testing electronic circuits?

Thx

 

[RoboWanabe]

Hi

For analogue electronics you basikly need to know algebra manipulation and For digital u need algebra manipulation and boolean algebra. These are what I needed the most . Laplace transform and fourier analysis are used for a number of things but the main one I can think of with filters. Sure therese lots more to say but thats all I can think of.

 

[crutschow]

Analog design generally requires more analytical mathematics such as calculus including Laplace transforms and Fourier analysis, but a good knowledge of Algebra and complex numbers can get you a long way. Laplace transforms are used to calculate the response of circuits with reactive impedances. Fourier Transforms are used to determine the frequency components and circuit response to complex signals such as pulses and square-waves. For analog circuit design, it helps to have a certain "intuitive" understanding of circuits to determine what circuits are needed to do a particular analog processing task. To develop that requires some experience with circuit design. A Spice analog simulator can help in experimenting with and understanding various circuit designs, but is not a substitute for building a circuit.

Digital design generally requires less analytical math other than Boolean algebra. You do need to develop a good understanding of what all the various gates, flip-flops, drivers, and registers do and which ones are best used to perform a specific digital function.

 

[MrAl]

Algebra
Geometry
Trigonometry
Analytic Geometry
Elementary Functions
Differential Calculus
Sequences and Series
Integral Calculus
Vector Analysis
Complex Variables
Fourier Series
Laplace Transforms
Probability and Statistics
For ordinary Digital, Boolean Algebra
For Digital Signal Processing, Z Transforms
Matrix Algebra
ODE's in Matrix Form

Laplace Transforms are used for analysis in the frequency domain.
Inverse Laplace for the time domain.
Differential equations are used for analysis in the time domain.

Matrices are used for general multidimensional analysis, algebraic or differential forms.

An example of the Laplace Transform for an RC filter:
Vout(s)=Vin(s)/(s*R*C+1)

 

[Winterstone]

An example of the Laplace Transform for an RC filter:

H(s)=Vin(s)/(s*R*C+1)

Vin(s) ??? Typo?

 

[panic mode]

that would be input voltage in frequency domain where

s=j*omega=j*2*pi*f

 

[MrAl]

Hi panic mode,


Im sure Winterstone is looking for the expression that looks closer to a 'book' example such as:

H(s)=Vout(s)/Vin(s)=1/(s*R*C+1)

 

[Winterstone]

Hi panic mode,

Im sure Winterstone is looking for the expression that looks closer to a 'book' example such as:

H(s)=Vout(s)/Vin(s)=1/(s*R*C+1)

No, sorry - without using any book I could remember that a transfer function H(s) cannot depend on the applied input voltage Vin. Thus, Vin must not appear in the numerator of H(s).

 

[MrAl]

Hello,


Yes, strictly speaking that is correct that is why i said 'book'. If H(s) is interpreted as the output however then we have:

Vout(s)=Vin(s)/(s*R*C+1)

and that is perfectly fine. And before you get in a huff over this last equation, yes, H(s) is usually referred to as the "Transfer Function".

So strictly speaking we have the two forms:
H(s)=1/(s*R*C+1)

and:
Vout(s)=Vin(s)/(s*R*C+1)

and those two are using the variable names that you are most used to seeing in text books.

If you would feel more comfortable with the first form above i can edit my previous post to reflect that.

 

[panic mode]

i wasn't sure what he was looking for, to me it seemed he was asking what is Vin(s)

No, sorry - without using any book I could remember that a transfer function H(s) cannot depend on the applied input voltage Vin. Thus, Vin must not appear in the numerator of H(s).

instead of memorizing things, the best is to derive the function yourselves.

for first order RC low pass filter we can simply use voltage divider rule giving

Vout(s)=Vin(s)*Z2/(Z1+Z2)


transfer function is defined as:

H(s)=Vout(s)/Vin(s)

once you divide Vout with Vin, you are left with something that does not depend on Vin (Vin cancels):


H(s)=Z2/(Z1+Z2)

where

Z1 = R
Z2 = 1/(sC)

etc.

Then you do Bode diagram...

 

[Winterstone]

instead of memorizing things, the best is to derive the function yourselves.
for first order RC low pass filter we can simply use voltage divider rule giving

Vout(s)=Vin(s)*Z2/(Z1+Z2)

transfer function is defined as:

H(s)=Vout(s)/Vin(s)

Panic mode - perfect! That's the way I like to exchange information. Thank you.
W.

 

[MrAl]

Hi,

Yes i was drawing the distinction between having an expression for Vout and one for H too. Strictly speaking the expression for H does not include Vin, when H is interpreted as the 'transfer function'. Most people are used to seeing H(s) as being the transfer function not the output itself that's why Winterstone commented. Variable names are just variable names however and as always the author gets to choose what variable names he/she wants to use The true meaning should be drawn from the context rather than from some predetermined idealized 'book' knowledge.
I'd still be willing to edit my previous post if Winterstone will feel more comfortable with the more common use.

Editing note:
The variable names used to represent certain quantities have more significant meaning to some people than other people so i've modified my original post to reflect the more common usage of the particular symbols usually associated with those quantities.