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Femme_physics
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I like Serena said:You can and should go through the minuses, but you should not go against the arrows.
I like Serena said:So why is the loop there?
Did someone tell you it should be there?
C/R = Sum of all the paths / 1- sum of all the loops
Where does the −G1 come from in the denominator?
This was for your basic exercise at that time.
However, I found it's not so simple for this circuit.
I tried to apply it. The result comes close, but is not quite what it should be.
I think you should build up your equations inside out, similar to the process of replacing resistors in series by one resistor, and replacing parallel resistors by one resistor.
Femme_physics said:
We weren't really taught how to do that, we were just told to use the fast path.
That one accounts for the +G1 in the denominator, but not for the −G1.
Well, I'll give you a hint of what I mean.
In your circuit you could replace the loop you just marked, by a block with G11+G1 in it, which is the response function of just that loop with the G1 block in it.
This simplifies the circuit.
Femme_physics said:You're right...
I really respect your methods and don't mind trying them but I have so much to study and relatively short period of time. Should I really try to understand this? I know it may not "sound" difficult but over the internet...u know how things can be.
Femme_physics said:I think I understand. There are two "reductors" (which I believe is the same as voltage sources) therefor your result makes sense. Thanks
Edit: That "IS" why you added that factor, yes?
Femme_physics said:By "reductors" I mean the circly-thingies with the plus and minus signs, like the one that appears right after "R".
Normally they wouldn't, but in this particular circuit they do.
Femme_physics said:Hmm...and how do you know when they do, and when they do not?
Femme_physics said:Also,...
In this case
http://img20.imageshack.us/img20/3033/clarify.jpg
(used a pencil to clarify text)
Should I use a factor of 3 on the routes because I have 3 summing junctions at the beginning?
Femme_physics said:I finally got it, and resolved that exercise and others and got the right result. So just wanted to say a belated thanks! Test is this tuesday :)
And your non-touching loops do not appear to be correct.
If I select the first 2 non-touching loops, I find G1G2H1 x G3H3.
But you have G3G4 after that??
Furthermore there are 4 combinations of 2 non-touching loops, but you have only 2 combinations...
I like Serena said:Looking at you first combination, G1G2H1 is a loop, but G4 is not a loop.
You should use G3G4 instead.
Same thing in your 3rd term.
That's all! You have the signs correct this time round! :)
A transfer function is a mathematical representation of the relationship between the input and output of a system. It is commonly used in control systems and signal processing to analyze and design systems.
To ensure the accuracy of your transfer function, you can compare it with the physical system it represents. This can be done through experiments or simulations. Additionally, you can check for mathematical errors in your derivation or consult with an expert in the field.
Yes, a transfer function can be simplified using various techniques such as pole-zero cancellation, partial fraction expansion, and factoring. Simplifying a transfer function can make it easier to analyze and design the system it represents.
A transfer function is a mathematical representation of a system's input-output relationship, while a frequency response is a plot of the system's output amplitude and phase as a function of frequency. The frequency response can be obtained by substituting complex numbers for the frequency variable in the transfer function.
No, a transfer function is only applicable to linear systems. Nonlinear systems have a more complex relationship between input and output, and therefore require different mathematical models for analysis and design.