Hey everyone, I would like it if someone could clarify whether I am doing the following correctly. Basically I have generated graphs in MATLAB and have changed one parameter at a time from the following formula. It should be noted that this formula is the non linear power density. I will post what all the parameters are but they shouldn't be required for my problem(my problem is generic but I am trying to explain it through this example):

\(
P_N_L = \frac{(2/3)^3.n_s.(\gamma)^2.L_e_f_f . log(\pi^2.B_2.L_e_f_f.B^2)}{\pi.B_2}
\)

So I first changed the value for \(\gamma\) (the fibre non linear parameter) for a range of values and kept all the other parameters the same. The graphs I produced look correct (again i could attach the image but is a slight tangent).

...okay here is my question. I am using another equation which measures the signal to noise ratio (SNR) and the equation is:

\( SNR = \frac{I.exp(-(I^2.P_N_L))}{I(1-exp(-I^2.P_N_L))}\)

So to summarise, \(P_N_L\) changes due to changing one parameter,\(\gamma\) and that alters the \( SNR\). What I want to do is look at the equations to see if my graphs make sense.

Here is my actual question. On the calculator I want to see the effect that \(P_N_L\) has on the \( SNR\) equation. Am I allowed to ignore all the other variables in the equation and put a number for \(P_N_L\), e.g. = 1, see if \( SNR\) increases or decreases and then set \(P_N_L = 2\) and see if it increases or decreases?

Basically i'm just trying to see how one variable effects the formula. Am I allowed to just put the value that changes in the formula and see if it increases or decreases in the next equation?

I hope i explained it well, I don't think I did...

 

You are allowed to try whatever you like, and for sure you get some change,
however, the SNR is calculated putting the PNL as exponent to e

So the graph will be different if you just use PNL.

Or do you mean you don't calculate PNL, but insert for instance {1,2} into the SNR formula? That's permitted yes.

Otherwise please explain what you intend to do write the formula as you would put it.

 

Yes I was including the exponential. So as an example, i was putting \(P_N_L = 1\) and on my calculator I just put \(SNR = \frac{exp(-P_N_L)}{ (1-exp(P_N_L))}\). Then i changed \(P_N_L = 2\). Thus I ignored the other terms in the expression as they were the same value for both times. Does that seem correct?

 

so you mean you want to construct a graph for SNR dependent on PNL, but not to calculate PNL as such, instead you run the SNR equation with a range of values: 1,2,3, etc.

And you don't take care of I as well.

I don't know if the resulting graph will be useful, but for sure you get some dependence on PNL.

Actually I is a constant factor here so you would obtain the result for 1A.
Yes I think the graph still would make some sense if it is only for 1A.
If I = electric current?

Also it would be helpful to know actual ranges of PNL, if this is really 1,2,3 or maybe 0.1, 0.2?

 

Yes I was including the exponential. So as an example, i was putting \(P_N_L = 1\) and on my calculator I just put \(SNR = \frac{exp(-P_N_L)}{ (1-exp(P_N_L))}\). Then i changed \(P_N_L = 2\). Thus I ignored the other terms in the expression as they were the same value for both times. Does that seem correct?

First, why do you keep the negative sign in the exponent in the numerator but not the one in the denominator?

What would your impression be if someone were to ask the similar but slightly different question: I have an expression:

\(
y = \frac{3^x}{1-3^x}
\)

I just want to know how this changes with x. Is it okay if I evaluate it on my calculator using '2' instead of '3'? Or 0.5? Or 1?

In other words, do you think they will get the desired information by using a different base for the exponential terms in the expression?

If the answer is no, then the answer to your question is no, because that is exactly what you are doing.

 

First, why do you keep the negative sign in the exponent in the numerator but not the one in the denominator?

It nullifies out when I remember college right?

 

It nullifies out when I remember college right?

How does it "nullify out"?

 

The negative sign was a mistake, sorry. Im trying yo see whether Pnl increases or decreases and see how that affects the next equation that depends on the prebious one. All I want to do is simplyfy it as much as possible to aviid having to put values in that are the same everytime.

 

Basically i'm just trying to see how one variable effects the formula. Am I allowed to just put the value that changes in the formula and see if it increases or decreases in the next equation?

First of all, I admit I haven't gone over all your math or even read the entire thread. I have only a minute. But, if you want to see how one variable affects an equation, look up the "sensitivity" equation. It involves taking deriviatives. I can't remember it exactly right now, but if you need help, I'll try to help look it up.

 

The negative sign was a mistake, sorry.

Not a problem.

Im trying yo see whether Pnl increases or decreases and see how that affects the next equation that depends on the prebious one. All I want to do is simplyfy it as much as possible to aviid having to put values in that are the same everytime.

So now consider the main question that I asked. It is very relevant to understanding yours.

Also, in general, to see how strongly an equation depends on a particular variable, you take the partial derivative with respect to that variable. This will let you see not only what direction the main equation will change, but by how much for small changes in the variable. I don't know if you have any calculus background yet or not.