Finding poles and zeros from TransferFunction

[ammu1]

Hi,
I have a Transfer function like this


V_s/J_s=[g_ds2 g_ds3 (-((-g_ds2 + g_m2)/g_ds3) + ((-s c_x - g_ds1 - g_ds2 + g_m2) (s c_y + g_ds2 + g_ds3 -g_m3))/(g_ds2 g_ds3)) ]/
[-g_ds2 (s C_L + g_ds3 + g_L) (-g_ds2 + g_m2) - (-s c_x - g_ds1 - g_ds2 + g_m2) (-(s C_L + g_ds3 + g_L) (s c_y + g_ds2 + g_ds3 - g_m3) - g_ds3 (-g_ds3 + g_m3))]

By using above Transfer function how to plot bode diagram and how to find pole and zeros .


Give me some suggestions !


Thanks

 

[barry]

That equation is next to impossible to read. Are all those "s"'s Laplacian "s" or something else? We have no idea what a term like "g_ds2_g_ds3" means. Maybe you can simplify that and repost it.

You understand that ZEROES are values of s where the transfer function=0, and POLES are where the TF goes to infinity, right?

 

[ammu1]

Hi,

By using MATHEMATICA Tool i find pole and zeros but it giving very big equations.

Is there any method to find pole zeros from the transfer function. I tried with different methods but am not understanding the results .
Please any one tell the method to find pole zeros .

Thanks

 

[LvW]

Is there any method to find pole zeros from the transfer function. I tried with different methods but am not understanding the results .
Please any one tell the method to find pole zeros .
Thanks

I know one method only:
*Zeros: Set the numerator equal to zero and solve for s
*Poles: Set the denominator equal to zero and solve for s

 

[ammu1]

Ya i tried like that only but its very difficult to find in my case.

So am searching for any other method is available.

Any suggestions ?


Thanks

 

[engrMunna]

Ya i tried like that only but its very difficult to find in my case.

So am searching for any other method is available.

Any suggestions ?


Thanks

Use matlab, You can use h = tf( [num],[den]) to get your transfer function. for eg h = tf( [1] , [1 0]) gives you h = 1 / s.
then use pzplot(h) ..it will give you a plot of your poles and zeros.

---------- Post added at 13:50 ---------- Previous post was at 13:43 ----------

**broken link removed**

See the above link on how to form a Transfer Function using tf ( )

 

[ammu1]

Hi, Thank u for reply and suggestions.
But the below command is gives the transfer function when u know the coefficients.
h = tf( [1] , [1 0])

I have transfer function like this
V_s/J_s=[g_ds2 g_ds3 (-((-g_ds2 + g_m2)/g_ds3) + ((-s c_x - g_ds1 - g_ds2 + g_m2) (s c_y + g_ds2 + g_ds3 -g_m3))/(g_ds2 g_ds3)) ]/
[-g_ds2 (s C_L + g_ds3 + g_L) (-g_ds2 + g_m2) - (-s c_x - g_ds1 - g_ds2 + g_m2) (-(s C_L + g_ds3 + g_L) (s c_y + g_ds2 + g_ds3 - g_m3) - g_ds3 (-g_ds3 + g_m3))]

from this i need to find pole and zeros.
If i give this command in matlab iam getting error
h = tf( [g_ds2* g_ds3 *(-((-g_ds2 + g_m2)/g_ds3) + ((-s *c_x - g_ds1 - g_ds2 + g_m2)* (s *c_y + g_ds2 + g_ds3 -g_m3))/(g_ds2* g_ds3))],[-g_ds2 *(s* C_L + g_ds3 + g_L) (-g_ds2 + g_m2) - (-s* c_x - g_ds1 - g_ds2 + g_m2)* (-(s* C_L + g_ds3 + g_L) *(s *c_y + g_ds2 + g_ds3 - g_m3) - g_ds3 (-g_ds3 + g_m3))])
**Undefined function or variable 's'.**

Please help me.

Thanks

 

[barry]

I think you need to simplify your transfer function. No offense, but what you have there is a mess. You've got underscores and capital letters and lowercase letters and spaces and parentheses and brackets. No wonder you can't figure this out. If those things like "g_ds2 g_ds3" are supposed be a single constant, then just use a single letter.

 

[ammu1]

HI barry sorry for inconvenience.
Actually my circuit is like below

By using small signal model i find the equations and after solving iam getting the output impedance. Finally iam getting the numerator and denominator shown as below

Num= g_ds2 g_ds3 (-((-g_ds2 + g_m2)/g_ds3) + ((-s c_x - g_ds1 - g_ds2 + g_m2) (s c_y + g_ds2 + g_ds3 _g_m3))/(g_ds2 g_ds3))
Den=-g_ds2 (s c_L + g_ds3 + g_L) (-g_ds2 + g_m2) - (-s c_x - g_ds1 - g_ds2 + g_m2) (-(s c_L + g_ds3 + g_L) (s c_y + g_ds2 + g_ds3 - g_m3) - g_ds3 (-g_ds3 + g_m3))

Now i want to find pole zeros from above symbolic expressions.

Please suggest something

Thanks

 

[LvW]

Ammu1, certainly one of the symbolic simulation programs can do the job.
For example, for similar tasks I have used the following software:

* Xfunc (**broken link removed**)
* Vissim (Vissim.com).

However, in both cases, it is - of course - necessary to rewrite your transfer function using the program-specific terms and notations.

I should add the information that both programs are free of charge (VISSIM as evaluation version)

 

[_Eduardo_]

........
By using small signal model i find the equations and after solving iam getting the output impedance. Finally iam getting the numerator and denominator shown as below

Num= g_ds2 g_ds3 (-((-g_ds2 + g_m2)/g_ds3) + ((-s c_x - g_ds1 - g_ds2 + g_m2) (s c_y + g_ds2 + g_ds3 _g_m3))/(g_ds2 g_ds3))
Den=-g_ds2 (s c_L + g_ds3 + g_L) (-g_ds2 + g_m2) - (-s c_x - g_ds1 - g_ds2 + g_m2) (-(s c_L + g_ds3 + g_L) (s c_y + g_ds2 + g_ds3 - g_m3) - g_ds3 (-g_ds3 + g_m3))

Now i want to find pole zeros from above symbolic expressions.

Num and Den are equivalents to:
Num(s) = a2 s^2 + a1 s + a0
Den(s) = b3 s^3 + b2 s^2 + b1 s + b0

By hand (or by symbolic software) you can easily find a symbolic expression for zeros (Num(s) = 0) because is a 2nd order equation.

But Den(s) is a 3rd grade polynomial --> the symbolic expression of the poles isn't compact as function of b3,b2,b1,b0 , and of course, as function of g_ds1,g_ds2....... is a useless nightmare.

Then, evaluate a0,a1...b0,b1... and continue with Bode plot, poles and zeros, whatever you want.