Finding the transfer function...

Discussion in 'Homework Help' started by snowfox, Nov 11, 2007.

  1. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    Hi guys,

    Need some help and input on one of my problems..

    Heres the values for the circuit diagram i posted:

    R1= 100ohms , R2= 125ohms, C1=.002F, C2=.002F

    Question being:

    A) Find the tranfer function H(s)=V(s)/E(s)

    B) Find the poles and zeroes of the transfer function

    ----------------------------------------------------------------------

    Heres what i got so far, but looks incorrect:

    H(s)= V(s)/E(s)

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

    Z1=(R1*C1*s+1)/(C1*s)

    Z2=R2/(R2*C2*s+1)

    therefore,

    H(s)= (R2*C1*s)/((R1*C1*s)(R2*C2*s)+(R2*C2*s)+(R1*C1*s)+1+(R2*C1*s)

    and then i plug in the values i get:

    H(s)=(.25s)/(.1s^2+.95s)

    For some reason this doesn't look like the function in the class examples to get poles and zeroes. Please see if you can figure out my error.. i might be totally on the wrong track.
     
  2. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    for pinnacle~~
    -----------------------------------------------------------------------------------
    for Z1 it is the resistor and capacitor in series right?

    therefore:

    Z1= R1 + (1/C*s)

    and then i get:

    Z1= ((R1*C1*s)+1)/(C1*S) -- when i put Z1 under the same common denominator.

    .. im confused...

    -------------------------------------------------

    u removed ur post pinnacle.. does that mean Z1 is right?
     
  3. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    I think you need to re-examine your expression for Z2. It looks as though the results is incorrect.

    If it were two resistors in parallel (Ra & Rb, for example) the expression would be (Ra*Rb)/(Ra + Rb).

    Your result for Z1 is correct.

    hgmjr
     
  4. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    Yes, thats the equation i used to derive Z2...

    orginally i got:

    Z2= ((R2)*(1/C2*s)) / (R2+(1/C2*s))

    then i simplified it to get---

    Z2= (R2) / (R2*C2*s+1)
     
  5. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    My bad. Your Z2 is correct. I jumped the gun.

    hgmjr
     
  6. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    As far as I can see your result for H(s) is correct also.

    Why do you believe your final answer is suspicious?

    hgmjr
     
  7. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    Just that in all the previous examples the professor showed us in class... the numbers came out to be integers. In this case they are all decimals... and it doesnt.. shall i say -- looks nice..

    my friend is saying there is a case where RC=1.. but that doesnt make sense.
     
  8. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    If it was correct..

    then ...

    zeroes would be

    s=0

    poles would be

    s=0 s=-9.5


    zeroes being the s in the numerator, and poles being the s's in the denominator...i think..


    ???
     
  9. The Electrician

    AAC Fanatic!

    Oct 9, 2007
    2,281
    326
    Your expressions for Z1 and Z2 are correct. Your expression for the numerator after plugging in the values is correct. But, your expression for the denominator after plugging in the values is incorrect. The correct expression is:

    .05*s^2 + .7*s + 1

    So after some prettyfying you should have:

    5*s
    ----------------
    s^2+ 14*s + 20
     
  10. RiJoRI

    Well-Known Member

    Aug 15, 2007
    536
    26
    Remember, the prof is going to use values that work nicely, so he has less of a chance of making some silly mistake, and the students have a better chance of "getting it."

    The homework will be more like the real world, so you can have some realistic practice, and not embarrass yourself (or the school) by asking "Why doesn't this work out as integers?" on your first job. ;)

    --Rich
     
  11. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    i reworked the calculation again.. and same thing... i can not get denominator to match up with yours, electrician....

    the denominator is Z1+Z2 righ?
     
  12. The Electrician

    AAC Fanatic!

    Oct 9, 2007
    2,281
    326
    You've got the denominator; it's:

    ((R1*C1*s)(R2*C2*s)+(R2*C2*s)+(R1*C1*s)+1+(R2*C1*s )

    and if you substitute the numerical values you should get:

    .05*s^2 + .7*s + 1

    rather than:

    (.1s^2+.95s)

    Notice that your result doesn't even have a constant term of 1; why not? Your expression for the denominator has one.
     
  13. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    Sorrie electrician.. yea i was doing this over and over again.. and i couldnt understand where my error came from, until i finally checked the values that i posted, and low and behold yea C2 was suppose to equal = .004F.

    But you did point out i left out the 1.

    With C2=.004, the denominator shuld work out to:

    .1s^2+.95s+1

    after factoring:

    =.1(s+1.202)(s+8.32)

    therefore,

    poles = -s=1.202 and -s=8.32

    if i am correct.

    can you double check my work electrician.
     
  14. The Electrician

    AAC Fanatic!

    Oct 9, 2007
    2,281
    326
    Looks good to me, except you don't have very many accurate digits in your final answer. I get -s = (19 - SQRT(201))/4 = 1.205638 and -s = (19 + SQRT(201))/4 = 8.294362.
     
  15. snowfox

    Thread Starter Member

    Oct 21, 2007
    18
    0
    Thanks man. Exam today. Wish me luck.
     
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