# Finding the transfer function...

#### snowfox

Joined Oct 21, 2007
18
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

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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.

#### snowfox

Joined Oct 21, 2007
18
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...

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

#### hgmjr

Joined Jan 28, 2005
9,027
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

#### snowfox

Joined Oct 21, 2007
18
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)

#### hgmjr

Joined Jan 28, 2005
9,027

hgmjr

#### hgmjr

Joined Jan 28, 2005
9,027
As far as I can see your result for H(s) is correct also.

hgmjr

#### snowfox

Joined Oct 21, 2007
18
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.

#### snowfox

Joined Oct 21, 2007
18
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..

???

#### The Electrician

Joined Oct 9, 2007
2,936
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

#### RiJoRI

Joined Aug 15, 2007
536
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.
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

#### snowfox

Joined Oct 21, 2007
18
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?

#### The Electrician

Joined Oct 9, 2007
2,936
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.

#### snowfox

Joined Oct 21, 2007
18
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.

#### The Electrician

Joined Oct 9, 2007
2,936
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.