# Transfer Funtion for a cascade system and sub system

• Sep 6th 2009, 03:14 PM
Geek and Guru
Transfer Funtion for a cascade system and sub system
In PART C I'm stuck ....

I need to find the Trafer funtion for H(s) -> For all the system

C)
H 'sub1' (s) =(1/(1+src))
H 'sub2' (s) =((sL)/(sL+r))
H(s) = ???

d1) ???

d2) ???

Any help will be appreciated ...

http://img186.imageshack.us/img186/6782/exx.th.jpg

http://img195.imageshack.us/img195/3793/exx1.th.jpg
• Sep 6th 2009, 11:01 PM
CaptainBlack
Quote:

Originally Posted by Geek and Guru
In PART C I'm stuck ....

I need to find the Trafer funtion for H(s) -> For all the system

C)
H 'sub1' (s) =(1/(1+src))
H 'sub2' (s) =((sL)/(sL+r))
H(s) = ???

$\displaystyle H(s)=H_2(s)H_1(s)$

CB
• Sep 6th 2009, 11:12 PM
CaptainBlack
Quote:

Originally Posted by Geek and Guru
d1) ???

d2) ???

If the system has transfer function $\displaystyle H(s)$ then the LT of the impulse response is also $\displaystyle H(t).$

To see this you need to know that $\displaystyle \mathcal{L}\delta(t)=1$.

For the time domain problem you need to know that $\displaystyle u'(t)=\delta(t)$ (I think, I usually do these things from first principles).

CB
• Sep 6th 2009, 11:17 PM
Geek and Guru
Thats correct, I solved that part of the problem and yes indeed I multiply those transfer function ... and was a little tricky because Partial Fraction have to be use but mission accomplish in that part ... also d1 and C3

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But !
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In the D2 is when the Apocalypse strike with the first horseman ...
A convolution integral have to be perform that i don't know how to handle.

d2) Find h(t) using h1(t) and h2(t) and using Time Convolution

Thanks CB, kudos for You bro !
• Sep 7th 2009, 05:13 AM
CaptainBlack
Quote:

Originally Posted by Geek and Guru
Thats correct, I solved that part of the problem and yes indeed I multiply those transfer function ... and was a little tricky because Partial Fraction have to be use but mission accomplish in that part ... also d1 and C3

-----
But !
-----

In the D2 is when the Apocalypse strike with the first horseman ...
A convolution integral have to be perform that i don't know how to handle.

d2) Find h(t) using h1(t) and h2(t) and using Time Convolution

Thanks CB, kudos for You bro !

Well $\displaystyle h(t)=h_2(t)*h_1(t)$, which translates into an integral, but to be honest its easier to do in the $\displaystyle s$-domain.

CB