Transfer Function

[jdd18vm]

Hey guys,

I realize this isn't likely to be a simple answer (well I mean "algebraically" is the answer but wont help), but can someone give me an idea how to get from initial equation for Z(s) to the final form for T(s) in the attached example from the EERM. Hope I'm not violating any copywrite. I think I understand how to write the equivalent s domain equations, and what to do with the roots once in the final as^2+bs+c form.

I need those steps covered by simply "after manipulating mathematically". This is where being out of school 24 yrs hurts.

As always, thanks in advance.

John

 

[benbo]

First, this is probably far more involved math than anything in the AM.

But, here's how I would do it.

First, don't worry about the 5 right off.

On the fraction, the "s" cancels out in the numerator. Then divide both the top and bottom by 2.67, and multiply top and bottom by s.

You will end up with (after rounding a little) = Z(s) = 5 + ((40s)/((s^2)+15))

Now, worry about the 5.

You have to put everything over the same denominator - s^2+15

So, it becomes -

Z(s) = (5*(s^2)+75+40s)/((s^2)+15)

Factor the 5 out of the top and then factor the binomial.

You should get the answer. Let me know if I need to clarify, and keep the questions coming.

You should be very proud to be able to teach yourself electrical engineering. It isn't easy.