Evening gents,

I am supposed to solve the transfer function for the lag-lead network in the figure attached and compare it to the following transfer function,

\(G_{c}(s) = K_{c} \frac{(s + \frac{1}{T_{1}})(s + \frac{1}{T_{2}})}{(s + \frac{\beta}{T_{1}})(s + \frac{1}{\beta T_{2}})}\)

Could someone verify that I solved the transfer function for the following circuit correctly?

Also, it doesn't quite compare to the above transfer function in the sense that it has an additional term in the denominator.

Is this correct?

 

I'm presuming you can expand the denominator in the general form and equate it to the denominator in the specific solution for the given circuit topology. One could then possibly find a set of conditions involving β that would satisfy the equality. One may need two different "β" values rather than one.

 

I'm presuming you can expand the denominator in the general form and equate it to the denominator in the specific solution for the given circuit topology.

This is the part I'm having trouble with. I can't seem to work my expression into the exact form they want.

Is it possible?