How to Design a Circuit from a Given Transfer Function?

[Lancelot59]

I'm given the following transfer function:
$$T(s)=\frac{50000s}{(s+50)(s+1000)}$$
and I need to constuct a circuit from it using opamps, resistors, capacitors, and inductors. Capacitors must be 100nF.

I'm not quite sure how to start here. I managed to get a time domain version of the transfer function:
$$T(t)=\frac{-50000}{19}e^{-50t}+\frac{100000}{19}e^{-1000t}$$

The problem is I have no idea how to get started. I know that the time function looks like a capacitor discharging, however I don't know how to start going about turning this function into a circuit.

 

[gneill]

You should familiarize yourself with the transfer functions of the simple RC filters (low pass and high pass).

hint: An op-amp can be used as a buffer between filter stages (keeps them from interfering with each others corner frequencies and gains).

 

[Lancelot59]

You should familiarize yourself with the transfer functions of the simple RC filters (low pass and high pass).

hint: An op-amp can be used as a buffer between filter stages (keeps them from interfering with each others corner frequencies and gains).

Ah, I see. So I can separate it into two systems with the following characteristics:

$$H_{1}=\frac{50000}{s+50} H_{2}=\frac{s}{s+1000}$$

and buffer them together?

 

[gneill]

Ah, I see. So I can separate it into two systems with the following characteristics:

$$H_{1}=\frac{50000}{s+50} H_{2}=\frac{s}{s+1000}$$

and buffer them together?

Yes, you could.

 

[Lancelot59]

Or I could interchange the numerators. Either way this puts me on a better track, I'll see what I can come up with.

 

[Lancelot59]

I managed to solve it! Thanks for pointing me in the right direction.