I have an assignment problem in my circuits class as follows;

Let us assume we have a DC voltage measured in a circuit, called Vin. We intend to build a circuit such that it has a transfer function defined as

H(s) = Vout(s) / Vin(s)
= (s^2 + s + 1) / s

Draw this electric circuit. The circuit can be composed of resistors, inductors, capacitors and opamps only. Then verify your circuit for any arbitrary DC voltage used instead of Vin by a simulator.

My workings so far;

H(s) could be simplified to = (s^2)/s + s/s + 1/s
= s + 1 + 1/s
= 1/(1/s) + (1/s)/(1/s) + (1/s^2)/(1/s)

I have assumed that Vin will be Vin(s) = 1/s which represents a u(t) step function in time domain - i.e. a DC voltage.

The Vout would therefore be Vout(s) = 1 + 1/s + 1/s^2
The inverse laplace of this would be the following in time domain;
delta(t) + t + 1

I would appreciate any guidance if I am approaching this the right way - and how would I possibly go about finding the circuit for such a function?

 

A circuit that diverges to ∞ for large values of t will be difficult to realize. What makes you think such a circuit is possible?

 

I don't think this is a practical circuit - just more to test theoretical knowledge. The simulation I would think should be over a small time period.

I have progressed through the problem further now. From my previous working,

Vout in time domain = t + 1 + delta(t)
Vin in time domain = u(t)

• t can be obtained using a integrator op-amp circuit with u(t) as the input
• delta(t) I think can be obtained with a differentiator op-amp circuit with a u(t) input
• the 1 output is simply the same as u(t)

So using a summing amplifier could I combine the output of these three circuits all using the same u(t) input in parallel?

 

The transfer function produces an output which is related to proportions of the actual input, the derivative of the input and integral of the input.

A typical application (say) in closed loop feedback control would the classic PID compensator. So there is indeed a practical use.

 

The integrator must be subjected to inputs of opposite sign or its output will diverge.

 

In the case of a PID compensator incorporated in a feedback control system the system error signal applied to the PID input could be of either positive or negative excursion. The integration term is used to null the system steady state error to zero.

 

Hi,

im also trying to solve the same problem for an assignment. Are you planning to use 3 op-amp circuits connected end to end?