Op amps

[tontod]

Excuse me for posting this, I am stuck on this, figured folks in here might be able to help or give me clues.

I'm taking an EE class after a number of years, and dont remember this material. It is about an output response of an op amp

"A standard inverting amplifier with gain of -10 is designed where the effects of the op amp input and output impedances may be ignored. The op amp has DC gain a0 = 10^5 and two break frequencies which are f1 = 1.5Hz and f1 = 1500Hz. For a unit step input, find the output response of the amplifier in the time domain. (Hint: Use the Laplace transform starting with the two-pole model of the op amp corresponding to the given data.)"

I just dont remember Laplace at all. If anyone can even give me general ideas/hints to proceed, that would be great also, thanks. Feel free to PM me regarding this problem.

Thanks.

 

[Special K]

Do you have a schematic for the circuit in question, or can you describe all the connections?

 

[tontod]

Originally posted by: Special K
Do you have a schematic for the circuit in question, or can you describe all the connections?

Its just a basic standard inverting amp, with the positive terminal grounded and having 2 resistors - a feedback resistor and a resistor connecting the inverting terminal.

 

[Special K]

Originally posted by: tontod

Originally posted by: Special K
Do you have a schematic for the circuit in question, or can you describe all the connections?

Its just a basic standard inverting amp, with the positive terminal grounded and having 2 resistors - a feedback resistor and a resistor connecting the inverting terminal.

I guess I figured if they are giving frequency response data, there must be a capacitor in there somwhere to make it an active filter.

 

[Special K]

Ah wait I think I know how to do it. Give me a few min...

 

[tontod]

Originally posted by: Special K

Originally posted by: tontod

Originally posted by: Special K
Do you have a schematic for the circuit in question, or can you describe all the connections?

Its just a basic standard inverting amp, with the positive terminal grounded and having 2 resistors - a feedback resistor and a resistor connecting the inverting terminal.

I guess I figured if they are giving frequency response data, there must be a capacitor in there somwhere to make it an active filter.

Yeah, you'd think, but I looked again, I dont see any mention of any caps. Thanks for the help. Much appreciated. 🙂

 

[Special K]

Argh I couldn't finish it, I got to the end but I'm not sure of my answer and I don't want to give you a wrong one. I'll let someone who is more sure of what they are talking about respond.

 

[tontod]

Originally posted by: Special K
Argh I couldn't finish it, I got to the end but I'm not sure of my answer and I don't want to give you a wrong one. I'll let someone who is more sure of what they are talking about respond.

Thats ok, its more than what I got. I'll look it over, maybe I'll be able to spot a mistake. Feel free to send it over.

 

[RaynorWolfcastle]

OK, here's how I'd go about it.

First, you need the transfer function of your input in the Laplace domain, that's easy enough, it's X(s) = 1/s with a region of convergence (ROC) Re{s} > 0

Next you you need to determine the transfer funcition of the inverting opamp in the Laplace domain.
Well that's easy enough it'll be H(s) = k/[(s - 1.5)(s-1500)]. To solve k, we know that H(0) = -10 = k/(1.5*1500) -> k = -22,500

So you now have H(s) and X(s), you can solve for Y(s) = X(s)H(s). Y(s) = 1/s * - 22,500/(s-1.5)(2-1500). Now do the inverse Laplace transform on Y(s) using partial fractions and you'll get y(t).

OK, this should give you a very close answer since your alpha is large. I don't really want to think about how you'd get a more accurate answer but you'd have to model your amplifier using a feedback loop using alpha_0 to determine your forward gain. Conceptually, it is the same problem but your H(s) would be messier since you're accounting for the non-ideality of a finite open loop op-amp gain.

I hope this helps you, 🙂

 

[Navid]

I think the two poles they have given you describe the op-amp itself without any components added to it. So, the poles are due to the parasitic capacitances internal to the op-amp.

You need to write down the characteristic of the op-amp alone first. It may help to remember that by replacing s in a Laplace transform with jw, you get the frequency response of the op-amp. Remember to put the poles on the left hand plane. Otherwise, you will have an unstable op-amp!

I have made the assumption that by "break frequency" you mean poles. That would be a downward break on the gain characteristic.

Then, you use control theory and consider 2 resistors one feedback and one from the input to the negative input of the op-amp with a ratio of 10 to give you a gain of 10 (20dB). You started with the open-loop characteristic of the op-amp. So, you will end up with the closed loop characteristic.

Then, you have to work on solving the equation for a unit step, which has a known Laplace transform.