I have two sample tasks for calculating transfer functions in a circuits with operational amplifiers. I can't find any good source for solving this type of problems apart of this http://cnx.org/content/m0036/latest/, which is helpful a bit. Where to take the reference for measured voltages, and how KVL may be of any use if the circuits are opened (or am I just missing something) ?

Task 1. Phase shifter.

In proper solution I have 3 equations describing this circuit :
U1=(R+1/sC)I2
U1=2RfI2 + U2
U2=-RfI1 + (1/sC)I2

But where do we get this equations from and why ? Why U2 is not equal -U1 just as it is stated on the page from the link ? On what basis do we write the 2 equations for U1 ? Do we somehow transform this circuit ?

Task 2.
Here in solution I have only voltage transfer function given, and there are no currents arrows.

And the voltage transfer function (U2/U1) for this circuit is :

So I've tried solving this on my own :
Current in upper most wire is I3, In the middle I2 and the bottom I1.

U1 = (R3+1/sC)I2 (similar to task 1)
U1 = (R1+R2)I2 + U2 (similar to task 1)
U1 = R4I3 + U2
U2 = no idea here

 

You need to go back to basic op-amps. Even that page you linked is a bit too deep I think.
Doing homework that's well above you doesn't really help, figure out the basics first.

First off, you don't sound very comfortable with circuit theory in general. Hopefully that you can pick up by doing these circuits.

Don't you have a textbook to review?

 

I do but nothing helpful in there. Just these systems don't look like circuits to me, I don't even know where to get the reference points for measured voltages from. And material from the page is pretty basic an clear to me.

 

I'll have to disagree with that if you think U1 should equal -U2 or that the results of that page are directly applicable to your circuits.

 

When the op-amp in the circuit is connected to degenerative feedback, the voltage of the positive input port U- and the voltage of the negative input port U+ are equal approximately.
Do you take this point into consideration?

 

I'm not sure if they're applicable or not. It is just the only useful thing I was able to find.

 

Ok I've found some youtube videos concerning analysis of op amp circuits. Hope this will help.

 

Try looking at textbook previews on Google books, such as this:
http://books.google.ca/books?id=sxmM8RFL99wC&dq=electric+circuits

(click 'preview this book')

You'll get a few pages before it cuts you off. Use the Contents browser at the top and select the chapter 5 on op-amps.

 

That is useful, thanks. Can samebody just tell me the directions of voltages in the second circuit ? I just need to check if I'm thinking right.

 

The additional key to solving such OP-amp circuits is to realize that the amplifier 'attempts' to regulate its output voltage such that the voltages at the input (+) and (-) terminals are equalized.

So one writes and then re-arranges the various equations with the final goal of finding a solution which meets the condition V(+)=V(-). This will lead to a relationship for U2/U1 which is a result of that condition.

In the circuit under consideration (Task 2) R4 will have no effect on the transfer function unless the (assumed) voltage source driving input U1 is non-ideal.