Hi, I am struggling to find the transfer function of the circuit (
https://www.dropbox.com/s/rfmu88nxkairjbm/Capture.PNG?dl=0)
If someone can help or provide a method of finding the transfer function it would be greatly appreciated
The end goal is to find the amplitude and phase response of the filter.
Thank you in advance.
To start with V- = V+ = Vo. Also, might try Y-Delta transform on the two passive networks.
First number the nodes as follows:
The node at the junction of C1, C2 as 1 and name the voltage there as V1
The node at the junction of R1, R3 as 2 and name the voltage there as V2
The node at the junction of +ve input of op-amp as 3 and name the voltage there as V3
Then write KCL equations for those three nodes. You will have 3 equations in 3 unknowns, V1, V2, V3.
Note that the output voltage is equal to V3.
Next, solve those equations by:
re-arranging the first equation for V1 and substituting this expression into the other two equations. This gives you two equations for V2 and V3.
Next:
re-arrange one of those two equations for V2 and substitute this expression for V2 into the other.
Now you have one equation for V3 alone in terms of the component values and the input voltage.
Next, re-arrange the expression you have for V3 in the form V3/Vin = function(all components).
Lastly try to arrange the function into some canonical form of a ratio of two polynomials.
You're done.