Reduce T-Network Feedback Resistance

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JasonHathaway
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Homework Statement


Reduce the feedback resistance for the following T-Network
Circuit schematic of an inverting op-amp amplifier with a T-network feedback: input V_IN through R1 to the inverting input, R2 from node X to the node junction, R4 shunt to ground at node Y, R3 feeding back to V_OUT, with the op-amp output labelled V_OUT.


Homework Equations


Basic circuit analysis (Thevenin maybe?)

The Attempt at a Solution


My first though was to use Thevenin, and actually I've found some book used that method:
Textbook excerpt with instructions for Thevenin equivalent at point X-Y, showing equations 3-15 (VTH = VOUT x R4/(R3+R4)) and 3-16 (RTH = R3 || R4), and an inverting op-amp circuit with VIN, R1, R2, RTH and VTH.

Textbook page titled Figure 3-8, Thevenin's Theorem Applied to T Network, showing equations 3-17, 3-18 and 3-19 relating Vout over Vin to resistors R1, R2, R3, R4 and RTH.
 
The Thevenin approach looks fine. Did you have some question about it?
 
Thank you for your quick respond. My question is whether this approach OK or not. And if the feedback resistance can be reduced more.
 
JasonHathaway said:
Thank you for your quick respond. My question is whether this approach OK or not. And if the feedback resistance can be reduced more.
The approach is good, and I doubt that the resistance can be simplified further (other than rearranging it algebraically) without plugging in actual values to reduce it to a number.
 
JasonHathaway said:
Thank you for your quick respond. My question is whether this approach OK or not. And if the feedback resistance can be reduced more.
Typically it is a good idea to get it in the form of

G=NUM/DEN.

in other words, simplify to get rid of R2*R3/R4 in the Numerator
 
As an alternative, you can apply the star-triangle transformation.
After applying this transformation there will be two resistors which do not influence the closed-loop gain (and can be neglected).