Inverting Op Amp Finding resistor value of voltage divider
The practical thinking engineer would immediately see in this configuration an inverting amplifier with a voltage divider included in the output. Usually R2 &gt;&gt; R3||R4 (i.e., the voltage divider has low output resistance); so the gain is simply -R2/R1 X (R3 + R4)/R3.
The name &quot;T network&quot; is misleading and it prevents understanding. It is much better to think of the circuit as a &quot;twice-disturbed operational amplifier with negative feedback&quot; (here these disturbances are useful). The first &quot;disturbance&quot; is caused by the R1-R2 summing circuit; the second &quot;disturbance&quot; is caused by the R3-R4 voltage divider. The two devices are cascaded attenuators that form the feedback network.
The &quot;golden rule&quot; is: if you take the output after a disturbance, it will be eliminated by the op-amp with excessive voltage before the disturbance; if you take the output before the disturbance, it will be an amplifying output. This trick is used in all the op-amp amplifying circuits with negative feedback to make a follower (inverter) amplify.
According to these explanations, V1 is &quot;undisturbed output&quot;, V2 - &quot;once-disturbed output&quot; and V3 is a &quot;double-disturbed output&quot;:) ... and V1 &lt; V2 &lt; V3.