P 6.4-7 Find v_o and i_o for the circuit shown in Figure P 6.4-7. Assume an ideal operational amplifier.

Figure P 6.4-7

First we need to simplify the circuit by replacing the bridge structure with a Thevenin equivalent circuit. So first the effective resistance can be found from redrawing the bridge with the voltage supply deactivated as

So from this drawing we can see we have two sets of a 10 kΩ and a 30 kΩ resistor in parallel and those two are in series. So

So the Thevenin Resistance which is result of adding two 7.5 kΩ resistors in series is

Now we need the open Circuit Voltage across the bridge. The circuit we will consider looks like

So if we find and then

So write out mesh currents

And

Solving for

Solving for

Solving for

So our Thevenin Circuit is

Connecting that into the op-amp circuit and adding some annotations to make solving it easier, we have the circuit

We know immediately

We also know from op-amp rules must be zero as there can be no currents into the inputs of the op-amps. Therefore

Also consider a current junction at

so

By doing a voltage walk from to , we can find

We find from

We find from

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This page last updated on March 15, 2019