operational amplifier - Solving a two op-amp circuit

We are supposed to find $R$ such that $I_S=0$ and then find the maximum $V_{SRC}$ for operation in the linear region. I tried to use KCL at the nodes but it didn't work out eventually since I got a value of R that is negative. And for the second part of the question how does one determine the maximum possible value in the linear range: I am not sure how to go about this. I would appreciate any help.

Answer

Step by step:

The current, from left to right, through $R$ is

$$I_R = \frac{V_{SRC} - V_{O2}}{R}$$

The current, from left to right, through the left-most 10k resistor is

$$I_{10k} = \frac{V_{SRC}}{10k\Omega}$$

KCL at the input node yields

$$I_S = I_R + I_{10k}$$

Using the well-known inverting op-amp gain formula, the two op-amp cascade has a gain of

$$\frac{V_{O2}}{V_{SRC}} = (-\frac{40k}{10k}) \cdot (-\frac{20k}{10k}) = 8$$

Now, set $I_S = 0$ and solve.

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A rewarding exercise is to solve for the input resistance seen by the input voltage source:

$$R_{IN} = \frac{V_{SRC}}{I_S} = \frac{V_{SRC}}{I_R + I_{10k}} = \frac{1}{\frac{1}{10k\Omega} - \frac{7}{R}}$$

Note that the input resistance is positive for $R > 70k\Omega$, is negative for $R < 70k\Omega$ (the circuit supplies power to the voltage source), and is 'infinite' (open circuit) for $R = 70k\Omega$