An ideal operational amplifier supplied from ± 12.0 V (saturation at the rails) is…

An ideal operational amplifier supplied from \(\pm 12.0\,\mathrm{V}\) (saturation at the rails) is connected as a transimpedance (current-to-voltage) stage. The noninverting input is grounded. An independent current source \(i_s=75.0\,\mu\mathrm{A}\) is connected between the inverting input and ground with the source arrow pointing toward ground, so that \(75.0\,\mu\mathrm{A}\) leaves the inverting node into the current source. Feedback is provided by \(R_f=80.0\,\mathrm{k}\Omega\) from the output to the inverting input. A load \(R_L=2.00\,\mathrm{k}\Omega\) is connected from the output to ground. In the linear region the input currents are zero and \(v_+=v_-\). Practical constraints: the transimpedance \(v_o/i_s\) must equal \(-R_f\) only while the device is linear; the pin-current limit is \(12.0\,\mathrm{mA}\). (a) Determine \(v_o\) and the current in \(R_f\). (b) Determine the current in \(R_L\) and the current leaving the output pin. (c) Decide whether the output is inside the rails and whether the pin-current limit is respected. (d) Determine the largest \(|i_s|\) for which the linear model remains valid with the given \(R_f\), considering only the voltage rails (ignore the pin-current limit in this part).

A transimpedance stage converts the current that the virtual earth must absorb (or supply) into \(v_o=\pm R_f i\); the sign follows the stated arrow.