Binary-weighted DAC (inverting) output voltage A binary-weighted DAC has a feedback resistor Rf = 12 kΩ. If 50 µA flows through Rf into the op-amp summing junction, what is the output voltage?

Introduction / Context:Many DACs use an inverting summing amplifier. The output voltage is set by the current entering the summing node and the feedback resistor value.

Given Data / Assumptions:

• Rf = 12 kΩ.
• Summing-node current I = 50 µA flowing through Rf.
• Ideal op-amp assumption with virtual ground at the summing node.

Concept / Approach:For an inverting configuration, Vout = −I * Rf. The sign is negative because current into the summing node produces an output that drives the inverting input to virtual ground.

Step-by-Step Solution:Convert units: 50 µA = 50 × 10^−6 A.Compute magnitude: V = I * R = 50 × 10^−6 * 12,000 = 0.6 V.Apply sign: Vout = −0.6 V.

Verification / Alternative check:Dimensional check: amperes × ohms = volts; 50e−6 × 1.2e4 = 0.6 confirms the value.

Why Other Options Are Wrong:0.6 V: wrong sign for inverting mode.±0.1 V: inconsistent with I * R calculation.

Common Pitfalls:Forgetting the negative sign of inverting amplifiers or mixing µA and mA.

Final Answer:–0.6 V