GATE 2022 IN – Question 42

Digital Electronics · ADC and DAC · 2 marks · Multiple choice

The resistor-ladder DAC has the switch state shown for its digital input. Its output-node Thevenin voltage $V_{th}$ and resistance $R_{th}$ are ______.

Diagram for GATE 2022 IN question 42

$V_{th}=0.5$ V, $R_{th}=1$ k$\Omega$
$V_{th}=0.5$ V, $R_{th}=2$ k$\Omega$
$V_{th}=1$ V, $R_{th}=1$ k$\Omega$
$V_{th}=1$ V, $R_{th}=2$ k$\Omega$

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Show answer and explanation

Correct answer: (C) $V_{th}=1$ V, $R_{th}=1$ k$\Omega$

Explanation

Only the middle switched branch is connected to 4 V, giving its one-quarter-scale contribution Vth=4/4=1 V. Suppress the source: the left 2k||2k=1k; successively adding 1k then paralleling 2k repeats to give **Rth=1 kΩ** at output.

Thus **C**.