A 3-bit DAC is implemented using ideal opamp and switches as shown in the figure. Each of the switches gets closed when its corresponding digital input is at logic 1. For a digital input of 110, the resistance $R_{in}$ seen from the reference source and the current $I$, are
The given problem involves a 3-bit Digital-to-Analog Converter (DAC) using an op-amp and switches, with input represented as a binary number. The task is to determine the input resistance \(R_{in}\) and the current \(I\) for the digital input "110".
- Identify Binary Digits for the Input "110":
- \(D_2 = 1\)
- \(D_1 = 1\)
- \(D_0 = 0\)
- Connect the Corresponding Resistors:
- \(3 \, \text{k}\Omega\) and \(6 \, \text{k}\Omega\) are connected since \(D_2\) and \(D_1\) are '1'.
- Calculate the Equivalent Resistance:
- Using parallel resistance formula: \(\frac{1}{R_{eq}} = \frac{1}{3} + \frac{1}{6} \, \text{k}\Omega\)
- \(R_{eq} = 2 \, \text{k}\Omega\)
- Determine the Total Current \(I\):
- Using Ohm's law: \(I = \frac{V}{R_{eq}} = \frac{6}{2} = 3 \, \text{mA}\)
- Conclusion:
- The input resistance \(R_{in}\) seen from the reference source is \(2 \, \text{k}\Omega\).
- The current \(I\) is \(3 \, \text{mA}\).
Therefore, the correct answer is
\(R_{in} = 2 \, \text{k}\Omega\) and \(I = 3 \, \text{mA}\)
.
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