Question

Let '$V_r$' be the reference voltage and 'n' be the number of bits then the resolution of R-2R ladder network is

• A. $V_r/n$
• B. $V_r / 2^n$
• C. $2V_r/n$
• D. $V_r / 2^n$

Hint:

Resolution is the "step size." Higher bit depth ($n$) means more steps and a smaller, more precise resolution.

Answer 1

The Correct Option is D

The R-2R ladder is a common architecture used in Digital-to-Analog Converters (DACs) because it only requires two precision resistor values ($R$ and $2R$), regardless of the number of bits. 1. Defining Resolution: Resolution in a DAC refers to the smallest possible change in the analog output voltage corresponding to a change of 1 LSB (Least Significant Bit) in the digital input. It determines the "fineness" or precision of the conversion.

2. Mathematical Derivation: The analog output voltage ($V_{out}$) for an $n$-bit DAC is generally given by: $$V_{out} = V_r \times \frac{\text{Digital Input}}{2^n}$$ The smallest step occurs when the digital input changes by 1. Therefore: $$\text{Resolution} = \frac{V_r}{2^n}$$

3. Physical Interpretation: If you have a 3-bit DAC ($n=3$) and a reference voltage of 8V, the resolution is $8 / 2^3 = 8/8 = 1V$. Each binary step increases the output by exactly 1V. As $n$ increases, the denominator $2^n$ grows exponentially, making the steps smaller and the resolution much finer. Note: Options 2 and 4 in the image appear identical ($V_r/2^n$); this is likely a typographical error in the original paper, but the formula itself is correct.