--- title: "Design 4-bit R-2R DAC; unipolar vs bipolar" subject: "Advanced Electronics" chapter: 3 key: "semester_4/advanced_electronics:design-4bit-r2r-unipolar-bipolar" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/design-4bit-r2r-unipolar-bipolar site: BCT Engineering --- # Design 4-bit R-2R DAC; unipolar vs bipolar Advanced Electronics · Chapter 3: Digital-to-Analog and Analog-to-Digital Conversion - Asked in: 2070 Asar, 5+2 marks - Video: [DAC (Digital to Analog Converter) | R - 2R ladder for 3 bit BINARY value](https://www.youtube.com/watch?v=8-Vu3NzK2V8) — Tech Blooms - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/design-4bit-r2r-unipolar-bipolar - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-3 ## Question Design a 4 bit voltage mode R-2R ladder type digital to analog converter and derive the expression for its analog output. Also differentiate between unipolar and bipolar DACs. ## Short answer A 4-bit R-2R ladder DAC outputs Vo = Vref (b3/2 + b2/4 + b1/8 + b0/16) = Vref·D/16. Unipolar DAC outputs 0 to +FS (straight binary), while bipolar DAC outputs -FS to +FS using offset binary, requiring an internal offset of half full scale. ## Answer A 4-bit voltage-mode R-2R ladder DAC uses only two resistor values, R and 2R. Each 2R leg is switched to Vref (bit 1) or ground (bit 0). The output is taken from the MSB end through a buffer. #### Design choices - Resistors: R = 10 kΩ, 2R = 20 kΩ (1 % metal film, matched) - Reference: Vref = 5 V - Switches: CMOS analog switches (for example CD4066) controlled by b3 … b0 - Output buffer: op-amp voltage follower (for example 741 or TL081) so the load does not disturb the ladder (ladder output resistance = R = 10 kΩ) ```text Vo<-+---10k---+---10k---+---10k---+ | | | | 20k 20k 20k 20k 20k | | | | | b3 b2 b1 b0 GND (MSB) (LSB) bit=1 -> Vref (5 V), bit=0 -> GND Vo --> (+) op-amp follower --> Vout = Vo ``` #### Derivation of output Looking towards the LSB from any node, the resistance is 2R. So each node splits the current equally, and each bit's effect at the output is half that of the previous bit. By superposition: ```text b3 alone -> Vref/2 b2 alone -> Vref/4 b1 alone -> Vref/8 b0 alone -> Vref/16 Vo = Vref (b3/2 + b2/4 + b1/8 + b0/16) = Vref · D / 16 (D = 8b3 + 4b2 + 2b1 + b0) ``` With Vref = 5 V: - Resolution = 5/16 = 0.3125 V - Full scale (1111) = 5 × 15/16 = 4.6875 V - Example: 1010 gives 5 × 10/16 = 3.125 V For a larger output, use a non-inverting amplifier: Vout = (1 + Rf/R1)·Vref·D/16. #### Unipolar vs bipolar DAC | Point | Unipolar DAC | Bipolar DAC | |---|---|---| | Output range | 0 to +FS (one polarity) | −FS to +FS (both polarities) | | Zero output at | Code 0000 | Mid-code 1000 | | Coding | Straight binary | Offset binary / 2's complement | | Extra circuit | None | Offset current/voltage of ½ FS | | Formula | Vref·D/2ⁿ | Vref(2D/2ⁿ − 1) | | Use | Positive-only signals | AC signals, audio, servo control | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For a 4-bit voltage-mode R-2R DAC: A. Vo = Vref D/8 B. Vo = Vref D x 16 C. Vo = Vref D/16 D. Vo = Vref(2D/16 - 1) Answer: C. Superposition gives Vref/2, /4, /8, /16 per bit. (Key point: Output expression) 2. Why is an op-amp follower used at the output? A. To increase Vref B. To make the output bipolar C. To remove the 2R resistors D. So the load does not disturb the ladder (output resistance R) Answer: D. The ladder has output resistance R, so loading would cause errors. (Key point: Buffer) 3. For Vref = 5 V, input 1010 gives: A. 3.125 V B. 2.5 V C. 4.6875 V D. 6.25 V Answer: A. 5 x 10/16 = 3.125 V. (Key point: Example) 4. Where is zero output for a bipolar DAC? A. At code 0000 B. At mid-code 1000 C. At code 1111 D. It is never zero Answer: B. Bipolar uses offset binary with output Vref(2D/2^n - 1); unipolar zero is at 0000. 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