---
title: "Non-inverted R-2R ladder DAC output"
subject: "Advanced Electronics"
chapter: 3
key: "semester_4/advanced_electronics:non-inverted-r2r-dac"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/non-inverted-r2r-dac
site: BCT Engineering
---

# Non-inverted R-2R ladder DAC output

Advanced Electronics · Chapter 3: Digital-to-Analog and Analog-to-Digital Conversion

- Asked in: 2074 Chaitra, 7 marks
- Video: [R-2R Ladder DAC Explained (with Solved Example)](https://www.youtube.com/watch?v=Pc1aFloxSMw) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/non-inverted-r2r-dac
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-3

## Question

Derive the expression for output voltage in non-inverted R-2R Ladder Type Digital to Analog converter.

## Short answer

The ladder’s superposition yields each bit contribution: MSB gives Vref/2, next Vref/4, LSB Vref/2^n. Summed, Vo = Vref * D / 2^n, with D the decimal input. Buffer may scale it.

## Answer

A non-inverted (voltage-mode) R-2R ladder DAC is built from only two resistor values, R and 2R. The digital bits switch each 2R leg between Vref (bit = 1) and ground (bit = 0). The output is taken at the MSB end of the ladder and is usually buffered by an op-amp.

#### Circuit (4-bit)
```text
 Vo <--+-----R-----+-----R-----+-----R-----+
       |           |           |           |
       2R          2R          2R          2R      2R
       |           |           |           |       |
      b3(MSB)     b2          b1          b0(LSB) GND
  (each switch: 1 -> Vref, 0 -> GND)
 Vo -> non-inverting buffer -> Vout
```

#### Key property
Looking from any node towards the LSB end, the resistance is **2R**. At the LSB node, its own 2R leg in parallel with the 2R termination gives R, and adding the series R gives 2R. This repeats at every node.

#### Derivation by superposition
Take one bit at a time with the other switches at ground.

1. **MSB (b3) alone.** The rest of the ladder seen from the output node is 2R to ground. The MSB leg 2R and the 2R to ground form a divider: V = Vref/2.
2. **b2 alone.** At node 2, the 2R leg (from Vref) and the 2R ladder section to its right form a Thevenin source of Vref/2 with resistance R. This passes through the series R to the output node, where the 2R MSB leg to ground forms a divider: V = (Vref/2)·2R/(R + R + 2R) = Vref/4.
3. In the same way b1 gives Vref/8 and b0 (LSB) gives Vref/16.

Adding the contributions:

```text
Vo = Vref (b3/2 + b2/4 + b1/8 + b0/16)
   = (Vref / 2⁴)(8·b3 + 4·b2 + 2·b1 + b0)
```

For an n-bit ladder:

```text
Vo = (Vref / 2ⁿ) · Σ bk·2ᵏ   (k = 0 … n−1)
   = Vref · D / 2ⁿ
```

Here D is the decimal value of the input word.

#### Results
- Resolution (1 LSB) = Vref/2ⁿ
- Full-scale output = Vref(2ⁿ − 1)/2ⁿ
- Output impedance of the ladder is always R, so a buffer with gain (1 + Rf/R1) can be added: Vout = (1 + Rf/R1)·Vref·D/2ⁿ.

**Example:** n = 4, Vref = 8 V, D = 1010 (10). Vo = 8 × 10/16 = 5 V.

#### Advantages
- Only two resistor values, so it is easy to trim and to make as an IC.
- The output resistance is constant at R.

**Drawback:** the voltage at each node changes as bits switch, so stray capacitances charge and discharge. This makes it slower than the inverted (current-mode) ladder.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In the non-inverted (voltage-mode) R-2R DAC, each 2R leg is switched to:
   A. Virtual ground or real ground
   B. Vref or -Vref
   C. Vref for bit 1 and ground for bit 0
   D. Open circuit
   Answer: C. The bits set the leg voltage to Vref or 0. (Key point: Switching)

2. The resistance looking toward the LSB end from any node is:
   A. R
   B. R/2
   C. 4R
   D. 2R
   Answer: D. 2R||2R = R plus series R = 2R, repeated at each node. (Key point: Key property)

3. The output due to the MSB alone is:
   A. Vref/2
   B. Vref/4
   C. Vref
   D. Vref/16
   Answer: A. The MSB leg 2R and the 2R to ground divide Vref by two. (Key point: MSB contribution)

4. The output for an n-bit ladder is:
   A. Vo = Vref D x 2^n
   B. Vo = Vref D/2^n
   C. Vo = Vref 2^n/D
   D. Vo = Vref D/(2^n - 1)
   Answer: B. Superposition of Vref/2, Vref/4, ... gives Vref D/2^n. (Key point: Final expression)

5. Why is voltage-mode slower than the inverted ladder?
   A. It has more resistors
   B. It has no buffer
   C. Node voltages change with the bits, charging stray capacitances
   D. Currents are constant
   Answer: C. Charging and discharging of stray capacitance causes delay. (Key point: Drawback)

## Close variants set in other exams

- [Inverted R-2R DAC output and advantages](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverted-r2r-dac-advantages) — Advanced Electronics, chapter 3, asked 4×

## Related in Advanced Electronics

- [4-bit inverted R-2R DAC and why better](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverted-r2r-4bit-better) — Advanced Electronics, chapter 3
- [Design 4-bit R-2R DAC; unipolar vs bipolar](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Adesign-4bit-r2r-unipolar-bipolar) — Advanced Electronics, chapter 3
- [5-bit R-2R DAC output for 10110](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ar2r-5bit-10110) — Advanced Electronics, chapter 3
- [4-bit R-2R ladder bit voltages and 1011 output](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ar2r-4bit-12v-1011) — Advanced Electronics, chapter 3
- [Current-mode R-2R preference; bipolar DAC](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Acurrent-mode-r2r-bipolar-dac) — Advanced Electronics, chapter 3
- [Bipolar DAC output and 3-bit transfer curve](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Abipolar-dac-transfer-curve) — Advanced Electronics, chapter 3

## Related in other subjects

- [R-2R ladder DAC versus weighted resistor](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Ar-2r-ladder-dac) — Instrumentation I, chapter 5
- [Analog and digital system block diagrams; linear and non-linear distortion](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-digital-block-linear-nonlinear-distortion) — Communication Systems, chapter 1