---
title: "Current-mode R-2R preference; bipolar DAC"
subject: "Advanced Electronics"
chapter: 3
key: "semester_4/advanced_electronics:current-mode-r2r-bipolar-dac"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/current-mode-r2r-bipolar-dac
site: BCT Engineering
---

# Current-mode R-2R preference; bipolar DAC

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

- Asked in: 2072 Kartik, 2+5 marks
- Video: [R-2R Ladder DAC: Current Switched Network in Digital Electronics](https://www.youtube.com/watch?v=QDhuW9jkx8Y) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/current-mode-r2r-bipolar-dac
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-3

## Question

Why current mode R-2R ladder type DAC is preferred over voltage mode R-2R ladder type DAC? Find expression for output voltage of Bipolar DAC and justify its name.

## Short answer

Current-mode keeps constant node voltages (virtual ground) so stray capacitances don’t slow settling, and Vref sees constant load. Bipolar output: Vo = Vref(2D/2^n −1) with offset binary, giving both positive and negative voltages, hence bipolar.

## Answer

#### Why current-mode R-2R is preferred over voltage-mode R-2R
In the current-mode (inverted) ladder, Vref drives the ladder and each 2R leg is switched between the op-amp virtual ground and true ground. Both are at 0 V.

- **Node voltages never change.** Every ladder node stays at a fixed voltage whatever the input code. Stray capacitances do not charge and discharge, so settling is much faster. In the voltage-mode ladder the node voltages change with each bit.
- **Constant current from Vref.** The reference sees a constant load of R, so it is not disturbed and glitches are smaller.
- **Switches work near ground potential.** Simple MOS switches can be used, with small and equal voltage drops, which gives better accuracy.
- The branch currents are fixed binary-weighted values (I/2, I/4, …) that are simply steered. This suits high-speed IC DACs.

#### Bipolar DAC
A bipolar DAC adds an offset current (half of full scale) of opposite sign to the ladder current. The output then covers both negative and positive values.

```text
 Vref -->[ current-mode R-2R ]--I_D--+
                                     |     Rf
 -Vref ---------[ 2R ]------I_os-----+--/\/\/--+
                                     |         |
                                   (-)\        |
                                       >-------+--> Vo
                                   (+)/
                                    GND
```

**Derivation (4-bit):**

1. The ladder current into the summing node:

```text
I_D = (Vref/R)(b3/2 + b2/4 + b1/8 + b0/16) = (Vref/R)(D/16)
```

2. The offset current from −Vref through 2R:

```text
I_os = −Vref / 2R
```

3. The op-amp gives Vo = −Rf (I_D + I_os). Take Rf = 2R:

```text
Vo = −2R [ (Vref/R)(D/16) − Vref/(2R) ]
   = −Vref (2D/16 − 1)
   = Vref (1 − D/8)
```

For n bits: Vo = −Vref(2D/2ⁿ − 1). A final unity inverter, or swapping the reference signs, gives Vo = Vref(2D/2ⁿ − 1).

| Code | D | Vo = Vref(2D/16 − 1) |
|---|---|---|
| 0000 | 0 | −Vref |
| 1000 | 8 | 0 |
| 1111 | 15 | +0.875 Vref |

#### Justifying the name
The output takes **both polarities**, negative for codes below 1000 and positive above it, with zero at mid-code. Because the output is two-polarity (bipolar), it is called a bipolar DAC. A unipolar DAC gives only 0 to +FS. The code used is offset binary, where the MSB acts as the sign bit.

## Check yourself

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

1. Why does the current-mode ladder settle faster?
   A. It has fewer resistors
   B. It uses a larger Vref
   C. Node voltages never change, so stray capacitances do not charge
   D. It uses a faster clock
   Answer: C. Switches move currents between two 0 V points. (Key point: Constant nodes)

2. What does Vref see in the current-mode ladder?
   A. A load varying with code
   B. An open circuit
   C. A short circuit
   D. A constant load of R
   Answer: D. So the reference is undisturbed and glitches are smaller. (Key point: Reference load)

3. How is a bipolar output obtained?
   A. An offset current of half full scale, of opposite sign, is added to the ladder current
   B. The ladder resistors are doubled
   C. Vref is set to zero
   D. Switches are removed
   Answer: A. Offset current from -Vref via 2R gives Vref/2R opposite to the ladder current. (Key point: Bipolar derivation)

4. Why is it called bipolar?
   A. It uses bipolar transistors
   B. Output takes both negative and positive values with zero at mid-code
   C. It has two op-amps
   D. It has two references of the same sign
   Answer: B. Codes below 1000 are negative and above are positive. (Key point: Name)

5. The bipolar output (final polarity) for n bits is:
   A. Vo = Vref D/2^n
   B. Vo = Vref(D - 2^n)
   C. Vo = Vref(2D/2^n - 1)
   D. Vo = 2Vref D
   Answer: C. From -Rf(ID + Ios) with Rf = 2R and an inversion. (Key point: Output expression)

## Related in Advanced Electronics

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

## 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
- [Zener circuit output voltage and current](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Azener-circuit-120v-5k) — Basic Electrical and Electronics Engineering, chapter 3
- [T/F: ACSR preferred over AAAC](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-acsr-vs-aaac) — Transmission and Distribution System Design, chapter 4
- [Justify higher voltage/more circuits for more power](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ajustify-higher-voltage-more-circuits) — Transmission and Distribution System Design, chapter 2