--- title: "Bipolar DAC output and 3-bit transfer curve" subject: "Advanced Electronics" chapter: 3 key: "semester_4/advanced_electronics:bipolar-dac-transfer-curve" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/bipolar-dac-transfer-curve site: BCT Engineering --- # Bipolar DAC output and 3-bit transfer curve Advanced Electronics · Chapter 3: Digital-to-Analog and Analog-to-Digital Conversion - Asked in: 2072 Chaitra, 7 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/bipolar-dac-transfer-curve - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-3 ## Question Derive the expression for output voltage in Bipolar type Digital to Analog converter (DAC). Draw the transfer curve for digital input and analog output for 3 bit bipolar type DAC. ## Short answer Vo = Vref(2D/2^n − 1). For 3-bit: D ranges 0–7, Vo steps from −Vref to +0.75 Vref with zero at D=4 (100). Transfer curve is a staircase crossing zero at mid‑code, demonstrating bipolar output. ## Answer A bipolar DAC produces both positive and negative output voltages. It adds a constant offset current equal to half of full scale, with opposite sign, to the current of a normal R-2R DAC. #### Circuit ```text Vref -->[ R-2R ladder ]--I_D----+ | Rf=2R -Vref -----[ 2R ]----I_os------+--/\/\/--+ | | (-)\ | >-------+--> Vo (+)/ GND ``` #### Derivation 1. The R-2R ladder (current mode) sends this current into the virtual ground: ```text I_D = (Vref/R)(b(n−1)/2 + b(n−2)/4 + … + b0/2ⁿ) = (Vref/R) · D/2ⁿ ``` 2. The offset branch from −Vref through 2R gives: ```text I_os = −Vref/(2R) ``` 3. The inverting summer output with Rf = 2R: ```text Vo = −Rf (I_D + I_os) = −2R [ (Vref/R)(D/2ⁿ) − Vref/(2R) ] = −Vref (2D/2ⁿ − 1) ``` Taking the polarity after an output inverter (or reversed references), the standard bipolar (offset binary) result is: ```text Vo = Vref (2D/2ⁿ − 1) = Vref (D − 2ⁿ⁻¹) / 2ⁿ⁻¹ ``` - D = 0 gives −Vref - D = 2ⁿ⁻¹ (MSB only) gives 0 - D = 2ⁿ − 1 gives Vref(1 − 2/2ⁿ) Step size = 2Vref/2ⁿ. #### Transfer curve for 3-bit bipolar DAC (n = 3) Vo = Vref(2D/8 − 1), step = Vref/4. | Input | D | Vo / Vref | |---|---|---| | 000 | 0 | −1.00 | | 001 | 1 | −0.75 | | 010 | 2 | −0.50 | | 011 | 3 | −0.25 | | 100 | 4 | 0 | | 101 | 5 | +0.25 | | 110 | 6 | +0.50 | | 111 | 7 | +0.75 | ```text Vo/Vref +0.75 | +--- +0.50 | +---+ +0.25 | +---+ 0.00 |----------------+---+----------- -0.25 | +---+ -0.50 | +---+ -0.75 | +---+ -1.00 +----+ 000 001 010 011 100 101 110 111 ``` The staircase goes from −Vref at 000 up through zero at 100 to +0.75 Vref at 111. Zero output falls at mid-code, which shows the bipolar nature of the output. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What current is added in a bipolar DAC? A. Ios = -Vref/(2R), half of full scale and opposite sign B. Ios = +Vref/R C. Ios = Vref/(4R) D. Ios = 0 Answer: A. It shifts the output by half full scale. (Key point: Offset current) 2. The standard bipolar output is: A. Vo = Vref D/2^n B. Vo = Vref(2D/2^n - 1) C. Vo = Vref(D + 2^n) D. Vo = -2Vref D Answer: B. From Vo = -Rf(ID + Ios) with Rf = 2R. (Key point: Derived output) 3. For the 3-bit DAC, output at 100 and at 000 are: A. +Vref and 0 B. 0 and +Vref C. 0 and -Vref D. -Vref/2 and -Vref Answer: C. D = 4 gives 0; D = 0 gives -Vref. (Key point: 3-bit values) 4. The step size of a 3-bit bipolar DAC is: A. Vref/8 B. Vref/2 C. 2Vref D. Vref/4 Answer: D. 2Vref/2^n = 2Vref/8 = Vref/4; the top code 111 gives +0.75 Vref. 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