--- title: "Band gap reference source and comparison with Zener" subject: "Electronics Devices and Circuit" chapter: 6 key: "semester_3/electronics_devices_and_circuit:bandgap-reference-vs-zener" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/bandgap-reference-vs-zener site: BCT Engineering --- # Band gap reference source and comparison with Zener Electronics Devices and Circuit · Chapter 6: Power Supplies, Breakdown Diodes, and Voltage Regulators - Asked in: 2080 Baisakh, 4+2 marks; 2072 Chaitra, 4+2 marks (asked 2 times) - Video: [Bandgap Reference Introduction](https://www.youtube.com/watch?v=nwxMivPmtuk) — Jordan Edmunds Chetty - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/bandgap-reference-vs-zener - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-6 ## Question Describe the band gap voltage reference source with the help of a relevant circuit. Compare band gap voltage reference source with Zener diode. ## Short answer A bandgap reference adds VBE (CTAT) and scaled VT (PTAT) to produce a temperature-stable voltage ~1.25V. Compared to a Zener, it has lower temperature coefficient, lower noise, works at lower supply voltages, but is more complex, requiring IC implementation. ## Answer #### Band gap voltage reference source A bandgap reference produces a stable dc voltage, about 1.25 V, which is almost independent of temperature, supply voltage and load. It is used in voltage regulators, ADCs, DACs and power supplies (like in the LM317). #### Principle It adds two voltages with opposite temperature coefficients so that they cancel: - **VBE of a transistor** has a negative temperature coefficient (CTAT): about −2 mV/°C. - **The thermal voltage VT = kT/q** has a positive temperature coefficient (PTAT): +0.086 mV/°C (VT = 25.85 mV at 300 K). Vref = VBE + K · VT, where K is a constant set by resistors and the area ratio. #### Circuit ```text +VCC [R3] [R3] | | +--+ +---+ op-amp inputs taken from the | | | | two collectors; its output Vref C1 | C2 | drives both bases Q1 (n x) Q2 (1 x) | B1-----+----B2 <---+--- Vref (op-amp output) E1 E2 [R1] | +---------+ | [R2] | GND ``` The op-amp (polarity chosen for negative feedback) makes the two collector voltages, and so the two collector currents, equal: I1 = I2 = I. Q1 has n times the emitter area of Q2. Both bases are at Vref. Applying KVL: VBE1 + I R1 + 2I R2 = VBE2 + 2I R2, so I R1 = VBE2 − VBE1 = VT ln n (the PTAT current I = VT ln n / R1) The reference voltage is the VBE of Q2 plus the drop across R2 caused by the total current 2I: **Vref = VBE2 + 2 I R2 = VBE2 + 2 (R2/R1) VT ln n** #### Temperature compensation d(Vref)/dT = dVBE/dT + K · dVT/dT = −2 mV/°C + K (0.0862 mV/°C) = 0 K = 2 (R2/R1) ln n = 2/0.0862 ≈ 23.2 Then Vref = VBE + 23.2 × 25.85 mV = 0.65 + 0.60 ≈ **1.25 V** This is about the bandgap voltage of silicon (1.12 eV, extrapolated 1.205 V at 0 K, with the final value near 1.25 V). For example, with n = 8 (ln 8 = 2.08), 2 (R2/R1)(2.08) = 23.2 gives R2/R1 ≈ 5.6. The reference voltage does not depend on temperature to the first order, and the circuit also has good supply rejection because the currents are set by the stable Vref. #### Comparison of bandgap reference and Zener diode | Point | Bandgap reference | Zener diode | |---|---|---| | Reference voltage | About 1.25 V (can be scaled by resistors) | Vz = 2.4 V to 200 V, fixed by the device | | Temperature coefficient | Very small (about 10 to 50 ppm/°C) | Larger (about ±2 mV/°C or more, 100 ppm/°C and above) | | Low-voltage use | Works from supplies of about 1.5 to 2 V | Needs Vin above Vz (at least 5 V or so) | | Noise | Low | High (avalanche noise, above 6 V) | | Bias current | Small, set by the circuit | Needs a few mA to stay in the breakdown | | Output resistance | Very low (with an op-amp) | rz of a few ohms to tens of ohms | | Construction | Part of an IC (transistors, resistors, op-amp) | A single discrete diode | | Cost and size | Integrated, more complex | Simple and cheap | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does a bandgap reference get a voltage that is almost independent of temperature? A. It subtracts two voltages that both rise with temperature B. It adds a VBE (negative temperature coefficient) and a PTAT voltage K*VT (positive coefficient) so the drifts cancel C. It uses a Zener diode biased at 6 V where drift is zero D. It keeps the transistor at a fixed temperature using a heater Answer: B. VBE falls about 2 mV/degC while VT rises, so a suitably scaled sum has zero first-order drift. (Key point: Principle of bandgap) 2. Using dVBE/dT = -2 mV/°C and dVT/dT = +0.0862 mV/°C, what value of K makes Vref independent of temperature, and what is Vref? A. K ≈ 23.2, Vref ≈ 0.65 + 0.60 ≈ 1.25 V B. K ≈ 2, Vref ≈ 0.7 V C. K ≈ 0.043, Vref ≈ 0.65 V D. K ≈ 58, Vref ≈ 2.2 V Answer: A. Setting -2 + K(0.0862) = 0 gives K = 23.2, so Vref = 0.65 V + 23.2 x 25.85 mV = 1.25 V. (Key point: Value of K) 3. Compared with a Zener diode, how does a bandgap reference behave with temperature? A. Larger temperature coefficient B. The same temperature coefficient C. It has no output at high temperature D. Much smaller temperature coefficient (about 10 to 50 ppm/°C) Answer: D. Cancellation of CTAT and PTAT gives low drift; Zener drift is larger. (Key point: Temperature stability) 4. Which comparison about operating supply is correct? A. A Zener works from 1.5 V; a bandgap needs 12 V B. Both need at least 20 V C. A bandgap works from about 1.5 to 2 V; a Zener needs Vin above Vz D. A bandgap needs a supply below 1 V Answer: C. A bandgap gives about 1.25 V and can operate from low supply; a Zener needs input above its Vz. 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