--- title: "Widlar emitter resistance for 10 μA" subject: "Advanced Electronics" chapter: 1 key: "semester_4/advanced_electronics:widlar-emitter-resistance-design" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/widlar-emitter-resistance-design site: BCT Engineering --- # Widlar emitter resistance for 10 μA Advanced Electronics · Chapter 1: Operational Amplifier Circuits - Asked in: 2071 Chaitra, 2+2+3 marks - Video: [Design a 100 μA Widlar Current Source](https://www.youtube.com/watch?v=7stq7MXo59w) — JJHanna - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/widlar-emitter-resistance-design - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-1 ## Question What are the basic requirements for current mirror circuit? Why is the output current of simple current mirror circuit not exactly equal to the input reference current? Determine the emitter resistance, RE for Widlar current source which supplies 10 μA from a reference current of 1 mA. ## Short answer Requirements: matched, same-temperature, equal-VBE, active-region, high-β transistors. IO≠IREF due to finite β, Early effect, mismatch. Using RE = (VT/IO)·ln(IREF/IO) with VT=26mV, IO=10μA, IREF=1mA, RE ≈ 11.97 kΩ. ## Answer #### Basic requirements for a current mirror - **Matched transistors:** Q1 and Q2 must have the same IS (same VBE–IC curve), same β and same Early voltage. This is easy in an IC because both are made in the same process steps, side by side. - **Same temperature:** both transistors must be at the same temperature (close together on one chip), so that VBE changes track each other. - **Equal VBE:** the bases are tied together and the emitters are tied together (or returned to the same rail), so VBE1 = VBE2 and therefore IC2 = IC1. - **Output transistor in the active region:** Q2 must have VCE2 > VCE(sat), i.e. the load must leave enough voltage across Q2. - **High β:** so that the base currents taken from the reference branch are negligible. #### Why the output current is not exactly equal to IREF - **Finite β:** IREF supplies IC1 plus both base currents, so IO = IREF/(1 + 2/β), slightly less than IREF. - **Early effect:** VCE2 is larger than VCE1 = VBE, so IO = IC1(1 + (VCE2 − VBE)/VA), slightly more than IC1 and dependent on the load voltage. - **Mismatch** in IS (area, doping) and temperature between Q1 and Q2. #### Emitter resistance for the Widlar source Given IREF = 1 mA, IO = 10 µA. Take VT = 26 mV (room temperature, about 27 °C) and neglect base currents. ```text +VCC IO (from load) | | R | | IREF | +------+ | | | | C1 | C2 Q1 B----+-------------B Q2 E1 E2 | | | RE | | GND GND ``` ```text VBE1 - VBE2 = IO·RE VT ln(IREF/IS) - VT ln(IO/IS) = IO·RE RE = (VT/IO) · ln(IREF/IO) = (0.026 / 10×10⁻⁶) · ln(1 mA / 10 µA) = 2600 × ln(100) = 2600 × 4.6052 = 11 973 Ω ``` **Answer: RE ≈ 11.97 kΩ (about 12 kΩ).** If VT = 25 mV is used, RE = 2500 × 4.6052 ≈ 11.51 kΩ. A simple mirror would need a resistor of about 1.4 MΩ (for VCC = 15 V) for the same 10 µA. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which formula gives RE of the Widlar source? A. RE = (VT/IO) ln(IREF/IO) B. RE = VT/(IREF − IO) C. RE = (VCC − VBE)/IO D. RE = IREF/IO Answer: A. From VBE1 − VBE2 = IO RE and VBE difference = VT ln(IREF/IO). (Key point: Design formula) 2. For IREF = 1 mA, IO = 10 µA and VT = 26 mV, what is RE? A. About 2.6 kΩ B. About 460 Ω C. About 12 kΩ D. About 26 kΩ Answer: C. RE = 2600 × ln(100) = 2600 × 4.605 ≈ 11.97 kΩ. (Key point: Calculation) 3. Which is NOT a reason why IO differs from IREF in a simple mirror? A. Mismatch of IS and temperature B. The diode-connected Q1 having its collector at the supply C. Early effect D. Finite β Answer: B. The causes are finite β, the Early effect and mismatch. (Key point: Mismatch) 4. About what resistor would a simple mirror need for 10 µA with VCC = 15 V? A. 140 Ω B. 14 kΩ C. 12 kΩ D. 1.4 MΩ Answer: D. R ≈ (15 − 0.7)/10 µA ≈ 1.4 MΩ, which is why the Widlar source is used. 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