--- title: "Series regulator circuit and stability factor" subject: "Electronics Devices and Circuit" chapter: 6 key: "semester_3/electronics_devices_and_circuit:series-regulator-stability-factor" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/series-regulator-stability-factor site: BCT Engineering --- # Series regulator circuit and stability factor Electronics Devices and Circuit · Chapter 6: Power Supplies, Breakdown Diodes, and Voltage Regulators - Asked in: 2081 Bhadra, 2+4 marks; 2080 Bhadra, 2+6 marks; 2079 Bhadra, 4 marks; 2078 Kartik, 6 marks; 2076 Chaitra, 5 marks; 2075 Chaitra, 6 marks; 2074 Ashwin, 6 marks; 2073 Shrawan, 4+4 marks; 2069 Chaitra, 6 marks; 2068 Baisakh, 6 marks; 2071 Chaitra, 7 marks; 2070 Chaitra, 5 marks (asked 12 times) - Video: [DC Power Supply : Transistorised series voltage regulator](https://www.youtube.com/watch?v=xNxpF1Lvw94) — ELECTRONICS BY PITALE SIR - 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/series-regulator-stability-factor - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-6 ## Question Draw the series DC voltage regulator circuit and find its stability factor. ## Short answer The circuit uses a pass transistor in series with the load, an error amplifier, and a Zener reference with a voltage divider R1-R2. Its stability factor S = ΔVo/ΔVi ≈ (1 + R1/R2)·rz/(R + rz), where rz is Zener dynamic resistance and R is the bias resistor. ## Answer A series regulator keeps the output dc voltage constant when the input voltage or the load changes. The control element (pass transistor) is in series with the load, and an error amplifier compares a sample of the output with a Zener reference. #### Circuit diagram ```text Vi o----+-------------------+ | | C [R] B +----| Q1 (pass) | | | E +--------------+ +------+---------+-----o Vo | | | | C [R1] [RL] Q2 |--B------------------+ | | | E | | GND | +----+ (Dz) Vz | | [R2] | | GND GND ``` Connections: Q1's collector goes to Vi and its emitter to Vo (an emitter-follower pass element). R, from Vi, supplies the base current of Q1 and the collector current of Q2. Q2's collector is connected to the base of Q1, its emitter is held at Vz by the Zener Dz, and its base is connected to the mid-point of the divider R1-R2 across Vo. #### Operation If Vo tends to rise, the base of Q2 rises, so Q2 conducts more and diverts current away from the base of Q1. Q1 conducts less, and Vo falls back. The opposite happens when Vo falls. #### Output voltage VB2 = Vo R2/(R1 + R2) = Vz + VBE2 **Vo = (Vz + VBE2)(1 + R1/R2)** #### Stability factor (line regulation factor) The stability factor S = ΔVo/ΔVi tells how much the output changes for a change in input. Vo depends only on Vz and VBE2. When Vi changes, the base of Q1 stays at about Vo + VBE1, so the current in R changes by about ΔVi/R. This extra current flows through Q2 into the Zener, and its dynamic resistance rz turns it into a change in Vz: ΔVz ≈ ΔVi · rz/(R + rz) ≈ ΔVi · rz/R Taking VBE2 as constant (it changes only with temperature, by about −2 mV/°C): ΔVo = (1 + R1/R2) ΔVz **S = ΔVo/ΔVi ≈ (1 + R1/R2) · rz/(R + rz)** Because rz is small (a few ohms to tens of ohms) compared with R (hundreds of ohms to kΩ), S is very small. For example, rz = 10 Ω, R = 1 kΩ and R1 = R2 give S = 2 × 10/1010 = 0.0198, about 2 % (20 mV per volt of input change). The regulation is improved by feeding the Zener from the regulated output, or by using a constant-current source in place of R. For the simple Zener-follower series regulator (Vo = Vz − VBE), S = ΔVo/ΔVi ≈ rz/(R + rz). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. If Vo tends to rise, what happens? A. Q2 conducts more, diverting base current from Q1, so Q1 conducts less and Vo falls B. Q1 conducts more C. Zener turns off D. Q2 turns off Answer: A. The error amplifier action reduces Q1 drive to restore Vo. (Key point: Operation) 2. What is the output voltage? A. (Vz + VBE2)(1 + R1/R2) B. Vz - VBE C. (Vz + VBE2) R2/(R1 + R2) D. Vz(1 + R2/R1) Answer: A. VB2 = Vo R2/(R1 + R2) = Vz + VBE2. (Key point: Output voltage) 3. What is the stability factor S? A. (1 + R1/R2) rz/(R + rz) B. (1 + R2/R1) R/(R + rz) C. rz R D. (R1/R2) R/rz Answer: A. ΔVz = ΔVi rz/(R + rz) and ΔVo = (1 + R1/R2)ΔVz. (Key point: Stability factor) 4. rz = 10 Ω, R = 1 kΩ, R1 = R2. What is S? A. 0.0198 B. 0.198 C. 0.0099 D. 0.02 V Answer: A. S = 2 x 10/1010 = 0.0198. 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