--- title: "Ebers-Moll model and ac T-model of BJT" subject: "Electronics Devices and Circuit" chapter: 2 key: "semester_3/electronics_devices_and_circuit:ebers-moll-t-model" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/ebers-moll-t-model site: BCT Engineering --- # Ebers-Moll model and ac T-model of BJT Electronics Devices and Circuit · Chapter 2: The Bipolar Junction Transistor - Asked in: 2068 Baisakh, 4 marks; 2071 Shrawan, 2+1+1 marks (asked 2 times) - Video: [Ebers Moll Model of BJT (Basics, Circuit, Current Equations & Working) Explained](https://www.youtube.com/watch?v=ujDaUymXBg0) — Engineering Funda - 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/ebers-moll-t-model - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-2 ## Question Draw Ebers Moll model and ac equivalent T-model for BJT. ## Short answer Ebers-Moll model uses two diodes (DE, DC) and two current sources αFIF and αRIR. AC T-model replaces BJT with resistor re = VT/IE between base and emitter, and a current source α ie from collector to base. Suitable for CB, CC, and CE with RE. ## Answer #### Ebers-Moll model The large-signal model uses two diodes (the emitter-base and collector-base junctions) and two current sources that show the transport of carriers between the junctions. ```text C o---+-----------+ | | ( ) αF·IF DC | IR | | B o---+-----------+ | | ( ) αR·IR DE | IF | | E o---+-----------+ ``` Simplified form: DE (BE diode) carries IF = IES[exp(VBE/VT) - 1] and DC (BC diode) carries IR = ICS[exp(VBC/VT) - 1]. The collector gets αF IF from the emitter diode, and the emitter gets αR IR from the collector diode: ```text IC = αF IF - IR , IE = -(IF - αR IR) , IB = (1-αF) IF + (1-αR) IR ``` #### AC equivalent T-model For small signals in the active region, the model is: ```text C | ( ) α ie (current source) | B -----+ | re (between base and emitter) | E ``` - A resistor **re = VT/IE** (the dynamic resistance of the forward-biased BE junction) is placed between the emitter and the base. - The collector current source is α ie, directed from collector to base (equivalently ic = α ie). - The base current is ib = ie/(β+1) = (1-α) ie. - ro = VA/IC may be added in parallel with the source. This model is best suited to circuits with resistance in the emitter (CB, CC and CE with RE), because re appears directly in the emitter path. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the Ebers-Moll large-signal BJT model consist of? A. One diode and one resistor B. A single voltage-controlled current source gm vpi C. Two diodes (BE and BC junctions) and two current sources for carrier transport D. Two resistors and one current source Answer: C. The model uses a diode for each junction plus two current sources (alphaF IF and alphaR IR) showing transport between the junctions. (Key point: Ebers-Moll structure) 2. In the ac T-model, what is the resistor re between emitter and base? A. re = beta VT/IC B. re = VCC/IE C. re = VT/IE, the dynamic resistance of the forward-biased BE junction D. re = VA/IC Answer: C. re = VT/IE is the small-signal resistance of the forward-biased base-emitter junction. (Key point: Value of re in T-model) 3. What is the collector current source in the T-model? A. gm vpi, from collector to base B. ie/(beta+1) from emitter to ground C. alpha ie, from collector to base (ic = alpha ie) D. beta ib, from base to emitter Answer: C. The T-model has the source alpha ie in the collector branch, so ic = alpha ie. (Key point: T-model current source) 4. The T-model is best suited to which circuits? A. Circuits with resistance in the emitter path, since re appears directly there B. Only circuits with no emitter resistor C. Only switching circuits in cut-off D. Only circuits at dc Answer: A. Because re sits in the emitter path, the model is convenient when RE or emitter-input (CB, CC) circuits are analysed. 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