--- title: "Hartley oscillator frequency" subject: "Electronics Devices and Circuit" chapter: 5 key: "semester_3/electronics_devices_and_circuit:hartley-oscillator" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/hartley-oscillator site: BCT Engineering --- # Hartley oscillator frequency Electronics Devices and Circuit · Chapter 5: Signal Generator and Waveform-Shaping Circuits - Asked in: 2083 Baisakh, 3+1 marks; 2079 Bhadra, 6 marks; 2076 Ashwin, 6 marks; 2073 Shrawan, 3 marks (asked 4 times) - Video: [Hartley Oscillator Circuit](https://www.youtube.com/watch?v=3B_sBX_11Zw) — The Organic Chemistry Tutor - 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/hartley-oscillator - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-5 ## Question Draw the circuit diagram of the Hartley Oscillator and write down the expression for its frequency of oscillation. ## Short answer The tank uses tapped inductance (L1, L2) and a capacitor C. Frequency f = 1/[2π√((L1+L2+2M)C)]. Feedback from the tap to base, with common‑emitter phase shift, gives positive feedback. Gain condition hfe ≥ L1/L2. ## Answer The Hartley oscillator is an LC oscillator in which the tank circuit has two inductors (a tapped coil) L1 and L2 and one capacitor C. The feedback signal is taken from the tap between the inductors. #### Circuit diagram (BJT, common emitter) ```text Collector o---+------+ | | [ L1 ] | | [ C ] Ground (tap) o| | | | [ L2 ] | | | Base o---+------+ ``` The tank has C across the series combination of L1 and L2; the junction of L1 and L2 is at ac ground. The transistor is a common-emitter stage with voltage-divider bias, an emitter resistor with bypass capacitor, an RF choke in the collector supply and coupling capacitors. - L1 is between the collector and the tap; L2 is between the tap and the base. The voltage across L2 is fed back to the base. - Because the tap is at ac ground, the collector and base voltages are 180° apart. This 180°, with the 180° shift of the common-emitter stage, gives 360° (positive feedback). #### Frequency of oscillation Total inductance with mutual inductance M between the coils: Leq = L1 + L2 + 2M **f = 1 / (2π √(Leq C)) = 1 / (2π √((L1 + L2 + 2M) C))** For no mutual coupling: f = 1/(2π √((L1 + L2) C)). #### Condition Gain: hfe ≥ L1/L2 (for a BJT amplifier with negligible loading), that is, the loop gain at least unity (Aβ ≥ 1), where β = L2/L1. Hartley oscillators are used for RF generation, and frequency is varied easily by a variable capacitor. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the tank circuit of a Hartley oscillator consist of? A. Two capacitors and one inductor B. Two inductors (tapped coil) and one capacitor C. One inductor and one resistor D. A quartz crystal and one capacitor Answer: B. The Hartley tank has a tapped coil (L1 and L2) with a capacitor C across it, and feedback is taken from the tap. (Key point: Tank of Hartley) 2. With mutual inductance M between the coils, the Hartley frequency is f = 1/(2π√(Leq C)). What is Leq? A. L1 + L2 - 2M B. L1 + L2 + 2M C. L1 L2/(L1 + L2) D. L1 + L2 + M Answer: B. The coils are series-aiding, so Leq = L1 + L2 + 2M; with no coupling it reduces to L1 + L2. (Key point: Frequency expression) 3. How is the 360° loop phase shift obtained in the Hartley oscillator? A. Common-emitter stage gives 180° and the grounded tap gives another 180° between collector and base B. Three RC sections give 180° and the transistor gives 180° C. The crystal supplies 180° and the stage supplies 180° D. The common-emitter stage alone gives 360° Answer: A. The tap is at ac ground, so collector and base voltages are 180° apart; with the CE stage's 180° this gives positive feedback. (Key point: Phase condition) 4. For a BJT Hartley oscillator with negligible loading, what condition on hfe is needed to sustain oscillation? A. hfe ≥ L2/L1 B. hfe ≥ L1/L2 C. hfe ≤ L1/L2 D. hfe = 1 Answer: B. Feedback factor is β = L2/L1, and Aβ ≥ 1 requires hfe ≥ L1/L2. 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