--- title: "Amplifier vs oscillator in terms of stability factor" subject: "RF and Microwave Engineering" chapter: 6 key: "semester_7/rf_and_microwave_engineering:amplifier-oscillator-stability-factor" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/amplifier-oscillator-stability-factor site: BCT Engineering --- # Amplifier vs oscillator in terms of stability factor RF and Microwave Engineering · Chapter 6: RF Design Practices - Asked in: 2071 Magh, 5 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/amplifier-oscillator-stability-factor - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-6 ## Question Discuss the difference between an amplifier circuit and an oscillator circuit in terms of stability factor. ## Short answer Amplifiers require unconditional stability, K > 1 and |Δ| < 1, with positive port resistances; oscillators need K < 1 and negative resistance. Amplifier terminations are chosen in the stable region, while an oscillator operates in the unstable region and satisfies ΓTΓin = 1 for oscillation. ## Answer An amplifier and an oscillator use the same active device, but they need opposite stability conditions: an amplifier must **never oscillate**, while an oscillator is **deliberately made unstable** at one frequency. Stability is measured by the Rollett factor and Δ: ```text Δ = S11S22 − S12S21 K = (1 − |S11|² − |S22|² + |Δ|²)/(2|S12S21|) ``` | Point | Amplifier | Oscillator | |---|---|---| | Required K | K > 1 (or μ > 1) | K < 1 | | Δ | Magnitude of Δ < 1 | Magnitude of Δ > 1 often helps | | Port reflection | Γin, Γout magnitude < 1 | Γin magnitude > 1 (negative R) | | Input/output R | Positive | Negative at port | | Γs, ΓL choice | In stable region | In unstable region | | Feedback | Avoided/neutralised | Positive feedback added | | Condition | No output without an input signal | Output with no input: ΓT·Γin = 1 | **Amplifier:** if K < 1, stability circles are drawn and Γs, ΓL are chosen in the stable region; resistive loading may be added. The aim is GT with no oscillation at any frequency. **Oscillator:** a transistor with K < 1 is chosen, or made so by adding series/shunt feedback (e.g. inductor in the common terminal). The terminating network ΓT is chosen inside the unstable region so that Rin < 0 and the oscillation condition holds: ```text Rin + RL = 0 and Xin + XL = 0 (start-up: |Rin| > RL, about 3×) ``` So the stability factor is a "design for stability" target in an amplifier and a "design for instability" target in an oscillator. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What stability factor does each circuit need? A. Amplifier K < 1, oscillator K > 1 B. Both need K > 1 C. Amplifier K > 1 (never oscillate), oscillator K < 1 (deliberately unstable) D. Both need K = 1 Answer: C. An amplifier is designed for stability and an oscillator for instability at one frequency. (Key point: Required K) 2. What is true about the port reflection and resistance? A. Oscillator: |Γin| > 1, giving negative input resistance; amplifier: |Γin| < 1, positive resistance B. Amplifier: negative resistance C. Both have |Γin| > 1 D. Oscillator: positive resistance Answer: A. Negative resistance (|Γin| > 1) supplies the energy needed for oscillation. (Key point: Port resistance) 3. Which condition must the oscillator terminating network satisfy? A. Rin + RL = 0 and Xin + XL = 0 (ΓT·Γin = 1), with |Rin| about 3 times RL for start-up B. Rin = RL only C. Xin = 0 only D. Rin + RL > 10 Answer: A. Oscillation needs the total resistance and reactance to cancel, with excess negative resistance for start-up. 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