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Understanding Maximum Power Gains and fmax in HF Circuits

This lecture clarifies power gains in HF circuits, including MAG, MSG, and U.MAG concepts, focusing on stability and feedback implications. Learn about maximum available gain and the significance of fmax for oscillator circuits. Explore concepts of inherent stability, maximum stable gain, and unilateral gain calculations.

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Understanding Maximum Power Gains and fmax in HF Circuits

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  1. HF power gains and fmax • LECTURE 19 • Clarification of power gains: MAG, MSG, U

  2. MAG: Maximum Available Gain YS conjugately matched to Yin YL conjugately matched to Yout MAG ρ is real part, and γ is any, of y-, z-, s-, etc

  3. MAG: lower-level equation

  4. MAG: oscillation MAG When MAG > 1, device is active; with appropriate feedback, an output could be maintained with no input – an oscillator. When MAG < 1, device is passive. The frequency at which MAG =1 is the maximum frequency at which oscillation can occur*, and is called fmax. fmaxis determined by extrapolation fromlower frequencies at -20dB/decade. BUT what if the FET is not stable? * with passive feedback

  5. Stability MAG can also be written as: MAG ≡ where k is the stability factor If k<1, the MAG is complex and unrealistic.

  6. Inherent stability MAG > 1 (and real, i.e., k ≥ 1) is needed for an amplifier. But, also, no oscillation is wanted. If both of the above can be obtained, with no external feedback, the device is inherently stable. Maximum Stable Gain If stability can only be obtained by incorporating external feedback and non-conjugately matching terminations, then the Maximum Stable Gain is realized when k=1. MSG MAG

  7. Example of MSG

  8. Unilateral gain When ρ32 = 0 for the transistor and any associated network, the system is unilateralized. In Section 14.4.1 of the text , Zin is computed, for conjugate-matching purposes, by assuming z32 ≈ 0. Obviously falls-off at -20dB/decade. The extrapolated fmax is

  9. Mason’s unilateral gain Quote from S.J. Mason, Trans. IRE, vol. CT-1, 20-25, 1954

  10. Mason’s unilateral gain: results

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