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HF power gains and fmax
LECTURE 19
• Clarification of power gains: MAG, MSG, U
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MAG: Maximum Available Gain
YS conjugately matched to Yin
YL conjugately matched to Yout
i1
y12 y21
Yin   y11 
v1
y22  yL
Yout
i2
y12 y21
  y22 
v2
y11  yS
MAG
ρ is real part, and γ is any, of y-, z-, s-, etc
MAG: lower-level equation
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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.
fmax is determined by extrapolation from lower frequencies at -20dB/decade.
BUT what if the FET is not stable?
* with passive feedback
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Stability
MAG can also be written as:
MAG
≡
where k is the stability factor
If k<1, the MAG is complex and unrealistic.
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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.
MAG
MSG
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Example of MSG
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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.
U BC 
gm
 2C gd C gg Rg
Obviously falls-off at -20dB/decade.
The extrapolated fmax is
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Mason’s unilateral gain
Quote from S.J. Mason, Trans. IRE, vol. CT-1, 20-25, 1954
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Mason’s unilateral gain: results