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Two-Port Impedance and Power Models 255
where stability factor K is defined by (7.57). The maximally efficient gain is
thus .
G = IY21IY,,1 2 -1 .
ME
2(KIY21/y"l-l)
(7.85)
Kotzebue makes the usual assumption that the sourCe is chosen as the
conjugate of the input impedance with the unique Y L in (7.82) in place; then
the efficiency is the same as the transducer gain. It is helpful to note that
IY21IYu! = !S21/Su!, Since K < 1 precludes obtaining the maximum possible
efficiency, note that the maximally efficient gain is finite for a nonzero
denominator in (7.85). The condition for avoiding an infinite G ME is that
K >1 ~~: 1=1 ~~: I·
(7.86)
Most practical transistors will satisfy (7.86), so that G ME will be finite even
when K< 1.
Program A7-4 for the HP-67/97 hand-held calculator computes the essential
relationships previously given. It also computes the overall stability factor
K':
2(G,+gll)(G L + g22) - Re(Y21Y ,,)
K'= (7.87)
IY21Yu!
Comparison with (7.57) shows that the overall stability factor takes into
account the additional damping effect of the source and load conductances.
These are seen at the ports in Figure 7.10. The overall stability factor is
significant, because bounded source and load admittances may ensure stability
for a transistor that otherwise might be unstable.
•
Example 7.8. Exercise Program A7-4 using the following short-circuit parameters
taken from 4-GHz transistor data:
Y = (10.64E- 3 /82.13" 0.8603E- 3 / - 88.68°).
34.54E-3 / -]6.68° 4.549E-3 /34.64 0 (7.88)
These are input individually into Program A7-4 using key a in the manner
described in Appendix A. In this case, the transistor is only conditionally
stable, since K=0.6317; G ME
= 15.19 dB, and the load and source reflection
coefficients are 0.6869 /16.34° and 0.8532 /71.92 0 , respectively. These reflection
coefficients for the load and SOurce correspond to Y L = 3.786 - j2.771 and
Y, = 2.415 - j 14.399 milJimhos. With these terminations in place, the overall
stability factor (7.87) is K'=2.2237. A model of the transistor employing the
conjugate terminations is useful for developing matching networks. This is
shown in Figure 7.16. The conjugate of the source impedance is 11.35 - j67.68
ohms; the model's series input representation is based on the impedance at 4
GHz. Similarly, the conjugate of the load impedance is 264.1311-j360.95