download searchable PDF of Circuit Design book - IEEE Global ...

Prohle"" 271
_merit is u=0.08; by (7.126), the ratio of true to maximum unilateral gain is
bounded between 0.86 and 1.18 (not dB). Input, device, and output gains by
(E.5), (E.14), and (E.6) are 1.31,2.92, and 1.94 dB, respectively. Therefore, the
maximum unilateral transducer gain is 6.17 dB, obtainable when r, = Sfl and
r,=S!,. According to (7.126), the actual transducer gain 0T is bounded
between 5.51 and 6.89 dB. The families of circles are shown in Figure 7.23.
Note that the O-dB circles always pass through the chart center. Also, the
centers of all input circles lie on the radial to Sfl' and the same is true for
output circles and S!,. The center of the input O.5-dB circle is 0.44 from the
Smith chart center, and its radius is 0.32.
7.5.4. Summary of Unilateral Scattering Gain. Considerable numerical and
conceptual simplification is available in unilateral amplifier design when the
assumption is valid. The unilateral figure of merit helps make this judgment
and provides bounds on the true value of transducer gain.
The optimal matching conditions are the source and load terminations of
Sf, and S!" respectively. Once device bias has been established. its S'I gain
term is an invariant factor in the unilateral gain formula. Two other factors
represent input and output mismatch. Even less-than-optimal matches can still
produce gain relative to the mismatch between 50 ohms and the input or
output scattering parameters.
The trend toward readily available computers and maximum required
performance reduces the attractiveness of the unilateral design technique.
However, there are certain conceptual advantages to recommend it, at least as
a first step in amplifier design.
Problems
7.1. Program coefficient equations (7.3)-(7.5) on a hand-held or desktop
personal computer. Use the subroutines in Program A2-1 of Appendix
A.
7.2. Verify the values of a;, where i= 1,2,3, in Table 7.1.
7.3. Find the impedance corresponding to reflection coefficient SII =
2.2 (-153° by plotting on a Smith chart and by computation. Assume
that SII is normalized to I ohm.
7.4. Consider the input impedance Zin of the pi network in Figure 7.8. For
Zi= 1+jO ohms, Zin= 1O.315823-j20.242819 ohms.
(a) Find the bilinear coefficients of Z;n as a function of Z;.
(b) Use this bilinear relation to show that Zin = 50 + jO when Zi = j50
ohms.