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Problems 333
For Z=O+jX, find (I) Zin' (2) VL/lin , and (3) IdVin' Assume IL= I
ampere.
8.3. Use ABCD parameters to show that a series impedance (Z) between
two unit inverters is equivalent to a shunt admittance (Y). In particular,
assume that Z=jwoLF; what is the equivalent Y?
8.4. A 12-element lowpass network is composed of six identical subsections,
each as in Figure 4.6 (Chapter Four), with Z = jw and Y = j2w. The
overall network is terminated by I-ohm resistors. Calculate the overall
ABCD matrix, S21' and L= -20 10g1S21I at w=l/fi, I, and fi
radians.
8.5. Derive the C expression in the overall ABCD matrix of an N = 3 ideal
prototype network. Compare your result to Equation (8.11).
8.6. Derive L(w) in Equation (8.14) in terms of the loaded QL values of an
N = 3 ideal prototype network. Compare your result to Equation (8.16).
8.7. A lowpass pi network has an equivalent two-port network that contains
an inverter, as shown below.
n"o'_.-..Y_'Y-,---+
--'A/'-4__Y,_-- __Y...,_~2_....R,
(a) For w= I radian, find expressions for Yo", YI' and Y2.
(b) For RL=I, C,=4, L2=!, and C 3 =3, find Vb' Y" and Yin'
8.8. Suppose that N=3, Qu=QL3=I, Q L2 =2, fo=50 MHz, and 60 dB is
required at 90 MHz using a doubly terminated network. For R 11 = 50
and R 33
= 100 ohms, find the element reactances at fo and the lumpedelement
values using (I) L", L 23 , and R 22 = 150 ohms; (2) L", C 23 , and
R 22 =75 ohms; and (3) C", C 23 , and R 22 :=75 ohms.
8.9. Design a direct-coupled filter that
(a) Uses only Land C components and no traps or end coupling.
(b) Has three resonators, and R 22 = 200 ohms.
(c) Is tuned to 100 MHz.
(d) Provides at least 60-dB attenuation at 150 MHz.
(e) Provides at least 52-dB attenuation at 70 MHz.
(f) Operates between two 50-ohm terminations.
(g) Has minimum midband loss for inductor QUL = 200 and lossless
capacitors.