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**Unformatted text preview: **ﬁwiﬁ—rﬂﬁé‘% a : %assﬁa 10:10 - 12:10 a mo ﬁiﬁ ° ﬁﬁﬁﬂﬁﬂﬁdﬂﬂﬁiﬁﬁﬁﬁf’ﬁﬁ ’ ﬁﬁﬁ
ﬁg . Liaseeaazneamaaae ., l) (10%) A ﬁlamentary wire carrying current I is closely
wound around a toroidal magnetic core of rectangular
cross section, as shown in Fig.1. The mean radius of the
toroidal core is a and the number of turns per unit length
along the mean circumference of the toroidal is N. Find
(a) the magnetic ﬁeld intensity in the core and (b) the
inductance of the toroid. Assume that b< <0. 2) (10%) Consider a wire of radius a=0.5mm in a height d=5mm
over a ground plane in the air as shown in Fig.2. Find the
per-unit-length capacitance, inductance, and the characteristic
impedance of the wire. Note that the per-unit—length
capacitance between two parallel cylindrical wires of radius a
and center-tc-center separation 2:! can be given by C=7reo/cosh (d/a) where cosh x: 1113+sz —- 1) 3) (15%) In a system shown" in Fig.3(a), the network N
consists of a single circuit element (R, L, or C). The
system is initially uncharged. The switch S is closed at
t=0, and the line voltage at 2:0 is observed to be as
shown in Fig.3(b). (a) Determine whether the circuit element is R, L, or C.
(in) Find the value onoy’Zm. ‘(c) Find an expression for the value of the circuit element
in terms of the area of the shaded region shown in the
ﬁgure, 29;, the reﬂection coefficient, and V0. 4) (15%) In Fig.4, a (+) wave carrying power P is incident
on the junction a—a’ from line 1. Find (a) the power-
reﬂected into line I; (b) the power transmitted into line 2;
and (c) the power transmitted into line 3. S) (20%) In the system shown in Fig.5, the switch is
closed at 1:0. Assume ng to be a direct voltage of
100V. (a) Draw the voltage bounce diagram. (b) Sketch the line voltage versus 1 (up to t=5us) at 2:312 40 '0 Z. = 6012.
(c) What is the line voltage at FE/Z as 1‘ tends to inﬁnity 1’00? T= [/19
(d) Sketch the line voltage versus 2 at t: I. 51.15. 6) (15%) Consider a typical CMOS buﬂ'er driver
circuit to a 5052 transmission line. A simpliﬁed
equivalent circuit for a high-to—low transition
can be represented by Fig.6(a) where R=OQ m I I 3’ (a) Plot the output voltage waveform Vgﬂ) versus
time (up to t=6us). Note that the transmission
line is originally charged up to V=3.8V for
KO. (b) Consider a voltage clamper D as shown in
Fig.6(b) is connected to the output port. The
diode D is clamped to —O.2V and having the 3’
VJ characteristics shown in Fig.6(c). Repeat Fig.6(b)
(a) and compare the results with those
obtained in (a). Discuss how the diode can Fig6(c)
improve the transition characteristics. (c) Another way is to add a series resistor at the source end, say R=40§2 in Fig.6(a). Repeat (a)
and compare the results with those obtained in (3). Discuss how the series resistance can
improve the transition characteristics. 7) (15%) Consider coupled transmission lines of length {=40cm as shown in Fig.7, for which the
mutual capacitance 0.20. 1C and mutual inductance L,,=0.15L where C and L are self
capacitance and self inductance, respectively, of the two isolated transmission lines. Let C and L
be such that the two transmission lines have characteristic impedance 20:50.0 and propagation
speed vp=20 cm/nsec. The line I is excited by a source voitage which is a ramped pulse of 2V
and with rise time tr=1 nsec, i.e., V36) =2 M, for Kr, and Vgﬁ) =2 for t > 1,. Find and sketch (8)
V2(z=0, r) and (b) was) when the iength oflines is e=40ch(c) Also discuss how the pulse
width and pulse height will change ifthe transmission lines are short lines, say £=5cm. 8) (15%) A section of transmission line can serve as a signal generator. Consider the circuit shown
in Fig.8. The switch S is closed to the shorted circuit at r=0.
(a)Sketch the line voltage versus time at z=£
(b)Design the length to give a periodic signal of frequency lGHz.
(c) Sketch the line voltage along the transmission line at I = if}; . '5' Ltd. Fig.7 Fig.8 ...

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- Fall '08