EM2_2001_Mid1.pdf - fiwifi—rflfié‘ a%assfia 10:10...

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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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