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ECE166 Homework 2 Fall 2010

# ECE166 Homework 2 Fall 2010 - ECE 166 — Microwave...

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Unformatted text preview: ECE 166 — Microwave Circuits and Systems Homework #2— Due Tuesday October 19, 2010 1. Consider a transmission line with length I, Zg=0, Z=inf, and with Vg=u(t). The line is lossless. 3) Calculate and plot the voltage in the middle of the line (point B). b) Redo (a) but assume that the line has a voltage loss of 0.8 (e'“]=0.8). It should converge quickly. :T—e—a———~—-—-° 15 E2 ’Q/I'U‘F: (0:43 we) 29 2. This problem is to give you experience in solving time-domain problems using L and C. Sketch VB and Vc and Vload for each of the cases shown below. Calculate the time constant. Va 3. On a single 50 Q Smith Chart, plot the following impedance points (Smith char! exercises for the mind and spirit). DO NOT USE A CALCULA TOR, only the Smith Chart. ZA = 30+j90 Q . What is TA? What is yA— normalized? Calculate VSWR on the line, Vmax, Vmin. FB = 0.5 4-100". What is 23'? What is yB— normalized? Calculate VSWR on the line, Vmax, Vmin. Zc = 80 —j 10 Q in series with 40 +j60 Q. What is I‘c? What is yc— normalized? 20 which is composed of(100 +j60) in parallel with (60 —j20) Q. What is FD? What is yD— normalized ZF is ZA but with a 0.1257» transmission -line in front of it. What is FF? All the locations for VSWR = 2.0 (what is F?) At least 4 impedances which will result in a VSWR of3 4. On a singie 50 Q Smith Chart, plot the following impedance points (Smith chart exercises for the mind and spirit). All locations for z=2+jx and y=2+jb (the y locations should be on a Z chart!) All locations for z=0.5-jx and y=0.5-jb (the y locations should be on a Z chart!) All locations for z=r+j0.3 and y=g+j0.3 (the y locations should be on a Z chart!) All locations for z=0.6 All locations for z= - 0.5j 5. This problem is to show you the impedance ioci ofreoi components used at microwave ﬁeqnencies. a) Consider a planar inductor with a model given below, and with L=10 nH, Rs=3 Q, Cs=60 fF, Cp=0.4 pF and Rp=300 .Q. Plot the impedance of this inductor from DC to 10 GHz (0.5 GHz steps) on a Smith chart with the inductor in series with 50 Q (port 2 is connected to 50 Q), and with the inductor connected to ground (port 2 is connected to ground). b) Plot in a rectangular plot X = Imag{Zin} from 0.1 to 10 GHz (logarithmic frequency in x-axis), and Q: llmag{Zin}|fRe{Zin} of the inductor when port 2 is grounded. In your opinion, what is the usable frequency of this inductor? Why? c) Plot on a Smith Chart with Zo=500 Q the impedance of a load composed of a 1000 Q resistor in parallel with 50 fF. At what frequency does the 1 k9. resistor stop behaving as a 1 k9? d) Plot the impedance loci on the Smith chart ofa “real” capacitor with C = 6 pF, R5 = 1 9, L5 = 0.25 nI-l (and Ls = 0 nH) from 0.5-6 GHZ in 0.5 GHZ steps. Determine the series resonant frequency of the capacitor with Ls = 0.25 nH. What is the Q at 0.5, 1 and 3 GHz for Ls = 011B and Ls = 0.4 nH? Models: Inductor Capacitor Resistor ‘35 n) ] (I) {2) C R I» Cp L Rs Cp F s I” Cp R Z Z- zin Ftp % % Rp m Ls "' w 6. This problem is to get you more comfortabie with the Smith Chart and how to use series and shunt elements and oiso t—iines sections. On a single 50 Q Smith Chart, ﬁnd and plot the following impedances and ﬁnd their values in normalized values and in Ohms. Also, ﬁnd the reﬂection coefﬁcients at every plane. All non~iabe|ed t—lines have zero electrical length. I, ___________ «P: 0, i253} _)/ £720,5—ﬁqo 29 But-Zn ...
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