Download review for elec 105 midterm exam #1 (fall 2001)

ELEC 477
Topics in Wireless System Design
Spring 2007
Review Topics for Exam #1
The following is a list of topics that could appear in one form or another on the exam. Not all of
these topics will be covered, and it is possible that an exam problem could cover a detail not
specifically listed here. However, this list has been made as comprehensive as possible.
Electromagnetic spectrum (rough idea of frequency ranges and wavelengths)
- MF, HF, VHF, UHF
- AM, FM, and TV/CATV broadcast services
- microwave region
- millimeter wave region
- usefulness of various parts of spectrum for specific services/purposes
Basic wireless system
- baseband signal
- upconverters (transmitters) and downconverters (receivers)
- the use of radio is a kind of frequency division multiplexing
- transmission lines
- antenna(s)
Decibels
- definition; advantage over using power ratios
- application to power gain vs. voltage gain
- overall gain/loss of a system
- mathematical identities involving logarithms
- dBm, dBW units
- use of dBm (or dBW) vs. dB – absolute vs. relative quantities
Insertion loss (IL) vs. Transducer loss (TL)
- available power (PA) from Thévenin equivalent circuit
- power absorbed by load without 2-port network
- power absorbed by load with 2-port network
Concept of , VSWR, and return loss as measures of impedance match (with or w/o xmsn line)
Pi and T network resistive attenuators
Realistic models of resistors, inductors, and capacitors
- stray (parasitic) resistance, inductance, and capacitance
- behavior of components at high frequencies (above intended freq. range)
- self resonances of inductor/capacitor
- inductors often have troublesome resistance even at low frequencies
- design of inductor for highest possible Q
Skin effect (increased resistance of wires at high frequencies)
Impedance matching methods
- LC networks
- quarter-wave transmission line sections
- transmission line stubs
- “good” match criteria often used: ||2 < 0.1, VSWR < 2, RL < −10 dB
Quarter-wave sections for impedance matching
- Zo = (ZLZin)1/2
- matching bandwidth depends on impedance transformation ratio
1
L networks for impedance matching (a type of LC matching network)
- concepts of “source” (or “generator”) and “load” impedance
- concept of “lumped element”
- underlying concept: series-to-parallel transformations of resistance and reactance
Rp
1
- Rp = Rs(Q2+1) or Q 
Rs
-
for series combination, Q 
Xs
Rs
Rp
for parallel combination, Q 
Xp
individual inductors and capacitors have component Q; Q of inductors is usually lowest
four L network topologies: two for RL > Rg, two for RL < Rg
L
Rin 
for all four topologies
RL C
1
 o2 
for all four topologies if Q is large
LC
matching bandwidth is inversely proportional to Q
matching bandwidth can be increased by using multiple L network stages
rstage = roverall1/n, where n = no. stages, r = impedance transformation ratio
methods for “absorbing” load reactance into matching network
X load X p ,total
o shunt element next to load: X p 
X load  X p ,total
o series element next to load: X s  X s ,total  X load
Impedance matching using pi and T networks
- consists of two back-to-back L networks
- concept of “virtual” resistance Rv:
o Rv < Rg and RL for pi network
o Rv > Rg and RL for T network
- additional degree of freedom (third component) allows designer to (choose one):
o control Q (bandwidth) – one side of network dominates Q
o avoid unreasonable L and C values
- choice of topology
o avoid or allow DC continuity between stages or to ground
o avoid problems with stray reactance
o avoid unreasonable L and C values
o avoid too many inductors (inductors have stray resistance and are susceptible to
mutual coupling)
Transmission lines
- common types of transmission lines (for basic geometries, see Figs. 4.1-2 and 4.1-3)
o coaxial cable
o two-wire line
o microstrip
- difference between transmission line and waveguide (two conductors vs. “pipe”)
2
-
voltage and current waves expressed as solutions of wave equation
~
o total phasor voltage: V x   VI e x  VR e x
~
o total phasor current: I x   I I e x  I R e x
o  
=   j
R   j L 
G   jC 
special case of lossless line
~
o total phasor voltage: V x   VI e  jx  VR e jx
~
o total phasor current: I x   I I e  jx  I R e jx
o
-
R  jLG  jC 
Zo 
o   j  j L C 
-
L
C
phase constant ()
-
phase velocity: v p 
-
characteristic impedance (Zo)
R′, L′, C′, G′ (and therefore vp, l and Zo) depend on geometry and materials
electrical length vs. physical length of transmission lines
1  L
complex reflection coefficient () and VSWR: VSWR 
1  L
o
-
Zo 
c
r
 v.f. c 
1
 o o r
, where v.f. = vel. factor (v.f. = r-1/2)
Z L  jZ o tan(  l )
Z o  jZ L tan(  l )
Y  jYo tan(  l )
- input admittance of terminated lossless line: Yin (l )  Yo L
Yo  jYL tan(  l )
- input impedance of terminated lossy line:
Z  Z o tanh(  l )
Z in (l )  Z o L
Z o  Z L tanh(  l )
- special cases
o properties of electrically-short lines (i.e., l << , which leads to Zin ≈ ZL)
o termination in a short (ZL = 0; line acts as a pure reactance)
o termination in an open (ZL = ; line acts as a pure reactance)
o design of short- or open-circuited line for a given pure reactance
o quarter-wave transformer (l = /4)
o impedances repeat every /2 along line
- wave traps
- loss in Np/m vs. loss in dB/m
- at low microwave frequencies and below, loss in xmsn lines is primarily due to the finite
conductivity (and shallow skin depth) of conductors
Short transmission lines as series inductances or parallel capacitances
- if Zo >> |ZL|tan(l) and tan(l) ≈ l, then Zin(−l) ≈ ZL + jZol, and Leff = lZo /
- if Yo >> |YL|tan(l) and tan(l) ≈ l, then Yin(−l) ≈ YL + jYol, and Ceff = l /Zo
- not effective in canceling shunt inductance or series capacitance
-
input impedance of terminated lossless line: Z in (l )  Z o
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Single-stub impedance matching
- shunt-stub matching (more common)
o place stub at any location where Re{Yin} = Yo = 1/Zo

 r  cos 1  L  , where
o two possible locations every /2: l main 
4
j r
L  L e


o can also use any location n/2 away from those given by formula
2 L
o Bmain  
Yo
2
1  L
-
series-stub matching (less common)
o place stub at any location where Re{Zin} = Zo

 r  cos 1  L
o two possible locations every /2: l main 
4
2 L
o X main  
Zo
2
1  L

-
design of short- and open-circuited stubs to cancel input susceptance Bmain or input
reactance Xmain
o design for Bstub = −Bmain or Xstub = Xmain
X  
 Y 

o short-circuited stub: l stub 
tan 1  stub  
tan 1  o 
2
 Z o  2
 Bstub 
o open-circuited stub: l stub 
-

  Zo  
B 

 
tan 1 
tan 1  stub 
2
 X stub  2
 Yo 
add /2 if formula for lmain or lstub gives a negative length (arises from the 180° ambiguity
with the tan-1 and cos-1 functions)
be able to find VSWR along stub, along line between stub and load, and along line
between source and stub (requires the calculation of different L values at various points)
Relevant coursework, textbook sections, and supplemental material:
Homework:
Labs:
Textbook:
#1-#4
#1-#4 (although little to nothing unique to the labs will be on the exam)
Chap. 1; Chap. 2 (except Sec. 2.14); Chap. 3 (little emphasis on Sec. 3.4);
Chap. 4 (except Sec. 4.16; little emphasis on Secs. 4.3, 4.7, and 4.8). Much of
this is important background material that was not covered explicitly in class.
Supplements: Trade Journal Article on Realistic Resistors, Inductors, and Capacitors
Pi, T, and Broadband Impedance Matching Networks
Single-Stub Impedance Matching (posted soon)
Mathcad:
Realistic Models of Lumped Elements
VSWR Bandwidth of Quarter-Wave Matching Sections
VSWR Bandwidth of L-Shaped LC Matching Networks
Canceling Reactance with Short Transmission Line Sections (posted soon)
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