EEE 445 Homework #7 Solutions 4.16 A four-port network has the scattering matrix shown below. (a) Is this network lossless? (b) Is this network reciprocal? (c) What is the return loss into port 1 when all other ports are terminated with matched loads? (d)
TRM Example 1: TEm0 Modes of Partially Loaded RWG
r k0 2 , 0 < x < t kx2 + k y 2 + kz 2 = k 2 = 2 k0 , t < x < a k xa = k0
2 2
0< x<t
k xd = r k0 2 2
At cutoff = 0: k = k xa c
t< x< a
y
b
r 0
0
x
k xd = r kc
t
a
TRM Example 1: TEm0 Modes of Partially L
3.3 Rectangular Waveguide 3.4 Circular Waveguide
To derive results for the TE and TM waves that can be supported by a rectangular waveguide. To derive results for the TE and TM waves that can be supported by a circular waveguide. Traditionally, TM is eas
Electric and Magnetic Fields
Assuming time convention jt e propagation in z-direction
E(r or E ( x, y , z ) = e ( x, y ) +zez ( x, y ) e j z (3.1a) H ( r ) = h ( x, y ) + zhz ( x, y ) e j z (3.1b)
EEE 591/445 Lecture 07 1
and
= e ( ) +zez ( ) e j z ) h
2.7 Lossy Transmission Lines
In practice, all transmission lines have some loss due to imperfect conductors and lossy dielectrics. Of course, we almost always want the loss to be as small as possible. In many situations, where small lengths of line are u
2.4 The Smith Chart
The Smith Chart is a very handy tool for working with impedances on a transmission line. It is so intuitive and useful that modern measurement equipment and simulation software still allow us to display data in the form of a Smith Char
2.1 Lumped circuit model for a transmission line
Chapter 2 Transmission Line Theory
To review transmission line concepts: distributed circuit, transmission line equations and parameters. Definition of Transmission Line
An arrangement of two or more cond
Power absorbed by good conductor
Power
1 Pav = Re E H * nds S0 2 2 1 = Rs H ds S0 2 1 1 Circuitanalogy P = Re cfw_VI = Re ( 2 2
*
(1.94) (1.97),(1.131)
2
Surfaceresistance
1 Z I )I * = R I cfw_ R + jX 2
1 Rs = Re cfw_ = Re (1 + j ) = 2 s 1 (1.114) s =
1.2 Maxwell Equations Maxwells Equations consist of six/four Eqs:
B E= M t D H= +J t D = B =0
(1.1a)
(1.1b)
(1.1c)
(1.1d)
Constituent eqs B = H
D = E
EEE591/445 Lecture 02
(1.2a) (1.2b)
1
Continuity eq
is obtained by taking (1.1b) and using vector identi
Lecture 1 Objectives
Motivate the study of microwave circuit design. Mention some of the aspects of microwave circuit design. Review some of the skills that students should have developed in previous classes (or from work experience).
EEE591/445
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What i
EEE 591/445 Homework 11 6.22. Solution 1. Analytical, using near resonance approximation
0
1 3.14185 1010 rad/sec LC Q 2 (5 109 )(1000)(0.804 1012 ) 25.2584 1 R 2Q jC0 1 j x /0 Let 0 (1 x)
Z in
0
e Z in
R Z 0 x 0.086281 1 (2Qx) 2 1 2QRx m Z in 0 0C0 (1
EEE 445 Homework #8 Solutions 5.1 Design lossless L-section matching networks for the following normalized load impedances: (a) z L 1.5 j 2.0 (c) z L 0.2 j 0.9 (b) z L 0.5 j 0.3 (d) z L 2.0 j 0.3
Solution: Using the Matlab function listed below, we obtain
3.19 Design a stripline transmission line for a 70 characteristic impedance. The ground plane separation is 0.316 cm, and the dielectric constant of the filling material is 2.20. What is the guide wavelength on this transmission line if the frequency is 3
EEE 445 Homework #4 Solutions 3.4 Compute the TE10 mode attenuation, in dB/m, for K-band waveguide operating at f = 20 GHz . The waveguide is made from brass, and is filled with a dielectric material having r = 2.2 and tan = 0.002 . Solution:
a = 1.07 cm
EEE 445 Homework #3 Solutions
2.19 Use the Smith chart to find the following quantities for the transmission line circuit below: (a) The SWR on the line. (b) The reflection coefficient at the load. (c) The load admittance. (d) The input impedance of the l
EEE 445 Homework #2 Solutions 2.2 A transmission line has the following per unit length parameters: L = 0.2 H/m, C = 300 pF/m, R = 5 /m, and G = 0.01 S/m. Calculate the propagation constant and characteristic impedance of this line at 500 MHz. Recalculate
EEE 445 Homework #1 Solutions
1.1 Assume that an infinite sheet of electric surface current density J s J 0 x A/m is placed on the z = 0 plane between free-space for z < 0, and a dielectric with r 0 for
z > 0, as shown below. Find the resulting E and H f
7.6 Coupled Line Directional Couplers
Side-by-side coupler
Realizable in both stripline and microstrip
Over/under coupler
Realizable in stripline only
EEE591/445
Lecture27
Lecture27
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Two-Conductor Transmission Line Concepts
Assume line is lossless:
7.2 T-Junction Power Divider
Overview of T-Junction Power Divider
A simple three-port network that can be implemented in any transmission media, microstrip and waveguide.
Recall that a three-port cannot be simultaneously matched, reciprocal, and lossle
Crystal Resonators, Waveguide Cavity Resonators and Dielectric Resonators Overview of crystal resonators
A crystal resonator consists of a small piece of quartz mounted between two metallic plates. Mechanical oscillations in the crystal are excited throu
5.7 Chebyshev Multi-Section Transformers
Design of multi-section transformers with equal-ripple passband responses. Chebyshev polynomials belong to orthogonal systems, including the Bessel, Legendre, Hermit, Laguerre functions and wavelets. Chebyshev min
5.5 Theory of Small Reflections
Rational
The /4 transformer can match real load impedance with any line impedance The bandwidth is narrow For more bandwidth, multi-section transformer
Review
Single-section transformer Multi-section transformer
EEE591/
5.4 Quarter-Wavelength Transformer
Like L-networks, single-stub and doublestub tuners, a quarter-wavelength transformer provides an inherently narrowband solution. The bandwidth of the solution can be increased through the use of multiple quarter-wavelen
Analytic and ADS solutions
Smith chart is handy, but only for a single frequency or narrow band. Analytic approach provides solutions in a given bandwidth.
Solving quadratic algebraic equation (next page). May convert into a simple program, e.g., Matlab
Transmission Line Stubs
5.2 Single stub tuning, 5.3 Double stub tuning For coax or waveguide, we usually prefer to use SC (short circuited) stubs since OC stubs tend to radiate. For planar transmission media (such as microstrip and stripline), we tend to
Multi-Port Networks
Two-port:
Definition of Port: A pair of terminals that carry equal currents in opposite directions.
EEE591/445 Lecture13
Lecture13
1
Examples of Multi-Port Networks
Two-ports: filters, amplifiers, transistor Three-ports: power divid
3.10 Wave Velocities and Dispersion 3.11 Summary: Power Handling Capacity of Waveguides To learn about the differences between various wave velocities and about dispersion. To learn about the power handling capability of transmission lines and waveguides.