The Terminated Lossless Line
EE 432 Lecture 5
IL
V (z) I(z)
Z ,
0
+
VL
_
ZL
z
0
Lecture 5 Page 1
Reflection Coefficient
EE 432 Lecture 5
Reflection coefficient is the ratio of the reflected wave to the incident wave:
Lecture 5 Page 2
Reflection Coefficien
Introduction to RF and Microwave Design
1
2
-2.5 dB
+18 dB
3
4
5
6
-9 dB
-3 dB
-2 dB
7
+13.5 dB
8
-9 dB
-1 dB
30 450
MHz
BPF
SP6T
SP6T
I
R
BPF
1 st LO Synthesizer
1960 2360 MHz
1 MHz steps
12
13
14
15
Anti-Alias LPF
+25 dB
-3.5 dB
-6 dB
R
-3 dB
I
-1 dB
LP
Communication over a Distance
EE 432 Lecture 3
Morse Telegraph
Early Radio:
American Morse Code (original Railroad Telegrapher's code)
Lecture 3 Page 1
Wireless Development
EE 432 Lecture 3
Cellular systems are deliberately designed so that adjacent cells
Transmission-Line Stubs
EE 432 Lecture 9
Purely reactive loads can be synthesized with lengths of
transmission line:
Z1
SHORTCIRCUITED
STUB
Lecture 9 Page 1
Z2
OPENCIRCUITED
STUB
Shorted Stubs
EE 432 Lecture 9
Use a length of shorted 100 transmission line
The Smith Chart
EE 432 Lecture 8
Philip Smith, 1939, Bell Labs
Polar Reflection Coefficient
Magnitude is distance from the chart center
Angle is measured around the circumference
Development:
Lecture 8 Page 1
The Normalized-Impedance Smith Chart
z = r + j
Distributed Matching Techniques
Although short lengths of open or shorted transmission lines
may be used in a matching network to replace capacitors and
inductors, this is not the best approach.
A stub tuner is a length of transmission line connected to a
The L Matching Network
EE 432 Lecture 16
There are four possible 2-element matching networks:
Lecture 16 Page 1.1
Design Equations for Matching RS < RL
Lecture 16 Page 2.1
EE 432 Lecture 16
Design Example
EE 432 Lecture 16
Design a network to match a 100
Linear Amplifier Design
EE 432 Lecture 24
Things to consider:
Specifications
Selection of an appropriate device
Bias circuit
Stability
Matching Network Design
Example: Design a single stage amplifier using the RF Microdevices FPD6836P70 pHEMT transis
Introduction to Transmission Lines
EE 432 Lecture 4
Transmission line effects are present at all frequencies
but are only noticed when the line length approaches a
fraction of a wavelength.
Return current:
Wavelength:
f
1 MHz 100 MHz 1 GHz 10 GHz
(m) 300
Multi-Element Matching Networks
T or Pi networks may be visualized as two L networks
connected back-to-back:
Adding a third element can potentially increase the Q, thus narrowing the bandwidth of the
match. However, the third element does provide an extra
Amplifier Stability
EE 432 Lecture 22
Depending on the s-parameters of the active device,
especially s12, the potential for oscillation exists.
Stability Criteria at the input:
Stability Criteria at the output:
Lecture 22 Page 1
Signal Flow Graphs
EE 432
Amplifier Nonlinear Distortion
EE 432 Lecture 26
The amount of nonlinear distortion that a system can
tolerate determines the largest signal that the amplifier
can process.
AM-AM Distortion
What is 1 dB gain compression?
Lecture 26 Page 1
AM-PM Distortion
Special Cases of Lossless Lines
Lecture 11 Page 1
EE 432 Lecture 11
Inductors and Capacitors Combined
EE 432 Lecture 11
Figure 4-23 A lowpass filter: (a) in the form of an LC ladder network; and (b)
realized using microstrip lines.
Lecture 11 Page 2
The Q
Applications of S-Parameter Analysis
An amplifier with an active device and input, M1, and output,
M2, matching networks. The biasing arrangement is not
shown, but usually this is done with appropriate choice of
matching network topology.
EE 432 Lecture 7
Impedance Matching Using Smith Charts
This is the preferred initial design approach since tradeoffs can be
easily visualized and evaluated before refining the design.
Lecture 19 Page 1
EE 432 Lecture 19
Graphical Matching Example
Match a 25 source to a 20
Impedance Matching
EE 432 Lecture 15
Reasons for matching:
For maximum power transfer
To minimize reflections on interconnecting lines
To achieve noise match
To achieve power match in a nonlinear amplifier
Some important design considerations:
Impedance r
Matching Complex Loads
EE 432 Lecture 17
Resonance Technique:
Absorption Technique:
Lecture 17 Page 1
Matching Network Design Using Resonance
Design a network to match a 50 source to the load shown at f = 1 GHz.
The network must block DC.
Start by ignorin
Measurement of S Parameters
EE 432 Lecture 10
S11 = Input Reflection Coefficient
S22 = Output Reflection Coefficient
S21 = Forward Insertion Gain
S12 = Reverse Insertion Gain
With
Lecture 10 Page 1
both ports driven from or terminated in Z0 as shown.
Netw
Introduction to Microwave Amplifiers
Devices in common use at microwave frequencies (alphabet soup):
Acronym
Name
Notes
BJT
Bipolar Junction Transistor
Realized in Silicon
HBT
Heterostructure Bipolar Transistor Realized in GaAs or other compound semicondu
Antennas and RF Link
EE 432 Lecture 2
An RF Link consists of everything between the output of the
transmitter and the input of the receiver.
Cable loss
Tx antenna gain
Path loss
Multipath, fading, scintillation, polarization rotation, rain loss,
atmospher
Microstrip Design Equations
EE 432 Lecture 12
0
r
Lecture 12 Page 1
h
Microstrip Design Tables
EE 432 Lecture 12
0
r
Lecture 12 Page 2
h
Microstrip Design Tables (Continued)
EE 432 Lecture 12
0
r
Lecture 12 Page 3
h
Other Microstrip References (Gonzalez)
Noise
EE 432 Lecture 25
Noise is due to random motion of electrons in conductors. White
noise contains equal energy at all frequencies. Its power spectral
density (in Watts/Hz) is uniform, as shown in the figure.
Noise in dB units:
Adjusting for observati
EE 432 UHF and Microwave Engineering
Spring 2011
Assignment 5
Coverage:
Due:
Material presented in lectures 10 12
Friday, February 18
S Parameter Measurements, Quarter-Wave Transformers, Microstrip Transmission Lines
The modern Vector Network Analyzer (VN
EE 432 UHF and Microwave Engineering
Spring 2011
Assignment 4
Coverage:
Due:
Material presented in lectures 8 9
Thursday, February 10
Microwave Network Analysis
The Smith Chart is one of the most useful graphical tools for solving transmission-line proble
EE 432 Assignment 1 Solutions
EE 432 Assignment 1 Solutions
EE 432 Assignment 1 Solutions
An equally valid, and perhaps better, choice of LO1 frequency is 2.1 GHz (high-side LO).
EE 432 Assignment 1 Solutions
If LO1 frequency was chosen to be 2.1 GHz then
EE 432 UHF and Microwave Engineering
Spring 2011
Assignment 2
Coverage:
Due:
Material presented in lectures 4 5
Thursday, January 27
Transmission Lines
One fundamental difference between circuit design at low frequencies (below 100 MHz) and at
microwave f