الفصل الدراسى السابع S-7. Microwave Engineering. هندسة ميكروموجية. 1. Microwave Engineering. هندسة ميكروموجية. 2. الهندسة الميكروموجية EE262 (2 س محاضرة+ 2 س تمرين+1س عملى) اسبوعياً. المنهج التفصيلى . نظرية أوساط النقل الميكروموجية . تقنيات الموائمة والتوليف.
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الهندسة الميكروموجية EE262 (2س محاضرة+2س تمرين+1س عملى) اسبوعياً
خطوط نقل الترددات العالية ، خريطة سميث ، تقنيات المواءمة باستخدام الخطوط المبتورة
، ادلة الموجة مستطيلة المقطع و الدائرية المقطع ، الخطوط الميكروشريطية ، المرنانات التجويفية ، فيزياء الضوء .
Regular attendance is critical for good success in the course
2.1 The Lumped-Element Circuit Model for a Transmission Line 48
Wave Propagation on a Transmission Line 50
The Lossless Line 51
2.2 Field Analysis of Transmission Lines 51
Transmission Line Parameters 51
The Telegrapher Equations Derived from Field Analysis of a Coaxial Line 54
Propagation Constant, Impedance, and Power Flow for the Lossless
Coaxial Line 56
2.3 The Terminated Lossless Transmission Line 56
Special Cases of Lossless Terminated Lines 59
2.4 The Smith Chart 63
The Combined Impedance–Admittance Smith Chart 67
The Slotted Line 68
2.5 The Quarter-Wave Transformer 72
The Impedance Viewpoint 72
The Multiple-Reflection Viewpoint 74
2.6 Generator and Load Mismatches 76
Load Matched to Line 77 Generator Matched to Loaded Line 77
Conjugate Matching 77
2.7 Lossy Transmission Lines 78
The Low-Loss Line 79 The Distortionless Line 80
The Terminated Lossy Line 81
The Perturbation Method for Calculating Attenuation 82
The Wheeler Incremental Inductance Rule 83
5th W. Impedance Matching & Tuning 228
5.1 Matching with Lumped Elements (LNetworks) 229
Analytic Solutions 230 Smith Chart Solutions 231
5.2 Single-Stub Tuning 234
Shunt Stubs 235 Series Stubs 238
5.3 Double-Stub Tuning 241
Smith Chart Solution 242 Analytic Solution 245
5.4 The Quarter-Wave Transformer 246
6th W. Microwave Network Analysis. 165
4.1 Impedance and Equivalent Voltages and Currents 166
Equivalent Voltages and Currents 166 The Concept of Impedance 170
Even and Odd Properties ofZ(ω)and(ω) 173
4.2 Impedance and Admittance Matrices 174
Reciprocal Networks 175 Lossless Networks 177
7th W. Microwave Network Analysis.
4.3 The Scattering Matrix 178
Reciprocal Networks and Lossless Networks 181
A Shift in Reference Planes 184
Power Waves and Generalized Scattering Parameters 185
4.4 The Transmission(ABCD)Matrix 188
Relation to Impedance Matrix 191
Equivalent Circuits for Two-Port Networks 191
8th W. Microwave Network Analysis.
4.5 Signal Flow Graphs 194
Decomposition of Signal Flow Graphs 195
Application to Thru-Reflect-Line Network Analyzer Calibration 197
4.6 Discontinuities and Modal Analysis 203
Modal Analysis of an H-Plane Step in Rectangular Waveguide 203
9th W. Microwave Network Analysis..
4.7 Excitation of Waveguides—Electric and Magnetic Currents 210
Current Sheets That Excite Only One Waveguide Mode 210
Mode Excitation from an Arbitrary Electric or Magnetic Current Source 212
4.8 Excitation of Waveguides—Aperture Coupling 215
Coupling Through an Aperture in a Transverse Waveguide Wall 218
Coupling Through an Aperture in the Broad Wall of a Waveguide 220
10th W. Power Divider and couplers..
POWER DIVIDERS AND DIRECTIONAL COUPLERS 317
7.1 Basic Properties of Dividers and Couplers 317
Three-Port Networks (T-Junctions) 318
Four-Port Networks (Directional Couplers) 320
7.2 The T-Junction Power Divider 324
Lossless Divider 324 Resistive Divider 326
11th W. Power Divider and couplers..
7.3 The Wilkinson Power Divider 328
Even-Odd Mode Analysis 328
Unequal Power Division andN-Way Wilkinson Dividers 332
7.4 Waveguide Directional Couplers 333
Bethe Hole Coupler 334 Design of Multihole Couplers 338
7.5 The Quadrature (90◦) Hybrid 343
Even-Odd Mode Analysis 344
12th W.. Power Divider and couplers..
7.6 Coupled Line Directional Couplers 347
Coupled Line Theory 347 Design of Coupled Line Couplers 351
Design of Multisection Coupled Line Couplers 356
7.7 The Lange Coupler 359
13th W. Power Divider and couplers..
7.9 Other Couplers 372
14th W. ACTIVE RF AND MICROWAVE DEVICES 524.
11.5 Microwave Tubes 552
15th W.. Review
Low frequency with high power (electrical machining, power generation, distribution electrical energy…) .
High frequency but low power (communications, radar, satellites, optical fiber…)
What happened if the frequency increase?
What is the relation between frequency of electro magnetic waves and dimension of electric elements?
Electrical length = Physical length/Wavelength (expressed in )
Phase delay = (2 or 360) * Physical length/Wavelength
f =10 kHz, = c/f = 3 x 108/ 10 x 103 = 30000 m
Electrical length =1 cm/30000 m = 0.33 x 10-6 , Phase delay = 0.00012
f =10 GHz, = 3 x 108/ 10 x 109 = 3 cm
Electrical length = 0.33 , Phase delay = 118.8
Electrically long - The phase of a voltage or current changes significantly over the physical extent of the device
EMC (electromagnetic comparable)
Electromagnetic field behave when the frequency of operation is large.
The phenomenon of electromagnetism is performed by the 4 Maxwell equations
Microwave frequency range between 3 and 300 GHz. With a corresponding electrical wavelength between ( λ=10 cm and λ=1 mm ) respectively.
(1 MHz = 106 Hz) & (1 GHz = 109 Hz)
f = 3 * 108/ 30 * 10-2 = 1 GHz
= 1 cm:
f = 3 * 108/ 1* 10-2 = 30 GHz
f= 30 GHz
= 3 * 108/ 30 * 109 = 10 mm
f= 300 GHz
= 3 * 108/ 300 * 109 = 1 mm
Complex reflecting and refracting environment
The first application of electromagnetic waves is the transmission line (TL).
Transit time effect cause a time delay
Then: Ignore transit time effect
Printed Circuit Trace
Propagation delay negligible
Transmission line section!
Propagation delay considered
Zo: characteristic impedance
(=+j): Propagation constant
At much lower frequencies the wavelength is large enough that there is insignificant phase variation across the dimensions of a component.
The lumped circuit element approximations of circuit theory may not be valid at high RF and microwave frequencies, where one must work with Maxwell’s equations and their solutions.
Transmission Line Theory
Transmission line theory bridges the gap between field analysis and basic circuit theory, which is important in the analysis of microwave circuits and devices.
Any physical structure that guide the electromagnetic wave from place to place is called a Transmission Line (TL).
Basic circuit theory & Transmission line theory
Electrical length = Physical length/Wavelength (expressed in )
Phase delay = (2 or 360) x Physical length/Wavelength
L=series inductance per unit length, for both conductors, in H/m.
G=shunt conductance per unit length, in S/m.
C=shunt capacitance per unit length, in F/m.
To define these parameters we can divide the T L into small segment and use Kirchhoff's lows as follows:
When V Is applied, some current I will flow in the circuit.
The changes in voltage and current can be written as:
All quantities have harmonic time variation
low freq. rang deals with the algebraic equations.
At high freq. rang, the differential equations are used
Dividing by Δz and taking the limits asΔz----0 gives the following differential equations
Theseare the time domain form of the transmission line equations, also known as the telegrapher equations.
Forsinusoidal steady-state condition, with cosine-based phasors, these Eqns can be simplified to:
The two equations can be solved simultaneously to give wave equations for V(z) and I(z) :
Traveling wave solutions can be found as
Is the complex propagation constant, which is a function of frequency.
The e−γz term represents wave propagation in the +z direction, and the eγz term represents wave propagation in the−z direction.
to the voltage of
gives the current on the line:
shows that a characteristic impedance, Z0, can be defined as
can be rewritten in the following form:
Converting back to the time domain, we can express the voltage waveform as
Where φ± is the phase angle of the complex voltageV0±
Using arguments similar to those in basic plane equation, we find that the wavelength on the line is:
And the phase velocity is: