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### Lecture notes -_microwaves_jwfiles

1. 1. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy - 2009These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).MicrowavesLecture NotesDr. Serkan Aksoyv.1.3.42009www.jntuworld.comwww.jntuworld.comwww.jwjobs.net
2. 2. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 2009These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).Content1. LUMPED CIRCUIT MODEL-----------------------------------------12. FIELD ANALYSIS of LINES -----------------------------------------12.1. Wave Propagation along the Line --------------------------------------------------------------------- 12.1.1. Lossless Transmission Lines------------------------------------------------------------------------------22.1.2. Lossy Transmission Lines---------------------------------------------------------------------------------32.2. Smith Chart-------------------------------------------------------------------------------------------------- 32.3. Slotted Line-------------------------------------------------------------------------------------------------- 42.4. Generator & Load Mismatches------------------------------------------------------------------------- 43. MICROWAVE NETWORKS -----------------------------------------53.1. Voltage, Current and Impedance ---------------------------------------------------------------------- 53.2. Impedance & Admittance Matrices ------------------------------------------------------------------- 53.2.1. Scattering Matrix --------------------------------------------------------------------------------------------53.2.2. Transmission (ABCD) Matrix ----------------------------------------------------------------------------63.3. Equivalent Circuits for 2 Port Networks------------------------------------------------------------- 63.4. Signal Flow Graphs --------------------------------------------------------------------------------------- 64. IMPEDANCE MATCHING ------------------------------------------84.1. L Networks Matching------------------------------------------------------------------------------------- 84.2. Quarter Wave Transformer------------------------------------------------------------------------------ 84.3. Single Stub Tuning---------------------------------------------------------------------------------------- 84.4. Double Stub Tuning -------------------------------------------------------------------------------------- 94.5. Tapered Lines----------------------------------------------------------------------------------------------- 95. POWER DIVIDERS & COUPLERS ------------------------------ 105.1. Three Port Networks (T Junction)--------------------------------------------------------------------105.1.1. T Junction Power Divider ------------------------------------------------------------------------------- 105.2. Four Port Networks (Directional Coupler)---------------------------------------------------------105.2.1. Waveguide Directional Coupler----------------------------------------------------------------------- 105.2.2. Wilkinson Power Divider ------------------------------------------------------------------------------- 115.2.3. Hybrid Coupler-------------------------------------------------------------------------------------------- 115.2.4. Hybrid ------------------------------------------------------------------------------------------------ 115.2.5. Coupled Line Directional Coupler -------------------------------------------------------------------- 115.2.6. Lange Coupler --------------------------------------------------------------------------------------------- 115.3. Other Couplers --------------------------------------------------------------------------------------------116. NOISE & ACTIVE COMPONENTS ----------------------------- 126.1. Noise Figure, --------------------------------------------------------------------------------------------126.2. Dynamic Range & Intermodulation Distortion---------------------------------------------------136.3. RF Diode Characteristics--------------------------------------------------------------------------------147. MICROWAVE AMPLIFIER DESIGN--------------------------- 157.1. Two-Port Power Gains ----------------------------------------------------------------------------------157.2. Stability -----------------------------------------------------------------------------------------------------157.3. Single Stage Amplifier Design------------------------------------------------------------------------167.4. Broadband Amplifier Design--------------------------------------------------------------------------167.5. Power Amplifiers -----------------------------------------------------------------------------------------167.5.1. Large Signal Characterization-------------------------------------------------------------------------- 16www.jntuworld.comwww.jntuworld.comwww.jwjobs.net
3. 3. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 20091These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).1. LUMPED CIRCUIT MODELFields Circuits: Real size of the circuit, : WavelengthCircuitTransmission Lineand will vary in magnitude and phase over its length.: Resistance per unit length ( ): Finite conductivity: Inductance per unit length ( ): Self inductance of two wires: Capacitance per unit length ( ): Proximity conductors: Conductance per unit length ( ): Dielectric lossesKirchoff Voltage LawKirchoff Current LawTaking the limit as , Telegraph equationsTime domainFrequency domain2. FIELD ANALYSIS of LINESThe idea is to find relations between and with .where , and , , , are time-averaged values calculated for length line and is the linecross-sectional area.2.1. Wave Propagation along the LineUsing the frequency domain Telegrapher equationwhere is propagation constant.The solution of Telegrapher equationThen, taking the derivation of , the calculation ofThenConverting to time domain by usingwhere , , is the phase.www.jntuworld.comwww.jntuworld.comwww.jwjobs.net
4. 4. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 20092These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).2.1.1. Lossless Transmission LinesWhen the lossless line is terminated by a loadReflected waves occur.Reflection coefficient at the load,where and consists of a superposition of an incidentand reflected waves called Standing Waves ( ).Time Average Power Flow:This shows is constant at anywhere on the line.When the line is matched  is constant.When the line is mismatched (   ReturnLossMatched load (No reflectedpower, maximum power is delivered).Total reflection, (All powerreflected).is not constant.The maximum value occurs when. The minimum valueoccurs when . When increases,increases as a measure of mismatch. Then Standing Wave Ratio( ) iswhen means matched line. In that case at , thereflection coefficient and input impedanceUsing the definition of , more useful form known asTransmission Line Impedance Equation as- Transmission Coefficient:Some part of EM wave is alsotransmitted to second region asInsertion Loss:Short Circuit:Open Circuit:The proper length of open or short circuited transmission linecan provide any desired reactance or susceptance.(No regard to ): The sameimpedance is observed at the input.(Quarter WaveTransform)- (Short circuit) Open circuit- (Open circuit)   Short circuitwww.jntuworld.comwww.jntuworld.comwww.jwjobs.net
5. 5. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 20093These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).2.1.2. Lossy Transmission LinesIn practice, finite conductivity (or lossy dielectrics) lines can beevaluated as a Lossy Line.Low-loss line , . Thenignoring the last term of  In the lossy line; , & can be approximated tolossless line.Distortionless Line: For the lossy line, in fact the exactis not a linear function of frequency meansdispersive. But specifically if the following conditionholdsthen , mean that the lossy linebehaves as lossless (distortionless) line.Terminated Lossy Line: Loss is assumed small thatPower lost in the line:Perturbation Method for Calculating AttenuationPower flow along lossy line:Power loss per unit length:Attenuation constant:Wheeler Incremental Inductance Rule:: Incremental inductance: Loss per unit length: Power at the .Then, Attenuation constant:where is skin depth and .Taylor series Inductance Rule:where .2.2. Smith Chartwhere is Resistance, is Reactance, is Conductance andis Susceptance. Whenever is normalized impedanceThe apsis and ordinate of Smith chart are and .Rearranging themwww.jntuworld.comwww.jntuworld.comwww.jwjobs.net
6. 6. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 20094These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).These are two families of circles as and . Superposition ofSmith Chart and its 180o( ) rotated version is known asCombined Impedance-Admittance Smith Chart.is the complete revolution of Smith chart. is the halfof Smith chart (180o). The images of is in Smith chart.2.3. Slotted LineThis device is used to find as first .- Measurement of on the distance from the line.- Calculate-- Using and , write- Calculate at .2.4. Generator & Load MismatchesThen, using thiswhere and .where and . Generally isfixed and three cases are considered asLoad Matched to Line: , , .Then .Generator Matched to Line: , .Conjugate Latching:Maximum power transfer . If one directlychose , it does not mean that the best efficiencydue to the phase differences. The efficiency can be improvedonly by making as small as possible.www.jntuworld.comwww.jntuworld.comwww.jwjobs.net
7. 7. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 20095These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).3. MICROWAVE NETWORKSAt low frequencies for electrically small circuits, lumped activeand passive circuit elements are enough for analyzing the circuitleading a type of a Quasi-Static solution (assumption ofnegligible phase change in any where of the circuit) ofMaxwells equations and to Kirchoff Current and Voltage Lawswith impedance concept. Moreover fields are considered asTEM type. But this way is not possible to analyze microwavecircuits. The circuit concept should modify and apply tomicrowave network theory developed in MIT in 1940. Thereasons of using it are as followMuch easier than field theory,Calculations are performed at terminals, not everywhere,Easy to modify and combine different problems,The field solution of Maxwells equation gives moreinformation at the every time and place of the network, butdifficult. At microwave frequencies, although thedefinition of the terminal pairs for line is relativelyeasy, the terminal pair for line does notstrictly exist.3.1. Voltage, Current and ImpedanceThe measurements of and at microwave frequencies aredifficult due to not easily defined terminals for non-TEM waves.Because of that the fields are measured and used asthan, the impedance can be defined as . Because thefields depend on the coordinates (like in waveguide), specialattenuation should be given for extraction of and . The way isto do thatthen, the impedance can be defined as. The impedance concept first usedby O. Heaviside, and then after application to transmission lines,to electromagnetics by Schelkunoff. In this manner, types of itIntrinsic Impedance, : It depends on only thematerial parameters.Wave Impedance, : TM, TE, TEMtypes are present which may depend on type of guide,material and frequency.Characteristic Impedance, : For TEM, it isunique, but for TE and TM, not unique because andcan not be determined, uniquely.It can be shown that the real parts of , and areeven in , but the imaginery parts of them are odd in .and are the even function in .3.2. Impedance & Admittance MatricesThe and of a port microwave network having th terminalThe impedance matrix is in the form ofSimilarly the admittance matrix is in the form ofClear that . It can be shown thatThen and are known as Input Impedance and TransferImpedance, respectively.If the network is reciprocal (no ferrites, plasmas andactive devices inside), and are the rightrelations.If the network is lossless, and are purelyimaginary.3.2.1. Scattering MatrixThe form of the scattering matrix gives thecomplete description of the port networks with the incidentand reflected waves asAny element of the scattering matrixwww.jntuworld.comwww.jntuworld.comwww.jwjobs.net
8. 8. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 20096These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).and are Reflection and Transmission Coefficient (fromport to port ), respectively. Network analyzer is used tomeasure parameters of a network. If network is reciprocal,is symmetric. If network is lossless, is unitary means that. Using the relations asand with between and matrixesIn the , all the and are defined as a reference point at theend of every lines. If the reference point is shifted, thenwhere is the electrical length of the outward shift.3.2.1.1. Generalized Scattering MatrixIn the previous chapter, is defined for networks with samecharacteristic impedance for all ports. Generally for not sameimpedance for all ports, a new set of wave amplitudes as,Then, generalized matrix- In reciprocal networks, is symmetric,- In lossless networks, is unitary and satisfies the equation3.2.2. Transmission (ABCD) MatrixMany microwave networks consisting cascade connection andneed building block fashion in practice. ABCD matrix is definedto satisfy this aswhere port 1 and port 2 are completely isolated in the equationmeans that cascade multiplication is possible. The currentdirection is also specially designed for ABCD matrix. Therelation between and matrix parameters are asIf the network is reciprocal ( ), then .3.3. Equivalent Circuits for 2 Port NetworksTransition between a coaxial line and microstrip line canbe chosen as an example of two port networks. Because ofdiscontinuity in the transition region, EM energy is storedin the vicinity of the transition leading to reactive effectsmean that the transition region should be modeled as blackbox (There is an unlimited way of equivalent circuits, butchoosing matrix equivalence), thenA nonreciprocal network can not be represented bypassive equivalent circuit using reciprocal elements. If thenetwork is reciprocal (there are six degrees of freedom, sixindependent parameters), the presentations lead naturallyto and equivalent circuits asIf the network is lossless, the impedance and admittancematrix elements are purely imaginary, the degrees offreedom reduces to three and the elements of andequivalent circuits should be constructed from purelyreactive elements.3.4. Signal Flow GraphsSignal flow graph is an additional technique to analysemicrowave networks in terms of reflected and transmittedwaves. Three different forms of it are given below with nodesand branches.www.jntuworld.comwww.jntuworld.comwww.jwjobs.net
9. 9. Microwaves - Lecture Notes - v.1.3.4 Dr. Serkan Aksoy – 20097These lecture notes are heavily based on the book of Microwave Engineering by David M. Pozar. For future versions or any proposals, please contact withDr. Serkan Aksoy (saksoy@gyte.edu.tr).The decomposition rules are also given belowwww.jntuworld.comwww.jntuworld.comwww.jwjobs.net