北京大学：《电路分析原理 Circuit Analysis》课程教学课件（英文版）第七章 链式网络与传输线 第一节 传输线

Article I of circuit analysis- Applications (Principles of Circuit Analysis) Chapter 7: Uniform Lossless Transmission Line uniform lossless transmission line (Chain Network and Transmission Line) Lecture 1 diode cire 2009.11.26 Chapter 7: Transmission Line Chapter 7: Transmission Line. 37-1 Transmission Line: Some history 87-1 Transmission Line: Some history 37-2 Chain Network and Transmission Line(conceptions) 7-2 Chain Network and Transmission Line(concept s7-3 Uniform Lossless Transmission Line(key points) 7-3 Uniform Lossless Transmission Line (key points) natural impedance, trand)is The natural parameter of natural impedance, transmission constant incident wave, reflected wave, reflectance incident wave, renected wave, refectance terminal: open, short terminal: open, short, matching 37-4 step response of transmission line 137- step response of transmission line "crowne Engineering", Third Edition David M.P Microwave Engineering", Thin Edition David M. Pozar (chapter 2 and 3 hapter 2 and 3) Transmission Line: Some history IEEE standard frequency spectrum allocation: Signal sending Signal receivin load which signals will we transmit? Lightwave: ...THz 0.633um, 1.3um. 1.5um

北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 第 ？讲： 复习 北京大学 北京大学 《Principles of Circuit Analysis》 Chapter 7: Uniform Lossless Transmission Line (Chain Network and Transmission Line) Lecture 1 2009.11.26 Interest Focus Persistence Originality 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 ＃ operational amplifier ＃ uniform lossless transmission line ＃ diode circuit ＃ triode circuit Equivalence, G-parameter Circuit analysis, A￾parameter piecewise linearity, Equivalent modeling H-parameter, Z-parameter Article Ⅱ of circuit analysis --- Applications 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 §7-1 Transmission Line: Some history §7-2 Chain Network and Transmission Line (conceptions) §7-3 Uniform Lossless Transmission Line (key points) natural impedance, transmission constant natural impedance, transmission constant incident wave, reflected wave, reflectance incident wave, reflected wave, reflectance terminal: open, short, matching §7-4 step response of transmission line Chapter 7: Transmission Line The natural parameter of transmission line The wave properties of transmission line Reference: “Microwave Engineering”，Third Edition David M.Pozar (chapter 2 and 3) Reference: “Microwave Engineering”，Third Edition David M.Pozar (chapter 2 and 3) 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 §7-1 Transmission Line: Some history §7-2 Chain Network and Transmission Line (conceptions) §7-3 Uniform Lossless Transmission Line (key points) natural impedance, transmission constant natural impedance, transmission constant incident wave, reflected wave, reflectance incident wave, reflected wave, reflectance terminal: open, short, matching §7-4 step response of transmission line Chapter 7: Transmission Line Reference: “Microwave Engineering”，Third Edition David M.Pozar (chapter 2 and 3) Reference: “Microwave Engineering”，Third Edition David M.Pozar (chapter 2 and 3) 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Transmission Line: Some history Signal source Signal processing and transmission load Signal source Signal processing load Signal processing Signal amplification Transmission Line (channel) Transmission Line (channel) Signal sending Signal receiving Which signals will we transmit? 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 IEEE standard frequency spectrum allocation: Lightwave: …THz 0.633um,1.3um, 1.5um

Problems at the high frequency: elements Problems at the high frequency: wire (Transmission Line)-Kelvin skin effec 0理担电阻 电感效应 电容效应 The relationship between the frequency and the absolute value of the 图14铜、铝和金的趋肤厚度特性,己=64.516×10sm impedance of a metalfilmresistor whose nominal value is 500Q electromagnetic field theory: Maxwell equations Transmission Line: some histor ×E=i()3kH VxH=J-ic-0)2kn'E v→(n2E)=° V·H=0 If what we concern is the input and output, not the internal electromagnetic Too difficult field the transmission 图2.5 of signals.? Cl-1:Introduction to Linear Circuit Anaeviey Cl-1: Introduction to Linear Circuit AnR Analysis of electronic signals E(t, z, H(t, z) umped Parameter Hypothe Circuit Analysis, Electromagnetic Field Theory When the physical object has dimensions that are much smaller than the wavelength of electronic signals( that is L<λor100L≤λ), we can assume f=50Hz, 2=c/f=6x10 L=1km< 址出时到 is concen No Maxwell equations! when l<<λ,andL~λ from the ports of the elements, such they are different- without regard to the electromagnetism inside the elements. TV f=100MHz, aF2xf, C=3X10-mis, 2=C/ f=3m L=1.5m, Va(t Vasinat, Va(t=ve(t) The distinguishing feature of of the elements

北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Problems at the high frequency: elements 5Ω The relationship between the frequency and the absolute value of the impedance of a metalfilmresistor whose nominal value is 500Ω. 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Problems at the high frequency: wire (Transmission Line) -- Kelvin skin effect 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 ∇ • = 0 ∇ • = ∇× = ∇× = H (n E) H J-i( ) kn E E i( ) kH 0 2 2 2 1 0 0 2 1 0 0 ε σ μ ε ε μ electromagnetic field theory: Maxwell equations Too difficult 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 If what we concern is the input and output, not the internal electromagnetic field Æ the transmission of signals…? Transmission Line: Some history 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Analysis of electronic signals: Circuit Analysis, Electromagnetic Field Theory E(t, z), H(t, z) TV f=100MHz， ω=2πf, C=3X108m/s，λ=C/ f=3m L=1.5m，VA(t)= Vmsinωt， VA(t)=-VB(t) A B C A B C f=50Hz，C=3X108m/s，λ=C/ f=6X107m L=1km<< 6X104km Analysis of electronic signals: when L << λ , and L ~ λ they are different~ C1-1: Introduction to Linear Circuit Analysis Review 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Lumped Parameter Hypothesis : When the physical object has dimensions that are much smaller than the wavelength of electronic signals, (that is L << λ or 100L ≤ λ )，we can assume that all the characters and parameters can be concentrated into one point. It means that electric fields is concentrated in capacitance, magnetic field is concentrated inductance and loss is concentrated in resistance. The wires for connection are considered lossless. The essence of Circuit Analysis is that we only consider the outer characteristics from the ports of the elements, such as voltage, electric current and power, without regard to the electromagnetism inside the elements. R L C *** C1-1：Introduction to Linear Circuit Analysis modeling equivalent The distinguishing feature of Circuit Analysis is we only consider the outer characteristics of the elements No Maxwell equations! Review

Cl-I Introduetion to Linear Cireuit an evie Cl-1: Introduction to Linear Circuit Analysis Analysis of electronic signals: Circuit Analysis, Electromagnetic Field Theory When l~λ,fdLλ&L~λ,andLA&1-2 conditions Condition It dL &L~λ,andL<<λ hey are different- Z+△Z I(z)RAZ LAZ Condition I:dL<<λ Condition 2: the plane wave characteristie of Electromagnetic Field Let R, G, L, C to be the parameters of unit length

北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 TV f=100MHz， ω=2πf, C=3X108m/s，λ=C/ f=3m L=1.5m，VA(t)= Vmsinωt， VA(t)=-VB(t) A B C’ A B C When L ~ λ ,……if dL λ & L ~ λ , and L λ & L ~ λ , We want to use the circuit analysis ? conditions ？ Condition 1：dL λ & L ~ λ , and L λ & L ~ λ , We want to use the circuit analysis ? conditions ？ Condition 1: dL << λ C1-1：Introduction to Linear Circuit Analysis Analysis of electronic signals: Circuit Analysis, Electromagnetic Field Theory 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Z ΔZ Z Z+ΔZ RΔz LΔz GΔz CΔz + V(z+Δz) - + V(z) - I(z) I(z+Δz) Let R,G,L,C to be the parameters of unit length dL << dL << λλ chain circuit → Transmission Line →uniform transmission line ***

Chain cireuit Transmission Line -Uniform transmission line Next lecture sOlving the problems about transmission line a87-1 Transmission Line: Some history orrectly needs the Maxwell equations 57-2 Chain Network and Transmission Line(conceptions) O If we solve the transmission line signals using circuit 37-3 Uniform Lossless Transmission Line(keyc analysis approximately, we can get qualitative or even comparatively correct transmission results--simplify natural impedance, transmission constar the solutions greatl O If the radiation of the whole transmission line is incident wave, reflected wave, reflectance small and can be equivalent to transmission loss terminal: open, short, matching homogeneously, the whole transmission line 87-4 step response of transmission line luding the two terminals can be considered a two- port network(chain circuit) "Microave Engineering", Thin Edition David M. Pozar

北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 ‰ If the radiation of the whole transmission line is small and can be equivalent to transmission loss homogeneously, the whole transmission line including the two terminals can be considered a two￾port network (chain circuit). ‰ If we solve the transmission line signals using circuit analysis approximately, we can get qualitative or even comparatively correct transmission results —— simplify the solutions greatly. ‰Solving the problems about transmission line correctly needs the Maxwell equations Chain circuit → Transmission Line →Uniform transmission line 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 §7-1 Transmission Line: Some history §7-2 Chain Network and Transmission Line (conceptions) 2 Chain Network and Transmission Line (conceptions) §7-3 Uniform Lossless Transmission Line (key points) (key points) natural impedance, transmission constant natural impedance, transmission constant incident wave, reflected wave, reflectance incident wave, reflected wave, reflectance terminal: open, short, matching §7-4 step response of transmission line Next lecture… Reference: “Microwave Engineering”，Third Edition David M.Pozar (chapter 2 and 3) Reference: “Microwave Engineering”，Third Edition David M.Pozar (chapter 2 and 3)