example of uniform lossless transmission li time delay, impulse response time delay, impulse response etermine the waveform of output signal Vo(t)(04G) zcτvo()= v(t) Z z=32 Solution 3: SoluboHoun t tal r=20us reflectance 即(Q口□ Vo(t) sorted:p Applieation example of uniform lossless transmission line Application example of uniform lossless tral time delay impulse response -time delay impulse response 300m, the natural impedance is 30022, the 'e velocity is3xlo°m/s L. Evaluate the voltage reflection coeff 2am即可(1AC出 deltae when the signals passes b the transmission line. esponse of the end terminals. 2. Evaluate the step response of the end terminals. i 3.Get the voltage waveform of the position within 0-5us, which is 75 m away 3. Get the voltage waveform of the position within 0-Sus, which is 75 m away from the end terminals v()=l(t)→V(s)=1/s v=(22)(z1+z)e P,(0)=2 Z∞-300 2(e z-z.0-300 )=+c==(-c+-”+)=5(rc Z+Z0+300 App datas. mampl r es aniserm Application example of uniform lossless transmission line: time delay, impulse response The length of transmission line is 1=300m, the natural impedance is 30042, the 图mpm=30 m, the natural impedance is 30002, the a. se reflection reflection coefficient of the end terminals(2-2)A0)and the Evaluate the voltage reflection coefficient of the end terminals(2-2)A(0)and the voltage reflection coefficient of input teminals(1-1)B/. Calculate th Evaluate the step response of the end terminals. 3. Get the voltage waveform of the position within0-SHs, which is 75 m away 39fromt age waveform of the position within 0-5us, which is 75 m away Solution: 2) (D)=()→F(s)=l1/1 (22)(z1+z)e zL)"(Z-Z)e""V 2()=2(-r)-u(-3r)+(-5r)+ 2x∑-1)au(-2kz-r) the voltage waveform of the position within 0-5p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 u(t) ZC τ + - ZL=∞ τ V+ V- 2τ 3τ V+ V0(t)=? t t V0(t) V- V+ V- Solution 3: Get the unit step response using the terminal’s reflectance Application example of uniform lossless transmission line: time delay, impulse response e.g.: ρ (0) -1 ρ (0) 1 V V = Terminal open: = Terminal shorted: 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 C Z L =3Z C V (t) + - τ t V 0 (t) 10us 0 x=0 8 V x = l + - Solution 2: Determine the waveform of output signal Vo(t) (04G) ( ) 2 1 3 1 3 1 0 = + − = + − = L c L c v Z Z Z Z ρ 1 1 oc c v oc c ZZ Z ZZ Z ρ − − = = =− + τ = 20μs 2τ 4 -4 τ V+ V- 3τ V+ V- V0(t) …… τ 8 4 -4 -2 12 -6 3 t t Application example of uniform lossless transmission line: time delay, impulse response 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 解：1) The length of transmission line is l = 300m, the natural impedance is 300Ω, the wave velocity is 3×108 m/s。 1.Evaluate the voltage reflection coefficient of the end terminals (2-2‘) ρv(0) and the voltage reflection coefficient of input terminals (1-1‘) ρv1. Calculate the time delay τ when the signals passes by the transmission line. 2.Evaluate the step response of the end terminals. 3.Get the voltage waveform of the position within 0 ~ 5μs, which is 75 m away from the end terminals. x l O u(t) + - 1' 2' 1 2 ( ) 1 300 300 0 = ∞ + ∞ − = + − = L c L c v Z Z Z Z ρ 1 0 300 1 0 300 o c v o c Z Z Z Z ρ − − = = =− + + ( )s v l τ 1 μ 3 10 300 8 = × = = Application example of uniform lossless transmission line: time delay, impulse response 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 The length of transmission line is l = 300m, the natural impedance is 300Ω, the wave velocity is 3×108 m/s。 1.Evaluate the voltage reflection coefficient of the end terminals (2-2‘) ρv(0) and the voltage reflection coefficient of input terminals (1-1‘) ρv1. Calculate the time delay τ when the signals passes by the transmission line. 2.Evaluate the step response of the end terminals. 3.Get the voltage waveform of the position within 0 ~ 5μs, which is 75 m away from the end terminals. Solution: 2) x l O u(t) + - 1' 2' 1 2 ( ) ( ) ∑( ) +∞ = − − − − + − − = − + + = − + = 0 3 5 (2 1) 2 2 1 2 2 1 2 k s s s k s k s s e s e e e e s e s V s τ τ τ τ τ τ L v t u t V s s i i ( ) = ( ) → ( ) =1/ (e e ) 2 V V (2Z ) (Z Z )e V (2Z ) (Z - Z )e V 2 L c 2 -1 L c 2 L -1 1 L τ τ τ τ s s s s − − = + = + + v t u t V s s i i ( ) = ( ) → ( ) =1/ (e e ) 2 V V (2Z ) (Z Z )e V (2Z ) (Z - Z )e V 2 L c 2 -1 L c 2 L -1 1 L τ τ τ τ s s s s − − = + = + + Application example of uniform lossless transmission line: time delay, impulse response 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 2 2 1 2 2 3 5 k k u t k V t u t u t u t τ τ τ τ τ L v t u t V s s i i ( ) = ( ) → ( ) =1/ L c 2 -1 L c 2 L -1 V1 (2Z L ) (Z Z )e V (2Z ) (Z - Z )e V sτ − sτ = + + Application example of uniform lossless transmission line: time delay, impulse response The length of transmission line is l = 300m, the natural impedance is 300Ω, the wave velocity is 3×108 m/s。 1.Evaluate the voltage reflection coefficient of the end terminals (2-2‘) ρv(0) and the voltage reflection coefficient of input terminals (1-1‘) ρv1. Calculate the time delay τ when the signals passes by the transmission line. 2.Evaluate the step response of the end terminals. 3.Get the voltage waveform of the position within 0 ~ 5μs, which is 75 m away from the end terminals. x l O u(t) + - 1' 2' 1 2 Solution: 2) 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 Solution: 3) x l O u(t) + - 1' 2' 1 2 τ τ τ 4 1 4 3 = + τ 2τ 3τ 4τ 5τ 1 2 O t Vx 4 3τ 距离2-2'端口75米处的电压波形 τ 2τ 3τ 4τ 5τ 1 2 O t Vx 4 3τ 距离2-2'端口75米处的电压波形 Application example of uniform lossless transmission line: time delay, impulse response The length of transmission line is l = 300m, the natural impedance is 300Ω, the wave velocity is 3×108 m/s。 1.Evaluate the voltage reflection coefficient of the end terminals (2-2‘) ρv(0) and the voltage reflection coefficient of input terminals (1-1‘) ρv1. Calculate the time delay τ when the signals passes by the transmission line. 2.Evaluate the step response of the end terminals. 3.Get the voltage waveform of the position within 0 ~ 5μs, which is 75 m away from the end terminals. the voltage waveform of the position within 0 ~ 5μs, which is 75 m away from the end terminals