Question Solved1 Answer 1. 5 5 a) i) A lossless coaxial cable has a characteristic impedance of 50 2. Explain what the characteristic impedance means. ii) The 50 2 lossless coaxial cable is filled with a dielectric material between the inner conductor and the outer conductor. The material has a dielectric constant of ε = 4. Another lossless coaxial cable has the same size as this cable but is filled with a new material having a dielectric constant of ε = 2. Is the characteristic impedance of the other cable smaller or greater than 50 s2? Justify your answer. 7 b) The top layer of a microstrip circuit is shown in Fig. Q1b. Apart from the input and output ports, the lengths of the other three microstrip lines are about half wavelength. i) Draw the equivalent circuit of this microstrip circuit using inductors and capacitors; ii) Explain the most likely function of the circuit. Describe what parameters are usually used to characterise such a circuit. Input Port 8 10 Output Port Fig. Q1b c) i) A lossy transmission line has the following primary constants: R = 55 m/m, G = 600 pS/m, L = 600 nH/m and C = 40 pF/m. The transmission line is used to transmit a signal at 1 kHz. Calculate the phase velocity of the 1 kHz signal. Also calculate how much in dB the magnitude of the signal will be attenuated after 10 km. ii) Will the attenuation and phase velocity be the same for a 2 kHz signal? What do you call this phenomenon? 5

VS3MI7 The Asker · Advanced Mathematics

Transcribed Image Text: 1. 5 5 a) i) A lossless coaxial cable has a characteristic impedance of 50 2. Explain what the characteristic impedance means. ii) The 50 2 lossless coaxial cable is filled with a dielectric material between the inner conductor and the outer conductor. The material has a dielectric constant of ε = 4. Another lossless coaxial cable has the same size as this cable but is filled with a new material having a dielectric constant of ε = 2. Is the characteristic impedance of the other cable smaller or greater than 50 s2? Justify your answer. 7 b) The top layer of a microstrip circuit is shown in Fig. Q1b. Apart from the input and output ports, the lengths of the other three microstrip lines are about half wavelength. i) Draw the equivalent circuit of this microstrip circuit using inductors and capacitors; ii) Explain the most likely function of the circuit. Describe what parameters are usually used to characterise such a circuit. Input Port 8 10 Output Port Fig. Q1b c) i) A lossy transmission line has the following primary constants: R = 55 m/m, G = 600 pS/m, L = 600 nH/m and C = 40 pF/m. The transmission line is used to transmit a signal at 1 kHz. Calculate the phase velocity of the 1 kHz signal. Also calculate how much in dB the magnitude of the signal will be attenuated after 10 km. ii) Will the attenuation and phase velocity be the same for a 2 kHz signal? What do you call this phenomenon? 5
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Transcribed Image Text: 1. 5 5 a) i) A lossless coaxial cable has a characteristic impedance of 50 2. Explain what the characteristic impedance means. ii) The 50 2 lossless coaxial cable is filled with a dielectric material between the inner conductor and the outer conductor. The material has a dielectric constant of ε = 4. Another lossless coaxial cable has the same size as this cable but is filled with a new material having a dielectric constant of ε = 2. Is the characteristic impedance of the other cable smaller or greater than 50 s2? Justify your answer. 7 b) The top layer of a microstrip circuit is shown in Fig. Q1b. Apart from the input and output ports, the lengths of the other three microstrip lines are about half wavelength. i) Draw the equivalent circuit of this microstrip circuit using inductors and capacitors; ii) Explain the most likely function of the circuit. Describe what parameters are usually used to characterise such a circuit. Input Port 8 10 Output Port Fig. Q1b c) i) A lossy transmission line has the following primary constants: R = 55 m/m, G = 600 pS/m, L = 600 nH/m and C = 40 pF/m. The transmission line is used to transmit a signal at 1 kHz. Calculate the phase velocity of the 1 kHz signal. Also calculate how much in dB the magnitude of the signal will be attenuated after 10 km. ii) Will the attenuation and phase velocity be the same for a 2 kHz signal? What do you call this phenomenon? 5
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c) Solution.The given parameters{:[R=55mOmega//m],[G=600 rhos//m],[L=600nH//m],[C=40pF//m],[" frequency "omega=2pi f=2pi xx10^(3)=2000 pird//s]:}(i) )The propagation constant gamma=sqrt((R+j omega L)(G+j omega C)){:[=sqrt((RG-omega^(2)LC)+j omega(RC+LG))],[=sqrt((-9.14 xx10^(-10))+j(2.2 xx10^(-12)))],[=sqrt(9.14 xx10^(-10)e^(-j(0.137)))],[=3.023 xx10^(-5)e^(-j(0.068))],[" attenuation constant "alpha=Re{gamma}=Re{3.023 xx10^(-5)exp(-j 0.068)}],[=Re{3.023 xx10^(-5)(cos(.068)+j sin(.068)}:}],[=3.023 xx10^(-5)]:}[Angles are taken is degree] Phase constant {:[beta=g_(m){gamma} ... See the full answer