電子學題解ch

1、6-6Solutions for Chapter 6 Problems1. Distributed Parameters ModelP6.1: RG-223/U coax has an inner conductor radius a = 0.47 mm and inner radius of the outer conductor b = 1.435 mm. The conductor is copper, and polyethylene is the dielectric. Calculate the distributed parameters at 800 MHz.P6.2: MATLAB: Modify MATLAB 6.1 to account for a magnetic conductive material. Apply this program to problem P6.1 if the copper conductor is replaced with nickel.Note that this program has also been modified f

2、or P6.04 as well.%Coax distributed parameters% Modified: P0602% add rel permeability% also modified for P0604%clearclcdisp(Calc Coax Distributed Parameters)%Some constant valuesmuo=pi*4e-7;eo=1e-9/(36*pi);%Prompt for input valuesa=input(inner radius, in mm, = );b=input(outer radius, in mm, = );er=input(relative permittivity, er= );sigd=input(dielectric conductivity, in S/m, = );sigc=input(conductor conductivity, in S/m, = );ur=input(conductor rel. permeability, = );f=input(input frequency, in Hz

3、, = );%Perform calulationsG=2*pi*sigd/log(b/a);C=2*pi*er*eo/log(b/a);L=muo*log(b/a)/(2*pi);Rs=sqrt(pi*f*ur*muo/sigc);R=(1000*(1/a)+(1/b)*Rs)/(2*pi);omega=2*pi*f;RL=R+i*omega*L;GC=G+i*omega*C;Gamma=sqrt(RL*GC);Zo=sqrt(RL/GC);alpha=real(Gamma);beta=imag(Gamma);loss=exp(-2*alpha*1);lossdb=-10*log10(loss);%Display resultsdisp(G/h = num2str(G) S/m)disp(C/h = num2str(C) F/m)disp(L/h = num2str(L) H/m)disp(R/h = num2str(R) ohm/m)disp(Gamma= num2str(Gamma) /m)disp(alpha= num2str(alpha) Np/m)disp(beta= nu

4、m2str(beta) rad/m)disp(Zo = num2str(Zo) ohms)disp(loss= num2str(loss) /m)disp(lossdb= num2str(lossdb) dB/m)Now run the program for Nickel:Calc Coax Distributed Parametersinner radius, in mm, = 0.47outer radius, in mm, = 1.435relative permittivity, er= 2.26dielectric conductivity, in S/m, = 1e-16conductor conductivity, in S/m, = 1.5e7conductor rel. permeability, = 600input frequency, in Hz, = 800e6G/h = 5.6291e-016 S/mC/h = 1.1249e-010 F/mL/h = 2.2324e-007 H/mR/h = 159.7792 ohm/mGamma= 1.78881+25

5、.252i /malpha= 1.7888Np/mbeta= 25.252rad/mZo = 44.6608-3.1637i ohmsloss=0.027942 /mlossdb=15.5374 dB/mSummarizing the distributed parameter data from this routine we have:P6.3: Modify (6.3) to include internal inductance of the conductors. To simplify the calculation, assume current is evenly distributed across the conductors. Find the new value of L for the coax of Drill 6.1.From Amperes Circuit Law we can find H versus r:Using the energy approach, , we findInserting the given values we findWit

6、h two significant digits we therefore have L = 330 nH/m.2. Time Harmonic Waves on Transmission LineP6.4: MATLAB: Modify MATLAB 6.1 to also calculate g, a, b and Zo. Confirm the program using Drill 6.2.See the solution for P6.2.Calc Coax Distributed Parametersinner radius, in mm, = 0.45outer radius, in mm, = 1.47relative permittivity, er= 2.26dielectric conductivity, in S/m, = 1e-16conductor conductivity, in S/m, = 5.8e7conductor rel. permeability, = 1input frequency, in Hz, = 1e9G/h = 5.3078e-01

7、6 S/mC/h = 1.0606e-010 F/mL/h = 2.3675e-007 H/mR/h = 3.8112 ohm/mGamma= 0.0403332+31.4857i /malpha= 0.040333Np/mbeta= 31.4857rad/mZo = 47.246-0.0605221i ohmsloss=0.9225 /mlossdb=0.35033 dB/mThis agrees with the results of Drill 6.2.P6.5: The impedance and propagation constant at 100 MHz for a T-Line are determined to be Zo = 18.6 j0.253 W and g = 0.0638 + j4.68 /m. Calculate the distributed parameters.P6.6: The specifications for RG-214 coaxial cable are as follows: 2.21 mm diameter copper inner

8、 conductor 7.24 mm inner diameter of outer conductor 9.14 mm outer diameter of outer conductor Teflon dielectric (er = 2.10)Calculate the characteristic impedance and the propagation velocity for this cable.P6.7: For the RG-214 coax of problem P6.6 operating at 1 GHz, how long is this T-line in terms of wavelengths if its physical length is 50 cm?P6.8: If 1 watt of power is inserted into a coaxial cable, and 1 microwatt of power is measured 100 m down the line, what is the lines attenuation in d

9、B/m?P6.9: Starting with a 1 mm diameter solid copper wire, you are to design a 75 W coaxial T-Line using mica as the dielectric. Determine (a) the inner diameter of the outer copper conductor, (b) the propagation velocity on the line and (c) the approximate attenuation, in dB/m, at 1 MHz.So the inner diameter of the outer conductor is 18 mm.To calculate a, will need g. Therefore we calculate R, L, G and C.Now, with w = 2pf,Finally, This is confirmed using MLP0602.P6.10: MATLAB: A coaxial cable has a soli

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