Tee (Not a Coupler) Open Circuit Line. Z Z Z jz d

Transcription

1 ECSE-2 Spring 22 Analysis Using Matlab Cable System R2 T2 Tee (Nt a Cupler) T TV Set Input R V T3 Open Circuit Line The basic principle f this signal blcker is relatively simple. The CATV cable (T2 in the figure abve) is interrupted with a Tee cupler t which is cnnected a shrt piece f cable (T3 abve) with nthing cnnected t it (pen circuited line). The input impedance f this extra piece f cable adds in parallel t the input impedance f the cable that runs frm the Tee t the TV set (T abve). Assuming that the cable is prperly matched t the TV, the input impedance f the cable cnnected t the TV (T) will be equal t the characteristic impedance f the cable. In this case, the impedance f the cable and the TV is 75 hms. Since the input impedance f any cable (Z in ) is a functin f the electrical length f the cable (thrugh the terms like tanβd where d is the length), the Z in f the pen-circuited cable (T3) will change with frequency. If the length f this cable is prperly selected, the signal frm ne CATV channel will be reflected frm the Tee while the signals frm ther channels will nt be reflected. A crude explanatin f hw this can wrk can be made by lking just at tw frequencies where Z in is either very small r very large. Fr example, assume that the extra piece f cable has a length = d. Als, assume that it is insulated with plyethylene ε r = Then the velcity f prpagatin n the line is v = 2 x 8 m/s. In the simulatin f this line, ne can either reduce the expressin fr Z in fr an pen circuit r just use a very large value fr Z L. T be as general as pssible, chse the latter apprach. Then Z Z Z jz d L + tan β in = jz ct β d. When this is Z + jz tan βd very large (ctβd ), adding it in parallel t the cable will have n effect. When this is very small (ctβd ), adding it in parallel t the cable will lk like a shrt circuit and which is as large an impedance mismatch as can be btained. The input impedance f an pen circuited cable is Z Z Z jz d L + tan β in = jz ct βd while the input impedance f a matched cable is Z + jzl tan βd Zin = Z. Ideally, at the lcatin f the Tee, these tw impedances will add in parallel. Since this is a parallel cmbinatin, it is easier t add them as admittances. Y in =/Z in and Y in =/Z, respectively. K. A. Cnnr Revised: 2/5/22 L

2 ECSE-2 Spring 22 Infrmatin n the Standard Cable-TV Frequencies can be fund at Cable TV frequencies run frm abut 5MHz t 65MHz, accrding t the reference abve. The fllwing Matlab m-file was written t analyze the blcker design. In this prgram, the frequency f is specified as a vectr cvering the entire range f CATV frequencies. Then Z and Z L (called Zl in the prgram) are given and β is determined fr each frequency frm the prpagatin velcity v. Next, the input impedance f the pen circuit line is determined at each f the frequencies. S far we have three vectrs f equal length f, β, and Z in. Next, the parallel cmbinatin f the tw impedances is determined. This cmbinatin (Zttal) is nw the lad seen by the riginal CATV cable. Zttal Z The reflectin cefficient n the riginal cable is then determined frm Γ =, Zttal + Z where we have used Ref instead f Γ due t Matlab limitatins. The transmissin cefficient is then determined frm τ = +Γ r Trans = +Ref in Matlab. The transmissin cefficient tells us what transmits past the Tee int the TV set. We then plt the real and imaginary parts f each f these terms alng with their magnitude. It is the magnitude that is f the mst interest. The utput plts frm this prgram fr d=.25m are shwn after the prgram listing. % Prgram fr mdeling a CATV channel blcker % K. A. Cnnr Nvember 999 f=[5:.:65]*e7; Z=75; d=.224; beta=2*pi*f/2e8;zl=e8; % Input impedance f the pen circuit line Zin=Z.*(Zl+j.*Z.*tan(beta.*d))./(Z+j.*Zl.*tan(beta.*d)); % Cmbinatin f Zin and Z Zttal=./(./Zin+./Z); % Reflectin Cefficient Ref=(Zttal-Z)./(Zttal+Z); % Transmissin Cefficient Trans=+Ref; %Pltting Results plt(f,real(zin),f,imag(zin),f,abs(zin)); title('input Impedance f Open Line');xlabel('');grid;figure; plt(f,real(ref),f,imag(ref),f,abs(ref)); title('reflectin Cefficient');xlabel('');grid;figure; plt(f,real(trans),f,imag(trans),f,abs(trans)); K. A. Cnnr 2 Revised: 2/5/22

3 ECSE-2 Spring 22 title('transmissin Cefficient');xlabel('');grid; Output Plts x 7 Input Impedance f Open Line x 8 Reflectin Cefficient x 8 K. A. Cnnr 3 Revised: 2/5/22

4 ECSE-2 Spring 22 Transmissin Cefficient x 8 Nte that, fr this chice f length, the blcked frequencies are at 2MHz and 6MHz. 4 x 5 Input Impedance f Open Line x 8 K. A. Cnnr 4 Revised: 2/5/22

5 ECSE-2 Spring 22 Reflectin Cefficient x 8 Transmissin Cefficient x 8 which blcks the particular frequency f 223.2MHz. K. A. Cnnr 5 Revised: 2/5/22

6 ECSE-2 Spring 22 The equipment in the studi differs frm the CATV test in frequency range (-5 MHz is pssible using the functin generatr) and cable characteristic impedance (Z =5hms). Set up the cnfiguratin shwn belw using three pieces f cax frm the cable bx. Cnnect t Tees as shwn. Measure the length f the pen circuit cable. If it is nt at least 4 meters lng, add anther piece f cable using a Tee t increase the ttal length. Measure the length f this cable cmbinatin. Input this length int the equatins used t mdel the blcker, using 5 hms fr Z. The mdified cde and the results f such analysis fllw. Functin Generatr R2 Tee T2 Tee T Tee 5 Ohm Terminatr R V 5 5 R4 Meg 'Scpe Channel Open Circuit Cax T3 R3 Meg 'Scpe Channel 2 % K. A. Cnnr Nvember 999 f=[.5:.:5]*e6; Z=5% Prgram fr mdeling a CATV channel blcker ; d=5; beta=2*pi*f/2e8;zl=e8; % Input impedance f the pen circuit line Zin=Z.*(Zl+j.*Z.*tan(beta.*d))./(Z+j.*Zl.*tan(beta.*d)); % Cmbinatin f Zin and Z Zttal=./(./Zin+./Z); % Reflectin Cefficient Ref=(Zttal-Z)./(Zttal+Z); % Transmissin Cefficient Trans=+Ref; %Pltting Results plt(f,real(zin),f,imag(zin),f,abs(zin)); title('input Impedance f Open Line');xlabel('');grid;figure; plt(f,real(ref),f,imag(ref),f,abs(ref)); title('reflectin Cefficient');xlabel('');grid;figure; K. A. Cnnr 6 Revised: 2/5/22

7 ECSE-2 Spring 22 plt(f,real(trans),f,imag(trans),f,abs(trans)); title('transmissin Cefficient');xlabel('');grid; 25 Input Impedance f Open Line x 6 Reflectin Cefficient x 6 K. A. Cnnr 7 Revised: 2/5/22

8 ECSE-2 Spring 22 Transmissin Cefficient x 6 Nte that this cmbinatin f cables (d=5meters) blcks frequencies arund MHz. Manually change the frequency f the functin generatr while bserving bth the input and utput t the cables as indicated. A very small utput vltage (relative t the input) shuld be bserved arund MHz, if the experiment is set up crrectly. K. A. Cnnr 8 Revised: 2/5/22