Cable System Network Design Considerations in Software

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Cable System Network Design Considerations
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Questions
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1 Explain the difference between telephone system local lines and trunk lines 2 What is the purpose for twisting the pairs of wires in a telephone cable 3 What is the purpose of placing loading coils (inductances) in telephone line circuits 4 What does the acronym CATV mean 5 Describe the network architecture for cable television systems 6 Describe cable system choices of method for the reverse of upstream network 7 Describe how optical- ber technology is used in the forward or downstream sections of a cable television plant 8 Explain an HFC network 9 What is the largest network protocol for LAN networks 10 Describe the three choices of network topology for LAN systems 11 What type of network topology is used for Ethernet 12 Explain the process used to transmit digital signals on a cable system
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APPENDIX A
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Proof and Discussion of Pertinent Equations
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1 The rst two equations are explained using the simple resistance capacitance circuit where the input voltage source is in series with a resistor of R ohms in series with a capacitor of C microfarads The output voltage is taken across the capacitor
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This circuit, in many applications, represents a voltage source where R is the equivalent resistance and C is the Miller capacitance of the ampli er input connected across the capacitance C When Vin is a sinusoidal signal voltage, the ac value of the capacitive reactance in ohms is Xc 1 _____ 2pfC when the magnitude of Xc 1/2pfC, f 1 ______ 2pRC R in solving for f
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where f is the frequency of the input voltage Vin (RMS) when Xc R This is called the cut-off frequency of this simple low-pass lter, which is often referred to as a basic integrator The attenuation in output voltage at this frequency may be calculated as follows using the voltage divider theorem: Vout Xc _____ (V ) in Rj Xc where RjX c is 90 leading
Converting to polar coordinates and solving,
out ______
V Vin
Xc _________________ (R2 Xc X 2)arctan___ c R
Copyright 2005 by The McGraw-Hill Companies, Inc Click here for terms of use
Since Xc R, Vout ____ Vin Vout |Xc| _______ (2X c)
2 1/2
Appendix A
|Xc| ________ (Xc)(2)1/2 Vout or ____ Vin
1 _____ (2)1/2 0707
0707Vin
Since Vout /Vin represents the circuit gain, Vout 20 log ____ Vin 20 log 0707 3 dB
where the minus sign means a negative gain or attenuation 2 Proof of the rise time equation for the same resistor capacitive circuit Since digital signal voltages vary between two values, the response of this circuit to sudden voltage changes is important The rise time is the measure of this response A short rise time means this circuit responds faster to sudden changes in input voltage This circuit follows the charging curve for the RC circuit where R C the circuit time constant where R is in ohms and C is in farads Since the output voltage is Vc, we may write Vc Vmax(1 e
t/RC
where RC
time constant
The IEEE stated that the rise time is the time it takes for Vc at 01Vmax to reach V at 09Vmax Vc and substituting, 01Vmax Multiplying, 01Vmax Combining terms, 09Vmax Vmaxe
t/RC
01Vmax
Vmax(1
t/RC
Vmax
Vmaxe
t/RC
Proof and Discussion of Pertinent Equations
Dividing by Vmax and multiplying by 09 1, e
t/RC
Taking the natural logarithm of both terms, ln Using the calculator, 09 So t 01RC at 01Vmax when Vc 09Vmax Multiplying, 09Vmax Vmax Vmaxe Dividing by Vmax, multiplying by e Taking the natural logarithm, ln e Solving for t, t ___ RC 23 at 09Vmax
t/RC
ln e
t/RC
t ___ RC
09Vmax Substituting, Vmax(1 e
t/RC
Vmaxe
t/RC
t/RC
01Vmax
1, and rearranging terms,
t/RC
ln 01
The rise time is de ned as the time it takes for the capacitor to charge from 10% Vmax to 90% Vmax Rise time tr t09 t01 01RC 22RC
23RC tr 22RC
Appendix A
To investigate the frequency response of this basic low-pass lter, recall that we previously derived fc Solving for the RC product, RC Substituting for RC tr/22, RC tr ___ 22 22 ____ 2pfc Solving for fc, fc 035 _____ tr 1 ____ 2pfc 035 _____ fc 1 ______ 2pfc 1 ______ 2pRC
Since the bandwidth (BW) is from zero frequency to the cut-off frequency, fc Substituting, BW 035 _____ tr BW
This result relates the low-pass lter circuit bandwidth to the rise time A shorter (quicker rise time) increases the bandwidth 3 Proof of the equation Pr ___ Pt Gt Gr 325 dB 20 log dkm 20 log fMHz
Consider a source of power at a point in space radiating electromagnetic energy into space in all directions the equation describing this action is
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