Transients on Transmission Line

8/13/2019 Transients on Transmission Line

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Terminated Transmission Lines



Transmission Line

Equivalent Circuit

v(z+D z, t)

i(z, t) i(z+D z, t)

RD z LD z

GD z C D z

v(z, t)

D z

+ +

--

02 F/m ; ln H/m;

ln 2

60

ln

o r

r

C L b ab a

L Zo b a

C

8

velocity factor

3 10 m/s

pv c

c

0 0

1 1 p

r

v LC



Two Types of Measuements

• Time Domain

– Step Excitation

–

Perform TDR• Frequency Domain

– Sinusoidal Response

•

Quarter wave tranformer• Impedanc matching



Experiments

• Measurement of output impedance:

• Measurement of phase velocity in the cable:

– Open circuit coaxial cable

– Step input



Choose proper period, nice time/div, and good trigger point!



Transmission line terminated in a resistive load:

Time domain response for three types of resistive loads, (a) Z L = Z 0,

(b) Z L 0.5 Z 0, (c) Z L 2 Z 0.



Transmission line with source mismatch: Open circuited transmission line

for two different values of source impedance (a) Z S > Z 0 ; this is achieved

by connecting a 150 resistor in series (between the signal source and the

transmission line input), and (b) Z S < Z 0 ; this is achieved by connecting a

22 resistor in shunt (across the transmission line input terminals



Transmission line with capacitive termination:

Choose a value of C such that the time constant is of the

order of a tenth of microsecond.



Capacitive discontinuity in a transmission line



A micro project:

Think of a real life situation where you could apply the time

domain measurement on transmission lines.

Now, conceive of some circuit elements that would simulate

the real life situation and measure the time domain response

of the line with circuit elements in place.

Comment on the accuracy and usefulness of this technique.

You may need to study the literature to find out the

correlation between the real life situation and the electrical

circuit elements



Frequency domain response of a terminated transmission

line:

Calculate the frequency ( f 0) at which the given length of the

cable is a quarter wavelength long. Use the phase velocityinformation obtained in the earlier measurement to calculate

the wavelength () in the cable.

Connect the signal source and apply a sinusoidal signal of

frequency f 0.

Measure the voltage at the input of the transmission line with

the other end open. Plot the voltage as a function of frequency

over 0.8 f 0 to 1.2 f 0.

Now, repeat the same measurement with the line terminatedin a short circuit.



Impedance matching with a quarter wave transmission line:

Connect a 150 resistor in series with the signal source so that the

source impedance is 200 .Use sinusoidal signal for these measurements, and set the

frequency to f 0 determined earlier.

Connect a 200 load resistor across the source and confirm that

the source impedance is indeed 200. Note down the voltage. Now connect a 12.5 resistor and measure the voltage.

A load resistance Z L = 12.5 can be matched to the source of ZS =

200 using a /4 transmission line of characteristic impedance Z 0

= 50.Connect a /4 long 50 cable between the 12.5 load and the

source. Measure the voltage at the input of the line and confirm that

the /4 transformer line is able to match the load to the source.

Transients on Transmission Line

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