about bounce diagram

7/28/2019 About Bounce Diagram

1/22

Bounce Diagrams

for Transmission Lines

Lectures 35


2/22

Solution to TL equation

V =V+

+V"

I= 1Z

0

(V+ "V") = I+ + I"

I+

=

V+

Z0

I"= "

V"

Z0

Solution to TL equation is summation of traveling waves

propagating in the +z or -z directions


3/22

Example

Z0

z=0 z=l

RLRg

V0

t=0, close

vp


4/22

Example, t=0

Rg

V0

+

-

V+

I+

At t=0, a wave originates at z=0 and starts to travel in

the +z direction

Until the wave propates to the end and reflects back,

there is no V- wave, and the load resistance RL has no

effect.

Z0


5/22

Example t=T

T=l

vpTime required for V+ wave to reach

load end of the TL

z=l

RL

+

-

(V++V-)

(I++ I-)

Wave reflects to set up a - wave IN ADDITION TO the

+ wave


6/22

Definition: Reflection Coefficient

Voltage Reflection Coefficient

Current Reflection Coefficient

" =V

#

V+=

RL# Z

0

RL + Z0

I"

I+=

"(V" /Z0)

(V+

/Z0)= "

V"

V+= "#


7/22

Example, t=2T

Rg

V0

+

-

V++V-+V-+ Z0

I++I-+I-+

Reflected wave travels back towards the source, and gets

there at t=2T

The wave gets RE-REFLECTED at the source end and

travels back toward the load as a + wave

The re-reflection process continues forever until steady

state conditions are reached


8/22

Special Case TL Terminations

Short-circuited line:

Open-circuited line:

Impedance-matched line:

RL=0

RL=infinity

RL= Z0

" =V

#

V+=

RL# Z

0

RL+ Z

0

=

0# Z0

0+ Z0

= #1

" =V

#

V+=

$# Z0

$+ Z0

=1

" =V

#

V+=

Z0# Z

0

Z0+ Z

0

= 0


9/22

Bounce Diagram

Z0=60

z=0 z=l

120 100V

t=0, close

T=1 sec40

First step: Calculate V+

, I+

, load, source

Second step: Construct 2 bounce diagrams

1. Voltage

2. Current


10/22

Voltage Current

z z

tt

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec


11/22

Voltage Current

z z

tt

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

=-1/5 =1/3 =-1/3=1/5


12/22

Voltage Current

z z

tt

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

I+

=1A

I= 0A

=-1/5 =1/3 =-1/3=1/5

V= 60V I= 1A


13/22

Question: What is V(z) at t=0.25 sec?

z

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

=-1/5 =1/3

V= 60V

z=0 z=l

V [volts]

60


14/22


z

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

=-1/5 =1/3

V= 60V

z=0 z=l

V [volts]

60


15/22

Voltage Current

z z

tt

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

I+

=1A

I= 0A

=-1/5 =1/3 =-1/3=1/5

V-=20V I-=-1/3 A

V= 60VI= 1A

V= 80V I= 2/3A


16/22


z

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

=-1/5 =1/3

V= 60V

z=0 z=l

V [volts]

60

V-=20V

V= 80V

80


17/22

Question: What is V(t) at z=0.25*l m?

z

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

=-1/5 =1/3

V= 60V

t=sec

V [volts]

60

V-=20V

V= 80V

80

0 1 2


18/22

Voltage Current

z z

tt

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

I+

=1A

I= 0A

=-1/5 =1/3 =-1/3=1/5

V-=20V I-=-1/3 A

V= 60VI= 1A

V= 80V I= 2/3A

V-+=-4V

V= 76V

I-+=-1/15 A

I= 2/3 - 1/15


19/22

Voltage Current

z z

tt

t=0

1 sec

2sec

3 sec

4 sec

5 sec

6 sec

V+

=60V

V= 0V

I+

=1A

I= 0A

=-1/5 =1/3 =-1/3=1/5

V-=20V I-=-1/3 A

V= 60VI= 1A

V= 80V I= 2/3A

V-+=-4V

V= 76V

I-+=-1/15 A

I= 2/3 - 1/15

V-+-=-1.33V

V= 74.6V

V-+-=0.26

V= 74.86V

I-=0.02 A

I-=0.004 A

I= 0.62A

I= 0.624A


20/22


21/22

Steady State

VSS

=VSS

+

+VSS

"= 75V

ISS

= ISS

+

+ ISS

"= 0.625A

VSS

+

= ISS

+

Z0

VSS

"= "I

SS

"Z

0

z=0 z=l

120

100V

40

Iss

+

-

Vss


22/22

Next time: TL Discontinuity

Z01 RLRg

V0

t=0, close

vp1 Z02 vp2

incident transmitted

reflected

about bounce diagram

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