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## PowerPoint Slideshow about ' 16.360 Lecture 4' - guinevere-burch

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- Transmission lines

- Transmission line parameters, equations
- Wave propagations
- Lossless line, standing wave and reflection coefficient
- Input impedence
- Special cases of lossless line
- Power flow
- Smith chart
- Impedence matching
- Transients on transmission lines

- Transmission line parameters, equations

B

A

VBB’(t) = VAA’(t)

VBB’(t)

Vg(t)

VAA’(t)

L

A’

B’

VAA’(t) = Vg(t) = V0cos(t),

Low frequency circuits:

VBB’(t) = VAA’(t)

Approximate result

VBB’(t) = VAA’(t-td) = VAA’(t-L/c)

= V0cos((t-L/c)),

A

VBB’(t)

Vg(t)

VAA’(t)

L

A’

B’

16.360 Lecture 4

- Transmission line parameters, equations

Recall: =c, and = 2

VBB’(t) = VAA’(t-td) = VAA’(t-L/c)

= V0cos((t-L/c))

= V0cos(t- 2L/),

If >>L, VBB’(t) V0cos(t) = VAA’(t),

If <= L, VBB’(t) VAA’(t), the circuit theory has to be replaced.

A

VBB’(t)

Vg(t)

VAA’(t)

L

A’

B’

16.360 Lecture 4

- Transmission line parameters, equations

e. g: = 1GHz, L = 1cm

Time delay

t = L/c = 1cm /3x1010 cm/s = 30 ps

Phase shift

= 2ft = 0.06

VBB’(t) = VAA’(t)

= 10GHz, L = 1cm

Time delay

t = L/c = 1cm /3x1010 cm/s = 30 ps

Phase shift

= 2ft = 0.6

VBB’(t) VAA’(t)

A

VBB’(t)

Vg(t)

VAA’(t)

L

A’

B’

16.360 Lecture 4

- Transmission line parameters

- time delay

VBB’(t) = VAA’(t-td) = VAA’(t-L/vp),

- Reflection: the voltage has to be treat as wave, some bounce back

- power loss: due to reflection and some other loss mechanism,

- Dispersion: in material, Vp could be different for different wavelength

E

16.360 Lecture 4

- Types of transmission lines

- Transverse electromagnetic (TEM) transmission lines

B

E

a) Coaxial line

b) Two-wire line

c) Parallel-plate line

d) Strip line

e) Microstrip line

- Types of transmission lines

- Higher-order transmission lines

a) Optical fiber

b) Rectangular waveguide

c) Coplanar waveguide

- Lumped-element Model

- Represent transmission lines as parallel-wire configuration

A

B

Vg(t)

VBB’(t)

VAA’(t)

B’

A’

z

z

z

R’z

L’z

L’z

R’z

L’z

R’z

Vg(t)

G’z

C’z

C’z

C’z

G’z

G’z

Definitions of TL dimensions

TEM (Transverse Electromagnetic): Electric and magnetic fields are orthogonal to one another, and both are orthogonal to direction of propagation

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