16.360 Lecture 9

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16.360 Lecture 9

• Last lecture

• Power flow on transmission line

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16.360 Lecture 9
Last lecture Power flow on a lossless
transmission line

• Instantaneous power
• Time-average power

j?z

e
V(z) V0 ( )

?
-
i(z)
)
?
At load z 0, the incident and reflected
voltages and currents
i
i

V V0
i
r
-
r
V V0
i
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16.360 Lecture 9

• Instantaneous power

i
i
i
P(t) v(t) i(t) ReV exp(j?t) Re i
exp(j?t)




ReV0exp(j? )exp(j?t) ReV0/Z0 exp(j?
)exp(j?t)


(V0²/Z0) cos²(?t ? )
r
r
r
P(t) v(t) i(t) ReV exp(j?t) Re i
exp(j?t)
-

-

ReV0exp(j? )exp(j?t) ReV0/Z0 exp(j?
)exp(j?t)


- ?²(V0²/Z0) cos²(?t ? ?r)
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16.360 Lecture 9

• Time-average

Time-domain approach
i
?
T
T
i
Pav
P (t)dt

2?
0
0

(V0²/2Z0)
r

Pav
-?² (V0²/2Z0)
Net average power
i
r
Pav
Pav
Pav

(1-?²) (V0²/2Z0)
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16.360 Lecture 9

• Time-average

Phasor-domain approach
Pav
(½)ReV i
i


Pav (1/2) ReV0 V0 /Z0
(V0²/2Z0)
r

Pav
-?² (V0²/2Z0)

Pav
(1-?²) (V0²/2Z0)
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16.360 Lecture 9
Pav
(½)ReV i
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16.360 Lecture 9
Today Smith chart

• parameter equations
• input impedance

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16.360 Lecture 9
Parameter equations
Unit circuit
.
Short Circuit load
B
Open Circuit load
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16.360 Lecture 9
Normalized impedance
Parameter equations
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16.360 Lecture 9
Parameter equations
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16.360 Lecture 9
An example
Smith Chart
Input impedance
Wavelength toward generator (WTG)
Smith Chart
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16.360 Lecture 9
An example
find Zin (-0.1?)
Smith Chart
Constant ? circle, SWR Circle
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16.360 Lecture 9
Next lecture

• SWR

• Voltage maxima and minima

• Impedance to Admittance transformations

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16.360 Lecture 9
SWR, voltage maximum and minimum
If
Smith Chart
Recall
when 2?z ?r 2n?.
when 2?z ?r (2n1)?.
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