The Smith Chart and S-Parameters Admittance or Y Smith Chart. 14 A ZY Smith Chart. 15. 16. Impedance...
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The Smith Chart and S-Parameters 1
Transcript of The Smith Chart and S-Parameters Admittance or Y Smith Chart. 14 A ZY Smith Chart. 15. 16. Impedance...
The Smith Chart and S-Parameters
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Reflection Coefficient
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1
1
nl
nl
o
l
o
l
ol
ol
zz
zzzz
zzzz
Constant Resistance
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Proof:assume: Z0 = R0 + JX0 , ZL =RL + JXL znl =rl + jxl = ZL ⁄ Z0
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1
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nl
nl
o
l
o
l
ol
ol
zz
zzzz
zzzz
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nl
nlnl
z
zz
ir
irll j
jjxr
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5
2222
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)1(2
)1(1
ir
i
ir
irll jjxr
ir
irll j
jjxr
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22
22
121
irr
irlr
222 )()( rbyax 2
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110
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l
il
lr rr
r
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Constant Reactance
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222 )()( rbyax
22212
irr
ilx
222 )1()1()1(ll
ir xx
2222
22
)1(2
)1(1
ir
i
ir
irll jjxr
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A Z Smith Chart
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An Admittance or Y Smith Chart
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A ZY Smith Chart
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Impedance Matching
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Eight Possible Impedance-Matching Networks
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Example#1
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Cont’d
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Match process of the first circuit:
Example#2
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Low-pass structure
High-pass structure
Cont’d
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Example#3
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Two-step matching(a,b’,d,d’,c)
One-step matching is performed in the previous example.(a,b,c)
Cont’d
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Cont’d
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Circuit Model for Transmission Line
)m/Ω(R:
L: (H/m)
C: (F/m)
G: (S/m)
v(z,t)-RΔz i(z,t)- LΔz ( , ) – v(z+Δz,t) = 0 KVL: i(z,t)-GΔz v(z+Δz,t)-CΔz ( , ) – i(z+Δz,t)=0KCL:
( , ) = -Ri(z,t) - L ( , )( , ) = -Gv(z,t) - C ( , )
( ) = -(R+jωL)I(z)( ) = -(G+jωC)V(z)Sinusoidal steady-State Analysis:
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Cont’d
( ) = -(R+jωL)I(z)( ) = -(G+jωC)V(z)² ( )² - γ²V(z) = 0² ( )² - γ²I(z) = 0γ = α+jβ = ( + )( + )
V(z) = + I(z) = + orV(z) = + I(z) = +
I(z) = ( - )
■
It is easily proven that:
Defining: Z0 = = I(z) = -v(z,t)=| |cos(ωt-βz+ ) + | |cos(ωt+βz+ )
Z-Parameters
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S-Parameters
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= , = , = , = = += +
S-Parameters
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