SP 5.4-1 soln - KU ITTCjstiles/723/handouts/SP 5.4-1 soln.pdf · 4/4/2008 SP 5.4-1 soln 1/2 Jim...
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4/4/2008 SP 5.4-1 soln 1/2 Jim Stiles The Univ. of Kansas Dept. of EECS Special Problem 5.4-1 A matching network has been constructed to match a complex load to a transmission line with characteristic impedance 0 50 Z = Ω . The design frequency of this matching network is 0 10 f MHz = . Note that this matching network is not specifically one of the standard designs that we studied. The capacitor has a capacitance of value: 9 10 2 C farads π − = Determine the complex admittance L Y of the load. Solution First, combine the capacitor and L Y to form an new load with admittance L Y ′ : 0 50 Z = Ω 01 100 Z = Ω L Y 4 λ 0 in Γ = C
Transcript of SP 5.4-1 soln - KU ITTCjstiles/723/handouts/SP 5.4-1 soln.pdf · 4/4/2008 SP 5.4-1 soln 1/2 Jim...
4/4/2008 SP 5.4-1 soln 1/2
Jim Stiles The Univ. of Kansas Dept. of EECS
Special Problem 5.4-1 A matching network has been constructed to match a complex load to a transmission line with characteristic impedance 0 50Z = Ω . The design frequency of this matching network is 0 10f MHz= . Note that this matching network is not specifically one of the standard designs that we studied. The capacitor has a capacitance of value:
9102
C faradsπ
−
=
Determine the complex admittance LY of the load. Solution First, combine the capacitor and LY to form an new load with admittance LY ′ :
0 50Z = Ω 01 100Z = Ω LY
4λ
0inΓ = C
4/4/2008 SP 5.4-1 soln 2/2
Jim Stiles The Univ. of Kansas Dept. of EECS
where:
( )0
97 102 10
20.01
L L
L
L
Y j C Y
j Y
j Y
ω
ππ
−
′ = +
⎛ ⎞= +⎜ ⎟
⎝ ⎠= +
Now, in order for 0inΓ = , we know that (because of the 4
λ
transformer):
201 0
20 01
L LZ ZZ YZ Z
′ ′= ⇒ =
And so if matched:
( )0
2201
50 0 005100L
ZY .Z
′ = = =
Therefore:
0.005 0.01 0.005 0.01L L LY j Y Y j⇒ = −′ = = +
0 50Z = Ω 01 100Z = Ω 0L LY j C Yω′ = +
4λ
