INF5481 RF Circuit, Theory and Design
Assignment #2
Problem 1
Z0 = 50 Ω
l0 = 0.4λ
ZL = 60 + j75 Ω
Zin
Figure 1: Diagram for problem 1
We have a 50 Ω line connected to a complex load as shown in figure 1.
Using a smith chart, we want to find ΓL , SWR, YL and Zin .
(a)
Normalize the load impedance and mark zL = ZL /Z0 on a smith chart. Read
of the reflection coefficient at the load.
(b)
Draw a circle that intersects with zL centered at z = 1 and read of the
standing wave ratio.
(c)
Use a ZY smith chart to read of the load admittance.
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INF5481: Assignment #2
(d)
Rotate the load reflection coefficient from l = 0 to l = 0.4λ, read of the input
impedance.
Problem 2
l7 = λ/4
C8 = 2.2 pF
l5 = λ/4
l6 = 0.4λ
l3 = 0.15λ
R4 = 33 Ω
L2 = 2 nH
R1 = 85 Ω
Z0 = 50 Ω
Zin
Figure 2: Diagram for problem 2, all transmission lines are lossless and 50 Ω.
In a patent for a GSM900 receiver circuit working at 940 MHz, you find
the circuit diagram in figure 2. You decide to investigate the circuit using
a smith chart. Start at the load and work you way to the input, show
intermediate steps and give the un-normalized input impedance Zin .
If you arrived around 30 Ω, can you think of a simpler circuit to transform
a 85 Ω load to 30 Ω?
Problem 3
We now study the shorted and open transmission lines in figure 3.
(a)
Find the required length l0 to achive an input impedance Zin = −25j Ω.
(b)
Find the required length l1 to achive an input admitance Yin = 0.04j Ω.
Is your answer unique?
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INF5481: Assignment #2
Z0 = 50 Ω
Z0 = 50 Ω
l0 =?
l1 =?
ZL = ∞
ZL = 0
Zin = −25j Ω
Yin = 0.04j Ω
(a) Short circuit
(b) Open
Figure 3: Diagrams for problem 3
Problem 4
We have the complex load in figure 4, which we want to match to Zin = 50 Ω.
Use a smith chart to find the required values for L and C at 100 MHz.
L
C
Zload = 10 + 40j Ω
Zin = 50 Ω
Figure 4: Diagram for problem 4
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