Download Tutorial 2 with answers

Tutorial 2: Matching Network
Matching Network:
1.
Considered the transmission line circuit shown below. Compute the incident
power, the reflected power and the power transmitted into the infinite 75Ω
line. Show that power conservation is satisfied.
(Answer: Power delivered by source: 0.4 W; Power dissipated in 50 Ohm
load = 0.16 W; Power transmitted down the line = 0.24 W; Incident
power = 0.25 W; Reflected power = 0.010 W)
2.
Use Smith chart to find the following quantities for the transmission line
circuit below:
(a) The SWR on the line
(b) The reflection coefficient at the load
(c) The load admittance.
(d) The input impedance of the line.
(e) The distance from the load to the first voltage minimum.
(f) The distance from the load to the first voltage maximum.
(Answer: From Smith chart, z L  1.2  j1.0 ; (a) SWR = 2.46; (b)
  0.42254 ; (c) YL  0.492  j0.41 / 50  9.84  j8.2 mS; (d)
Z in  24.5  j 20.3 ; (e)  min  0.325
(f)  max  0.075 )
EKT 441: Microwave Communications
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Tutorial 2: Matching Network
3.
Use the Smith chart to find the shortest lengths of a short-circuited 75Ω line to
give the following input impedance:
(a) Zin = 0.
(b) Zin = ∞.
(c) Zin = j75 Ω.
(d) Zin = -j50 Ω.
(e) Zin = j10 Ω.
(Answers: (a)   0 or   0.5 ;(b)   0.25 ; (c)   0.125 ;
(d)   0.406 ; (e)   0.021 )
4.
Repeat question 3 for an open-circuited length of 75 Ω line.
(Answers: (a)   0.25 ; (b)   0. or   0.5 ; (c)   0.375 ; (d)
  0.656  0.5  0.156 ; (e)   0.271 )
5.
A slotted line experiment is performed with the following result: distance
between successive minima = 2.1cm; distance of first voltage minimum from
load = 0.9 cm; SWR of load = 2.5. If the Z0 = 50 Ω, find the load impedance?
(Answers:   4.2cm ; 
6.
min
 0.214 ; z  2  j 0.9  Z  100  j 45 )
L
L
A single stub tuner is to match a lossless line of 400Ω to a load of 800 – j300
Ω. The frequency is 3 GHz.
(a) Find the distance in meters from the load to the tuning stub.
(b) Determine the length in meters of the short circuited stub.
3  10 8
(Answers: y L  0.438  j 0.164 ;  
 0.1m ; d  0.0124m ;
3  10 9
  0.0138m )
7.
Calculate the electrical lengths of a single stub matching network with open
circuit stub that will match a load impedance of 30 + j70 Ω to a 50 Ω input
transmission line.
(Answers: z L  0.6  j1.4 ; y L  0.26  j0.6 ; d = 0.275λ; l = 0.328λ)
8.
(a) Calculate the position and characteristic impedance of a quarter-wave
transformer that will match a load impedance, (15 + j25)Ω to a 50Ω input
line.
(b) What is the magnitude of the reflection coefficient within the transformer?
(Answers: (a) Z  102.8 ; d= 0.171λ; (b)   0.346 )
T
EKT 441: Microwave Communications
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Tutorial 2: Matching Network
9.
With the line lengths given in wavelengths where appropriate, match a (15 –
j25)Ω load to a 50Ω source with the quarter-wave transformer matching with
the transformer impedance less than 50Ω.
(Answer: Z  24.5 ; d= 0.078λ)
T
8.
Using the Smith chart, calculate the component values in figure below that
will match a 150Ω to a 50Ω source impedance at 100MHz.
(Answers: y  0.333  j 0.47 ; C  15.0 pF , z  1.0  j1.414 ; L  113nH )
9.
What capacitance values are required for the network to match a (30 + j50)Ω
load to a 50Ω source impedance at 1.0 GHz?
(Answers: y  0.441  j 0.5 ; C2  1.59 pF ; z  1.0  j1.14 ; C1  2.79 pF )
EKT 441: Microwave Communications
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