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Test: Smith Chart - Electronics and Communication Engineering (ECE) MCQ


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10 Questions MCQ Test Electromagnetics - Test: Smith Chart

Test: Smith Chart for Electronics and Communication Engineering (ECE) 2024 is part of Electromagnetics preparation. The Test: Smith Chart questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Smith Chart MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Smith Chart below.
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Test: Smith Chart - Question 1

Consider the following statements regarding the Smith's chart:

1. Smith's chart is a graphical indication of the impedance of a transmission line and of the corresponding reflection coefficient as one moves along the line.

2. λ distance on the line corresponds to a 720° movement on the Smith's chart.

3. The admittance chart can be obtained by shifting each and every point on the impedance chart by 90°.

4. Counter-clockwise movement on the chart corresponds to moving towards the generator.

which of the above statements are correct?

Detailed Solution for Test: Smith Chart - Question 1

Smith's chart → The smith's chart provides a graphical representation of the impedance of the transmission line and of the corresponding reflection coefficient (Γ) (option 1 is correct)

It is the intersection of two circles→

(1) constant R-circles

 

(2) constant x-circles 

complete circle in smith's chart i.e R = ∞ to R = ∞ is λ /2

360° = λ/2→ λ = 720°  (option 2 is correct)

every point on the impedance Smith chart can be converted into its admittance counterpart by taking a 180° rotation (option 3 is incorrect)

clockwise movement on the chart corresponds to moving towards the generator. (option 4 is incorrect)

Test: Smith Chart - Question 2

When the load impedance is equal to the characteristic impedance of the transmission lines, then the reflection coefficient and standing wave ratio are, respectively _________.

Detailed Solution for Test: Smith Chart - Question 2

The voltage standing wave ratio is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current).

VSWR is also given by:

Γ = Reflection coefficient, defined as:

ZL = Load impedance

Z0 = Characteristic Impedance

For ΓL varying from 0 to 1, VSWR varies from 1 to ∞.

Application:

Given ZL = Z0

The reflection coefficient is calculated to be:

VSWR for Γ = 0 equals 1, which is the minimum value (because it varies from 1 to ∞)

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Test: Smith Chart - Question 3

Identify the type of load, at lossless transmission line if the Voltage standing wave pattern is found to be

Detailed Solution for Test: Smith Chart - Question 3

Concept: Consider the points in diagrams shown below. 

Now According to VSWR identify where do load can exist. if VSWR is Infinite then load will be anywhere on outer circle otherwise inside the circle.

1. If VSWR is infinite and Maxima at load then load will be Open circuit.

2. If VSWR is infinite and Minima at load then load will be Short circuit.

3. If VSWR is infinite and neither maxima nor minima occur at load,  now  if we move away from the load and minima comes first  then load will be Purely capacitive.

4. If VSWR is infinite and neither maxima nor minima occur at load,  now  if we move away from the load and maxima comes first  then load will be Purely inductive.

5. If VSWR is finite(not equal to 1) and Maxima occur at load then load will be Purely resistive with RL > Z0

6. If VSWR is finite(not equal to 1) and Minima at load then load will be Purely resistive with RL < Z0.

7. If VSWR is finite(not equal to 1) and neither maxima nor minima occur at load,  now  if we move away from the load and minima comes first  then load will be capacitive.

8. If VSWR is finite(not equal to 1) and neither maxima nor minima occur at load,  now  if we move away from the load and maxima comes first  then load will be inductive.

9. If VSWR is finite and equal to 1 then Load is purely resistive with RL = Z0

Solution: 

1. we can see VSWR is finite so we are somewhere inside the circle and as there is minima at load so we are on the line of minima. 

2. So load is purely Resistive. Moreover R< Z0.

Hence option C is correct.

Test: Smith Chart - Question 4

The impedances Z = jX, for all X in the range (-∞, ∞), map to the Smith chart as

Detailed Solution for Test: Smith Chart - Question 4

Concept:

For drawing a smith chart:

First, we calculate normalized impedance (z)

     …1)

Then we solve for constant R circles and constant X-circles by using the following formulas:

Const. R circles:

Const. X circles:

Where, ΓR = Real part of reflection coefficients.

ΓI = Imaj part of reflection coefficients.

Calculation:

Given: Z = j X

Compare this with equation (1), we can write:

R = 0

After putting this value in equation (2), we get:

R)2 + (ΓI)2 = 1     …4)

Equation (4) represents the equation of a unit circle with center (0, 0). Hence option (a) is correct.

Test: Smith Chart - Question 5

A transmission line having characteristic impedance ‘Z1’ of varying length in series with a load impedance  ‘ZL’ appears in a Smith Chart on

Detailed Solution for Test: Smith Chart - Question 5

The reflection coefficient at the load is defined as:

, where ZL = load impedance and Z0 = characteristic impedance.

Also, VSWR = 

Clearly, VSWR is a function of ZL and Z0.

For the given transmission line, Z0 = Zt and ZL = ZL

So, VSWR is constant and it doesn’t change with the length of the line, In the smith chart, this is represented as a constant VSWR circle.

Test: Smith Chart - Question 6

Impedance characteristics on a Smith Chart repeat after a distance of

Detailed Solution for Test: Smith Chart - Question 6

Concept

Where β = 2π/λ

Application:

When l = 0 (i.e. at the load),

When l = λ2

Hence the input impedance (or the Smith Chart) repeats itself every half-wavelength, i.e. a half-wavelength along the transmission line corresponds to a complete rotation on the Smith chart.

Test: Smith Chart - Question 7

Which is indicated the Reflection coefficient, If ‘n’ is refractive index of incident medium and n1 is the refractive index of transmitted medium?

Detailed Solution for Test: Smith Chart - Question 7

Concept:

Normal Incidence is as shown:

The Reflection coefficient is defined as:

Where:

η1 = intrinsic impedance of medium 1

η2 = intrinsic impedance of medium 2

Note:

This question is given wrongly in the official paper and full marks was awarded to all. 

Test: Smith Chart - Question 8

In the following Smith Chart, Constant VSWR circle

the movement from y along a constant VSWR circle to y1 needs addition of

Detailed Solution for Test: Smith Chart - Question 8

Concept:

VSWR: Voltage standing wave ratio is a measure of low-efficiency radio frequency power is transmitted from a power source through a transmission line into a load.

Range of VSWR is from 1 to ∞

In the smith chart clockwise movement represents the increase in impedance and its represent towards the generator.

Solution:

Capacitive reactance should be connected in shunt to increase the reactance

So movement from y to y1 is clockwise so correct option is (b) i.e. capacitance should be connected in shunt with y

Important Points:

Inductive reactance should be connected in series for clockwise movement in the smith chart.

More information on about smith chart:

(1) One complete movement is represented (360°) represent λ/2 distance λ → 720°

(2) Smith's chart is used for both impedance and admittance chart.

Test: Smith Chart - Question 9

The Smith chart consists of the

Detailed Solution for Test: Smith Chart - Question 9

The Smith chart consists of the constant resistance circles and the constant reactance circles. The impedances are plotted using these circles. Also stub matching can be done using the Smith chart.

Test: Smith Chart - Question 10

The best stub selection for the transmission line will be

Detailed Solution for Test: Smith Chart - Question 10

Normally series stubs are not preferred as modification of the stub parameters requires changing the whole stub setup. Shunt stubs enable modification with ease. Open circuited stubs are not preferred as it will radiate power like an antenna, which is undesirable. Hence shorted stubs are used.

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