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

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)

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:

Z_L = Load impedance

Z₀ = Characteristic Impedance

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

Application:

Given Z_L = 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 ∞)

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 R_L > Z₀. 

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

Hence option C is correct.

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, Γ_R = Real part of reflection coefficients.

Γ_I = I_maj 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:

(Γ_R)² + (Γ_I)² = 1     …4)

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

The reflection coefficient at the load is defined as:

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

Also, VSWR = 

Clearly, VSWR is a function of Z_L and Z₀.

For the given transmission line, Z₀ = Z_t and Z_L = Z_L

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.

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.

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. 

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.

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.

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.