Smith Chart Exam

Smith chart is based on the polar plot of:

• Reactance

• Voltage

• Current

• Voltage reflection co-efficient

Answer explanation

Let the reflection co-efficient be expressed in terms of magnitude and direction as ┌=|┌|e^jθ. Magnitude is plotted as radius from the center of the chart, and the angle is measured in counter clockwise direction from the right hand side. Hence, smith chart is based on the polar pot of voltage reflection co-efficient.

Any passively realizable reflection coefficient can be plotted as a unique point on the smith chart. This statement implies that:

• Reflection co-efficient less than or equal to 1 can be plotted

• Reflection co-efficient greater than or equal to 1 can be plotted

• Transmission co-efficient has to be less than or equal to one for the point to be located

• T=Г+1

Answer explanation

Reflection co-efficient is defined as the ratio of reflected voltage /current to the incident voltage or current. Hence reflection co-efficient can never be greater than 1. Hence, only reflection co-efficient less than or equal to 1 can be plotted.

Reflection coefficient of a transmission line in its polar form can be represented as:

• ┌=|┌|e^jθ

• ┌=|┌|e^jθ-1

• ┌=|┌|e^jθ+1

• ┌=|┌|e^jθ+α

Answer explanation

Reflection c co-efficient is defined as the ratio of reflected voltage /current to the incident voltage or current. It is a complex value consisting of both real and imaginary parts. Converting it to polar form, it takes the form of ┌=|┌|e^jθ, Consisting of both magnitude and phase θ.

If the characteristic impedance of a λ/2 transmission line is 50 Ω and reflection coefficient 0.3, then its input impedance

• 26.92 Ω

• 30 Ω

• 40 Ω

• 34.87 Ω

Answer explanation

Given the characteristic impedance and reflection coefficient of a transmission line, input impedance is given by Zₒ (1+Гe^-2jβL)/ (1- Г^e-2jβL). Substituting the given values, the input impedance of the line is 26.92 Ω

If the normalized input impedance of a transmission line is 0.5 Ω, then he reflection coefficient of a λ/2 transmission line is

• 0.3334

• 0.5

• 0.6667

• 1

Answer explanation

Given the characteristic impedance and reflection coefficient of a transmission line, input impedance is given by Zₒ (1+Гe^-2jβL)/ (1- Г^e-2jβL). Substituting the given values in the above equation, reflection coefficient is 0.3334.

Normalized impedance of 0.3+j0.4 lies in the:

• Upper half of the impedance smith chart

• Lower half of the impedance smith chart

• Horizontal line of the chart

• None of the mentioned

Answer explanation

In the impedance smith chart, the upper part of the smith chart refers to positive reactance or inductive reactance. Hence, the given point lies in the upper half of the smith chart corresponding to the intersection of circles r=0.3 and r=0.4

Normalized impedance of 1-j is:

• In the upper half of the impedance smith chart

• In the Lower half of the impedance smith chart

• On the outer most circle of the smith chart.

• On the horizontal line of the smith chart

Answer explanation

In the impedance smith chart, the lower half of the smith chart corresponds to negative reactance or capacitive reactance. Hence the given point lies in the lower half of the smith chart.

If a transmission line of a characteristic impedance 100 Ω is terminated with a load impedance of 300+j200 Ω, then the normalized load impedance is:

• 1+j

• 1-j

• 3+2j

• 2-3j

Answer explanation

Normalized load impedance is obtained by dividing the load impedance with the characteristic impedance of the transmission line. Dividing 300+200j from 100, we get 3+2j.

If the normalized load impedance of a transmission line is 0.3-j0.4 with a characteristic impedance of 50 Ω, then the load impedance is:

• 15-j20

• 15+j20

• 1-j

• 0.3-0.4j

Answer explanation

Load impedance is the product of characteristic impedance and normalized load impedance. Hence taking the product of characteristic impedance and load impedance, we get 15-j20Ω.

To get an admittance chart from an impedance chart:

• Smith chart has to be rotated by 90⁰

• Smith chart has to be rotated by 180⁰

• Admittance chart cannot be obtained from the impedance chart anyway.

• None of the mentioned

Answer explanation

Impedance and admittance parameters, both are a reciprocal of one another. Hence one chart can be obtained from the other chart. By rotating the impedance smith chart by an angle of 180⁰, admittance chart is obtained.