# Objective Questions on Scattering Matrix

## Objective Questions on Scattering Matrix

Objective Questions on Scattering Matrix, MCQ on Scattering Matrix in Microwave Engineering, Mulitple Choice Questions on Scattering Matrix, Gate MCQ on Scattering Matrix in Microwave Engineering.

### Multiple Choice Questions

1. When the co-planar arm lengths are not the same, then outputs in the H-plane tee can be
• in phase
• out of phase
• with phase difference
• None of the above

2. When the co-planar arm lengths are not the same, then outputs in the E-plane tee can be

• in phase
• out of phase
• with phase difference
• None of the above

3. The outputs of directional couplers have a phase difference of

• 90°
• 45°
• 80°
• none

4. Co-planar arm ports in 3-port junctions can be

• matched to junction
• mismatched
• either
• none

5. For its S matrix to be unitary, the circuit should be

• reciprocal
• lossless
• both
• none

6. Chain S parameters are similar to

• ABCB parameters
• transmission-line parameters
• both
• none

7. An E-plane tee is

• a voltage junction
• a series junction
• both
• none

8. An H-plane tee is

• a voltage junction
• a shunt Junction
• both
• none

9. A microwave junction is supposed to be matched at all ports if in the S matrix

• All the diagonal elements are zero
• All the diagonal elements are equal but not zero
• All the diagonal elements are complex
• is hermition

Answer: All the diagonal elements are zero

10. There is a directional coupler consisting of two waveguides with a common side wall (the one parallel to E-field) having two holes space S cm in the common-well. Then

• coupling factor is independent of spacing S
• coupling factor is a function of spacing S
• directivity is independent of spacing S
• none of the above

Answer: coupling factor is independent of spacing S

11. A 3-port circulator is shown in the figure. Which one of the following scattering matrices relates to this circulator?

• $\begin{bmatrix} 0 & 0 & 1\\ 1 & 0 & 0\\ 0 & 1 & 1 \end{bmatrix}$
• $\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix}$
• $\begin{bmatrix} 1 & 0 & 1\\ 0 & 0 & 0\\ 1 & 0 & 1 \end{bmatrix}$
• $\begin{bmatrix} 1 & 1 & 1\\ 1 & 0 & 1\\ 1 & 1 & 1 \end{bmatrix}$

Answer: $\begin{bmatrix} 0 & 0 & 1\\ 1 & 0 & 0\\ 0 & 1 & 1 \end{bmatrix}$

12. Which of the following relations would be true for the magic tee shown in the given figure?

1. S13 = S23
2. S14 = S24
3. S12 = 0
4. S34 = 0

Select the correct answer using the codes given below:

Codes:

• 1, 2 and 3
• 1, 2 and 4
• 2, 3 and 4
• 1, 3 and 4

13. The scattering matrix of a magic tee, shown in the given figure is

• $\frac{1}{\sqrt{2}}\begin{bmatrix} 0 & 0 & 1 & 1\\ 0 & 0 & -1 & 1\\ 1 & -1 & 0 & 0\\ 1 & 1 & 0 & 0 \end{bmatrix}$
• $\frac{1}{\sqrt{2}}\begin{bmatrix} 0 & 0 & 1 & 1\\ 0 & 0 & 1 & 1\\ 1 & 1 & 0 & 0\\ 1 & 1 & 0 & 0 \end{bmatrix}$
• $\frac{1}{2}\begin{bmatrix} 0 & 0 & 1 & 1\\ 0 & 0 & -1 & 1\\ 1 & -1 & 0 & 0\\ 1 & 1 & 0 & 0 \end{bmatrix}$
• $\frac{1}{2}\begin{bmatrix} 0 & 0 & 1 & 1\\ 0 & 0 & 1 & 1\\ 1 & 1 & 0 & 0\\ 1 & 1 & 0 & 0 \end{bmatrix}$

Answer: $\frac{1}{\sqrt{2}}\begin{bmatrix} 0 & 0 & 1 & 1\\ 0 & 0 & -1 & 1\\ 1 & -1 & 0 & 0\\ 1 & 1 & 0 & 0 \end{bmatrix}$

14. According to symmetry property, which is true?

• S12 = S21
• S13 = S31
• S23 = S32
• All

15. Which property is associated with S matrix?

• [S] is always a square matrix of order (nxn)
• [S] is a symmetric matrix.
• [S] is a unitry matrix.
• all of above