Electronics & Communications Test - 3

Q₀: Toggle at every clock

Q₁: when Q̅₀ changes from 0 → 1 (positive edge) OR Q₀ changes from 1 → 0

Truth Table:

00 → 01 → 10 → 11 → 00 → 01 → 10 → 11 → 00 …

Therefore option 2 is correct.

Concept:

For a second-order differential function, the characteristic equation will have two roots D₁ and D₂. The roots can have three possible forms, ie.

1) Real, distinct roots, D₁ ≠ D₂

2) Complex Roots, D₁, D₂ = a + ib

3) Double roots, D₁ = D₂ = 0

If two roots are real and distinct (i.e. D₁ ≠ D₂), the general solution will be:

Important Point:

If the roots of the characteristic equation are complex (i.e. D_{1, 2} = a ± ib), the general solution to the differential equation will be:

The solution for the second-order differential equation with equal roots of the characteristic equation is given by:

The given circuit can be redrawn as

For unique solution

Rank (A|B) = Rank (A) = No. of unknowns

For No solution

Rank (A|B) = Rank(A) < No.of unknows

For No solution

Rank (A|B) ≠ Rank (A)

Calculation:

Now the augmented matrix A|B is

The correct answer is 1750 Hz

Concept: 

(1) If the signal is a multiply in the time domain then in the frequency domain we get convolution.

(2) The duration/ extension property of convolution says that if

x₁(ω) is non-zero for ω₁<ω<ω₂ 

x₂(ω) is non-zero for ω3<ω<ω4

Now for Y(ω) = x₁(ω) * x₂(ω)

then

Y(ω) is non-zero for (ω₁ + ω₃)<ω<(ω2 + ω₄)

Solution:

x1(ω) is non zero for -1500π<ω<1500π  

x2(ω) is non zero for -2000π<ω<2000π 

Now for

Y(ω) = x1(ω) * x2(ω)

then

Y(ω) is non-zero for (-1500π-2000π )<ω<(1500π +2000π)

Concept:

The transfer function for a control system is defined as:

where H(s) = Transfer function

Y(s) = Output function

X(s) = Input function

The impulse response for a control system is also known as the transfer function of the system.

Explanation:

Concept:

The reflection coefficient gives the percentage of incident voltage reflected from the load.

Mathematically, this is defined as: