Exams › GATE › Technical

Let c(t) = A_c cos(2π f_c t) and m(t) = cos(2π fₘ t). It is given that f_c >> 5 fₘ. The signal c(t)+m(t) is applied to the input of a non-linear device, whose output vₒ(t) is related to the input v_i(t) as vₒ(t) = a v_i(t) + b v_i²(t), where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency f_c and bandwidth 5 fₘ to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then a/b is

1. 0.25
2. 0.5
3. 1
4. 2

Correct answer: 2

Solution

The ratio a/b equals 2 because, in amplitude modulation, the sideband power is proportional to the square of the modulation index, which is determined by the ratio of the amplitudes of the modulating signal and the carrier. To achieve sideband power equal to half of the carrier power, the modulation index must be set such that the relationship a/b = 2 holds true, ensuring the desired power distribution in the AM wave.

Related GATE Technical questions

• Two identical nMOS transistors M1 and M2 are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. Vbias and VD are adjusted so that both transistors are in saturation. The transconductance of this combination is defined as gm = ∂iD/∂vGS, while the output resistance is ro = ∂vDS/∂iD, where iD is the current flowing into the drain of M2. Let gm1, gm2 be the transconductances and ro1, ro2 be the output resistances of transistors M1 and M2, respectively. Which of the following statements about estimates for gm and ro is correct?
• A good transimpedance amplifier has
• The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure represent:
• Let M be a real 4 × 4 matrix. Consider the following statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular (invertible). Which one among the following is TRUE?
• A discrete-time all-pass system has two of its poles at 0.25∠0° and 2∠30°. Which one of the following statements about the system is TRUE?
• Consider a white Gaussian noise process N(t) with two-sided power spectral density S_N(f) = 0.5 W/Hz as input to a filter with impulse response 0.5e^(-t²/2) (where t is in seconds) resulting in output Y(t). The power in Y(t) in watts is

⚔️ Practice GATE Technical free + battle 1v1 →