List of top Electromagnetics Questions on Impedance transformation asked in GATE EC

A digital communication system transmits through a noiseless bandlimited channel \([-W, W]\). The received signal \(z(t)\) at the output of the receiving filter is given by: \[ z(t) = \sum_n b[n] x(t - nT), \] where \(b[n]\) are the symbols and \(x(t)\) is the overall system response to a single symbol. The received signal is sampled at \(t = mT\). The Fourier transform of \(x(t)\) is \(X(f)\). The Nyquist condition that \(X(f)\) must satisfy for zero intersymbol interference at the receiver is:

Consider the Earth to be a perfect sphere of radius \(R\). Then the surface area of the region, enclosed by the \(60^\circ N\) latitude circle, that contains the north pole in its interior is \(\_\_\_\_\).

A uniform plane wave with electric field: \[ \vec{E}(x) = A_y \hat{a}_y e^{-\frac{j2\pi x}{3}} \, {V/m}, \] is traveling in the air (relative permittivity, \(\epsilon_r = 1\), and relative permeability, \(\mu_r = 1\)) in the \(+x\) direction. It is incident normally on an ideal electric conductor (conductivity, \(\sigma = \infty\)) at \(x = 0\). The position of the first null of the total magnetic field in the air (measured from \(x = 0\), in meters) is \(\_\_\_\_\).

Let \(z\) be a complex variable. If \(f(z) = \frac{\sin(\pi z)}{z^2 (z - 2)}\) and \(C\) is the circle in the complex plane with \(|z| = 3\), then: \[ \oint_C f(z) \, dz \] is \(\_\_\_\_\).

The radian frequency value(s) for which the discrete-time sinusoidal signal: \[ x[n] = A \cos(\Omega n + \pi/3) \] has a period of 40 is/are \(\_\_\_\_\).

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is____.

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is \(\_\_\_\_\).