GATE EC question library

The system moded described by the state equations is $$\begin{array}{l} \mathrm{X}=\left[\begin{array}{cc} 0 & 1 \\ 2 & -3 \end{array}\right] x+\left[\begin{array}{l} 0 \\ 1 \end{array}\right] u \\ \mathrm{Y}=\left[\begin{array}{ll} 1 & 1 \end{array}\right] x \end{array}$$

The gain margin (in $d \mathrm{B}$ ) of a system a having the loop transfer function $$\mathrm{G}(s) \mathrm{H}(s)=\frac{\sqrt{2}}{s(s+1)} \text{ is }$$

For a second-order system with the closed-loop transfer function $$T(s)=\frac{9}{s^{2}+4 s+9}$$ the settling time for $2$ - percent band, in seconds, is

The resolution of a $4$ - bit counting $\text{ADC}$ is $0.5$ volts. For an analog input of $6.6$ volts, the digital output of the $\text{ADC}$ will be

Commercially available $\text{ECL}$ gears use two ground lines and one negative supply in order to

A Darlington emitter - follower circuit is sometimes used in the output stage of a $\text{TTL}$ gate in order to

The logical expresion $y=\mathrm{A}+\overline{\mathrm{A}} \mathrm{B}$ is equivalent to

Crossover distortion behaviour is characteristic of

In the cascade amplifier shown in the given figure, if the common - emitter stage $\left(Q_{1}\right)$ has a transconductance $\mathrm{gm}_{1}$, and the common base stage $\left(Q_{2}\right)$ has a transconductance $\mathrm{gm}_{2^{\prime}}$, then the overall transconductance $g\left(=i_{0} / v_{1}\right)$ of the cascade amplifier is

Negative feedback in an amplifier

The first dominant pole encountered in the frequency response of a compensated $\text{op - amp}$ is approximately at

The early effect in a bipolar junction transistor is caused by

A $2$-port network is shown in the given figure. The parameter $h_{21}$ for this network can be given by

If $[f(t)]=\mathrm{F}(s)$, then $[f(t-\mathrm{T})]$ is equal to

The $z$-transform $\mathrm{F}(z)$ of the function $f(n \mathrm{T})=a^{\prime \prime T}$ is

A plane wave propagating through a medium $\left[\varepsilon_{\mathrm{r}}=8, v_{\mathrm{r}}=2\right.$, and $\left.\sigma=0\right]$ has its electric field given by $\overrightarrow{\mathrm{E}}=0.5 \hat{\mathrm{X}} \mathrm{e}^{-(z / 3)} \sin \left(10^{8} t-\beta z\right) \mathrm{V} / \mathrm{m}$. The wave impedance, in ohms is

In air, a lossless transmission line of length $50 \mathrm{~cm}$ with $\mathrm{L}=10 \; \mu \mathrm{H} / \mathrm{m}, \mathrm{C}=40 \; \mathrm{pF} / \mathrm{m}$ is operated at $25 \; \mathrm{MHz}$. Its electrical path length is

A trasmitting antenna radiates $251 \mathrm{~W}$ isotropically. A receiving antenna, located $100 \mathrm{~m}$ away from the transmitting antenna, has an effective aperture of $500 \mathrm{~cm}^{2}$. The total received by the antenna is

In a twin-wire transmission line in air, the adjacent voltage maxima are at $12.5 \mathrm{~cm}$ and $27.5 \mathrm{~cm}$. The operating frequency is

Four independent messages have bandwidths of $100 \mathrm{~Hz}, 200 \mathrm{~Hz}$, and $400 \mathrm{~Hz}$, respectively. Each is sampled at the Nyquist rate, and the samples are time division multiplexed ($\text{TDM}$) and transmitted. The transmitted sample rate (in $\mathrm{Hz}$ ) is