GATE EC 2015 Question Paper (31-Jan-2015) (Shift 1)

The circuit shown in the figure has an ideal Op-Amp. The oscillation frequency and the condition to sustain the oscillations, respectively, are

In the circuit shown, I₁ = 80 mA and I₂ = 4 mA. Transistors T₁ and T₂ are identical. Assume that the thermal voltage V${}_T$ is 26 mV at 27°C. At 50°C, the value of the voltage V₁₂ = V₁ – V₂ (in mV) is ______

Two sequences $\left[\mathrm{a},\mathrm{b},\mathrm{c}\left]\mathrm{and}\right[\mathrm{A},\mathrm{B},\mathrm{C}\right]$ are related as,

≤ft[ {*20c \\ \\ } ] = ≤ft[ {*20c 1&1&1\\ 1&{_3^ - 1}&{_3^ - 2}\\ 1&{_3^ - 2}&{_3^ - 4} } ]≤ft[ {*20c \\ \\ } ]{_3} = {^{{{2π }}3}}

If another sequence $\mathrm{p},\mathrm{q},\mathrm{r}$ is derived as,

≤ft[ {*20c \\ \\ } ] = ≤ft[ {*20c 1&1&1\\ 1&{_3^1}&{_3^2}\\ 1&{_3^2}&{_3^4} } ]≤ft[ {*20c 1&0&0\\ 0&{_3^2}&0\\ 0&0&{_3^4} } ]≤ft[ {*20c {{}3}\\ {{}3}\\ {{}3} } ] ,

Then the relationship between the sequences $\left[\mathrm{p},\mathrm{q},\mathrm{r}\left]\mathrm{and}\right[\mathrm{a},\mathrm{b},\mathrm{c}\right]\mathrm{is}$

For the discrete-time system shown in the figure, the poles of the system transfer function are located at

The pole – zero diagram of a causal and stable discrete – time system is shown is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n] . If h[0] = 1, we can conclude.