GATE ECE 1988
GATE ECE
1
The quiescent collector current Ic, of a transistor is increased by changing resistance. As a result
2
Each transistor in the Darlington pair (see Fig. below) has hfe = 100. The overall hfe of the composite transistor neglecting the leakage current is
3
The amplifier circuit shown below uses a compostie transistor of a MOSFET and BIPOLAR in cascade. ALL capacitance are large. gm of the MOSFET = 2 mA/V , and hfe of the BIPOLAR = 99. The overall Transconductance gm of the composite transistor is
4
The transistor in the amplifier shown below has following parameters:
$$${h_{fe}}\, = \,100,\,{h_{ie}}\, = \,2k\Omega ,\,{h_{re}}\, = \,0,$$$
$${h_{oe}}\, = \,0.05\,\,m\Omega .\,\,C$$ is very large.
The output impedance is
5
The OP-AMP shown in fig. below is ideal. $$R\, = \,\sqrt {L/C.} $$ The phase angle between V0 and Vi at $$\omega = 1/\sqrt {LC} $$ is
6
The Op-Amp in the Fig below is ideal. Find the output when Vi = (1-exp($$ - \alpha t$$)) u(t). Assume the capacitor to be uncharged when the input is applied and $$ - \alpha $$ = 1/CR1. $$\left[ {u(t)\,\,is\,the\,unit\,step\,function.} \right]$$
7
In a digital communication system, transmissions of successive bits through a noisy channel are assumed to be independent events with error probability p. The probability of at most one error in the transmission of an 8 - bit sequence is
8
The transfer function of a zero - order hold is
9
The message bit sequence input to a DPSK modulator is 1, 1, 0, 0, 1, 1. The carrier phase during the reception of the first two message bits is $$\pi ,\,\,\pi $$. The carrier phase for the remaining four message bits is
10
White Gaussian noise with zero mean and double - sided power spectral density $$\eta /2$$ is the input $$x(t)$$ to a linear system with impulse response $$h(t)$$ $$ = exp\left( { - t/RC} \right)\,\,\,\,\,\,\,\,u\left( t \right)$$. The output is $$y(t)$$ . Evaluate $$E\left[ {x\left( {t + \tau } \right)y\left( t \right)} \right]$$ for $$\tau > 0.$$ (Note: $$u(t)$$ is the unit step function)
11
A signal having uniformly distributed amplitude in the interval ( -V, +V ) is to be encoded using PCM with uniform quantization. The signal - to - quantizing noise ratio is determined by the
12
A critically damped, continuous-time, second order system, when sampled, will have ( in Z domain)
13
Consider a characteristic equation given by
s4 + 3s3 + 5s2 + 6s + K + 10 = 0.
The condition for stability is
s4 + 3s3 + 5s2 + 6s + K + 10 = 0.
The condition for stability is
14
Consider a closed-loop system shown in fig. (a) below. The root locus for it is shown in fig. (b). The closed-loop transfer function for the system is
15
The circuit given below is a
16
The minimum number of 2-input NAND gates required to implement the Boolean function Z=A$$\overline {B\,} $$C, assuming that A, B and C are available, is
17
Minimum number of 2-input NAND gates required to implement the function, f=($$\overline X $$+$$\overline Y $$)(Z+W) is
18
For the circuit shown below the output Fis given by
19
The Boolean function A+BC is a reduced form of
20
For the identity AB+$$\overline A $$ C + BC= AB + $$\overline A $$ C, The dual form is
21
Implement the function $$F=\left(\overline A+\overline B\right)\left(\overline C+\overline D\right)$$ using two open collector TTL 2-input NAND gates.
22
The circuit shown below uses TTL flip-flops. The flip-flops are triggered at the negative transitions of the clock. It is desired that when M = 1 the circuit should function as an up-counter (in 8421 BCD) and when M=0, as a down-counter. Design the combinational circuit interposed between the flip-flops so that the circuit works as desired. (i.e. find F as a function of Q,$$\overline Q $$, M, $$\overline M $$).
23
For the circuit shown in the figure below, sketch V0 against time. Assume that all flip-flops are reset to zero before the clock is applied.
24
In a good conductor the phase relation between the tangential components of electric field Et and the magnetic field Ht is as follows
25
A two - wire transmission line of characteristic impedance $$Z_0$$ is connected to a load of impedance $${Z_L}({Z_L}\, \ne \,\,{Z_0})$$. Impedance matching cannot be achieved with
26
Vector potential is a vector
27
On either side of a charge-free interface between two media,
28
For a normal mode EM wave propagating in a hollow rectangular wave guide
29
The electric field E and the magnetic field H of a short dipole antenna satisfy the condition
30
A rectangular waveguide with cross-section dimensions 5 cm by 3 cm is filled with a dielectric of relative permittivity 3.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
31
A rectangular waveguide with cross-section dimensions 5 cm by 3 cm is filled with a dielectric of relative permittivity 3.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
32
For a microprocessor system using I/O-mapped I/O the following statement(s) is NOT true
33
A microprocessor with a 16-bit address bus is used in a linear memory selection configuration (i.e. Address bus lines are directly used as chip selects of memory chips) with 4 memory chips. The maximum addressable memory space is
34
In register index addressing mode the effective address is given by
35
A 8bit $$\mu $$p has 16bit address bus. A 1KB memory chip is interfaced to processor as shown ib figure. The address range for the chip is _____________.
36
The circuit shown below is initially in a steady state condition. At $$t = 0$$, the switch '$$S$$' is opened.
(i) Determine the initial voltage $${V_c}\left( {{0^ - }} \right)$$ across the capacitor and initial current $${i_L}\left( {{0^ - }} \right)$$ through the inductor.
(ii) Find the voltage $${v_L}\left( t \right)$$ across the inductor for $$t > 0$$.
37
Two two-port networks are connected in parallel. The combination is to be represented as a single two-port network. The parameters of this network are obtained by addition of the individual
38
If an impedance ZL is connected across a voltage source V with source impedance ZS, then for maximum power transfer, the load impedance must be equal to
39
The Laplace transform of a function f(t)u(t), where f(t) is periodic with period T, is A(s) times the Laplace transform of its first period. Then
40
The transfer function of a zero-order hold is
41
Consider the system shown in the Fig.1 below. The transfer function $$Y\left( z \right)/X\left( z \right)$$ of the system is
42
The output of a system is given in difference equation form as $$y\left( k \right) = \,a\,\,y\left( {k - 1} \right) + x\left( k \right),$$ where $$x\left( k \right)$$ is the input. If $$x\left( k \right)$$ $$\, = \,\,0$$ for $$k\, \ne \,0,\,\,x\left( 0 \right)\, = \,1,$$ and $$y\left( 0 \right)\, = \,0,$$ find $$y\left( k \right)$$ for all $$k.$$
Determine the range of $$'a'$$ for which $$y\left( k \right)\,$$ is bounded.
43
Specify the filter type if its voltage transfer function H(s) is given by
H(s) = $${{K({s^2} + {\omega _0}^2)} \over {{s^2} + ({\omega _0}/Q)s + {\omega _0}^2}}$$
44
A signal containing only two frequency components (3 kHz and 6 kHz) is sampled at the rate of 8 kHz, and then passed through a low pass filter with a cutoff frequency of 8 kHz. The filter output
45
A signal x(t) = $$\exp ( - 2\pi Bt)\,u(t)$$ is the input to an ideal low pass filter with bandwidth B Hz. The output is denoted by y(t). Evaluate $$\int\limits_{ - \infty }^\infty {{{[y(t) - x(t)]}^{2\,}}dt} $$.