AFCAT (Air Force Common Admission Test) EKT - Computer Science and Electronics Stream Syllabus

State the Nyquist sampling theorem.

A band-limited signal with maximum frequency fm can be perfectly reconstructed if the sampling rate fs >= 2*fm. 2*fm is the Nyquist rate.

What is the difference between an energy signal and a power signal?

An energy signal has finite, non-zero total energy and zero average power (e.g., a pulse). A power signal has finite, non-zero average power and infinite energy (e.g., periodic signals).

Define a Linear Time-Invariant (LTI) system.

A system that satisfies both linearity (superposition: scaling and additivity) and time-invariance (a time shift in input produces an identical time shift in output).

What operation relates the input, impulse response, and output of an LTI system?

Convolution: y(t) = x(t) * h(t), where h(t) is the impulse response. In the frequency domain this becomes multiplication: Y(f) = X(f)·H(f).

What are the conditions for BIBO stability of an LTI system in terms of impulse response?

A system is BIBO stable if and only if its impulse response is absolutely integrable: integral of |h(t)| dt is finite (continuous), or sum of |h[n]| is finite (discrete).

What is the relationship between the gain (directivity) and effective aperture of an antenna?

G = (4*pi / lambda^2) * Ae, where Ae is the effective aperture and lambda is the wavelength.

What is the length of a half-wave dipole antenna and its radiation resistance?

Physical length is approximately lambda/2 (about 0.95*lambda/2 accounting for end effects); radiation resistance is approximately 73 ohms.

Name the three main modes/layers of radio wave propagation.

Ground wave (surface) propagation, sky wave (ionospheric) propagation, and space wave (line-of-sight/tropospheric) propagation.

What is the critical frequency in ionospheric propagation?

The highest frequency that is reflected back by an ionospheric layer when a wave is sent vertically (straight up); above it the wave penetrates and escapes.

What is the relationship between the radar range equation's maximum range and transmitted power?

Rmax is proportional to the fourth root of transmitted power (Rmax proportional to Pt^(1/4)); doubling range requires 16 times the power.

Why are waveguides used instead of coaxial cables at microwave frequencies?

Waveguides have much lower losses at high frequencies, can handle high power, and avoid the dielectric/conductor losses of coax. They act as high-pass filters with a cutoff frequency.

What is the dominant mode in a rectangular waveguide?

The TE10 mode, which has the lowest cutoff frequency of all modes in a rectangular waveguide.

What is the Doppler shift used for in radar, and what does it measure?

The Doppler shift (frequency change of the reflected signal) is used in CW/MTI/pulse-Doppler radar to measure the radial velocity of a moving target. fd = 2v/lambda.

For a standard second-order system, how is damping ratio (zeta) classified by response type?

zeta = 0: undamped (oscillatory); 0 < zeta < 1: underdamped; zeta = 1: critically damped (fastest non-oscillatory); zeta > 1: overdamped.

What is the relationship between bandwidth and rise time in a first-order system?

Bandwidth is inversely related to rise time: tr * BW is approximately 0.35 (for a first-order/low-pass system). Higher bandwidth gives faster rise time.

Define gain margin and phase margin in frequency-response stability analysis.

Gain margin is the additional gain (in dB) allowed before instability, measured at the phase crossover (-180 deg) frequency. Phase margin is the additional phase lag allowed before instability, measured at the gain crossover (0 dB) frequency.

What does the Routh-Hurwitz criterion determine, and what indicates instability?

It determines the number of closed-loop poles in the right-half s-plane without solving for roots. A sign change in the first column of the Routh array indicates RHP poles, meaning instability (number of sign changes = number of RHP poles).

Compare the effects of negative feedback versus positive feedback in a control system.

Negative feedback reduces gain, increases bandwidth and stability, reduces distortion/noise, and stabilizes operation. Positive feedback increases gain but reduces stability and is used in oscillators.

What is the Barkhausen criterion for sustained oscillation?

For sustained oscillations, the loop gain magnitude must equal 1 (|A*beta| = 1) and the total loop phase shift must be 0 or 360 degrees (an integer multiple of 360).

What is a transducer, and what distinguishes active from passive transducers?

A transducer converts one form of energy/physical quantity into another (usually electrical). Active transducers generate their own output (e.g., thermocouple, piezoelectric); passive transducers need external excitation power (e.g., strain gauge, thermistor, LVDT).

What physical quantity does an LVDT measure and what is its output characteristic?

An LVDT (Linear Variable Differential Transformer) measures linear displacement; its output is an AC voltage proportional to displacement, with phase indicating direction of movement.

Define accuracy versus precision in measurement.

Accuracy is closeness of a measurement to the true value. Precision is the repeatability/consistency of measurements (closeness of repeated readings to each other), regardless of the true value.

What is the time complexity of binary search and what is its precondition?

O(log n) time complexity; it requires the array/list to be sorted beforehand.

Compare a stack and a queue data structure.

A stack is LIFO (Last In First Out) with push/pop at one end. A queue is FIFO (First In First Out) with enqueue at rear and dequeue at front.

What are the average and worst-case time complexities of QuickSort?

Average case: O(n log n); worst case: O(n^2) (e.g., already sorted data with poor pivot choice). It is in-place with O(log n) average stack space.

What traversal of a Binary Search Tree yields elements in sorted ascending order?

In-order traversal (Left, Root, Right) yields the nodes in ascending sorted order.

What is the difference between a microprocessor and a microcontroller?

A microprocessor is a single CPU chip requiring external RAM, ROM, and I/O. A microcontroller integrates CPU, RAM, ROM/flash, I/O ports, timers, and peripherals on one chip, designed for embedded control.

What is the size of the address bus and data bus of the Intel 8085 microprocessor, and how much memory can it address?

16-bit address bus and 8-bit data bus, allowing it to address 2^16 = 64 KB of memory.

List the seven OSI model layers in order from Layer 1 to Layer 7.

1 Physical, 2 Data Link, 3 Network, 4 Transport, 5 Session, 6 Presentation, 7 Application.

Compare TCP and UDP transport protocols.

TCP is connection-oriented, reliable, ordered, with flow/error control and acknowledgements (slower). UDP is connectionless, unreliable, unordered, with no handshake (faster, lower overhead), used for streaming and DNS.

What are ACID properties in a database management system?

Atomicity (all-or-nothing transactions), Consistency (valid state to valid state), Isolation (concurrent transactions do not interfere), and Durability (committed changes persist despite failures).