UPSC IES/ESE (Engineering Services) Electronics, Communication and Control Systems Syllabus

How do negative feedback with gain $A$ and feedback factor $\beta$ affect gain and bandwidth?

Closed-loop gain $$A_f = \frac{A}{1+A\beta}$$ Bandwidth increases by factor $(1+A\beta)$; gain-bandwidth product stays constant. Distortion and gain sensitivity reduce by $(1+A\beta)$.

Compare Class A, B, AB, and C power amplifiers by conduction angle and max efficiency.

Class A: $360^\circ$, $\eta_{max}=25\%$ (50% transformer-coupled). Class B: $180^\circ$, $\eta_{max}=78.5\%$. Class AB: slightly $>180^\circ$ (removes crossover distortion). Class C: $<180^\circ$, $\eta > 78.5\%$ (tuned RF).

Convert decimal $45$ to binary, octal and hexadecimal.

$45_{10} = 101101_2 = 55_8 = 2D_{16}$.

State De Morgan's theorems in Boolean algebra.

$$\overline{A+B} = \bar{A}\cdot\bar{B}, \qquad \overline{A\cdot B} = \bar{A}+\bar{B}$$ Generalized: complement the whole expression, complement each variable, and swap AND $\leftrightarrow$ OR.

What is the 2's complement of an 8-bit number, and why is it used?

2's complement $=$ (1's complement) $+ 1$, i.e. invert all bits and add 1. It allows subtraction by addition and gives a unique representation of zero; range for $n$ bits is $-2^{n-1}$ to $+2^{n-1}-1$.

Why are NAND and NOR called universal gates?

Any Boolean function can be implemented using only NAND gates or only NOR gates, since each can realize NOT, AND, and OR. This makes them universal building blocks.

Distinguish combinational and sequential logic circuits.

Combinational: output depends only on present inputs, no memory (e.g. adders, MUX, decoders). Sequential: output depends on present inputs and past state, uses memory/feedback and a clock (e.g. flip-flops, counters, registers).

Give the sum and carry equations for a full adder.

$$S = A \oplus B \oplus C_{in}$$ $$C_{out} = AB + (A \oplus B)C_{in}$$

What is the characteristic (next-state) equation of a JK flip-flop?

$$Q_{n+1} = J\bar{Q}_n + \bar{K}Q_n$$ With $J=K=1$ it toggles; $J=K=0$ holds; $J=1,K=0$ sets; $J=0,K=1$ resets.

Distinguish a multiplexer from a demultiplexer and give line counts.

MUX: $2^n$ data inputs $\to$ 1 output, selected by $n$ select lines (data selector). DEMUX: 1 input $\to 2^n$ outputs via $n$ select lines (data distributor).

Compare synchronous and asynchronous (ripple) counters.

Asynchronous/ripple: clock applied only to first FF, others triggered by previous output; cumulative propagation delay, slower. Synchronous: all FFs share a common clock, faster, no cumulative delay but more logic.

What is the modulus of a counter and how many flip-flops are needed for a mod-N counter?

Modulus = number of unique states before repeating. A mod-$N$ counter needs $n$ flip-flops where $2^{n-1} < N \leq 2^{n}$, i.e. $n = \lceil \log_2 N \rceil$.

Compare SRAM, DRAM, and the meaning of volatile vs non-volatile memory.

SRAM: flip-flop based, fast, no refresh, low density, used for cache. DRAM: capacitor based, needs periodic refresh, high density, slower, main memory. Both are volatile (lose data on power off); ROM/Flash/EEPROM are non-volatile.

Name the register types by data transfer and give examples.

SISO, SIPO, PISO, PIPO shift registers. SIPO does serial-to-parallel conversion; PISO does parallel-to-serial. A universal shift register can do all modes plus bidirectional shifting.

State the basic functional units of a microprocessor (e.g. 8085) architecture.

ALU, registers (accumulator, general-purpose, temporary), instruction register/decoder, program counter, stack pointer, timing and control unit, address/data bus, flag register. Buses: address (output), data (bidirectional), control.

Differentiate a microprocessor from a microcontroller.

Microprocessor: CPU only; memory, I/O, timers are external (general-purpose). Microcontroller: CPU + RAM + ROM + I/O ports + timers + serial on one chip (embedded, application-specific, lower cost/power).

Differentiate Von Neumann and Harvard architectures.

Von Neumann: single shared memory and bus for instructions and data (simpler, bus bottleneck). Harvard: separate memories and buses for instructions and data (parallel fetch, faster; used in many microcontrollers/DSPs).

Classify signals: continuous vs discrete-time, and energy vs power signals.

Continuous-time: defined for all $t$; discrete-time: defined only at integer $n$. Energy signal: $0 < E < \infty$, $P=0$ (aperiodic). Power signal: $0 < P < \infty$, $E=\infty$ (periodic/random).

State the conditions for a system to be linear and time-invariant (LTI).

Linear: satisfies superposition (additivity + homogeneity). Time-invariant: a time shift in input produces an identical shift in output, $x(t-t_0) \to y(t-t_0)$. LTI systems are fully characterized by their impulse response $h(t)$.

How is the output of an LTI system obtained from input and impulse response?

By convolution: $$y(t) = x(t) * h(t) = \int_{-\infty}^{\infty} x(\tau)h(t-\tau)\,d\tau$$ Discrete: $y[n] = \sum_{k=-\infty}^{\infty} x[k]h[n-k]$.

State the BIBO stability condition for a continuous-time LTI system.

The impulse response must be absolutely integrable: $$\int_{-\infty}^{\infty} |h(t)|\,dt < \infty$$ Equivalently, all poles of $H(s)$ lie in the left half of the $s$-plane.

Define the Fourier transform pair for a continuous-time signal.

$$X(\omega) = \int_{-\infty}^{\infty} x(t)e^{-j\omega t}\,dt$$ $$x(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} X(\omega)e^{j\omega t}\,d\omega$$

Define the bilateral Laplace transform and its relation to the Fourier transform.

$$X(s) = \int_{-\infty}^{\infty} x(t)e^{-st}\,dt, \quad s = \sigma + j\omega$$ Setting $\sigma=0$ (i.e. $s=j\omega$) gives the Fourier transform, valid when the ROC includes the $j\omega$-axis.

Define the Z-transform and the region of convergence (ROC) significance.

$$X(z) = \sum_{n=-\infty}^{\infty} x[n]z^{-n}$$ The ROC determines causality/stability: for a causal system the ROC is outside the outermost pole; stability requires the ROC to include the unit circle $|z|=1$.

State the Nyquist sampling theorem.

A bandlimited signal with maximum frequency $f_m$ is fully recoverable if sampled at $$f_s \geq 2 f_m$$ The minimum rate $f_s = 2f_m$ is the Nyquist rate; the bound $f_s/2$ is the Nyquist frequency.

What is aliasing and how is it prevented?

Aliasing is the overlap of spectral images when $f_s < 2f_m$, causing high frequencies to masquerade as lower ones (irrecoverable distortion). Prevented by an anti-aliasing low-pass filter before sampling and/or sampling above the Nyquist rate.

For AM (DSB-FC) $s(t)=A_c[1+\mu\cos\omega_m t]\cos\omega_c t$, give the power efficiency and transmission bandwidth.

Efficiency $$\eta = \frac{\mu^{2}}{2+\mu^{2}}$$ (max $33.3\%$ at $\mu=1$). Bandwidth $BW = 2f_m$. Total power $P_t = P_c\left(1+\frac{\mu^{2}}{2}\right)$.

Define modulation index for FM and PM, and give Carson's rule bandwidth for FM.

FM: $\beta = \Delta f / f_m$; PM: $\beta = k_p A_m$. Carson's rule: $$BW \approx 2(\Delta f + f_m) = 2 f_m(\beta + 1)$$

Define noise figure and give Friis' formula for cascaded stages.

Noise figure $F = \dfrac{(S/N)_{in}}{(S/N)_{out}} \geq 1$. Cascade: $$F = F_1 + \frac{F_2-1}{G_1} + \frac{F_3-1}{G_1 G_2} + \cdots$$ so the first stage gain/noise dominates.

Compare ASK, FSK and PSK digital modulation schemes.

ASK: amplitude switched (simple, noise-sensitive). FSK: frequency switched (constant envelope, more bandwidth). PSK: phase switched (best noise immunity for given power; BPSK is most robust). PSK/FSK outperform ASK in BER.

Outline the PCM process and give the quantization SNR for an n-bit uniform quantizer.

Steps: sample $\to$ quantize $\to$ encode (binary). For $n$ bits with a sinusoidal full-scale input: $$\text{SNR}_{dB} \approx 6.02n + 1.76$$ (about 6 dB improvement per added bit).

Compare DPCM and Delta Modulation, and name the two distortions of delta modulation.

DPCM encodes the difference between a sample and its prediction (multi-bit), reducing bit rate. Delta modulation is 1-bit DPCM transmitting only sign of the difference. DM distortions: slope-overload (step too small for fast changes) and granular/hunting noise (step too large for slow changes).