Importance of Modulation Index in AM (Amplitude

Modulation):
THE MODULATION INDEX (M) IN AM IS A KEY PARAMETER THAT INDICATES THE EXTENT TO WHICH
THE CARRIER WAVE IS VARIED BY THE MODULATING SIGNAL. IT IS DEFINED AS THE RATIO OF THE
PEAK AMPLITUDE OF THE MODULATING SIGNAL (AMA_MAM) TO THE PEAK AMPLITUDE OF THE
CARRIER WAVE (ACA_CAC):
M=AMACM = \FRAC{A_M}{A_C}M=ACAM
IMPORTANCE OF MODULATION INDEX:
1. DETERMINES SIGNAL STRENGTH AND QUALITY:
O A PROPER MODULATION INDEX ENSURES THAT THE SIGNAL IS STRONG ENOUGH
TO BE TRANSMITTED OVER LONG DISTANCES WITHOUT DISTORTION.
2. PREVENTS OVERMODULATION:
O IF M>1, OVERMODULATION OCCURS, LEADING TO DISTORTION AND LOSS OF
INFORMATION.
O IF M<1, THE SIGNAL IS UNDER-MODULATED, WHICH RESULTS IN LOW SIGNAL
STRENGTH AND INEFFICIENT USE OF POWER.
3. AFFECTS BANDWIDTH:
O THOUGH THE BANDWIDTH IN AM IS TYPICALLY TWICE THE HIGHEST FREQUENCY
OF THE MODULATING SIGNAL, THE MODULATION INDEX AFFECTS THE POWER
DISTRIBUTION ACROSS THE SPECTRUM.
4. IMPACTS POWER EFFICIENCY:
O MODULATION INDEX AFFECTS HOW POWER IS DISTRIBUTED BETWEEN THE
CARRIER AND SIDEBANDS. A HIGHER MMM (UP TO 1) IMPROVES THE EFFICIENCY
OF AM TRANSMISSION.

TYPES OF MODULATION BASED ON MODULATION INDEX:

1. UNDER-MODULATION ( 0<M<1 ):
O THE CARRIER IS NOT FULLY MODULATED.
O THE ENVELOPE OF THE AM WAVE DOES NOT REACH ZERO.
O LOW EFFICIENCY AND WEAKER SIGNAL STRENGTH.
O LESS CHANCE OF DISTORTION, BUT MAY RESULT IN A SIGNAL THAT IS DIFFICULT TO
DETECT CLEARLY.
2. PERFECT MODULATION ( M=1 ):
O THE CARRIER IS EXACTLY 100% MODULATED.
O THE ENVELOPE JUST TOUCHES THE ZERO AXIS.
O IDEAL SCENARIO FOR MAXIMUM CLARITY AND EFFICIENCY WITHOUT DISTORTION.
3. OVER-MODULATION ( M>1 ):
O THE MODULATING SIGNAL IS TOO STRONG RELATIVE TO THE CARRIER.
O ENVELOPE CROSSES THE ZERO AXIS, CAUSING PHASE REVERSAL AND SEVERE
DISTORTION.
O DIFFICULT TO DEMODULATE CORRECTLY; INFORMATION MAY BE LOST.

SUMMARY:
TYPE MODULATION CHARACTERISTICS RESULT
INDEX MMM
UNDER- 0<M<1 INCOMPLETE MODULATION LOW EFFICIENCY,
MODULATED WEAK SIGNAL
PERFECTLY M=1 IDEAL ENVELOPE SHAPE MAXIMUM CLARITY,
MODULATED NO DISTORTION
OVER- M>1 ENVELOPE DISTORTION DUE SIGNAL DISTORTION
MODULATED TO PHASE REVERSAL AND LOSS
UNDERSTANDING AND CONTROLLING THE MODULATION INDEX IS CRUCIAL FOR EFFECTIVE AM
COMMUNICATION, AS IT DIRECTLY INFLUENCES SIGNAL QUALITY, TRANSMISSION EFFICIENCY, AND
RECEIVER PERFORMANCE.

Concept of Threshold Reduction in FM System:

2.
IN FREQUENCY MODULATION (FM) SYSTEMS, THRESHOLD REDUCTION REFERS TO TECHNIQUES
USED TO IMPROVE THE PERFORMANCE OF FM RECEIVERS AT LOW SIGNAL-TO-NOISE RATIOS
(SNRS), ESPECIALLY AROUND THE FM THRESHOLD.

WHAT IS THE FM THRESHOLD?

 IN FM SYSTEMS, NOISE PERFORMANCE IS EXCELLENT AT HIGH SNRS.
 HOWEVER, BELOW A CERTAIN SNR LEVEL, KNOWN AS THE THRESHOLD POINT, NOISE
INCREASES RAPIDLY, AND THE DEMODULATED SIGNAL BECOMES SEVERELY DISTORTED.
 THIS SUDDEN DEGRADATION IS CALLED THE FM THRESHOLD EFFECT.
 THE FM THRESHOLD TYPICALLY OCCURS AROUND AN INPUT SNR OF 10 DB.

THRESHOLD REDUCTION:
THRESHOLD REDUCTION IS THE PROCESS OF LOWERING THE SNR LEVEL AT WHICH THIS SUDDEN
DETERIORATION IN PERFORMANCE OCCURS.

PURPOSE OF THRESHOLD REDUCTION:

 TO MAINTAIN GOOD SIGNAL QUALITY EVEN WHEN THE RECEIVED SIGNAL IS WEAK.
 TO DELAY THE ONSET OF DISTORTION CAUSED BY THE THRESHOLD EFFECT.
 TO EXTEND THE EFFECTIVE OPERATING RANGE OF FM RECEIVERS.

METHODS OF THRESHOLD REDUCTION:

1. USE OF LIMITERS AND DE-EMPHASIS CIRCUITS:
O LIMITERS CLIP AMPLITUDE VARIATIONS, MAKING THE SYSTEM LESS SENSITIVE TO
AMPLITUDE NOISE.
O DE-EMPHASIS FILTERS REDUCE HIGH-FREQUENCY NOISE AFTER DEMODULATION.
2. PHASE-LOCKED LOOPS (PLL):
O PLL FM DEMODULATORS CAN TRACK THE FREQUENCY CHANGES MORE
ACCURATELY, ESPECIALLY IN NOISY CONDITIONS.
O THEY PERFORM BETTER THAN CONVENTIONAL DISCRIMINATORS AT LOW SNRS.
3. PRE-EMPHASIS IN TRANSMITTER:
O BOOSTING HIGH-FREQUENCY COMPONENTS BEFORE TRANSMISSION (PRE-
EMPHASIS) AND ATTENUATING THEM AT THE RECEIVER (DE-EMPHASIS) HELPS
IMPROVE OVERALL SNR.
4. USE OF NARROWBAND FM (NBFM):
O IN SYSTEMS WHERE BANDWIDTH EFFICIENCY IS MORE IMPORTANT, NBFM CAN
OPERATE AT LOWER THRESHOLDS COMPARED TO WIDEBAND FM.

BENEFITS OF THRESHOLD REDUCTION:

 IMPROVED AUDIO QUALITY UNDER WEAK SIGNAL CONDITIONS.
 GREATER COVERAGE AREA FOR FM TRANSMISSIONS.
 BETTER PERFORMANCE IN MOBILE AND PORTABLE FM RECEIVERS.

SUMMARY:
CONCEPT DESCRIPTION
FM THRESHOLD POINT BELOW WHICH FM PERFORMANCE DROPS RAPIDLY DUE TO NOISE
THRESHOLD TECHNIQUES TO REDUCE THIS THRESHOLD SNR TO EXTEND GOOD
REDUCTION PERFORMANCE INTO LOWER SIGNAL CONDITIONS
KEY TECHNIQUES LIMITERS, PLL DEMODULATORS, PRE-EMPHASIS/DE-EMPHASIS
RESULT BETTER NOISE RESISTANCE AND IMPROVED SIGNAL QUALITY AT LOW SNRS
THRESHOLD REDUCTION IS AN ESSENTIAL CONCEPT IN FM RECEIVER DESIGN FOR ENSURING
RELIABLE COMMUNICATION, ESPECIALLY IN WEAK SIGNAL OR HIGH-NOISE ENVIRONMENTS.

Major Non-Linear Effects in FM Systems:

1. HARMONIC DISTORTION
 OCCURS WHEN THE SYSTEM PRODUCES HARMONICS (INTEGER MULTIPLES) OF THE
ORIGINAL SIGNAL FREQUENCY.
 IN FM, HARMONIC DISTORTION CAN LEAD TO SPURIOUS FREQUENCY COMPONENTS,
AFFECTING BANDWIDTH AND SIGNAL CLARITY.
 OFTEN CAUSED BY NON-LINEAR AMPLIFIERS IN THE TRANSMITTER OR RECEIVER.

2. INTERMODULATION DISTORTION (IMD)

 HAPPENS WHEN TWO OR MORE SIGNALS MIX IN A NON-LINEAR DEVICE, PRODUCING SUM
AND DIFFERENCE FREQUENCIES (E.G., F1±F2F_1 \PM F_2F1±F2, 2F1±F22F_1 \PM F_22F1
±F2, ETC.).
 IN FM SYSTEMS, IMD CAN CREATE UNDESIRED SIDEBANDS, CAUSING ADJACENT CHANNEL
INTERFERENCE.
 COMMON IN SYSTEMS WITH MULTIPLE CARRIERS OR STRONG NEARBY SIGNALS.

3. CAPTURE EFFECT DISTORTION

 FM RECEIVERS OFTEN EXHIBIT THE CAPTURE EFFECT, WHERE THE RECEIVER LOCKS ONTO
THE STRONGER OF TWO SIGNALS ON THE SAME FREQUENCY.
 IF THE SYSTEM IS NON-LINEAR, IT MAY NOT CORRECTLY DISTINGUISH BETWEEN SIGNALS,
LEADING TO SIGNAL DISTORTION OR LOSS WHEN MULTIPLE FM SIGNALS ARE PRESENT.

4. PHASE NON-LINEARITY
 PHASE DISTORTION OCCURS WHEN THE PHASE RESPONSE OF THE SYSTEM IS NON-LINEAR
ACROSS FREQUENCIES.
 IN FM, SINCE INFORMATION IS ENCODED IN FREQUENCY (AND INDIRECTLY IN PHASE),
PHASE NON-LINEARITY CAN DISTORT THE DEMODULATED SIGNAL.
 PARTICULARLY AFFECTS SYSTEMS USING WIDEBAND FM OR COMPLEX MODULATION
SCHEMES.

5. AMPLITUDE-TO-PHASE CONVERSION (AM-TO-PM)

 A NON-LINEAR DEVICE MAY UNINTENTIONALLY CONVERT AMPLITUDE VARIATIONS INTO
PHASE VARIATIONS.
 IN FM, EVEN THOUGH THE SIGNAL IDEALLY HAS CONSTANT AMPLITUDE, SOME RESIDUAL
AM OR SYSTEM IMPERFECTIONS CAN TRIGGER THIS EFFECT, INTRODUCING PHASE NOISE.

6. LIMITER NON-LINEARITY
 FM RECEIVERS USE LIMITERS TO REMOVE AMPLITUDE VARIATIONS.
  IF THE LIMITER ITSELF IS NON-LINEAR OR NOT FUNCTIONING CORRECTLY, IT MAY CLIP OR
DISTORT THE FREQUENCY CONTENT, AFFECTING THE DEMODULATED OUTPUT.

EFFECTS OF NON-LINEARITY ON FM PERFORMANCE:

EFFECT CONSEQUENCE
HARMONIC DISTORTION EXTRA FREQUENCY COMPONENTS, SPECTRAL SPREADING
INTERMODULATION DISTORTION ADJACENT CHANNEL INTERFERENCE
CAPTURE EFFECT ISSUES LOSS OF WEAKER SIGNAL, FALSE LOCKING
PHASE NON-LINEARITY SIGNAL DISTORTION, REDUCED INTELLIGIBILITY
AM-TO-PM CONVERSION PHASE/FREQUENCY JITTER AND NOISE
LIMITER NON-LINEARITY LOSS OF FIDELITY IN DEMODULATION

SUMMARY:
NON-LINEAR EFFECTS IN FM SYSTEMS PRIMARILY ORIGINATE FROM NON-IDEAL ELECTRONIC
COMPONENTS AND HIGH SIGNAL LEVELS THAT PUSH SYSTEMS OUT OF THEIR LINEAR OPERATING
RANGE. THESE EFFECTS CAN DISTORT THE TRANSMITTED INFORMATION, CAUSE INTERFERENCE,
AND REDUCE THE OVERALL SIGNAL QUALITY AND RELIABILITY OF COMMUNICATION. MITIGATING
THEM INVOLVES CAREFUL SYSTEM DESIGN, LINEAR AMPLIFICATION, FILTERING, AND PROPER
MODULATION TECHNIQUES.

Noise Performance of AM (Amplitude Modulation)

In AM systems, noise significantly affects the performance, especially since AM transmits both
amplitude and frequency components, but only the amplitude carries the message signal. This
makes AM particularly sensitive to additive noise, such as thermal noise or atmospheric noise.
We can analyze the noise performance of AM by looking at the Signal-to-Noise Ratio (SNR) at both
the input and output of the receiver.

📌 1. AM Signal with Noise

Let the transmitted AM signal be:
s(t)=Ac[1+m⋅cos⁡(2πfmt)]⋅cos⁡(2πfct)s(t) = A_c \left[ 1 + m \cdot \cos(2\pi f_m t) \right] \cdot
\cos(2\pi f_c t)s(t)=Ac[1+m⋅cos(2πfmt)]⋅cos(2πfct)
Where:
 AcA_cAc = carrier amplitude
 mmm = modulation index
 fmf_mfm = modulating frequency
 fcf_cfc = carrier frequency
Assume the received signal is corrupted by additive white Gaussian noise (AWGN) n(t)n(t)n(t):
r(t)=s(t)+n(t)r(t) = s(t) + n(t)r(t)=s(t)+n(t)

📌 2. Envelope Detection and Noise

In AM with envelope detection:
 The detector follows the envelope of the incoming signal.
 Since the information is in amplitude, any amplitude noise directly degrades the signal.

📌 3. Signal Power and Noise Power

Signal Power (PsP_sPs) of the AM wave:
An AM signal consists of a carrier and two sidebands.
Ps=Ac22+Ac2m24=Ac22(1+m22)P_s = \frac{A_c^2}{2} + \frac{A_c^2 m^2}{4} = \frac{A_c^2}{2}
\left(1 + \frac{m^2}{2} \right)Ps=2Ac2+4Ac2m2=2Ac2(1+2m2)
 Ac22\frac{A_c^2}{2}2Ac2 → power in carrier
 Ac2m24\frac{A_c^2 m^2}{4}4Ac2m2 → power in sidebands (contains the actual
information)
Signal Component After Detection:
Only the sideband power carries useful information. So we define useful signal power after
detection as:
Puseful=Ac2m24P_{\text{useful}} = \frac{A_c^2 m^2}{4}Puseful=4Ac2m2

📌 4. Output SNR Expression

Let the input noise power spectral density be N0/2N_0/2N0/2 (for AWGN).
After envelope detection and filtering, the output noise power (assuming a bandwidth BBB) is:
Pn=N0BP_n = N_0 BPn=N0B
So, the Output SNR is:
(SN)out=Ac2m24N0B\left( \frac{S}{N} \right)_{\text{out}} = \frac{A_c^2 m^2}{4 N_0 B}(NS)out
=4N0BAc2m2

📌 5. Input SNR Expression

Total input signal power (as calculated earlier):
Ps=Ac22(1+m22)P_s = \frac{A_c^2}{2} \left(1 + \frac{m^2}{2} \right)Ps=2Ac2(1+2m2)
Noise power at the input over bandwidth BBB:
Pn=N0BP_n = N_0 BPn=N0B
So, Input SNR:
(SN)in=Ac22N0B(1+m22)\left( \frac{S}{N} \right)_{\text{in}} = \frac{A_c^2}{2 N_0 B} \left(1 +
\frac{m^2}{2} \right)(NS)in=2N0BAc2(1+2m2)

📌 6. Noise Figure (NF)

Noise figure quantifies the degradation of SNR from input to output:
Noise Figure (NF)=(S/N)in(S/N)out\text{Noise Figure (NF)} =
\frac{(S/N)_{\text{in}}}{(S/N)_{\text{out}}}Noise Figure (NF)=(S/N)out(S/N)in
Substitute values:
NF=Ac22N0B(1+m22)Ac2m24N0B=2(1+m22)m22=4(1+m22)m2NF = \frac{\frac{A_c^2}{2 N_0 B}
\left(1 + \frac{m^2}{2} \right)}{\frac{A_c^2 m^2}{4 N_0 B}} = \frac{2\left(1 + \frac{m^2}{2}
\right)}{\frac{m^2}{2}} = \frac{4\left(1 + \frac{m^2}{2} \right)}{m^2}NF=4N0BAc2m22N0BAc2
(1+2m2)=2m22(1+2m2)=m24(1+2m2)

✅ Conclusion:
 AM is noise-sensitive, especially at low modulation index.
 Only sidebands carry information, but carrier uses most power.
 SNR improves with higher modulation index (up to m=1m = 1m=1).
 Envelope detection is simple but doesn't reject noise well.
 For better noise performance, DSB-SC or SSB (suppressed carrier/sideband) or FM systems
are preferred.

✍️ Summary Table:
Parameter Expression
AM signal power Ac22(1+m22)\frac{A_c^2}{2} \left(1 + \frac{m^2}{2} \right)2Ac2(1+2m2)
Useful signal
Ac2m24\frac{A_c^2 m^2}{4}4Ac2m2
power
Output SNR Ac2m24N0B\frac{A_c^2 m^2}{4 N_0 B}4N0BAc2m2
Ac22N0B(1+m22)\frac{A_c^2}{2 N_0 B} \left(1 + \frac{m^2}{2} \right)2N0BAc2
Input SNR
(1+2m2)
Noise Figure 4(1+m22)m2\frac{4(1 + \frac{m^2}{2})}{m^2}m24(1+2m2)
Topics Syllabus

 English grammar

 Vocabularies
Verbal Aptitude
 Reading and comprehension

 Narrative sequencing

 Data interpretation

 2 & 3-dimensional plots

 Maps & tables

 Numerical computation & estimation that includes ratios, percentage

Quantitative Aptitude
powers, exponents & logarithms

 Permutations & combinations

 Mensuration & geometry

 Elementary statistics & probability

 Logic: Deduction & induction Analogy

Analytical Aptitude
 Numerical relations & reasoning

 Transformation of shapes like translation, mirroring , rotation & scali

Spatial Aptitude  Assembling & grouping

 Paper folding, cutting, and patterns (2 & 3 dimensions)

GATE ECE Syllabus 2026 For Engineering Mathematics

Engineering Mathematics is going to be an important part of the GATE ECE syllabus. It covers basic
ideas and mathematical methods that are used in electronics and communication engineering. It
improves aspirants' abilities to solve problems, think logically, and deal with challenging engineering
problems effectively.

Here are the major topics covered in the GATE syllabus 2026 for ECE:

GATE ECE Syllabus 2026 For Engineering Mathematics

Sub-topics Syllabus

 Linear dependence and independence

 Vector space

Linear Algebra  Matrix algebra, eigen values and eigen vectors

 Solution of linear equations- existence and uniqueness

 Rank .
  Mean value theorems

 Theorems of integral calculus

 Evaluation of definite and improper integrals

Calculus
 Partial derivatives, maxima and minima

 Multiple integrals, line, surface and volume integrals

 Taylor series

 First order equations (linear and nonlinear)

 Higher order linear differential equations

 Cauchy's and Euler's equations

 Methods of solution using variation of parameters

Differential Equations
 Complementary function and particular integral

 Partial differential equations

 Variable separable method

 initial and boundary value problems

 Vectors in plane and space

 Vector operations
Vector Analysis
 Gradient, divergence and curl

 Gauss's, Green's and Stokes’ theorems.

 Analytic functions

 Cauchy’s integral theorem

Complex Analysis
 Cauchy’s integral formula, sequences, series, convergence tests

 Taylor and Laurent series, residue theorem.

 Mean, median, mode, standard deviation

 Combinatorial probability

 Probability distributions

 Binomial distribution
Probability and Statistics
 Poisson distribution

 Exponential distribution

 Normal distribution

 Joint and conditional probability.

GATE ECE Syllabus 2026 For Core Subjects

The core section covers the questions from the specific subjects learn by students in the
undergraduate level studies. The list of subjects and sub-topics are mentioned below:

GATE ECE Syllabus 2026 For Core Subjects

Subject Name Sub-topics Syllabus

 Node and mesh analysis

 Superposition, Thevenin's theorem, Norton’s theorem &

reciprocity.

 Sinusoidal steady state analysis: phasors, complex power

Circuit Analysis  Maximum power transfer.

 Time and frequency domain analysis of linear circuits such

RL, RC and RLC circuits

 Solution of network equations using Laplace transform

Networks , Signal &  Linear 2-port network parameters, wye-delta transformati
Systems
 Fourier series

Continuous-time Signals  Fourier transform

 Sampling theorem and applications.

 DTFT, DFT, z-transform

 Discrete-time processing of continuous-time signals.

Discrete-time Signals  LTI systems: definition and properties, causality & stability
their impulse response & convolution, poles & zeroes,

 Frequency response, group delay, phase delay

 Energy bands in semiconductors

Semiconductors  Equilibrium carrier concentration

 Direct and indirect band-gap semiconductors

 Diffusion current & drift current

Electronic Devices  Mobility and resistivity
Carrier Transport
 Generation and recombination of carriers

 Poisson and continuity equations.

 P-N junction & Zener diode

Diode
 BJT, MOS capacitor & MOSFET
  LED, photo diode & solar cell

 Clipping, clamping & rectifiers

Diode Circuits
 BJT & MOSFET

 Biasing

Amplifiers  Ac coupling, small signal analysis & frequency response

Analog Circuits  Current mirrors & differential amplifiers

 Amplifiers

 Summers, differentiators & integrators

Op-amp Circuits
 Active filters

 Schmitt triggers & oscillators

 Binary Number system

Number Representations
 Integer & floating-point- numbers

 Boolean algebra

 Minimization of Boolean functions using Boolean identitie

Karnaugh map

Combinatorial circuits  Logic gates & their static CMOS implementations

 Arithmetic circuits

 Code converters

 Multiplexers & decoders.

 Latches & flip-flops

Digital Circuits
 Counters & shift-registers

Sequential Circuits  Finite state machines

 Propagation delay & critical path delay

 Setup and hold time

Data Converters  Sample & hold circuits

Semiconductor  ADCs & DACs

 ROM

Memories  SRAM

 DRAM

Computer Organization  Machine instructions & addressing modes

  ALU, data-path & control unit

 Instruction pipelining

 Feedback principle

Basic control system  Transfer function

components  Block diagram representation

 Signal flow graph

 Frequency response
Control Systems
 Routh-Hurwitz & Nyquist stability criteria

Transient and steady-state  Bode and root-locus plots

analysis of LTI systems  Lag, lead & laglead compensation

 State variable model

 Solution of state equation of LTI systems.

 Auto correlation & power spectral density

Random Processes  Properties of white noise

 Filtering of random signals through LTI systems.

 Amplitude modulation & demodulation

 Angle modulation & demodulation

Analog Communications
 Spectra of AM & FM

 Super heterodyne receivers.

 Entropy
Communications Information Theory  Mutual information

 Channel capacity theorem

 PCM, DPCM

 Digital modulation schemes (ASK, PSK, FSK, QAM) & their

bandwidth

Digital Communications  Inter-symbol interference,

 MAP & ML detection,

 Matched filter receiver

 SNR and BER

 Fundamentals of error  Hamming codes
correction  CRC.

 Differential and integral forms and their interpretation

 Boundary conditions
Maxwell’s Equations
 Wave equation

 Poynting vector.

 Reflection and refraction polarization

 Phase and group velocity

Plane Waves and Properties
 Propagation through various media

 Skin depth.

 Equations
Electromagnetics
 Characteristic impedance

 Impedance matching
Transmission Lines
 Impedance transformation,

 S-parameters

 Smith chart.

 Rectangular and circular waveguides

 Light propagation in optical fibers

Waveguides and Antenna
 Dipole and monopole antennas

 Linear antenna arrays.

Check: GATE ECE Previous Year Question Papers