Formula Sheet: Electronics | GATE ECE (Electronics) Mock Test Series 2025 - Electronics and Communication Engineering (ECE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Amplitude Modulation :
DSB-SC :
u (t) =
m(t) cos 2p
t
Power P =
Conventioanal AM :
u (t) =
[1 + m(t)] Cos 2p
t . as long as |m(t)| = 1 demodulation is simple .
Practically m(t) = a m
(t) .
Modulation index a =
( )
( )
, m
(t) =
( )
| ( )|
Power =
+
SSB-AM :
? Square law Detector SNR =
( )
Square law modulator
?
= 2a
/ a
? amplitude Sensitivity
Envelope Detector R
C (i/p) < < 1 /
R
C (o/P) >> 1/
R
C << 1/?
=
Frequency & Phase Modulation : Angle Modulation :-
u (t) =
Cos (2p
t + Ø (t) )
Ø (t)
( ) ?
2p
m(t)
. dt ?
phase & frequency deviation constant
? max phase deviation ?Ø =
max | m(t) |
? max requency deviation ? =
max |m(t) |
Bandwidth :
Effective Bandwidth
= 2 (ß + 1)
? 98% power
Noise in Analog Modulation :-
? (SNR)
=
=
=
R = m(t) cos 2p
?
=
/ 2
Page 2
Amplitude Modulation :
DSB-SC :
u (t) =
m(t) cos 2p
t
Power P =
Conventioanal AM :
u (t) =
[1 + m(t)] Cos 2p
t . as long as |m(t)| = 1 demodulation is simple .
Practically m(t) = a m
(t) .
Modulation index a =
( )
( )
, m
(t) =
( )
| ( )|
Power =
+
SSB-AM :
? Square law Detector SNR =
( )
Square law modulator
?
= 2a
/ a
? amplitude Sensitivity
Envelope Detector R
C (i/p) < < 1 /
R
C (o/P) >> 1/
R
C << 1/?
=
Frequency & Phase Modulation : Angle Modulation :-
u (t) =
Cos (2p
t + Ø (t) )
Ø (t)
( ) ?
2p
m(t)
. dt ?
phase & frequency deviation constant
? max phase deviation ?Ø =
max | m(t) |
? max requency deviation ? =
max |m(t) |
Bandwidth :
Effective Bandwidth
= 2 (ß + 1)
? 98% power
Noise in Analog Modulation :-
? (SNR)
=
=
=
R = m(t) cos 2p
?
=
/ 2
? (SNR)
=
/
/
=
=
=
=
= (SNR)
? (SNR)
=
/
/
=
=
=
= (SNR)
.
=
.
= ?
? =
Noise in Angle Modulation :-
=
PCM :-
? Min. no of samples required for reconstruction = 2? =
; ? = Bandwidth of msg signal .
? Total bits required = v
bps . v ? bits / sample
? Bandwidth = R
/2 = v
/ 2 = v . ?
? SNR = 1.76 + 6.02 v
? As Number of bits increased SNR increased by 6 dB/bit . Band width also increases.
Delta Modulation :-
? By increasing step size slope over load distortion eliminated [ Signal raised sharply ]
? By Reducing step size Grannualar distortion eliminated . [ Signal varies slowly ]
Digital Communication
Matched filter:
? impulse response a(t) =
( T – t) . P(t) ? i/p
? Matched filter o/p will be max at multiples of ‘T’ . So, sampling @ multiples of ‘T’ will give max SNR
(2
nd
point )
? matched filter is always causal a(t) = 0 for t < 0
? Spectrum of o/p signal of matched filter with the matched signal as i/p ie, except for a delay factor ;
proportional to energy spectral density of i/p.
Ø
( ) =
(f) Ø(f) = Ø(f) Ø*(f) e
Ø
( ) = |Ø( )|
e
Page 3
Amplitude Modulation :
DSB-SC :
u (t) =
m(t) cos 2p
t
Power P =
Conventioanal AM :
u (t) =
[1 + m(t)] Cos 2p
t . as long as |m(t)| = 1 demodulation is simple .
Practically m(t) = a m
(t) .
Modulation index a =
( )
( )
, m
(t) =
( )
| ( )|
Power =
+
SSB-AM :
? Square law Detector SNR =
( )
Square law modulator
?
= 2a
/ a
? amplitude Sensitivity
Envelope Detector R
C (i/p) < < 1 /
R
C (o/P) >> 1/
R
C << 1/?
=
Frequency & Phase Modulation : Angle Modulation :-
u (t) =
Cos (2p
t + Ø (t) )
Ø (t)
( ) ?
2p
m(t)
. dt ?
phase & frequency deviation constant
? max phase deviation ?Ø =
max | m(t) |
? max requency deviation ? =
max |m(t) |
Bandwidth :
Effective Bandwidth
= 2 (ß + 1)
? 98% power
Noise in Analog Modulation :-
? (SNR)
=
=
=
R = m(t) cos 2p
?
=
/ 2
? (SNR)
=
/
/
=
=
=
=
= (SNR)
? (SNR)
=
/
/
=
=
=
= (SNR)
.
=
.
= ?
? =
Noise in Angle Modulation :-
=
PCM :-
? Min. no of samples required for reconstruction = 2? =
; ? = Bandwidth of msg signal .
? Total bits required = v
bps . v ? bits / sample
? Bandwidth = R
/2 = v
/ 2 = v . ?
? SNR = 1.76 + 6.02 v
? As Number of bits increased SNR increased by 6 dB/bit . Band width also increases.
Delta Modulation :-
? By increasing step size slope over load distortion eliminated [ Signal raised sharply ]
? By Reducing step size Grannualar distortion eliminated . [ Signal varies slowly ]
Digital Communication
Matched filter:
? impulse response a(t) =
( T – t) . P(t) ? i/p
? Matched filter o/p will be max at multiples of ‘T’ . So, sampling @ multiples of ‘T’ will give max SNR
(2
nd
point )
? matched filter is always causal a(t) = 0 for t < 0
? Spectrum of o/p signal of matched filter with the matched signal as i/p ie, except for a delay factor ;
proportional to energy spectral density of i/p.
Ø
( ) =
(f) Ø(f) = Ø(f) Ø*(f) e
Ø
( ) = |Ø( )|
e
? o/p signal of matched filter is proportional to shifted version of auto correlation fine of i/p signal
Ø
(t) = R
Ø
(t – T)
At t = T Ø
(T) = R
Ø
(0) ? which proves 2
nd
point
Cauchy-Schwartz in equality :-
|g
(t) g
(t) dt|
= g
(t)
dt |g
(t)|
dt
If g
(t) = c g
(t) then equality holds otherwise ‘<’ holds
Raised Cosine pulses :
P(t) =
(
)
(
)
.
(
)
P(f) =
| | =
cos
| |
=| | =
| |
? Bamdwidth of Raised cosine filter
=
? Bit rate
=
a ? roll o actor
? signal time period
? For Binary PSK
= Q
= Q
=
erfc
.
? 4 PSK
= 2Q
1
FSK:-
For BPSK
= Q
= Q
=
erfc
? All signals have same energy (Const energy modulation )
? Energy & min distance both can be kept constant while increasing no. of points . But Bandwidth
Compramised.
? PPM is called as Dual of FSK .
? For DPSK
=
e
/
Page 4
Amplitude Modulation :
DSB-SC :
u (t) =
m(t) cos 2p
t
Power P =
Conventioanal AM :
u (t) =
[1 + m(t)] Cos 2p
t . as long as |m(t)| = 1 demodulation is simple .
Practically m(t) = a m
(t) .
Modulation index a =
( )
( )
, m
(t) =
( )
| ( )|
Power =
+
SSB-AM :
? Square law Detector SNR =
( )
Square law modulator
?
= 2a
/ a
? amplitude Sensitivity
Envelope Detector R
C (i/p) < < 1 /
R
C (o/P) >> 1/
R
C << 1/?
=
Frequency & Phase Modulation : Angle Modulation :-
u (t) =
Cos (2p
t + Ø (t) )
Ø (t)
( ) ?
2p
m(t)
. dt ?
phase & frequency deviation constant
? max phase deviation ?Ø =
max | m(t) |
? max requency deviation ? =
max |m(t) |
Bandwidth :
Effective Bandwidth
= 2 (ß + 1)
? 98% power
Noise in Analog Modulation :-
? (SNR)
=
=
=
R = m(t) cos 2p
?
=
/ 2
? (SNR)
=
/
/
=
=
=
=
= (SNR)
? (SNR)
=
/
/
=
=
=
= (SNR)
.
=
.
= ?
? =
Noise in Angle Modulation :-
=
PCM :-
? Min. no of samples required for reconstruction = 2? =
; ? = Bandwidth of msg signal .
? Total bits required = v
bps . v ? bits / sample
? Bandwidth = R
/2 = v
/ 2 = v . ?
? SNR = 1.76 + 6.02 v
? As Number of bits increased SNR increased by 6 dB/bit . Band width also increases.
Delta Modulation :-
? By increasing step size slope over load distortion eliminated [ Signal raised sharply ]
? By Reducing step size Grannualar distortion eliminated . [ Signal varies slowly ]
Digital Communication
Matched filter:
? impulse response a(t) =
( T – t) . P(t) ? i/p
? Matched filter o/p will be max at multiples of ‘T’ . So, sampling @ multiples of ‘T’ will give max SNR
(2
nd
point )
? matched filter is always causal a(t) = 0 for t < 0
? Spectrum of o/p signal of matched filter with the matched signal as i/p ie, except for a delay factor ;
proportional to energy spectral density of i/p.
Ø
( ) =
(f) Ø(f) = Ø(f) Ø*(f) e
Ø
( ) = |Ø( )|
e
? o/p signal of matched filter is proportional to shifted version of auto correlation fine of i/p signal
Ø
(t) = R
Ø
(t – T)
At t = T Ø
(T) = R
Ø
(0) ? which proves 2
nd
point
Cauchy-Schwartz in equality :-
|g
(t) g
(t) dt|
= g
(t)
dt |g
(t)|
dt
If g
(t) = c g
(t) then equality holds otherwise ‘<’ holds
Raised Cosine pulses :
P(t) =
(
)
(
)
.
(
)
P(f) =
| | =
cos
| |
=| | =
| |
? Bamdwidth of Raised cosine filter
=
? Bit rate
=
a ? roll o actor
? signal time period
? For Binary PSK
= Q
= Q
=
erfc
.
? 4 PSK
= 2Q
1
FSK:-
For BPSK
= Q
= Q
=
erfc
? All signals have same energy (Const energy modulation )
? Energy & min distance both can be kept constant while increasing no. of points . But Bandwidth
Compramised.
? PPM is called as Dual of FSK .
? For DPSK
=
e
/
? Orthogonal signals require factor of ‘2’ more energy to achieve same
as anti podal signals
? Orthogonal signals are 3 dB poorer than antipodal signals. The 3dB difference is due to distance b/w 2
points.
? For non coherent FSK
=
e
/
? FPSK & 4 QAM both have comparable performance .
? 32 QAM has 7 dB advantage over 32 PSK.
? Bandwidth of Mary PSK =
=
; S =
? Bandwidth of Mary FSK =
=
; S =
? Bandwidth efficiency S =
.
.
? Symbol time
=
log
? Band rate =
Page 5
Amplitude Modulation :
DSB-SC :
u (t) =
m(t) cos 2p
t
Power P =
Conventioanal AM :
u (t) =
[1 + m(t)] Cos 2p
t . as long as |m(t)| = 1 demodulation is simple .
Practically m(t) = a m
(t) .
Modulation index a =
( )
( )
, m
(t) =
( )
| ( )|
Power =
+
SSB-AM :
? Square law Detector SNR =
( )
Square law modulator
?
= 2a
/ a
? amplitude Sensitivity
Envelope Detector R
C (i/p) < < 1 /
R
C (o/P) >> 1/
R
C << 1/?
=
Frequency & Phase Modulation : Angle Modulation :-
u (t) =
Cos (2p
t + Ø (t) )
Ø (t)
( ) ?
2p
m(t)
. dt ?
phase & frequency deviation constant
? max phase deviation ?Ø =
max | m(t) |
? max requency deviation ? =
max |m(t) |
Bandwidth :
Effective Bandwidth
= 2 (ß + 1)
? 98% power
Noise in Analog Modulation :-
? (SNR)
=
=
=
R = m(t) cos 2p
?
=
/ 2
? (SNR)
=
/
/
=
=
=
=
= (SNR)
? (SNR)
=
/
/
=
=
=
= (SNR)
.
=
.
= ?
? =
Noise in Angle Modulation :-
=
PCM :-
? Min. no of samples required for reconstruction = 2? =
; ? = Bandwidth of msg signal .
? Total bits required = v
bps . v ? bits / sample
? Bandwidth = R
/2 = v
/ 2 = v . ?
? SNR = 1.76 + 6.02 v
? As Number of bits increased SNR increased by 6 dB/bit . Band width also increases.
Delta Modulation :-
? By increasing step size slope over load distortion eliminated [ Signal raised sharply ]
? By Reducing step size Grannualar distortion eliminated . [ Signal varies slowly ]
Digital Communication
Matched filter:
? impulse response a(t) =
( T – t) . P(t) ? i/p
? Matched filter o/p will be max at multiples of ‘T’ . So, sampling @ multiples of ‘T’ will give max SNR
(2
nd
point )
? matched filter is always causal a(t) = 0 for t < 0
? Spectrum of o/p signal of matched filter with the matched signal as i/p ie, except for a delay factor ;
proportional to energy spectral density of i/p.
Ø
( ) =
(f) Ø(f) = Ø(f) Ø*(f) e
Ø
( ) = |Ø( )|
e
? o/p signal of matched filter is proportional to shifted version of auto correlation fine of i/p signal
Ø
(t) = R
Ø
(t – T)
At t = T Ø
(T) = R
Ø
(0) ? which proves 2
nd
point
Cauchy-Schwartz in equality :-
|g
(t) g
(t) dt|
= g
(t)
dt |g
(t)|
dt
If g
(t) = c g
(t) then equality holds otherwise ‘<’ holds
Raised Cosine pulses :
P(t) =
(
)
(
)
.
(
)
P(f) =
| | =
cos
| |
=| | =
| |
? Bamdwidth of Raised cosine filter
=
? Bit rate
=
a ? roll o actor
? signal time period
? For Binary PSK
= Q
= Q
=
erfc
.
? 4 PSK
= 2Q
1
FSK:-
For BPSK
= Q
= Q
=
erfc
? All signals have same energy (Const energy modulation )
? Energy & min distance both can be kept constant while increasing no. of points . But Bandwidth
Compramised.
? PPM is called as Dual of FSK .
? For DPSK
=
e
/
? Orthogonal signals require factor of ‘2’ more energy to achieve same
as anti podal signals
? Orthogonal signals are 3 dB poorer than antipodal signals. The 3dB difference is due to distance b/w 2
points.
? For non coherent FSK
=
e
/
? FPSK & 4 QAM both have comparable performance .
? 32 QAM has 7 dB advantage over 32 PSK.
? Bandwidth of Mary PSK =
=
; S =
? Bandwidth of Mary FSK =
=
; S =
? Bandwidth efficiency S =
.
.
? Symbol time
=
log
? Band rate =
? Energy of a signal |x(t)|
dt = | [ ]|
? Power of a signal P = lim
?
|x(t)|
dt = lim
?
|x[n]|
? x
(t) ?
; x
(t) ?
x
(t) + x
(t) ?
+
iff x
(t) & x
(t) orthogonal
? Shifting & Time scaling won’t effect power . Frequency content doesn’t effect power.
? if power = 8 ? neither energy nor power signal
Power = 0 ? Energy signal
Power = K ? power signal
? Energy of power signal = 8 ; Power of energy signal = 0
? Generally Periodic & random signals ? Power signals
Aperiodic & deterministic ? Energy signals
Precedence rule for scaling & Shifting :
x(at + b) ? (1) shift x(t) by ‘b’ ? x(t + b)
(2) Scale x(t + b) by ‘a’ ? x(at + b)
x( a ( t + b/a)) ? (1) scale x(t) by a ? x(at)
(2) shift x(at) by b/a ? x (a (t+b/a)).
? x(at +b) = y(t) ? x(t) = y
? Step response s(t) = h(t) * u(t) = h(t)dt
S’ (t) = h(t)
S[n] = [ ]
h[n] = s[n] – s[n-1]
? e
u(t) * e
u(t) =
[ e
- e
] u(t) .
?
Rect (t / 2
) *
Rect(t / 2
) = 2
min (
,
) trapezoid (
,
)
? Rect (t / 2T) * Rect (t / 2T) = 2T tri(t / T)
Hilbert Transform Pairs :
e
/
dx
= s 2p ; x
e
/
dx = s
2p s > 0
Laplace Transform :-
Read More
|
25 docs|263 tests
|
FAQs on Formula Sheet: Electronics - GATE ECE (Electronics) Mock Test Series 2025 - Electronics and Communication Engineering (ECE)
| 1. What are some common electronic components used in Electronics and Communication Engineering? |  |
Ans. Some common electronic components used in Electronics and Communication Engineering are resistors, capacitors, inductors, transistors, diodes, and integrated circuits.
| 2. How does a transistor work in electronic circuits? | |
Ans. A transistor is a semiconductor device that can amplify or switch electronic signals. It works by controlling the flow of current between its terminals based on the voltage applied to its input terminal.
| 3. What is the purpose of using capacitors in electronic circuits? | |
Ans. Capacitors are used in electronic circuits to store and release electrical energy, filter out noise and ripple in power supplies, and block DC signals while allowing AC signals to pass through.
| 4. How do integrated circuits (ICs) differ from discrete electronic components? | |
Ans. Integrated circuits (ICs) are miniature electronic circuits fabricated on a small piece of semiconductor material, while discrete electronic components are individual components like resistors and capacitors that are not integrated into a single package.
| 5. How do communication systems use modulation and demodulation techniques? | |
Ans. Modulation is the process of encoding information onto a carrier signal, while demodulation is the process of extracting the original information from the modulated signal. Communication systems use modulation and demodulation techniques to transmit and receive information efficiently over long distances.
Related Exams
About this Document
|
1.3K Views |
|
4.61/5 Rating |
|
Dec 22, 2024 Last updated |
Document Description: Formula Sheet: Electronics for Electronics and Communication Engineering (ECE) 2024 is part of GATE ECE (Electronics) Mock Test Series 2025 preparation.
The notes and questions for Formula Sheet: Electronics have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Formula Sheet: Electronics covers topics
like and Formula Sheet: Electronics Example, for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Formula Sheet: Electronics.
Introduction of Formula Sheet: Electronics in English is available as part of our GATE ECE (Electronics) Mock Test Series 2025
for Electronics and Communication Engineering (ECE) & Formula Sheet: Electronics in Hindi for GATE ECE (Electronics) Mock Test Series 2025 course.
Download more important topics related with notes, lectures and mock test series for Electronics and Communication Engineering (ECE)
Exam by signing up for free. Electronics and Communication Engineering (ECE): Formula Sheet: Electronics | GATE ECE (Electronics) Mock Test Series 2025 - Electronics and Communication Engineering (ECE)
Description
Full syllabus notes, lecture & questions for Formula Sheet: Electronics | GATE ECE (Electronics) Mock Test Series 2025 - Electronics and Communication Engineering (ECE) - Electronics and Communication Engineering (ECE) | Plus excerises question with solution to help you revise complete syllabus for GATE ECE (Electronics) Mock Test Series 2025 | Best notes, free PDF download
Information about Formula Sheet: Electronics
In this doc you can find the meaning of Formula Sheet: Electronics defined & explained in the simplest way possible. Besides explaining types of
Formula Sheet: Electronics theory, EduRev gives you an ample number of questions to practice Formula Sheet: Electronics tests, examples and also practice Electronics and Communication Engineering (ECE)
tests
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Sample Paper
,Exam
,Formula Sheet: Electronics | GATE ECE (Electronics) Mock Test Series 2025 - Electronics and Communication Engineering (ECE)
,Semester Notes
,Previous Year Questions with Solutions
,Viva Questions
,video lectures
,MCQs
,Important questions
,Objective type Questions
,mock tests for examination
,past year papers
,Free
,shortcuts and tricks
,Formula Sheet: Electronics | GATE ECE (Electronics) Mock Test Series 2025 - Electronics and Communication Engineering (ECE)
,practice quizzes
,Extra Questions
,Formula Sheet: Electronics | GATE ECE (Electronics) Mock Test Series 2025 - Electronics and Communication Engineering (ECE)
,study material
,ppt
,Summary
;
Additional Information about Formula Sheet: Electronics for Electronics and Communication Engineering (ECE) Preparation
Formula Sheet: Electronics Free PDF Download
The Formula Sheet: Electronics is an invaluable resource that delves deep into the core of the Electronics and Communication Engineering (ECE) exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Formula Sheet: Electronics now and kickstart your journey towards success in the Electronics and Communication Engineering (ECE) exam.
Importance of Formula Sheet: Electronics
The importance of Formula Sheet: Electronics cannot be overstated, especially for Electronics and Communication Engineering (ECE) aspirants.
This document holds the key to success in the Electronics and Communication Engineering (ECE) exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Formula Sheet: Electronics Notes
Formula Sheet: Electronics Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Formula Sheet: Electronics.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Formula Sheet: Electronics Notes on EduRev are your ultimate resource for success.
Formula Sheet: Electronics Electronics and Communication Engineering (ECE) Questions
The "Formula Sheet: Electronics Electronics and Communication Engineering (ECE) Questions" guide is a valuable resource for all aspiring students preparing for the
Electronics and Communication Engineering (ECE) exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Formula Sheet: Electronics on the App
Students of Electronics and Communication Engineering (ECE) can study Formula Sheet: Electronics alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Formula Sheet: Electronics,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Formula Sheet: Electronics is prepared as per the latest Electronics and Communication Engineering (ECE) syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup