Formula Sheet: Electronics
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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 MoreFAQs on Formula Sheet: Electronics
| 1. What are the most important semiconductor formulas I need to memorise for GATE ECE? |  |
Ans. Essential semiconductor formulas include intrinsic carrier concentration (ni), drift velocity, conductivity, and the Shockley diode equation. Memorise transconductance (gm), output resistance, and gain expressions for BJTs and FETs. Master depletion-width calculations and built-in potential equations. Use flashcards or mind maps from EduRev to organise these electronics fundamentals by device type for faster recall during exams.
| 2. How do I remember all the transistor biasing formulas without getting confused? | |
Ans. Transistor biasing formulas differ based on circuit configuration-common-emitter, common-base, and common-collector each have distinct voltage and current relationships. Group formulas by configuration rather than learning them randomly. Focus on the relationship between VBE, IC, and β first, then derive secondary expressions. Visual aids like PPTs or mind maps help distinguish between active-region and saturation-region operating points effectively.
| 3. What's the difference between small-signal and large-signal analysis formulas in electronics? | |
Ans. Large-signal analysis uses exact nonlinear transistor equations for circuit behaviour across the full operating range. Small-signal analysis linearises these equations around a bias point, producing simplified formulas for voltage gain, input impedance, and output resistance. Small-signal models assume incremental changes only. Refer to detailed notes or flashcards that compare both approaches side-by-side to avoid mixing up their applications during problem-solving.
| 4. Why do I keep making mistakes with filter circuit formulas and cutoff frequency calculations? | |
Ans. Filter formulas depend on circuit topology-RC, RL, RLC filters each have different cutoff-frequency expressions. Students often confuse -3dB bandwidth with passband gain or mix up highpass and lowpass corner frequencies. Remember: cutoff frequency (fc) = 1/(2πRC) for passive filters, but active filters require additional gain factors. Double-check whether your circuit is first-order or second-order before applying the formula.
| 5. How should I organize all electronics formulas for quick revision before my GATE exam? | |
Ans. Organise formulas by functional blocks: semiconductor devices, amplifiers, filters, and oscillators. Create a systematic formula sheet grouping DC analysis, AC small-signal analysis, and frequency-response equations together. Use colour-coded categories for different device types. Access MCQ tests and visual worksheets on EduRev to test your formula application under exam-like conditions and identify weak areas needing reinforcement.
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