Ece Formula List

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  • Topic: Orthogonal matrix, Matrices, Normal matrix
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Institute Of Engineering Studies (IES,Bangalore)

Formulae Sheet in ECE/TCE Department

Communication Systems
Amplitude Modulation : DSB-SC : u (t) = m(t) cos 2π t Power P = Conventioanal AM : u (t) = [1 + m(t)] Cos 2π 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 / ≥ Frequency & Phase Modulation : Angle Modulation :u (t) = ∅ (t) Cos (2π t + ∅ (t) ) ( ) → 2π m(t) . dt → phase & frequency deviation constant R C (o/P) >> 1/ R C x} = 1 – P { X ≤ x} = 1- (x)

PDF :Pdf =

(x) =

(x)

7

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Institute Of Engineering Studies (IES,Bangalore)

Formulae Sheet in ECE/TCE Department

Pmf = (x) = Properties: (x) ≥ 0    (x) = (∞) = (x) * u(x) =

= x } δ(x = x )

(x) dx

(x) dx =1 so, area under PDF = 1 (x)dx

P{x 1 (over damped) :-

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Institute Of Engineering Studies (IES,Bangalore)

Formulae Sheet in ECE/TCE Department

C(t) = 1 T= > > >

Time Domain Specifications :           Rise time t = Peak time t = / Max over shoot % =e × 100 Settling time t = 3T 5% tolerance = 4T 2% tolerance . Delay time t = ∅

∅ = tan

Damping actor

=

( (

) )

Time period of oscillations T = No of oscillations =
/

= ; ω =ω 2 + 1 2 + 2)
/

t ≈ 1.5 t t = 2.2 T Resonant peak = Bandwidth ω = ω (1

ω > ω ) → good conductor Complex permittivity = 1 = -j . Tan = = .

Plane wave in loss less dielectric :- ( σ ≈ 0)  α=0;β=ω ω= λ = 2π/β  E & H are in phase in lossless dielectric = , = )

η=

/

∠ .

Free space :- (σ = 0,

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Institute Of Engineering Studies (IES,Bangalore)

Formulae Sheet in ECE/TCE Department
η= / < = 12 π ∠

 α=0,β=ω ; u = 1/ Here also E & H in phase . Good Conductor :σ >>ω σ/ω → ∞ ⇒ σ = ∞      

, λ = 2π/β

=

= ∠

α = β = π σ ; u = 2ω/ σ ; λ = 2π / β ; η = Skin depth δ = 1/α η= 2e / = Skin resistance R = R R = = .

=

.

Poynting Vector :( ) ds =  S   δ (z) =
| |

[ v cos a

+

] dv – σ

dv

e

Total time avge power crossing given area

= S

(s) ds

Direction of propagation :- ( a ×a =a

)

a ×a =a → Both E & H are normal to direction of propagation → Means they form EM wave that has no E or H component along direction of propagation . Reflection of plane wave :(a) Normal incidence Reflection coefficient Γ = = coefficient Τ = =

Medium-I Dielectric , Medium-2 Conductor :> :Γ there is a standing wave in medium Max values of | | occurs = - nπ/β = n = 1 2…. = ( )

wave in medium ‘2’.

=

(

)

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Institute Of Engineering Studies (IES,Bangalore)
( )

Formulae Sheet in ECE/TCE Department
=
( )

<

:-

occurs @ β β = nπ ⇒

= =



=

(

)

=

Since |Γ| < 1 ⇒ 1 ≤ δ ≤ ∞

min occurs...
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