Ece Formula List

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) :-

11

No.1 Training center for GATE/IES/JTO/PSUs in Bangalore @ Malleshwaram & Jayanagar, Bangalore. Ph: 0 99003 99699/ 0 97419 00225 / 080-32552008 Email : [e-mail] Site: www.onlineIES.com Google+: http://bit.ly/gplus_iesgate FB: www.facebook.com/onlineies

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