Institute Of Engineering Studies (IES,Bangalore)

Formulae Sheet in ECE/TCE Department

Communication SystemsAmplitude Modulation : DSB-SC : u (t) = m(t) cos 2 t Power P = Conventioanal AM : u (t) = [1 + m(t)] Cos 2 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 (2 t + (t) ) ( ) 2 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)

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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 } (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 =/

= ; = 2 + 1 2 + 2)/

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

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

Plane wave in loss less dielectric :- ( 0) =0;= = = 2/ E & H are in phase in lossless dielectric = , = )

=

/

.

Free space :- ( = 0,

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No.1 Training center for GATE/IES/JTO/PSUs in Bangalore @ Malleshwaram & Jayanagar, Bangalore. Ph: 0 99003 99699/ 0 97419 00225 / 080-32552008 Email : onlineies.com@gmail.com 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= / < = 12

=0,= ; u = 1/ Here also E & H in phase . Good Conductor : >> / =

, = 2/

=

=

= = ; u = 2/ ; = 2 / ; = Skin depth = 1/ = 2e / = Skin resistance R = R R = =.

=

.

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

[ v cos a

+

] dv

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 = = coefficient = =

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

wave in medium 2.

=

(

)

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No.1 Training center for GATE/IES/JTO/PSUs in Bangalore @ Malleshwaram & Jayanagar, Bangalore. Ph: 0 99003 99699/ 0 97419 00225 / 080-32552008 Email : onlineies.com@gmail.com 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=( )

Shorted line :- = -1 , S =

=

=j

tan l

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No.1 Training center for GATE/IES/JTO/PSUs in Bangalore @ Malleshwaram & Jayanagar, Bangalore. Ph: 0 99003 99699/ 0 97419 00225 / 080-32552008 Email : onlineies.com@gmail.com 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

= -1 , S =

=

=j

tan l.

may be inductive or capacitive based on length 0 If l < / 4 inductive ( +ve) < l < /2 capacitive ( -ve)

Open circuited line := = -j cot l =1 s= =

l < / 4 capacitive < l < /2 inductive

Matched line : ( = ) = = 0 ; s =1 No reflection . Total wave

. So, max power transfer possible .

Behaviour of Transmission Line for Different lengths :l = /4 l = /2 : = impedance inverter @ l = /4 impedance reflector @ l = /2

Wave Guides :TM modes : ( = ) = sin x sin h =k +k =

ye + where k =

m no. of half cycle variation in X-direction n no. of half cycle variation in Y- direction . Cut off frequency = k < k > = k + u = phase velocity = + + + = 0; = 0 =

Evanscent mode ; = ; = 0 Propegation mode = =

=

is lossless dielectric medium

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No.1 Training center for GATE/IES/JTO/PSUs in Bangalore @ Malleshwaram & Jayanagar, Bangalore. Ph: 0 99003 99699/ 0 97419 00225 / 080-32552008 Email : onlineies.com@gmail.com 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

=u/ =

( )

( )

=

1

= / W

= phase constant in dielectric medium.

u = / = 2/ = u /f phase velocity & wave length in side wave guide = == = 1

=

1 = 0) cos

impedance of UPW in medium

TE Modes :- ( = cos

e

= >

= / 1

Dominant mode

Antennas :Hertzian Dipole :Half wave Dipole :=

=

sin

e

=

;

=

EDC & Analog Energy gap =/ /

. .

. .

. .

Energy gap depending on temperature

- KT ln

=

+ KT ln (KT in ev)/

)/ No. of electrons n = N e ( )/ No. of holes p = N e ( Mass action law n = n = N N e Drift velocity = E (for si 1

cm/sec)

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No.1 Training center for GATE/IES/JTO/PSUs in Bangalore @ Malleshwaram & Jayanagar, Bangalore. Ph: 0 99003 99699/ 0 97419 00225 / 080-32552008 Email : onlineies.com@gmail.com 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 charge density = qN = ne = N .n .

Hall voltage

=

. Hall coefficient R = 1/ . = N .n

Conductivity = ; = R . Max value of electric field @ junction Charge storage @ junction =-

= qA x N = qA x N EDC

Diffusion current densities J = - q D

J =-qD

Drift current Densities = q(p + n )E , decrease with increasing doping concentration . = = KT/q 25 mv @ 300 K Carrier concentration in N-type silicon n = N ; p = n / N Carrier concentration in P-type silicon p = N ; n = n / N Junction built in voltage Width of Depletion region * = 12.9 = Charge stored in depletion region q = Depletion capacitance C = C =C / 1+ C = 2C (for forward Bias) + ; = Aq n = Aq n/ / .

=

ln = x +x = + ( + )

.A./

; C =

Forward current I =

1 1

Saturation Current

= Aq n

+ /D ; = /D = , = = mean transist time I = .g C I.

Minority carrier life time = Minority carrier charge storage Q= + = I Diffusion capacitance C =

carrier life time , g = conductance = I / )/ = 2( Junction Barrier Voltage = = (open condition) = - V (forward Bias) = + V (Reverse Bias) Probability of filled states above E f(E) = ( )/

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No.1 Training center for GATE/IES/JTO/PSUs in Bangalore @ Malleshwaram & Jayanagar, Bangalore. Ph: 0 99003 99699/ 0 97419 00225 / 080-32552008 Email : onlineies.com@gmail.com 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

Drift velocity of e Poisson equation =

1 =

cm/sec =E=

Transistor : = + = = +

Active region (1- e / ) = . = - 0.25 mv / C

Common Emitter : = (1+ ) +

= Collector current when base open Collector current when = 0 > or - 2.5 mv / C ; Large signal Current gain = D.C current gain ( =h = =h >C R

) when

Small signal current gain = Over drive factor =

= h =

(

)

h C

=

Conversion formula :CC CE h =h ; h =1; CB CE h =

h = - (1+ h ) ;

h

=h

; h =

-h

;h =

; h

=

CE parameters in terms of CB can be obtained by interchanging B & E . Specifications of An amplifier : = = =h +h =h = =.

= =

.

=.

.

.

Choice of Transistor Configuration : For intermediate stages CC cant be used as 10 R

For thermal stability [

- 2 (R + R )] [ 0.07

. S] < 1/

;

>

Ebress moll model :=- + (1- e =- = + (1- e

/ /

) )

Multistage Amplifiers : * = 2 / 1 ; Rise time t = t = 1.1 t = 1.1.

=. .