Electronics and Communication Engineering Formula sheet.pdf
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Transcript of Electronics and Communication Engineering Formula sheet.pdf
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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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
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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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
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.
=. .