Analog Electronics Formulas

7/28/2019 Analog Electronics Formulas

1/9

Institute Of Engineering Studies (IES,Bangalore) Formulae Sheet in ECE/TCE Department

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

Email : [email protected] Site:www.onlineIES.comGoogle+: http://bit.ly/gplus_iesgate FB:www.facebook.com/onlineies

x Hall voltage = . . Hall coefficient R= 1/ . charge density = qN= ne x Conductivity = ; = R.x Max value of electric field @ junction E = - N. n = - N. n .x

Charge storage @ junction Q

= - Q

= qA x

N

= qA x

N

EDCx Diffusion current densities J = - q D J = - q Dx Drift current Densities = q(p + n)Ex , decrease with increasing doping concentration .x = = KT/q 25 mv @ 300 Kx Carrier concentration in N-type silicon n = N ; p = n / N x Carrier concentration in P-type silicon p = N ; n = n / Nx Junction built in voltage

V=

Vln

x Width of Depletion region W = x + x = + (V + V)* = 12.93

x = x Charge stored in depletion region q = . . A . Wx Depletion capacitance C = ; C = /

C =

C/

1 +

C = 2C (for forward Bias)x Forward current I = I + I ; I = Aq n / 1I = Aq n / 1x Saturation Current I = Aq n + x Minority carrier life time = L / D ; = L / Dx Minority carrier charge storage Q = I , Q = I

Q = Q + Q = I = mean transist timex Diffusion capacitance C = I = .g C I.

carrier life time , g = conductance = I /

x I = 2()/Ix Junction Barrier Voltage V = V = V (open condition)= V - V (forward Bias)= V + V (Reverse Bias)

x Probability of filled states above E f(E) = ()/


2/9




x Drift velocity of e 10 cm/secx Poisson equation = = = E = Transistor :-

xI

=

I+

I

x I = II Active regionx I =I + I (1- e/ )Common Emitter :-

x I = (1+ ) I + I = x I = Collector current when base openx I Collector current when I = 0 I > I .x V, or V, - 2.5 mv / C ; V,, = - 0.25 mv /Cx Large signal Current gain = x D.C current gain

=

=

h

x (= h ) when I > Ix Small signal current gain = ICIR = h = ( )hFEIC x Over drive factor = I = I Conversion formula :-

CC CEx h = h ; h = 1 ; h = - (1+ h) ; h = hCB CEx h = ; h = - h ; h = ; h = CE parameters in terms of CB can be obtained by interchanging B & E .

Specifications of An amplifier :-

x A = Z = h + hAZ A = . = . = . A = Y = h - A = . = .

Choice of Transistor Configuration :-x For intermediate stages CC cant be used as A < 1x CE can be used as intermediate stagex CC can be used as o/p stage as it has low o/p impedancex CC/CB can be used as i/p stage because of i/p considerations.


3/9




Stability & Biasing :- ( Should be as min as possible)

x For S = , S = , S = ,

I= S.

I+

S

V+

S

x For fixed bias S = = 1 + x Collector to Base bias S = 0 < s < 1+ = x Self bias S = 1+ R > 10 Rx

R=

;

R=

x For thermal stability [ V - 2I (R + R)] [ 0.07 I . S] < 1/ ; V <

Hybridpi()- Model :-g = |I | / V

r = h / gr

=

h-

r

r = r / hg = h - (1+ h ) gFor CE :-

x f = ( ) = ( )x f = hf ; f= = C = C + C (1 + gR )f = S.C current gain Bandwidth productf= Upper cutoff frequency

For CC :-

xf= = = ( )

For CB:-

x f = ( ) = (1 + h) f = (1 + ) f


4/9




x f = f f > f > fEbress moll model :-I = - I + I (1- e/)

I = - I + I (1- e/) I = I

Multistage Amplifiers :-

x f* = f2/ 1 ; f = /x Rise time t = . = ..x

t = 1.1

t

+ t

+

x f = 1.1 f + f + x = 1.1 + +

Differential Amplifier :-

x Z = h + (1 + h) 2R = 2 hR 2Rx

g=

||

=

=

gof BJT/4

DC value of

x CMRR = ; R , Z , A & CMRR Darlington Pair :-

x A = (1 + ) (1 + ) ; A 1 ( < 1)x Z = () [ ifQ & Q have same type ] = ARx R = () + x g = (1 + ) g

Tuned Amplifiers : (Parallel Resonant ckts used ) :

x f = Q Q factor of resonant ckt which is very high


5/9




x B.W = f /Qx f = f - x

f=

f+

x For double tuned amplifier 2 tank circuits with same f used . f = f f.

MOSFET (Enhancement) [ Channel will be induced by applying voltage]

x NMOSFET formed in p-substratex If VV channel will be induced & i (Drain source )x V +ve for NMOSx i (V- V ) for small Vx V channel width @ drain reduces .

V= V- V channel width 0 pinch off further increase no effectx For every V> V there will be V,x i = K [ (V- V ) V- V ] triode region ( V< V- V)

K = Cx i = K [ V ] saturationx

r=

( )

Drain to source resistance in triode region

PMOS :-

x Device operates in similar manner except V, V, V arevex i enters @ source terminal & leaves through Drain .

VV induced channel VV- V Continuous channeli = K [(V V ) - V ] K = C

V

V-

V

Pinched off channel .

x NMOS Devices can be made smaller & thus operate faster . Require low power supply .x Saturation region Amplifierx For switching operation Cutoff & triode regions are usedx NMOS PMOS


6/9




VV VV induced channelV- V> V V- V< V Continuous channel(Triode region)

V

V-

V V

V-

V

Pinchoff (Saturation)

Depletion Type MOSFET :- [ channel is physically implanted . i flows with V= 0 ]x For n-channel V +ve enhances channel . -ve depletes channelx i - Vcharacteristics are same except that V isve for n-channelx Value of Drain current obtained in saturation when V= 0 I.

I=

K

V .

MOSFET as Amplifier :-

x For saturation V > V- Vx To reduce non linear distortion < < 2(V- V )x i = K (V V ) g = K (V V )x = - gR x Unity gain frequency

f =

()

JFET :-

x VV i = 0 Cut offx V V 0, VV- V

i = I21 Triodex V V 0 , V V- V

|| ||

Saturation

Zener Regulators :-

x For satisfactory operation I + I


7/9




x R = x Load regulation = - (r || R )x Line Regulation =

.

x For finding min R take V & V , I (knee values (min)) calculate according to that .Operational Amplifier:- (VCVS)

x Fabricated with VLSI by using epitaxial methodx High i/p impedance , Low o/p impedance , High gain , Bandwidth , slew rate .x FET is having high i/p impedance compared to op-amp .x Gain Bandwidth product is constant .x Closed loop voltage gain A = feed back factorx V = V dt LPF acts as integrator ;x V = dt ; V = (HPF)x For Op-amp integrator V = dt ; DifferentiatorV = - x Slew rate SR = = . = A. x Max operating frequency f = . = .x In voltage follower Voltage series feedbackx In non inverting mode voltage series feedbackx In inverting mode voltage shunt feed backx V = -V ln x V = - V

= - V ln x Error in differential % error = 100 %


8/9




Power Amplifiers :-

x Fundamental power delivered to load P = R = Rx Total Harmonic power delivered to load P =

+

+ . .

= P1 + + + = [ 1+ D] P

Where D = +D + . . + D D = D = total harmonic Distortion .

Class A operation :-

x o/p I flows for entire 360x Q point located @ centre of DC load line i.e., V = V / 2 ; = 25 %x Min Distortion , min noise interference , eliminates thermal run wayx Lowest power conversion efficiency & introduce power drainx P = IV - iV if i = 0, it will consume more powerx P is dissipated in single transistors only (single ended)Class B:-

x Iflows for180; Q located @ cutoff ; = 78.5% ; eliminates power drainx Higher Distortion , more noise interference , introduce cross over distortionx Double ended . i.e ., 2 transistors . I = 0 [ transistors are connected in that way ] P = iVx P = iV = 0.4 P P power dissipated by 2 transistors .Class AB operation :-

x Iflows for more than 180 & less than 360x Q located in active region but near to cutoff ; = 60%x Distortion & Noise interference less compared to class B but more in compared to class Ax Eliminates cross over DistortionClass C operation :-

x Iflows for < 180 ; Q located just below cutoff ; = 87.5%x Very rich in Distortion ; noise interference is high .Oscillators :-

x For RC-phase shift oscillator f = h 4k + 23 + where k = R/Rf =

> 29


9/9




x For op-amp RC oscillator f = | A| 29 R 29 RWein Bridge Oscillator :-

f =

h

3

3A 3 R 2 R

Hartley Oscillator :-

f = () |h| | | |A|

Colpits Oscillator :-

f =

|

h|

| | | A |

Documents

Analog Electronics Formulas