ECE Formula Sheet
Content
Communication Systems Amplitude Modulation : DSB-SC : u (t) = m(t) cos 2
Power P =
π t
Conventioanal AM :
[1 + m(t)]mCos( )2π t . as long as |(m()t)| ≤ 1 demodulation is simple . () m |()|
u (t) = Practically m(t) = a
(t) .
Modulation index a = Power =
+
(t) =
,
→ Square law Detector SNR = ( ) ↓ a a → amplitude Sensitivity R R RC << 1/ω ≥ Cos (2π t + ∅ (t) ) ∅→(maxt) 2πphase devi(m()a ttio)→n.d∆∅t →= → max requency deviation ∆ = = 2 (β + 1) → 98% power → (SNR) R = m(t) cos 2π ∴
SSB-AM : :
Square law modulator = 2 / Envelope Detector
Frequency u (t) =
C (i/p) < < 1 /
C (o/P) >> 1/
Phase Modulation : Angle Modulation :
phase & frequency deviation constant
max | m(t) | max |m(t) |
Bandwidth : : Effective Bandwidth
Noise in Analog Modulation :- :- =
=
=
=
/ 2
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Formulae Sheet in ECE/TCE Department
→ (SNR) // (SNR) → (SNR) // (SNR) η η → ω ω → → → R ω → → → =
=
=
=
=
.
=
=
=
=
=
=
=
=
.
=
Noise in Angle Modulation :-
=
PCM : Min. no of samples samples required for reconstruction reconstruction = 2 =
Total bits required = v Bandwidth =
/2 = v
bps . /
v
;
= Bandwidth of msg signal .
bits / sample
2 = v .
SNR = 1.76 + 6.02 v
As Number of bits increased SNR increased by 6 dB/bit . Band width also increases.
Delta Modulation :-
By increasing step size slope over load distortion eliminated [ Signal raised sharply ]
By Reducing step size Grannualar distortion eliminated . [ Signal Signal varies slowly ]
Digital Communication
→ → →→
Matched filter: impulse response a(t) =
( T – T – t) . P(t)
→
i/p
Matched filter o/p will be max at multiples of ‘T’ . So, sampling @ multiples of ‘T’ will give max SNR (2 point ) matched filter is always always causal causal a(t) = 0 for t < 0 Spectrum of o/p signal of matched filter with the matched signal as i/p ie, except for a delay factor ; proportional to to energy spectral density density of i/p. nd
∅() ∅ ∅ ∅ e ∅() |∅() | e = =
=
(f) (f) = (f) *(f)
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Formulae Sheet in ECE/TCE Department
o/p signal of matched filter is proportional to shifted version of auto correlation fine of i/p signal
∅∅ RR∅∅ → |g(t) g(t) ddtt| ≤ g(t) dt |g(t)| g g (t – (t – T) T) (0) which proves 2nd point
(t) = (T) =
At t = T
Cauchy-Schwartz in equality :-
If
dt (t) then equality equality holds holds othe otherwise rwise ‘<’ holds
(t) = c
Raised Cosine pulses :
(()) () | | ≤ cos || | | ≤| | ≤ ⇒ α → rol o actor P(t) =
.
P(f) =
Bamdwidth of Raised cosine filter
=
Bit rate
→ signal time period → → 1 → → →→ e/
For Binary PSK
= Q
= 2Q
4 PSK
= Q
= erfc
=
.
FSK:For BPSK
= Q
= Q
= erfc
All signals have same energy (Const energy modulation )
Energy & min min distance both can be kept constant while increasing no. of points . But Bandwidth Compramised. PPM is called as Dual of FSK . For DPSK
=
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→ → → →
Formulae Sheet in ECE/TCE Department
Orthogonal signals require factor of ‘2’ more energy to achieve same
as anti podal signals
Orthogonal signals are 3 dB poorer than antipodal signals. The 3dB difference is due to distance b/w 2 points. For non coherent FSK
e/ =
FPSK & 4 QAM both have comparable performance . 32 QAM has 7 dB advantage over 32 PSK.
.
Bandwidth of Mary PSK =
Bandwidth of Mary FSK =
Bandwidth efficiency efficiency S =
Symbol time
Band rate =
log =
=
=
; S=
;S=
.
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Formulae Sheet in ECE/TCE Department
Signals & Systems
→ |x(t)| ddtt |[]| lim→ |x(t)| ddtt lim→ |x[n]| → →→ x(t) →x(t) →x → x x → ∞ →⇒ ⇒ → ∞ → → → → →→ → →→ → ⇒ h(t)ddtt e e [e] e = =
Energy of a signal
= =
Power of a signal signal P =
(t) ; + + iff
(t) orthogonal
(t) &
power. Shifting & Time scaling won’t effect power . Frequency content doesn’t effect power. if power = neither energy nor power signal Power = 0 Energy signal Power = K power signal
Energy of power signal =
; Power of energy signal = 0
Generally Periodic & random signals Aperiodic & deterministic deterministi c
Power signals Energy signals
Precedence rule for scaling & Shifting :
x(at + b)
(1) shift x(t) by ‘b’ x(t + b) (2) Scale x(t + b) by ‘a’ x(at + b)
x( a ( t + b/a))
(1) scale x(t) by a x(at) (2) shift x(at) by b/a x (a (t+b/a)).
x(at +b) = y(t)
x(t) = y
Step response response s(t) = h(t) * u(t) =
S[n] =
u(t) *
u(t) =
Rect (t / 2
)*
S’ (t) = h(t) h(t) h[n] = s[n] s[n] – – s[n-1] s[n-1]
[
Rect(t / 2
-
] u(t) .
) = 2
,
min (
) trapezoid (
,
)
Rect (t / 2T) * Rect (t / 2T) = 2T tri(t / T)
Hilbert Transform Pairs :
e // dx σ 2π x e/ ddxx σ 2π σ =
;
=
> 0
Laplace Transform :-
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(s) e x(t) e
x(t) =
Formulae Sheet in ECE/TCE Department
ds
ds
X(s) =
Initial & Final value Theorems : x(t) = 0 for t < 0 ; x(t) doesn’t doesn’t contain any impulses impulses /higher /higher order singularities singularities @ t =0 then then
x(
∞ lliimm→→(()) )=
x( ) =
Properties of ROC :-
ω
1. X(s) ROC has strips parallel to j axis 2. For rational laplace transform ROC has no poles
→ →→
3. x(t)
finite duration & absolutely integrable then ROC entire s-plane
4. x(t)
Right sided then ROC right side of right most pole excluding pole s =
5. x(t) 6. x(t)
left sided
ROC left side of left most pole excluding s= -
two sided
ROC is a strip
∞ ∞ ∞
7. if x(t) causal
ROC is right side of right most pole including s =
8. if x(t) stable
ROC includes j -axis
Z-transform
x[n] = X(z) =
ω
:-
x() x[n]
dz
Initial Value theorem : If x[n] = 0 for n < 0 then x[0] =
lim→ [] lim→(1)
Final Value theorem : = =
lim→ ()
X(z) X(z)
Properties of ROC :-
1.ROC is a ring or disc centered @ origin 2. DTFT of x[n] converter if and only if ROC includes unit ci circle rcle 3. ROC cannot contain any poles
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Formulae Sheet in ECE/TCE Department
→→
4. if x[n] is of finite duration then ROC is enter Z-plane except poss possibly ibly 0 or 5. if x[n] right sided then ROC outside of outermost outermost pole excluding excluding z = 0 6. if x[n] left sided then ROC inside of innermost pole including z =0 7. if x[n] & sided then ROC is ring 8. ROC must be connected region 9.For causal LTI system ROC is outside of outer most pole including 10.For 10. For Anti Causal system ROC is inside of inner most pole including ‘0’ ‘0’
∞
∞
11. System said to be stable if ROC includes unit circle . 12. Stable & Causal if all poles inside unit circle 13. Stable & Anti causal if all poles outside unit circle. Phase Delay & Group Delay :- When a modulated signal is fixed through a communication channel , there are two different delays to be considered.
∅ ω ∅ ω ↓ω ↓ ∅()
(i) Phase delay: Signal fixed @ o/p lags the fixed signal by (
∅() = -
where (
) phase
) = K H(j )
Frequency response of channel for narrow Band signal signal
=
Group delay
Signal delay / Envelope delay
Probability & Random Process:-
→→ →→
P (A/B) =
(()) (())
⇒
Two events A & B said to be mutually exclusive /Disjoint if P(A B) =0 Two events A & B said to be independent independent if P (A/B) = P(A) P(A B) = P(A) P(B) P(Ai / B) =
=
() ()
≤ ∞∞ ≤ ∞ x≤ ≤ x x x ≤
CDF :- Cumulative Distribution function
(x) = P { X
x x }
Properties of CDF :
( ) = P { X } = 1 (- ) = 0 ( X ) = ( ) - ( ) Its Non decreasing function P{ X > x} = 1 – 1 – P P { X x} = 1- (x)
PDF :-
Pdf =
(x) (x) =
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= x δ x ≥ ∞ x ≤ x (x )dxdx x σ () x → g(x) ( x ) ≤ < 1 << (a) x e()/ σ x e() / (x) =
Pmf =
} (x =
Formulae Sheet in ECE/TCE Department
)
Properties:- (x) 0
(x) =
( )=
P{
(x) * u(x) =
(x) dx =1 so, area under PDF = 1
<X
(x) dx
} =
Mean & Variance :-
Mean
(x) dx
= E {x} =
Variance
= E {
} = E {
E{g(x)} =
}-
dx
Uniform Random Variables :
Random variable X ~ u(a, b) if its pdf of form as shown below (x) =
(x) =
Mean =
Variance =
/ 12
E{
} =
Gaussian Random Variable :-
(x) =
X ~ N (
Mean =
)
dx =
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Formulae Sheet in ECE/TCE Department
x e()/ σ λ e ee|| ∞ ≤≤ ≤ ∞ (x ) ∞ (xx y) ∞ ∞ ∞ ()) / ( ) / ≤x ( ) dx =
Variance =
Exponential Distribution :-
(x) =
u(x)
) u(x)
(x) = ( 1-
Laplacian Distribution :-
(x) =
Multiple Random Variables :-
(x , y) = P { X x , Y y } ( , y) = P { Y < y } = (x , ) = P { X x } = (x) ; (- , y) = (x, - ) = (- , - ) = 0
dy ;
= =
=
(y/x) =
(y)
(x, y) dx
(y) =
=
Independence :- X & Y are said to be independent if (x, y) = (x) . (y) P{X
≤ ≤ ≤ ≤
⇒ ⇒ → t t t ) t t t → → R t t t t
(x , y) = (x) (y) x, Y y} = P { X x} . P{Y
y}
Correlation: (x, y). xy. dx dy Corr{ XY} = E {XY} = If E { XY} = 0 then X & Y are orthogonal orthogonal .
Uncorrelated :- Covariancee = Cov {XY} = E { (X Covarianc ( X - ) (Y- } = E {xy} – {xy} – E E {x} E{y}. If covariance = 0 E{xy} = E{x} E{y}
Independence
uncorrelated but converse is not true.
Random Process:- Take 2 random process X(t) & Y(t) and sampled @
X(
, X( ) , Y( ) , Y ( ) ,
Auto correlation
( ,
,
random variables
) = E {X( ) X( ) }
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Formulae Sheet in ECE/TCE Department
→→ CRtttt tt tt t t R t t t t → C t t t t t t R t t t t → C t t ⇒ R t t t t → → RR t ttxt⇒ t t → RR R≤ R → RR ≤RR R R S≤ωR RR () e (ω)edω R S ω RS ω |(ω)|(ω) ddωω R δ → Auto covariance cross correlation correlation cross covariance
( , ) = E { X( ) - ( )) (X( ) ( , ) = E { X( ) Y( ) } ( , ) = E{ X( ) - ( )) (Y( ) -
( )}=
( )}=
( ,
( ,
)-
)-
( )
( )
( )
( )
( , ) = 0 ( , )= ( ) ( ) Un correlated ( , ) = 0 Orthogonal cross correlation correlation = 0 (x, y ! , ) = (x! ) (y ! ) independent
Properties of Auto correlation :-
(0) = E { } ( ) = (- ) even | ( ) | (0)
Cross Correlation
( )= (- ) ( ) (0) . (0) ( )| (0) + (0) 2|
Power spectral Density :-
P.S.D
( )=
(j ) =
(j ) =
(j )
Power = (0) = ( ) = k ( ) white process
d
Properties : (j ) even (j ) 0
S ω ≥
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Formulae Sheet in ECE/TCE Department
Control Systems nd
Time Response of 2 order system :-
Step i/P :
→
C(t) = 1-
(sin
t ±
sin ω 1 tan tan e lim sin tan →→ ω → Damping actor tan ω e(1+ ω e(t) =
=
)
Damping ratio ;
< 1( nder damped damped ) :C(t) = 1- =
Sin
= 0 (un damped) :c(t) = 1- cos
t
= 1 (Critically damped ) :C(t) = 1 -
t)
> 1 (over damped) :-
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Formulae Sheet in ECE/TCE Department
t∅ ∅ t a n t e/ t . t () / () Dampi n g a ct o r t ≈ t t ω ω 12 ω ω (12 + + 2)//
C(t) = 1 -
T=
>
>
>
Time Domain Specifications :-
Rise time
=
Peak time
=
Max over shoot % = Settling time = 3T
× 100 5% tolerance 2% tolerance
= 4T
Delay time
=
=
=
Time period of oscillations T = No of osci oscillations llations = =
1.5 = 2.2 T = Resonant peak
=
ω ω ω
;
Bandwidth
=
<
<
Static error coefficients :-
Step i/p :
e lim→ () lim→ () lim→ () e e lim→ lim(→)((()) () t e lim→ s ()(() →→ee ∞ → e/ =
= =
= =
=
(positional error)
=
Ramp i/p (t) :
=
Parabolic i/p ( /2) :
Type < i/p Type = i/p Type > i/p
Sensitivity S =
= 1/
=
=
= finite = 0
/
sensitivity of A w.r.to K.
Sensitivity of over all T/F w.r.t forward path T/F G(s) :
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Open loop:
S =1
Closed loop :
S=
Formulae Sheet in ECE/TCE Department
(()(()
Minimum ‘S’ value preferable
Sensitivity of over all T/F T/F w.r.t feedback T/F H(s) : S =
Stability RH Criterion :-
()(() (()(()
Take characteristic characteristic equation 1+ G(s) H(s) = 0 All coefficients should have same sign There should not be missing ‘s’ term . Term missed means presence of at least one +ve real part root If char. Equation contains either only odd/even terms indicates roots have no real part & posses only imag parts there fore sustained oscillati oscillations ons in response. Row of all zeroes occur if (a) Equation has at least one pair of real roots with equal image but opposite sign (b) has one or more pair of imaginary roots (c) has pair of complex conjugate conjugate roots forming symmetry about origin.
Electromagnetic Fields
→→ →→
Vector Calculus:- A. (B × C) = C. (A × B) = B. (C × A) A×(B×C) = B(A.C) – B(A.C) – C(A.B) C(A.B) Bac – Bac – Cab Cab rule
→ a (|.|) a (.|.|)
Scalar component of A along B is
= A Cos
= A .
Vector component of A along B is
= A Cos
.
=
..ds ((..)) →→ ergencevatliovsse/pot .ential. → source . < ⇒ sink .==→ →sol.ir)eonoitatdioalnal/Di/vconser |(|) R |() ∞ ρ ρa a→ a
Laplacian of scalars : = = A = (
=
Divergence theorem Stokes theorem
= 0
Harmonic .
Electrostatics :-
Force on charge ‘Q’ located @ r F =
E @ point ‘r’ due to charge located @
E due to
=
line charge @ distance ‘ ‘ E =
E due to surface charge
is E =
;
.
..
=
.
(depends on distance)
unit normal to surface (independent (independent of distance)
For parallel plate capacitor @ point ‘P’ b/w 2 plates of 2 opposite charges is
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a ( a Ψ s .
E=
-
Formulae Sheet in ECE/TCE Department
)
‘E’ due to volume charge c harge E =
→ → →Ψ ρ= .⇒D D .ds ρ. dvdv → a a .d | | → → ∝ ∝ ∝ D. dv dv ρ ρ e/ σ
Electric flux density D = Flux =
.
D
independent of medium
Gauss TotalLaw flux:-coming out of any closed surface is equal to total charge enclosed by surface . = = = =
Electric potential
(independent (independent of path)
= = -
= -
=
. dr
-
(for point charge )
r
Potential @ any point (distance = r), where Q is located same where , whose position is vector @
V=
V(r) =
+ C . [ if ‘C’ taken as ref ref potential potential ]
× E = 0, E = - V For monopole E
V
; Dipole E
;
V
.
Electric lines of force/ flux /direction of E always normal to equipotenti equipotential al lines . = = Energy Density =
Continuity Equation
.J = -
=
where
.
= Relaxation / regeneration time =
/ (less for good conductor )
Boundary Conditions : = Tangential component of ‘E’ are continuous across dielectric-dielectric dielectric -dielectric Boundary . Tangential Components of ‘D’ are dis continues across Boun dary .
=
;
=
/
.
D D ρ → .d .ds
Normal components components are are of ‘D’ are are continues continues , where as ‘E’ are dis continues. continues. = ; = ; = =
=
=
=
=
t
Maxwell’s Equations :-
faraday law
=
Transformer emf =
= =
= -
ds ⇒
× E = -
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→
.d
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Formulae Sheet in ECE/TCE Department
s
→ →
×
Motional Motion al emf emf = × H = J +
= × ( × B).
Electromagnetic wave propagation :- × H = J + D= E × E = - B= H
. D = ρ J =σ . = ⊥ / ρ ρ ω(σ+ω) α β βα ω 1 + +1 e ω β η η / η η / σ ω η α β α → σ α → N| log β → σ ω σ →ωω1→β λ πβ α β ω ω = λ = 2π/β η = / ∠
= -
=
; E.H = 0
For loss less medium
-
=
E(z, t) =
=
| |=
cos( t – z) ;
| | <
E H in UPW
E=0
=
= =
= + j .
=
=
/ .
tan 2
= /
.
= + j attenuation constant Neper /m . For loss less medium = 0; = 0. phase shift/length ; = / ; = 2 / .
|
= 20 =
= 8.686 dB
= = / = tan loss tanjent = 2 If tan is very small ( < < ) good (lossless) dielectric If tan is very large ( >> ) good conductor Complex permittivity = = - j ..
Tan =
=
.
Plane wave in loss less dielectric :- ( σ ≈ 0)
= 0 ; =
.
E & H are in phase in lossless dielectric
Free space :- ( = 0, =
, =
)
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Formulae Sheet in ECE/TCE Department
α β ω λ = 2π/β η = = / < = 12π ∠ σ ω σ/ω → ∞ ⇒ σ = ∞ = = αSkiη =nβdept 2 πh eδσ/= 1/α 2ω/σ λ π β η ∠ R RR . ( ) ds + – σ | δ | e a (s) a a a →→a a a
Good Conductor :- >>
= =
,
; u = 1/ = 0 , = Here also E & H in phase .
; u =
; = 2 / ;
=
=
Skin resistance
=
=
=
=
[
.
Poynting Vector :-
=-
S
] dv
dv
v
(z) = cos Total time avge power crossing given area
=
ds ds
S
)
Direction of propagation :- ( × =
× = 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 =
=
Τ Γ there is a standing wave in medium wave in medium ‘2’. (nπ/β) () n = 1 2…. coefficient
=
=
Medium-I Dielectric , Medium-2 Conductor : > :-
Max values of |
| occurs
= -
=
=
=
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Formulae Sheet in ECE/TCE Department
β () ⇒ () β π ⇒ || || ||t |Γ| ⇒||≤δ ≤ |∞ | Γ r σ r Γ ( R+ R+ ωe))(+ (+ωωC)β α β e ω β <
=
occurs @
:-
= n
=
=
=
=
()
min occurs when there is | |max
Since | | < 1
1
; | | =
=
=
S=
Transmission Lines :- Supports only TEM mode LC = ; G/C = / .
= 0 ;
-
= V(z, t) =
= = + j cos ( t- z) +
=
= 0
-
=
=
=
cos ( t + z)
Lossless Line : (R = 0 =G; σ = 0)
→ γ α/C β ω C α = β = w w C λ = 1/ C C → α = = R β = ω ω = ωCωC = ω C → λ = 1/ C // γ β ⇒ β β Γ Γ |||| |||| /S = =
+ j = j
, u = 1/
Distortion less :(R/L = G/C)
=
=
; u =
=
; u = 1/C , u
= 1/L
i/p impedance :-
=
=
for lossless lossless line
= j
tan hj l = j tan l
VSWR =
=
CSWR = - Transmissio Transmission n coefficient S = 1 + SWR = = = =
(
=
=S
=
=
Shorted line :-
= -1 , S =
>
=
=
) (
<
)
= j
tan
l
Γ ∞ β
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Γ
= -1 , S =
∞ β
=
= j
tan l.
may be inductive or capacitive based on length ‘0’
λλ/2 → capacitive( Γ ∞ β λ λ Γ If
Formulae Sheet in ECE/TCE Department
<
l
/ 4
inductive (
+ve)
l
< <
Open circuited line :- = -j cot l = = 1 s =
l < <
/ 4 capacitive
< l < <
-ve)
/2 inductive
=
Matched line : ( = ) = 0 ; s =1 = No reflection reflection . Total Total wave
. So, max power transfer possible .
Behaviour of Transmission Line for Different lengths :-
λ λ λλ → ⇒→ = ) e h k k ∴ γ + ω ω → k +ω → + γγ α αβ β k + → γ = β α = β = k + u = /4
l
l
= /2 :
=
Wave Guides :TM modes : (
=
sin
=
+
impedance reflector @ l = = /2
x x
impedance inverter @ l = = /4
sin
y
=
where k =
m no. of half cycle variation in X-direction
n no. of half cycle variation in Y- direction . = Cut off frequency
<
Evanscent mode ;
>
Propegation mode
= 0;
= 0 =
= ;
= 0
=
= phase velocity =
is lossless dielectric medium
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Formulae Sheet in ECE/TCE Department
λ u ( )() β β 1 β ω β uη ωβ λ πβ u →1 η η 1 η → → e → η η η 1 → e η η
/ =
=
=
=
/
=
= -
=
phase velocity & wave length in side wave guide
impedance of UPW in medium
cos
=
>
Dominant mode
/
=
= phase constant in dielectric medium.
= 0)
cos
=
/f
=
TE Modes :- (
/ W
= 2 / =
=
= =
Antennas :-
Hertzian Dipole :-
=
=
sin
Half wave Dipole :-
=
;
=
EDC & Analog
//... .... Ne( )/ Nn e(n N)/N e/ ≤ 1
Energy gap
=
- KT ln
Energy gap depending on temperature Energy
=
+ KT ln
No. of electrons electrons n = No. of holes holes p = Mass action law = = Drift velocity = E (for si
(KT in ev)
cm/sec)
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σ ρ. σR R ρ ρ → N N n N n xN xN J D J D ≈ np NN np nn NN
Hall voltage
=
. Hall coefficient
= 1/ .
. Conductivity = ; = Max value of electric field @ junction
= -
Charge storage @ junction
Formulae Sheet in ECE/TCE Department
charge density = q
.
.
.
= qA
= qA
= -
= -
= ne … …
EDC
Diffusion current densities = - q = - q Drift current current Densities Densities = q(p + n )E , decrease with increasing doping concentration .
=
= KT/q
25 mv @ 300 K
Carrier concentration in N-type silicon Carrier concentration in P-type silicon
Junction built in voltage
=
ln =
=
= =
= =
/
= =
+
=
. A .
=
(for forward forward Bias) Bias) ;
/ = Aq
= Aq
n D +n D 1 C ⇒ C ∝ → 2()/ Q=
+
=
I
Diffusion capacitance
= =
;
Saturation Current = Aq Minority carrier life time = Minority carrier charge storage
Forward current I =
/ /
Depletion capacitance
= =
Charge stored in depletion region
; ;
=12.9 qx .x + ( + ) C C / CC 2CC1+1 + + n / 1
*
= =
Width of Depletion region
=
/
;
=
/
= , = = mean transist time I = .g
I.
carrier life time , g = conductance = I / = = = (open condition) Junction Barrier Voltage = = - V (forward Bias) = + V (Reverse Bias)
Probability of of filled states states above ‘E’ f(E) =
( )/
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Drift velocity of
e ≤ 1 ⇒
Poisson equation
=
= E =
= = – – +
=
Collector current when base open
Collector current when
= 0
>
- 2.5 mv
C ;
or
D.C current gain
(
=
)
=
=
when
>
C
=
=
Conversion formula :- CC ↔ CE = ; = 1 ;
= - 0.25 mv
Over drive factor =
.
=
Small signal current gain
)
(1-
Large signal Current gain
Active region
Common Emitter :- = (1+ ) +
cm/sec
α α → e/ β → β β = → → / → / β h β β h ≈ β h h C R C ( ) h ∵ β β → h h h h h h h h h h h h
Transistor :- = + = – –
=
Formulae Sheet in ECE/TCE Department
= - (1+
=
);
=
= =
CB ↔ CE
=
;
=
-
;
=
;
=
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 can’t be used as < 1 CE can be used as intermediate stage CC can be used as o/p stage as it has low o/p impedance CC/CB can be used as i/p stage because of i/p considerations.
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Formulae Sheet in ECE/TCE Department
Stability & Biasing :- ( Should be as min as possible)
∆∆ S ∆∆ S ∆∆ ∆ ∆ S ∆ S ∆ββ β ≈ βR R R R
For S =
= S.
+
= =
+
For fixed bias S =
=1+
Self bias S =
=
=
;
Collector to Base bias S =
= =
1+
0 < s < 1+ =
> 10
For thermal stability [
- 2 (
+
g rr hh rg rg hr hh g (h ) ( ) C C g R ≈ () ( ) 1 + h 1 + β = = = =
<
R R
Hybrid – Hybrid – pi( pi(π)- Model :-
= | | /
. S] < 1/ ;
)] [ 0.07
/
/ - (1+
)
For CE :-
= =
=
= =
=
;
+
C=
(1 +
)
= S.C current gain Bandwidth product = Upper cutoff cutoff frequency frequency
For CC :-
=
=
=
For CB:-
=
=(
)
= (
)
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Formulae Sheet in ECE/TCE Department
α e/ α α e/ t2 / .1 . / . t t + t +
=
Ebress moll model : (1 + = -
= -
+
>
>
)
(1-
)
=
Multistage Amplifiers :-
* =
;
Rise time
=
=
= 1.1
= 1.1
= 1.1
=
+ +
Differential Amplifier :-
h| | h R h R ≈ βR g g α → α R ↑ → ↑ ↑ CRR ↑ (β ) Ωβ ≈ R R () g β g = =
=
=
CMRR =
)2
+ (1 +
+
= (1 +
)
DC value of
1 ( < 1)
);
= =
=
,
;
Darlington = (1Pair + ):-(1 +
2
of BJT/4
=
= 2
[ if
&
have same type ] =
Tuned Amplifiers : (Parallel Resonant ckts used ) :
=
Q
‘Q’ factor of resonant ckt which is very high high
→
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Formulae Sheet in ECE/TCE Department
∆ ∆
B.W = /Q
=
-
=
+
For double tuned amplifier 2 tank circuits with same
used .
=
.
MOSFET (Enhancement) [ Channel will be induced by applying voltage]
→ ≥ i → i ∝ ↑ → ≈→ i → C i → r ( ) →
p-substrate NMOSFET formed in p-substrate channel will be induced & If +ve for NMOS ( - ) for small
=
channel width
-
For every
>
[ (
0
there will be
-
)
-
pinch off further increase no effect
triode region (
]
=
source )
channel width @ drain reduces .
=
(Drain
=
[
=
]
<
-
)
saturation
Drain to source resistance in triode region
PMOS : are – – v vee , are , Device operates in similar manner except enters @ source terminal & leaves through Drain .
i ≤ → ≥ → i ( ) C ≤ → →
=
induced channel [
-
]
=
-
Continuous channel
- Pinched off channel . NMOS Devices Devices can be made made smaller smaller & thus operate operate faster faster . Require low power supply supply . Saturation region Amplifier For switching operation Cutoff & triode regions are used
NMOS
PMOS
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≥ ≤ ≥ →→ ≤ →→ i ∴
-
>
-
→ → →
Formulae Sheet in ECE/TCE Department
induced channel
-
<
-
Continuous channel(Triode region) Pinchoff (Saturation) (Saturation)
i ⇒
Depletion Type MOSFET :- [ channel is physically implanted .
For n-channel
-
+ve -ve
characteristics are same except that
=
= 0 ]
enhances channel . depletes channel
is – is – ve ve for n-channel
Value of Drain current obtained in saturation when
flows with
= 0
.
.
MOSFET as Amplifier :-
i ( ) ⇒ g ( ) g R () ≤ ⇒ i → → ≤ ≤ i ≤= 21 ≤ ≤ ≥ ⇒ → || || ≥
- > For saturation To reduce non linear distortion
=
=-
-
) )
=
Unity gain frequency
< < 2(
=
JFET :-
= 0 Cut off 0,
Triode
0 ,
-
Saturation
Zener Regulators :-
For satisfactory operation
+
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R r R =
Load regulation regulation = - ( ||
Line Regulation =
Formulae Sheet in ECE/TCE Department
For finding min
)
.
R take
&
,
(knee values (min)) calculate according to that .
Operational Amplifier:- (VCVS)
Fabricated with VLSI by using epitaxial method High i/p impedance , Low o/p impedance , High gain , Bandwidth , slew rate . FET is having high i/p impedance compared to op-amp . Gain Bandwidth product is constant .
Closed loop voltage gain
β →
=
LPF acts as integrator ;
=
=
=
.
dt ;
= A.
Max operating frequency
feed back factor
dt ;
=
Slew rate SR =
⇒ ⇒ dtdt → ∆∆ ∆∆ ∆∆ ∆∆ . ∆ ∆
For Op-amp integrator
=
Differentiator Differentiator
(HPF) = -
=
=
.
In voltage follower Voltage series feedback
In non inverting mode voltage series feedback
In inverting mode voltage shunt feed back
η η = -
ln
= -
= -
ln
Error in differential % error =
× 100 %
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Power Amplifiers :-
Fundamental power delivered to load
R+ +. R.
=
Total Harmonic power delivered to load
Formulae Sheet in ECE/TCE Department
=
=
=
1D+ + + … …
= [ 1+
]
+D +. . + D D η
Where D =
=
D = total harmonic Distortion .
Class A operation :o/p flows for entire ‘Q’ point located @ centre of DC load line i.e., = / 2 ; = 25 % Min Distortion , min noise interference , eliminates thermal run way Lowest power conversion efficiency & introduce power drain = - if = 0, it will consume more power
i i 18 η i → 18
is dissipated in single transistors only (single ended)
Class B:-
flows for ; ‘Q’ located @ cutoff ; = 78.5% ; eliminates power drain Higher Distortion , more noise interference , introduce cross over distortion = 0 [ transistors are connected connected in that way ] Double ended . i.e ., 2 transistors . power dissipated by 2 transistors tr ansistors . = = 0.4
i
=
Class AB operation :-
flows for more than & less than ‘Q’ located in active active region region but near to cutoff cutoff ; = 60% Distortion & Noise interference less compared compared to class ‘B’ but more in compared to class ‘A’ Eliminates cross over Distortion Eliminates
ηη h ≥
Class ‘C’ operation : flows for < 180 ; ‘Q’ located just b below elow cutoff ; = 87.5% Very rich in Distortion ; noise interferenc interferencee is high . Oscillators :-
RC-phase shift oscillator oscillator f = For RC-phase
f=
4k + 23 +
where k =
R/R
> 29
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For op-amp RC oscillator f =
| ≥
|
29
Formulae Sheet in ECE/TCE Department
⇒ R ≥ R
29
Wein Bridge Oscillator :-
f=
h ≥
3
3 A 3
≥
⇒ R ≥ R
2
Hartley Oscillator :-
f=
h | ≥ ( ) ↓| ≥ h | ≥ | ≥ | ≥ |
|
|A
Colpits Oscillator :-
f=
|
|
|A
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Formulae Sheet in ECE/TCE Department
MatheMatics Matrix :- If |A| = 0 Singular matrix ; |A| 0 Non singular matrix Scalar Matrix is a Diagonal matrix with all diagonal elements are equal Unitary Matrix is a scalar matrix with Diagonal e element lement as ‘1’ ( = = ) If the product of 2 matrices are zero matrix then at least one of the matrix has det zero Orthogonal Matrix if A = .A = I = A= Symmetric A= Skew symmetric
→ →→
≠
⇒
()
Properties :- (if A & B are symmetrical ) A + B symmetric KA is symmetric AB + BA symmetric AB is symmetric symmetric iff AB = BA BA symmetric ; A skew symmetric. For any ‘A’ A + Diagonal elements of skew symmetric matrix are zero If A skew symmetric symmetric matrix ; skew symmetric If ‘A’ is null matrix then then Rank of A = 0. 0.
→ →
≠
→
Consistency of Equations :r(A, B) r(A) is consistent consistent r(A, B) = r(A) consistent consistent & if r(A) = no. of unknowns then unique solution r(A) < no. of unknowns then solutions .
∞
Hermition , Skew Hermition , Unitary & Orthogonal Matrices :-
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Formulae Sheet in ECE/TCE Department
→→
= then Hermition = then Hermition Diagonal elements of Skew Hermition Matrix must be purely imaginary or zero Diagonal elements of Hermition matrix always real . A real Hermition matrix is a symmetric matrix. |KA| = |A|
λλ λλis λig……en valλ ue o then 1/ λ → || → λ λ …….. λ λ → λ →λλ…………. λ . λ ( ) → (λ k) (λ k) λ λ λ | | ||()
Eigen Values & Vectors :- Char. Equation |A – |A – I| = 0. Roots of characteristic equation are called eigen values . Each eigen value correspo nds to non zero solution X such that (A – (A – I)X = 0 . X is called Eigen vector . Sum of Eigen values is sum of Diagonal elements (trace) Product of Eigen values equal to Determinent of Matrix . Eigen values of & A are same
&
are Eigen values of A then
,
.
,
A + KI
, K
is Eigen value of adj A.
+ k ,
+ k , …….. , ………
+ k
Eigen values of orthogonal matrix have absolute value of ‘1’ . . Eigen values of symmetric matrix also purely real . Eigen values of skew symmetric matrix are purely imaginary or zero . , , …… distinct eigen values of A then corresponding eigen vectors
linearly independent set . ; adj (adj A) =
| adj (adj A) | =
,
, .. …
for
Complex Algebra :-
Cauchy Rieman equations
()/(a) ( ( ) ( () ⇓ ( () a ( ) a ( ) Neccessary & Sufficient Conditions Conditio ns for f(z) to be analytic
dz =
f(z) = f( ) +
)
[
+
(a) ] if f(z) is ana analytic lytic in region region ‘C’ & Z =a is single single point )
+ …… +
)
+ ………. Taylor Series Series
if
= 0 then it is called Mclauren Series f(z) =
; when
=
If f(z) analytic in closed curve ‘C’ except @ finite no. of poles poles then
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( ) dd π lΦim→( () → ( ) ) a) lim
Formulae Sheet in ECE/TCE Department
= 2 i (sum of Residues @ singular points within ‘C’ ) )
Res f(a) =
=
(a) /
(a) (a)
=
((
f(z) )
Calculus :-
Rolle’s theorem ::-
If f(x) is (a) Continuous in [a, b] (b) Differentiable in (a, b) (c) f(a) = f(b) then there there exists exists aatt least least one value C (a, b) such that
( )()
= 0 .
( c )
Langrange’s Mean Value Theorem ::-
If f(x) is continuous in [a, b] and differentiable differentiable in (a, b) then there exists exi sts atleast one value ‘C’ in (a, b) such that
(c) = (c)
Cauchy’s Mean value theorem ::-
If f(x) & g(x) are two function such that (a) f(x) & g(x) continuous in [a, b] (b) f(x) & g(x) differentiable differentiable in (a, b)
g ≠ ∀ ( c ) g(c) ( ( ))((()) ( ) ( ) ( x ). dxdx x . dx d x x . dx d x ( x )ddxx ( a x)ddxx
(c)
(x) (x)
0
x in (a, (a, b)
Then there exist atleast one value C in (a, b) such that //
=
Properties of Definite integrals :-
a<c<b
+
=
=
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( x ). dxdx ( x )ddxx
= 2
f(x) is even
= 0
f(x) is odd
( x ). dxdx (x )dxdx ( x ). ddxx ( x )ddxx a +x).dx ( x ). dxdx ( a+x) x (x ). dxdx ( x ).dx / sinx / cosx ()())())())())……….…)…….……………… ) )() ) )………. …………….… () ) ) () )………() ………(…()() ) )……… )…….… ….( )). / sinx cosx ())()())……..()) () π
= 2
if f(x) = f(2a- x)
= 0
if f(x) = - f(2a – f(2a – x) x)
= n
if f(x) = f(x + a)
=
=
if f(a - x) = f(x)
=
=
if ‘n’ odd odd
=
Formulae Sheet in ECE/TCE Department
.
.
if ‘n’ even even
. dx =
Where K = / 2 when both m & n are even otherwise k = 1 Maxima & Minima :-
A function f(x) has maximum maximum @ x = a if A function f(x) has minimum minimum @ x = a if Constrained Maximum or Minimum :-
(a) = 0 and (a)
(a) = 0 and
(a) < 0 (a)
(a) > 0
To find maximum or minimum of u = f(x, y, z) where x, y, z are connected by Working Rule :-
Φ
(x, y, z) = 0
λϕ
(i) Write F(x, y, z) = f(x, f (x, y, z) + (x, y, z) (ii) Obtain
= 0,
= 0 ,
= 0
(ii) Solve above equations along with
= 0 to get stationary point .
ϕ
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Formulae Sheet in ECE/TCE Department
Laplace Transform :-
L
()) s s s = =
( ) t⇔ (s)( dds1)s (u) du ⇔ ( ) ( )
L{
f(s) -
f(t) } =
f(0) -
(0) (0) ……
(0)
f(s)
f(s) / s .
Inverse Transforms :-
=
t sin at
=
[ sin at at + at cos at at]]
=
[ sin at at - at cos at]
()
= Cos hat
= Sin hat
Laplace Transform of periodic function : L { f(t) } = Numerical Methods :-
( )
Bisection Method :-
x xx x x x x x x x x ( )() x)
(1) Take two values of & suc such h that that f( ) is +ve & f( ) is – is – ve ve then +ve then root lies between & otherwise it lies between & . Regular falsi method :-
Same as bisection except
=
-
f(
=
x x
find f(
) if f(
Newton Raphson Method :-
x x (( )) =
– –
Pi cards Method :-
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)
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Formulae Sheet in ECE/TCE Department
y y (xy) ←
+
=
= f(x, y)
Taylor Series method :-
y y y() y y() y
( ) y x ( y ) (y) x y ← x y x + h y x y x y()
= f(x, y)
y=
+ (x-
)
+
+ ………….
Euler’s method ::-
)
,
+ h f(
=
=
+ [f(
,
) + f(
=
+ [f(
,
) + f(
:
,
,
= f(x, y
( ) (y)
)
)]
: Calculate till two consecutive value of ‘y’ agree agree
y() y x + h y y y x + h y x + 2h y =
+ h f(
=
)
,
+ [f(
,
) + f(
,
)
……………… ………………
Runge’s Method ::-
k x x +y yy +k k x y k = h f(
,
)
= h f(
= h f( =
,
+h ,
= h ( f (
)
+
+h ,
)
+
finally compute K = (
+4
+
)
)) ))
Runge Kutta Method :-
k x y k x + y + = h f(
= h f(
,
)
,
)
+
finally compute K = (
+2
+ 2
)
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k x + y + k x y k = h f(
= h f (
,
)
+
+h ,
∴
)
Formulae Sheet in ECE/TCE Department
approximation vale
y y =
+ K .
Trapezoidal Rule :-
( x ). dxdx y yyy y y y x x x ( x ). ddxx y y y y y y + y +…. + y) (x ). ddxx y y y y y y y y + y ++….…. + y) =
) + 2 ( +
+
[ (
f(x) takes values
,
,
,
@
+ …….
)]
) + 2 (
….. …..
…….. ……..
Simpson’s one third rule ::-
=
+
[ (
)+4(
+
+ …….
)+3(
+
+
]
Simpson three eighth rule : -
=
[ (
+
+
+ …….
)+ 2 (
]
Differential Equations :- Variable & Seperable :-
General form is
ϕ (y) dy ϕ(x) dx f(y) dy =
Sol:
(x) dx
=
+C.
Homo generous equations :-
General form
=
f(x, y) &
⇒(()
Sol : Put y = Vx
= V + x
Homogenous of same degree
ϕ(xx y)
& solve
Reducible to Homogeneous :-
General form
≠
=
(i) Sol : Put
x=X+h
y=Y+k
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⇒ (() ) =
(ii)
=
Choose h, k such that
() ) ⇒
Sol : Let
=
Formulae Sheet in ECE/TCE Department
becomes homogenous then solve by Y = VX
=
=
Put ax + by = t
=
/b
Then by variable & seperable solve the equation . Libnetz Linear equation :-
e. .(.) +py = Q
General form I.F =
where P & Q are functions of “x” “x”
Sol : y(I.F) =
dx + C . dx
Exact Differential Equations :-
M
General form M dx + N dy = 0
If
N
y Nx =
→ →
f (x, (x, y)
f(x, y)
then
.dx (terms o N () e () e ( ) e
Sol :
+
containing x ) dy dy = C
( y constant )
Rules for finding Particular Integral :-
=
= x =
if f (a) = 0
x ( ) e
if
(a) = 0 (a)
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()
() ( ) () x [ (D )] x ( ) () e e () sin (ax + b) = sin
sin (ax + b)
= x
=
sin (ax + b)
=
f(x) =
f(-
a ≠ a )
f(-
Formulae Sheet in ECE/TCE Department
0
)= 0
Same applicable for cos (ax + b)
sin (ax (ax + b)
f(x)
Vector Calculus :Green’s Theorem ::-
(ϕ dx+ dy) Ψx ϕy =
dx dy
This theorem converts a line integral around a closed curve into Double integral which is special case of Stokes theorem . Series expansion :Taylor Series :-
( ) ( ) (xa) ( ) (xa) ( ) ( ) x ( ) x (1+x) () x e →
f(x) = f(a) +
(x-a) +
f(x) = f(0) +
x +
= 1+ nx +
= 1 + x +
+ …………+
+ …………+
+ ……. (mc lower series ) )
+ …… | nx| < 1
+ …….. ……..
Sin x = x -
+ +
- ……..
Cos x = 1 -
+ +
- ……..
Digital Electronics
Fan out of a logic gate =
or
or Noise margin margin : = Power Dissipation
-
=
when o/p low
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Formulae Sheet in ECE/TCE Department
→
→
when o/p high .
TTL , ECL & CMOS are used for MSI or SSI Logic swing : RTL , DTL , TTL saturated logic ECL Un saturated logic Advantages of Active pullup ; increased speed of operation , less power consumption . For TTL floating i/p considered as logic “1” & for ECL it is logic “0” .
→
“MOS” mainly used for LSI & VLSI . fan out is too high ECL is fastest gate & consumes more power . CMOS is slowest gate & less power consumption NMOS is faster faster than CMOS . Gates with open collector o/p can be used for wired AND operation (TTL) Gates with open emitter o/p can be used for wired OR operation (ECL) ROM is nothing but combination of encoder & decoder . This is non volatile memory . SRAM : stores binary information informatio n interms of voltage uses FF. DRAM : infor stored in terms of charge on capacitor . Used Transistors & Capacitors . SRAM consumes more power & faster than DRAM . CCD , RAM are volatile memories memories . 1024 × 8 memory can be obtained by using 1024 × 2 memories No. of memory memory ICs of capacity capacity 1k × 4 required to construct memory of capacity 8k × 8 are “16”
11
DAC
FSV =
Resolution =
ADC
=
/ =
Accuracy = ± LSB = ± Analog o/p = K. digital o/p
1%
* LSB = Voltage range / * Resolution =
2
* Quantisation Quantisation error =
%
PROM , PLA & PAL :-
AND Fixed
OR Programmable
PROM
Programmable fixed
PAL
Programmable Programmable
PLA
Flash Type ADC :
Fastest ADC :-
22 → → 2 →
comparators resistors × n Encoder
Successive approximation ADC : n clk pulses Counter type ADC : - 1 clk pulses
2
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Dual slope integrating type :
Flip Flops :-
2
Formulae Sheet in ECE/TCE Department
clock pulses .
R
a(n+1) = S +
Q Q
=D = J + Q = T + Q Excitation tables :-
J
K
0
0 0
x
0
0 0
0
0 0
0
0
1 1
x
0
1 1
0
1 1
1 0
1
0 x 1 x
1 0
1
0 0 1 1
1
0 1 1 0
S
R
0
0 0
x
0
1 1
0 0 1 1 x
1
1
T
D
1
1
For ring counter total no.of states = n
t t
For twisted Ring counter = “2n” (Johnson counter counter / switch tail Ring counter ) . . To eliminate race around condition << . In Master slave master is level triggered & slave is edge triggered
Combinational Circuits :Multiplexer : AB 00 01 I1 I0 _ 2 OC 0
I0
10 I2
11 I3
4
6
3 5
7
_ C
1
I1
C
I
1C 1
2
I3
0 A B
C
(2, 5, 6, 7)
2
i/ps ; 1 o/p & ‘n’ select lines. It can be used to implement Boolean function by selecting select lines as Boolean variables For implementing ‘n’ variable Boolean function × 1 MUX is enough enough . For implementing “n + 1” variable Boolean × 1 MUX + NOT gate is required . For implementing “n + 2” variable Boolean function × 1 MUX + Combinational Ckt is required If you want to design × 1 MUX using × 1 MUX . You need × 1 MUXes
2
2 2 2 2
2 2
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Decoder :-
Formulae Sheet in ECE/TCE Department
2
n i/p & o/p’s used to implement the Boolean function . It will generate required min terms @ o/p & those terms
should be “OR” ed to get the result . Suppose it consists of more min terms then connect the max terms to NOR gate then it will give the same o/p with less no. of gates . If you want to Design m × Decoder using n × Decoder . Then no. of n × Decoder
required =
.
2 2 t 2 t
In Parallel (“n” bit ) total time delay = For carry look ahead adder delay = 2
.
.
2
Microprocessors
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Clock frequency = crystal frequency Hardware interrupts
Software interrupts
→
TRAP (RST 4.5) RST 7.5 RST 6.5 RST 5.5
0024H both edge level Edge triggered 003CH 0034 H level triggered 002C
INTR
Non vectored
RST 0 RST 1 2 : : 7
Formulae Sheet in ECE/TCE Department
0000H 0008H 0010H 0018H
Vectored
0038H
S1 S 0
0
0
Halt
0
1
write
1
0
Read
1
1
fetch
HOLD & HLDA used for Dir ect Memory Access . Which has highest priority over all interrupts .
Flag Registers :S
AC X P X Z X CY
Sign flag :- After arthematic operation MSB is resolved for sign flag . S = 1
-ve result
If Z = 1 Result = 0 AC : Carry from one stage to other stage is there then AC = 1 P : P =1 even no. of one’s in result . CY : if arthematic operation Results in carry then CY = 1 For INX & DCX no flags effected In memory mapped I/O ; I/O Devices are treated as m memory emory locations . You can connect max max of 65536 devices in this technique . In I/O mapped I/O , I/O devices are identified by separate 8-bit address . same address can be used to identify i/p & o/p device . Max of 256 i/p & 256 o/p devices can be connected .
⇒
→
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Formulae Sheet in ECE/TCE Department
Programmable Interfacing Devices :-
→ →→ →
8155 programmable peripheral Interface with 256 bytes RAM & 16-bit counter 8255 Programmable Interface adaptor 8253 Programmable Interval timer 8251 programmable Communication interfacing Device (USART) 8257 Programmable DMA controller (4 channel) 8259 Programmable Interrupt controller 8272 Programmable floppy Disk controller CRT controller Key board & Display interfacing Device
D D D D D D
RLC :- Each bit shifted to adjacent left position .
becomes
.
CY flag modified according to
RAL :- Each bit shifted to adjacent left position . ROC :-CY flag modified according RAR :-
D
becom becomes CY & CY becomes
D
.
becomes CY & CY becomes
CALL & RET Vs PUSH & POP POP :- CALL & RET
When CALL executes , p p automatically automatically stores stores
16 bit address of instruction instruction next to CALL on the Stack CALL executed , SP decremented by 2 RET transfers contents of top 2 of SP to PC RET executes “SP” incremented by 2
PUSH & POP
* Programmer Programmer use PUSH to save the the contents contents rp on stack * PUSH executes “SP” decremented by “2” . * same here but to specific “rp” . * same here
Some Instruction Set information :CALL Instruction
CALL CC CM CNC CZ
→ → → → →
18T states SRRWW
Call on carry
9 – 18 18 states
Call on minus
9-18
Call on no carry Call on Zero ; CNZ call on non zero zero
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CP CPE
→ → →
Call on +ve
CPO
Formulae Sheet in ECE/TCE Department
Call on even parity
Call on odd parity
RET : - 10 T RC
: - 6/ 12 ‘T’ states states
Jump Instructions :-
JMP JC JNC JZ JNZ JP JM JPE JPO
→ → → → →→ → →
10 T
Jump Jump on Carry
7/10 T states states
Jump on no carry
Jump on zero
Jump on non zero
Jump on Positive Jump on Minus Jump on even parity
Jump on odd parity .
PCHL : Move HL to PC 6T PUSH : 12 T ; POP : 10 T SHLD : address : store HL directly to address 16 T SPHL : Move HL to SP 6T STAX : store A in memory 7T STC : set carry 4T XCHG : exchange DE with HL “4T” “4T”
R
XTHL :- Exchange stack with HL 16 T
→→ →→ → →
For “AND “ operation “AY” flag will be set & “CY” Reset Reset For “CMP” if A < Reg/mem : CY 1 & Z 0 (Nothing but A-B)
A > Reg/mem : CY
0 & Z
A = Reg/mem : Z
1 & CY
→
0 0 .
“DAD” Add HL + RP (10T) fetching , busidle , busidle DCX , INX won’t effect any flags . (6T) (6T)
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DCR, INR effects all flags except carry flag . “Cy” wont be modified “LHLD” load “HL” pair directly “ RST “ 12T states SPHL , RZ, RNZ …., PUSH, PCHL, INX , DCX, CALL fetching has 6T states PUSH – PUSH – 12 12 T ; POP – POP – 10T 10T
Formulae Sheet in ECE/TCE Department
→
→
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