number-systems
Base and place value
new symbol for new numbers
Better and easier
decimal (indo arabic)
hexadecimal base 16
octal base 8
binary base 2
How to inter convert and perform operations
understand and recall decimal system then connect the others
Specific technique for base 2to n power
Idea of Bits
Group bits
Break into group of bits or bits
Think of them as a building block
Digital electronics
Boolean algebra
Very similar to set theory but not the same
Find how different from set theory
Use of truth table
For proof
True equal 1
False 0
Operations on bools
Or a+b
Not ā
And a.b
Universal operation/gates
NOR
NAND
Laws
Important
A+1=1
A +A.B =A
Distributive law 2
A + B.C = (A+B).(A+C) proof use
A.(A+B)
XOR
Given the truth table for a boolean function can you get the expression
Yes two ways
Use boolean laws
Kaunaugh maps
Express the result an SOP or POS of the inputs
Always a unique expression NO
Its map of the min ormax terms
ANY LOGIC (TRUTH TABLE) CAN BE REPRSENTED
POS
SOP
Product (intersection)of any number of items false if at least one is false
important Exclusivity of the products for being true at a time only one will be true
Exclusivity of sum for being false at a time only one can be false
adjacent expressions must have something in common
order of the column and row names matters
rows
colums
from top to bottom
from left to right
WHY becuz we need to use idea of pairs, quad etc.
WHY
i think so it doesn't matter maybe just convention ? to just start with 00 but the order changes to accomodate the adjacent criteria
WHY you should use this and what it does ?minimize the number of gates or equivalently the terms in the sop or pos to implement a logic(truth tabel )
each possible product involving all the inputs is called the min term
each possible sum which involves all the inputs is called the max term
how many max terms possible
Idea union (or) of any number of items will be true if any one of them is true
simplify and reduce the SOP OR POS
SEMICONDUCTORS
BJT WHAT IS BIPLOAR , JUNCTION ,TRANSISTOR
RELATIONS ALPHA BETA ARE THEY VALID FOR BOTH NPN OR PNP
Semiconductor diode
Pn junction diode
Diffusion
Drift
Reverse
Potential barrier
Forward
Diffusion current increase exponentially as the dec of potential barrier
Voltage across diode constant WRONG
Small drift current which is independent of the voltage
Voltage maximum is fixed but voltage not constant
P has to be at higher potential than n but not more than a maximum like Si 0.7
Thickness c>e>b
Doping e>c>b
Why
More heat generated in collector so inc surface area to dissipate it
Heat generated depends on the power power =vi so now v across the collector is very high at almost all the emmitter current goes through the collector
Different modes in which it can operated
Why
Because two diodes therefore 4 combinatione
Configrations in which we can connect it in a circuit
MODES of operation (related to biasing )
DIFFERENCE
BJT CURRENTS
Directions are very important
All the relationships between the currents depend on the direction
ICBO
Collector to base leakage current with emiitet open circuit
Reverse saturation current
ICEO DOUBT
Ask do we need to remember the qualitative summary of bjt configrations
Characteristics note only DC BEHAVOIUR
Input
Output characteristics
Vary one thing only
But what can you vary voltage only
Because only DC input and output voltages are dc
Input or output depend configration of tranisi
Application
Rectifier
Full wave
Half wave
Bridge
Centre tap
Avg voltage
Avg voltage
Capacitor filter
Ripple voltage
For finding take approximation of the time constant vs time period
avg current
assuming ideal diode
if not assume that load includes the diode resistance
finding the required capacitance
assuming RL >>>>>T
keep in min the voltage
HOW DO I MAKE SURE THAT THE TRANISITORS I MAKE WITH SOME FINITE PROBABILITY OF ERRORS TO HAVE SIMILAR OR SAME CHRACTERISTICS
PROBLEM
MANUFUCATURE TRANSISITOR
beta make not remain constant
HOW TO SOLVE IT
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WHAT FACTORS DETRERMINE THE CHARCTERISTICS
INPUT VOLTAGE
OUTPUT CHAR
OUTPUT CURRENT
BEACUSE OUT VOLTAGE IS OUTCURREDNT* LOAD
BIASING VOLTAGES
IT DEPENDS ON THE IF iIc ouput currengt
depnds ib
with beta B
B OR aplha
beta alpha depnd on the manfacturing of ttrab=nsitor
bascially depned on ratio of carriers reaching collectkr vs base
beta depnds
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solution
we want ouput nearly independent beta
we use self biasing circuit
Simplify
Exp involving minterms
Exp involving max terms
Make a map of minterms
Make a map of max terms
Group the 0
Why
Because they were there in your original exp
Why adjacent
In case max
In case of min
Which things I can combine
Last and first of row
Don't learn the cases
Learn why combine and how
Idea
Always combine in powers of two
Why
Its not magic it is the boolean laws only
always take the maximum number of common squares even if some squares are common
note that we are allowed to overlap as long as all the squares are not common in the two groups
maximize the size of each group
note that you can in pricple find the pos expression from the karnaugh map of the min terms
if f function
f complement t
truth table invert
0 corresponfind min terms in karnaiugh mnap of min terms of f
will become 1
and to find the fcomplomnet as a sop you would group them
now f comp cmop = f and sop cjange to pos
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