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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
CHAPTER 1 To find forc in n!"on# E$c% for&'%( in co%'&n H i#)
%ormula &-& *D1+,E1+,F1+.1+/0 1 2 3 2 12
CHAPTER 1 To find c'rrn" in (&3r# E$c% for&'%( in co%'&n H i#)
%ormula &-' I=Q/T *D14E14 5 2 02
CHAPTER 0 To find cro##-#c" (r( in circ'%(r &i%# E$c% for&'%( in co%'&n H i#)
%ormula '-& *D15/0 4 14
CHAPTER 0 To find r#i#"(nc in o6&# E$c% for&'%( in co%'&n H i#)
%ormula '-' 10.4 250 39.75 4271
CHAPTER + To find c'rrn" in (&3r# E$c% for&'%( in co%'&n H i#)
%ormula (-& I = V/R 10 5 0
CHAPTER + To find 8o%"(9 in 8o%"# E$c% for&'%( in co%'&n H i#)
%ormula (-' 2 5 1:
CHAPTER + To find r#i#"(nc in o6&# E$c% for&'%( in co%'&n H i#)
%ormula (-( R = V/I 10 2 2
CHAPTER + To find !or; in foo" 3o'nd# E$c% for&'%( in co%'&n H i#)
%ormula (-) Work (ft lbs)=Force x Distance 100 100 1::::
CHAPTER + To find 3o!r in !(""# E$c% for&'%( in co%'&n H i#)
%ormula (-* Power = Energy / Time 100 10 1:
CHAPTER + To find nr9< in !(""6o'r# E$c% for&'%( in co%'&n H i#)
%ormula (-+ Energy (Watthours)= Power x Time 200 3 4::
CHAPTER + To find 3o!r in !(""# E$c% for&'%( in co%'&n H i#)%ormula (- 10 0.05 :2
CHAPTER + To find 3o!r in !(""# E$c% for&'%( in co%'&n H i#)
%ormula (- 0.05 200 :2
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
k ?cn#"n" Q1 ?co'% Q
0 ?co'% d ?&"r
F =k x Q x Q
!/d !
Q ?co'% T ?#c
d ?&i%#
A = d !
ρ ?CM-Ω f" l ?f" A ?CM
R = ρl /" *D00,E00F00
V ?8o%"# R ?o6&#
*D02E02
I ?(&3# R ?o6&#
V = I x R *D0,E0
V ?8o%"# I ?(&3#
*D+1E+1
F ?%# D ?f"
*D+7,E+7
E ?o'%# T ?#c
*D+E+
P ?!(""# T ?6o'r#
*D7:,E7:
V ?8o%"# I ?(&3# P = V x I *D7+,E7+
I ?(&3# R ?o6&#
P = I !x R *D74/0,E74
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER + To find 3o!r in !(""# E$c% for&'%( in co%'&n H i#)
%ormula (-7 10 200 :2
CHAPTER 7 E$c% for&'%( in co%'&n H i#)
%ormula )-& 10 10 10 +:
CHAPTER 7 E$c% for&'%( in co%'&n H i#)
%ormula )-'
*D22E22 70 2 +2
CHAPTER 7 E$c% for&'%( in co%'&n H i#)
%ormula )-( 0.002 100,000 0::
CHAPTER 7 E$c% for&'%( in co%'&n H i#)
%ormula )-) 4700 17400 50 1+21
CHAPTER 7 E$c% for&'%( in co%'&n H i#)
%ormula )-* 20 30 10 4:
CHAPTER 7 E$c% for&'%( in co%'&n H i#)
%ormula )-+ 40 200 160 7::
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *-& 3 1.5 1 22
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *-' 22 33 47 ::5
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *-( 10000 27000 20000 2+742+
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *-) 0.1 0.2 0.1 :7
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *-* 3900 6800 072:
V ?8o%"# R ?o6&#
P = V ! /R *D75/0E75
To find "o"(% 0 in o6&# R1 ?o6&# R
0 ?o6&# R
+ ?o6&#
RT = R
+R
!…+R
n *SUM?D20)F20
To find "o"(% 0 in o6&# V T ?8o%"# I
T ?(&3#
RT = V
T / I
T
To find 8 (cro## ( #3cific 0 I 0 1
?(&3# R1 ?o6&#
V = I
R x R
*D2,E2
To find 8 x '#in9 8 di8idr r'% R
X ?o6&# R
T ?o6&# V
T ?8o%"#
V X
= R X /R
T x V
T *D41E41,F41
To find 8 T in ( #ri# circ'i" V
1 ?8o%"# V
0 ?8o%"# V
+ ?8o%"#
V T = V
+ V
! …+V
n *SUM?D47)F47
To find 9 T in ( #ri# circ'i" P
R1 ?!(""# P
R0 ?!(""# P
R+ ?!(""#
P T = P
# P
! $# P
n *SUM?D4)F4
To find / T in ( 3(r(%%% circ'i" I
1 ?(&3# I
0 ?(&3# I
+ ?(&3#
I T = I
# I
! # I
% $# I
n *SUM?D:)F:
To find 1 T in ( 3(r(%%% circ'i" R
1 ?o6&# R
0 ?o6&# R
+ ?o6&#
G T = / R
# / R
! $#/ R
n *1D+G1E+G1F+
To find 0 T in ( 3(r(%%% circ'i" R
1 ?o6&# R
0 ?o6&# R
+ ?o6&#
RT =/(/ R
#/ R
!#/ R
%&&&/ R
n) *1?1D4G1E4G1F4
To find 1 T in ( 3(r(%%% circ'i" G
1 ?S G
0 ?S G
+ ?S
G T = G
# G
! # G
% *SUM?D5)F5
To find 0 T in ( 3(r(%%% circ'i" R
1 ?o6&# R
0 ?o6&#
RT = R
x R
!/ R
# R
! *D0,E0?D0GE0
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *-+ 10 6 12
To find 0 u for ( 3(r(%%% circ'i" R
?o6&# R
e ?o6&#
Ru = R
k x R
e/ R
k ' R
e *D2,E2?D2-E2
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *- 550 1000 0.0055 :::+:02
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *- 10000 11000 0.05 ::0415
CHAPTER 2 E$c% for&'%( in co%'&n H i#)
%ormula *-7 10000 11000 0.05 ::0+1
CHAPTER 4 R("io $3r##ion in co%'&n H i#)
%ormula +-& D5,.5*E5,F5 10 20 30 60 An# 6r i# 4::*4::
CHAPTER 4 E$c% for&'%( in co%'&n H i#)
%ormula +-' 10 20 30 4:
CHAPTER To find fficinc< of 3o!r "r(n#fr E$c% for&'%( in co%'&n H i#)
%ormula -& 8.84 26.6 ++0+
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -' 13 12 100 ::1
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -( 50 25 25 1
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -) 25 25 25 50 02
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -* 25 25 75 2 :2
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -& *??D11,E11G?E11,F11G?F11,D11D11 3.3 4.7 5.6 10
CHAPTER E$c% for&'% in co%'&n H i#)
%ormula -' *??D101,E101G?E101,F101G?F101,D101E101 3.3 4.7 5.6 10+
To find / ; in ( #3cific r(nc6 R
T ?o6&# R
; ?o6&# I
T ?(&3#
I X
= RT /R
X x I
T *DE,F
To find / & in ( 3(r(%%% circ'i" R
1 ?o6&# R
0 ?o6&# I
T ?(&3#
I = R
!/ R
# R
! x I
T *E51?D51GE51,F51
To find / ' in ( 3(r(%%% circ'i" R
1 ?o6&# R
0 ?o6&# I
T ?(&3#
I ! = R
/ R
# R
! x I
T *D57?D57GE57,F57
To find (%(ncd rid9 0 # R1 ?o6&# R
0 ?o6&# R
+ ?o6&# R
7 ?o6&#
R/ R
! = R
%/ R
To find 0 ;
in (%(ncd rid9 R1 ?o6&# R
0 ?o6&# R
+ ?o6&#
R X
( R here) = R
! x R
%/ R
*E1::,F1::D1::
P o'"
?!(""# P in ?!(""#
Efficiency () = P out
/ P in x ** *D1:+E1:+,1::
To find in"rn(% 0 of ( #o'rc V ?no-%o(d V ?%o(dd I ?%o(d A
r int
= V (no'loa+) ' V (loa+e+)/ I (loa+) *?D1:4-E1:4F1:4
To find / %o(d '#in9 T68nin# T6 V T$
?8o%"# RT$
?o6&# R< ?o6&#
I L
= V TH
/ RTH
+ R L *D1:5?E1:5GF1:5
To find 8 %o(d '#in9 T68nin# T6 R< ?o6&# R
< ?o6&# R
T$?o6&# 8
T$ ?8
V L
= R L /R
L + R
TH x V
TH *D110?E110GF110,.110
To find / %o(d '#in9 Nor"on# T6 RN ?o6&# R
N ?o6&# R
< ?o6&# I
N ?(&3#
I L
= R N
/R N
+ R L
x I N *D112?E112GF112,.112
To find 0 5 in d%"( n"!or; R
1 ?o6&# R
0 ?o6&# R
+ ?o6&#
R A
= ( Rx R
!) # ( R
!x R
%) # ( R
%x R
)/ R
To find 0 # in d%"( n"!or; R
1 ?o6&# R
0 ?o6&# R
+ ?o6&#
R B
= ( Rx R
!)#( R
!x R
%)#( R
%x R
)/ R
!
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -( *??D107,E107G?E107,F107G?F107,D107F107 3.3 4.7 5.6 1:
To find 0 " in d%"( n"!or; R
1 ?o6&# R
0 ?o6&# R
+ ?o6&#
RC = ( R
x R
!)#( R
!x R
%)#( R
%x R
)/ R
%
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -) *E10,F10?D10GE10GF10 18.28 12.83 10.77 ++:
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -* *F1+:,D1+:?D1+:GE1+:GF1+: 18.28 12.83 10.77 7:
CHAPTER E$c% for&'%( in co%'&n H i#)
%ormula -+ *D1++,E1++?D1++GE1++GF1++ 18.28 12.83 10.77 24:
CHAPTER 5 To find forc of (""r(c" or r3'%#ion E$c% for&'%( in co%'&n H i#) P ,trength P! ,trength
%ormula 7-& 1 2 0.05 ::
CHAPTER 5 To find &(9n"o&o"i8 forc E$c% for&'%( in co%'&n H i#)
%ormula 7-' mmf = NI 100 5 2::
CHAPTER 5 To find &(9n"ic fi%d in"n#i"< E$c% for&'%( in co%'&n H i#) &"r#
%ormula 7-( 5 100 0.1 2:::
CHAPTER 5 To find ind'cd 8o%"(9 3r "'rn E$c% for&'%( in co%'&n H i#)
%ormula 7-) 2 1 0
CHAPTER 5 To find ind'cd 8o%"(9 in coi% E$c% for&'%( in co%'&n H i#)
%ormula 7-* 100 3 1 +::
CHAPTER 1: Note: No formulas used in this chapter
CHAPTER 11 To find "i& of on 3riod in (c E$c% for&'%( in co%'&n H i#)
%ormula &&-& 1000 :::1
CHAPTER 11 To find fr'nc< fro& "i& of 1 3r E$c% for&'%( in co%'&n H i#)
%ormula &&-' 0.0001 1::::
CHAPTER 11 To find ffc"i8 8(%' fro& 3(; E$c% for&'%( in co%'&n H i#)
%ormula &&-( Effecti-e -alue (rms) = *&.*. x k& -al& 0.707 100 :
To find 0 1 in !< n"!or; R
5 ?o6&# R
# ?o6&# R
" ?o6&#
R = R
B x R
C / R
A # R
B # R
C
To find 0 0 in !< n"!or; R
5 ?o6&# R
# ?o6&# R
" ?o6&#
R! = R
C x R
A/ R
A # R
B # R
C
To find 0 + in !< n"!or; R
5 ?o6&# R
# ?o6&# R
" ?o6&#
R% = R
A x R
B/ R
A # R
B # R
C
d ?&"r#
Force = Pole ,trng& x Pole ! ,trng&/d ! *D1+4,E1+4F1+4/0
N ?= of "rn# I ?(&3#
*D1+5,E1+5
A ?(&3# T ?"'rn#
H = AT /meter *D170,E170F170
∆f%'$ ? ∆time( sec)
V nd
= 0 of lines of flux cut/er unit time *D172E172
N ?= of "'rn# ∆f%'$ ? ∆time( sec)
8 ind
= N (0 of turns) x ∆
flux/∆
time *D17,E17F17
f ?HJ
T (sec) = / f (12) *1D12+
T ?"i& in #c
f (12) = /T (sec) *1D124
V !k" ?8o%"#
*D125,E125
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 11 To find (89 8(%' ?10 c<c% fro& 3; E$c% for&'%( in co%'&n H i#)
%ormula &&-) "-g& -alue (/! cycle) = *&3%. x k& -al& 0.637 100 4+
V !k" ?8o%"#
*D140,E140
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 11 E$c% for&'%( in co%'&n H i#) #n$le
%ormula &&-* 141 30 0.5 :2
CHAPTER 11 To find K d'"< c<c of non-#in !(8# E$c% for&'%( in co%'&n H i#)
%ormula &&-+ 4 20 0:
CHAPTER 11 E$c% for&'%( in co%'&n H i#) B#%eln &#lue du'( )()le !k*!k &l'%
%ormula &&- 2 0.1 5 02
CHAPTER 10 Note: No formulas used in this chapter
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)%ormula &(-& *D14,E14F14 500 2 1 1:::
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-' *D15,E15F15 10 5 1 2:
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-( *D10?E10F10 5 12 6 02
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-) *::::::102,D12,E12/0,F12.12 1 2000 0.001 0.01 :2:0
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-* *::::::102,D1/0,E1F1 2000 0.001 0.01 :2:0
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-+ * SUM?D151)F151 10 5 2.5 12
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)%ormula &(- *1D157G1E157G1F157 10 5 10 :7
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(- *1?1D15G1E15G1F15 10 5 10 02
To find in#"(n" 8 of #in !(8 V !k" ?8o%"# %n θ
& inst = V x sin of angle -alue *D142,F142
' ! ?
µ
#c T ?µ#c
+uty cycle = tw (ulse wi+&)/T ( er&) x ** *D14E14,1::
To find 8 (89
of non-#in !(8#
4a-g
= 5aseln -al& # (+uty cycle x ' am&) *D11G?E11,F11
To find 8 ind'cd in ( coi% N ?= "rn# d φ
? d t ?#c#V
in+ = N (0 of trns) x +φ /+'
To find 8 < 8(%' of 9i8n < L ?H d ?(&3# d' ?#c#
V 6 = L x d /d'
To find < fro& 8 < (nd di>dt V
L ?8o%"# d ?(&3# d' ?#c#
L = V 6/ d/d'
To find < fro& 36<#ic(% 3(r(&"r# µ
r N ?= "rn# A ?# &"r# l ?&"r# L=!&7. x *'.x µ
r x N ! x A / l
To find < of (ir-cor ind'c"or N ?= "rn# A ?# &"r# l ?&"r#
L = !&7. x *'. x N ! x A / l
To find <T in ( #ri# circ'i" L
1 ?H L
0 ?H L
+ ?H
LT = L
# L
! & & & # L
n
To find 3(r circ'i" rci3roc(% of <T L1 ?H L0 ?H L+ ?H/ L
T = / L
# / L
! # / L
%$#/ L
n
To find <T in ( 3(r(%%% circ'i" L
1 ?H L
0 ?H L
+ ?H
LT = / / L
# / L
! # / L
%$#/ L
n
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-7 *D0::,E0::?D0::GE0:: 10 10 2
To find <T of 0 3(r(%%% <# L
1 ?H L
0 ?H
LT = L
x L
!/ L
# L
!
A B C D E F G H
1
2
3
4
5
67
8
9
10
199
200
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 1+ To find (&o'n" of #"ord nr9< E$c% for&'%( in co%'&n H i#)
%ormula &(-&? *D0:+,E0:+,F0:+/0 0.5 20 5 02:
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-&& *D0:4E0:4 10 12 :+
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-&' 10 10000 0.001 10 :::1
CHAPTER 1+ E$c% for&'%( in co%'&n H i#)
%ormula &(-&( 6 2200 0.000068 0.05 ::::1+
CHAPTER 17 E$c% for&'%( in co%'&n H i#)
%ormula &)-& *D012,E012,F012 6.28 60 5 17
CHAPTER 17 E$c% for&'%( in co%'&n H i#)
%ormula &)-' *D01?E01,F01 2000 6.28 1500000 ::::010
CHAPTER 17 E$c% for&'%( in co%'&n H i#)
%ormula &)-( *D001?E001,F001 4000 6.28 0.00003 010+170+
CHAPTER 17 E$c% for&'%( in co%'&n H i#)
%ormula &)-) *1?D007G1?E007G1?F007 2000 4000 6000 ::::51
CHAPTER 17 E$c% for&'%( in co%'&n H i#)
%ormula &)-* *1?1D00G1E00 5000 5000 02::
CHAPTER 17 E$c% for&'%( in co%'&n H i#)
%ormula &)-+ *D0+:,E0+:?D0+:GE0+: 5000 5000 02::
CHAPTER 17 E$c% for&'%( in co%'&n H i#)
%ormula &)- *D0++E0++ 3140 50 40
CHAPTER 12 P<"6(9or(n T6or& E$c% for&'%( in co%'&n H i#) # ,
%ormula &*-& *D0+4/0GE0+4/0 10 10 0::
L ?H I ?(&3#
Energy = *&7 LI !
To find 0 < circ'i" "i& con#"(n" L ?H R ?o6&#
8ne time constant = L/ R
To find in#" incr i in (n 0 < circ'i" V
# ?8o%"# R ?o6&# ' ?#c L ?H
= V s/ R x ( ' ε
-0t < *D0:5E0:5,??1-010/ -?E0:5,F0:5.0:5
To find in#" dc i in (n 0 < circ'i" V
# ?8o%"# R ?o6&# ' ?#c L ?H
= V s/ R x (ε-0t < *D010E010,??010/ -?E010,F010.010
To find 8(%' of ; < in (n (c circ'i" -π f ?HJ L ?H
X L
= !π fL
To find < ? ; < (nd f ;no!n X
< ?o6&# -π f ?HJ
L= X L
/!π f
To find fr'nc< ? ; < (nd < ;no!n X
< ?o6&# -π L ?H
f = X L/!π L
To find 1 ; <T
in ( 3(r(%%% (c circ'i" X <1
?o6&# X <0
?o6&# X <+
?o6&#
/ X LT
=/ X L
#/ X L!
#/ X L%
$
To find ; <T
in ( 3(r(%%% (c circ'i" X <1
?o6&# X <0
?o6&#
X LT
=/(/ X L
#/ X L!
#$)
To find ; <T
of 0 3(r(%%% <# X <1
?o6&# X <0
?o6&#
X LT
= X L
x X L!
/ X L
# X L!
To find @ in (n 0< (c circ'i" X < ?o6&# R ?o6&#
Q = X L
/ R
)! = #! # ,!
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
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234
235
236
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 12 E$c% for&'%( in co%'&n H i#)
%ormula &*-' *SQRT?D0+5/0GE0+5/0 10 10 1717
CHAPTER 12 E$c% for&'%( in co%'&n H i#)
%ormula &*-( *SQRT?D070/0GE070/0 5 8.66 1:::
CHAPTER 12 E$c% for&'%( in co%'&n H i#)
%ormula &*-) *SQRT?D072/0GE072/0 3 5 2+
CHAPTER 12 E$c% for&'%( in co%'&n H i#)
%ormula &*-* *D07,E07SQRT?D07/0GE07/0 50 30 020
CHAPTER 12 E$c% for&'%( in co%'&n H i#) .ne
%ormula &*-+ *D021E021 1 1500 ::::44
CHAPTER 12 To find ind'c"i8 #'#c3"(nc E$c% for&'%( in co%'&n H i#)
%ormula &*- *D027E027 1 1005 ::::552
CHAPTER 12 To find (d&i""(nc E$c% for&'%( in co%'&n H i#)
%ormula &*- *D02E02 1 835 :::115
CHAPTER 12 E$c% for&'%( in co%'&n H i#)
%ormula &*-7 *SQRT?D04:/0GE04:/0 0.000667 0.000995 :::115
CHAPTER 12 To find &(9ni"'d of 36(# (n9% E$c% for&'%( in co%'&n H i#)
%ormula &*-&? *DE.REES?ATAN?D04+E04+ 1500 1005 241
CHAPTER 14 To find &'"'(% ind'c"(nc E$c% for&'%( in co%'&n H i#) k
%ormula &+-& *D044,SQRT?E044,F044 1 3 3 +
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-' *D045GE045G0,F045 8 8 4 07
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-( *D00GE00-0,F00 8 4
To find 8 T in ( #ri# 0< circ'i" V
0 ?8o%"# V
< ?8o%"#
V T = √ V
R! # V
L!
To find A in ( #ri# 0< circ'i" R ?o6&# X < ?o6&#
0 = √ R! # X L
!
To find / T in ( 3(r(%%% 0< circ'i" I
0 ?(&3# I
< ?(&3#
I T = √
Ι
R! # I
L!
To find A in ( 3(r(%%% 0< circ'i" R ?o6&# X < ?o6&#
0 = R x X L
/ √ R! # X L
!
To find 1 in ( 3(r(%%% 0< circ'i" R ?o6&#
1 = 1 >0
X < ?o6&#
#<
= 1 ; <
0 ?o6&#
B = 1 >A
To find B in ( 3(r(%%% 0< circ'i" G ?S B< ?S
1 T = √.! # 5
L
!
R ?o6&# X < ?o6&#
θ ?&(9ni"'d * "(n-1 0 ; <
L1 ?H L
0 ?H
2 = k √ L x L
!
To find <T of #ri# <!s ?(id L
1 ?H L
0 ?H 2 ?H
LT = L
# L
! # ! 2
To find <T of #ri# <# ?o33 L
1 ?H L
0 ?H 2 ?H
LT = L
# L
! ' ! 2
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 14 E$c% for&'%( in co%'&n H i#) ?(id +:
%ormula &+-) *D02GE020,F02 10 10 5 ?o33 1:
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-* *1??1?D0GF0G1?E0GF0 8 8 4 4
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-+ *1??1?D01-F01G1?E01-F01 8 8 4 0
CHAPTER 14 To find cofficin" of co'3%in9 E$c% for&'%( in co%'&n H i#)
%ormula &+- *F07SQRT?D07,E07 8 8 4 :2
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+- or * D0,.0*E0,F0 20 280 1 14 1
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-7 or * D05:,.05:*E05:,F05: 20 280 1 14 1
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-&? or * D05+,.05+ * E05+,F05+ 5 1 0.5 0.1 1
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-&& or *D054,.054*E054,F054 5 1 0.5 0.1 1
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-&' or *?D055E055/0*F055.055 1 4 8 128 1
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-&( *D+:0,?E+:0F+:0/0 2000 2 1 :::
CHAPTER 14 E$c% for&'%( in co%'&n H i#)
%ormula &+-&) *SQRT?D+:2E+:2 1000 10 1:
CHAPTER 14 To find "r(n#for&r fficinc< E$c% for&'%( in co%'&n H i#)
%ormula &+-&* *D+:E+:,1:: 86 100 4
.nr(% <T for&'%( ?(id or o33 L
1 ?H L
0 ?H 2 ?H
LT = L
# L
! ± ! 2
To find <T of 0 3(r(%%% <# ?(id L
1 ?H L
0 ?H 2 ?H
LT = // L
# 2 # / L
! # 2
To find <T of 0 3(r(%%% <# ?o33 L
1 ?H L
0 ?H 2 ?H
LT = // L
' 2 # / L
! ' 2
L1 ?H L
0 ?H 2 ?H
k = 2 / √ L x L
!
8 r("io co&3(rd "o T r("io V P ?8o%"# V
3 ?8o%"# N
P ?"rn# N
3 ?"rn#
V P
/V 3 = N
P / N
3
T r("io co&3(rd "o 8 r("io N P ?"rn# N
3 ?"rn# V
P ?8o%"# V
3 ?8o%"#
N P
/ N 3 = V
P /V
3
T r("io co&3(rd "o / r("io N P
?"rn# N 3 ?"rn# I
3 ?(&3# I
P ?(&3#
N P
/ N 3 = I
3 / I
P
8 r("io co&3(rd "o / r("io V P ?8o%"# V
3 ?8o%"# I
3 ?(&3# I
P ?(&3#
V P
/V 3
= I 3 / I
P
N r("io co&3(rd "o A r("io N 3 ?"rn# N
P ?"rn# 0
3 ?o6&# 0
P ?o6&#
( N 3 / N
P )! = 0
3 / 0
P
To find A 9 fro& A
S (nd T r("io 0
3 ?o6&# N
P ?"rn# N
3 ?"rn#
0 P
= 0 3 ( N
P / N
3 )!
To find T r("io fro& A r("io 0 P ?o6&# 0
3 ?o6&#
N P
/ N 3 = √ 0
P / 0
3
P o'" ?!(""# P in ?!(""#
Efficiency = P out
/ P in x **
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-& *D+11E+11 10 2 2
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-' *D+17,E+17 5 2 1:
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-( V = Q/C *D+1E+1 10 5 0
CHAPTER 1 To find nr9< in o'%# E$c% for&'%( in co%'&n H i#)
%ormula &-) *:2,D+0:,E+0:/0 0.000005 250 :12402
CHAPTER 1 To find di%c"ric con#"(n" E$c% for&'%( in co%'&n H i#)
%ormula &-* *D+0+E+0+ 6 1 4
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-+ *2,D+04?1:/10,E+04 0.01 0.001 2E-:11
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &- *2,D+05,E+05?1:/10,F+05 3 0.01 0.001 0422E-:1:
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &- *002,D++0,E++01:/,F++0,?.++0-1 100 2 0.005 2 :::5
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-7 *D++2,E++2?D++2GE++2 3 6 0
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-&? *D++.++ 10 10 10 3 +++
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-&& *1?1D+71G1E+71G1F+71 10 5 10 02
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-&' *D+77,E+77F+77 60 7.5 15 +:
To find " 8(%' ?@ (nd 8 ;no!n Q ?co'% V ?8o%"#
C = Q/V
To find @ 8(%' ?" (nd 8 ;no!n C ?f(r(d# V ?8o%"#
Q = C x V
To find 8 8(%' ?@ (nd " ;no!n Q ?co'% C ?f(r(d#
C ?f(r(d# V ?8o%"#
Energy = *&7 x CV !
ε
o ?(# ε
8 ?8(c
k = ε
o/ε
-
To find " ?fro& 36<#ic(% f(c"or# A ?# &"r# % ?&"r#
C = 9&97 x A/*!%
To find " ?fro& 36<#ic(% f(c"or# k ?n'&r A ?# &"r# % ?&"r#
C = 9&97 x k x A/*! x %
To find " in µ% ?fro& 36<# f(c"or# k ?n'&r A ?# in % (in&) n?= 3%("#
C = !&!7:k : A/*. x % x (n')
To find " T of 0 #ri# c(3# C
1 ?µF C
0 ?µF
C T = C
x C
!/ C
# C
!
To find " T of * 8(%' #ri# " # C
1 ?µF C
0 ?µF C
+ ?µF n?= 3%("#
C T = C / N
To find " T of (n< 8(%' #ri# " # C
1 ?
µ
F C 0 ?
µ
F C + ?
µ
F
C T = //C
#/C
!#/C
%&&&#/C
n
To find 8 " x
in c(3 8 di8idr circ'i" V 3 ?8o%"# C
T ?'F C
X ?µ
F
V X
= V 3 x C
T /C
X
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
309
310
311
312313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-&( *D+7GE+7GF+7G.+7 15 10 10 3 +
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-&) *D+2:,E+2: 1000 0.000001 :::1
CHAPTER 1 E$c% for&'%( in co%'&n H i#) ε
%ormula &-&* *D+2+,??E+2+/-?F+2+.+2+ 50 2.71828 10000 10000 1+5
CHAPTER 1 E$c% for&'%( in co%'&n H i#) ε
%ormula &-&+ *D+24,???1-?E+24/-?F+24.+24 50 2.71828 18000 10000 717
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-& *?D+25,1:/-10,E+25?F+25,1:/-4 100 100 100 ::::1
CHAPTER 1 E$c% for&'%( in co%'&n H i#) 2π
%ormula &-' *1?D+40,E+40,F+40 6.28 120 0.000002 44+7
CHAPTER 1 E$c% for&'%( in co%'&n H i#) 2π
%ormula &-( *1?D+42,E+42,F+42 6.28 5E-010 1000 +171
CHAPTER 1 E$c% for&'%( in co%'&n H i#) 2π
%ormula &-) *1?D+4,E+4,F+4 6.28 2000 3180 ::::::::02
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-* *1?1D+1G1E+1G1F+1 1000 2000 3000 27272
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &-+ *D+7,E+7?D+7GE+7 1000 2000 4444
CHAPTER 1 E$c% for&'%( in co%'&n H i#)
%ormula &- *D+E+ 1000 5 0::
CHAPTER 15 E$c% for&'%( in co%'&n H i#)
%ormula &7-& *SQRT?D+:/0GE+:/0 50 50 :1
To find " T of 3(r(%%% c(3(ci"or# C
1 ?
µ
F C 0 ?
µ
F C + ?
µ
F C 7 ?
µ
F
C T = C
# C
! # C
%$#C
n
To find 1 "i& con#" in (n 0" circ'i" R ?o6&# C ?f(r(d#
T; (T) = R x C
To find in#" v 0 in ( dc 0" circ'i" V
S ?8o%"# ' ?µ#c τ ?µ#c
& R
= V 3 x (ε't/T)
To find in#" v " in ( dc 0" circ'i" V
S ?8o%"# ' ?µ#c τ ?µ#c
&C = V
, x ( ' ε
't/T)
To find i " ;no!in9 " (nd dv>dt C ?8(%' d& ?8o%"# d' ?#c
C = C x d&/d'
To find ; " ;no!in9 f (nd " f ?HJ C ?f(r(d#
X C = /!
π
x f x C
To find f ;no!in9 " (nd ; " C ?f(r(d# X
" ?o6&#
f = /!π x C x X C
To find " ;no!in9 f (nd ; " f ?HJ X
" ?o6&#
C = /!π
x f x X C
To find ; "T
of 3(r(%%% " # X " 1
?o6&# X " 0
?o6&# X " +
?o6&#
X CT
= // X C
# / X C !
# / X C %
$/<Cn
To find ; "T
of 0 3(r(%%% " # X " 1
?o6&# X " 0
?o6&#
X CT
= X C
x X C !
/ X C
# X C-
To find ; "T
of * 8(% 3(r(%%% " # X " 1
?o6&# N ?n'&r
X CT
= X C
/ N
To find 8 T in ( #ri# 0" circ'i" V
0 ?8o%"# V
" ?8o%"#
V T = √ V
R! # V
C !
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 15 E$c% for&'%( in co%'&n H i#)
%ormula &7-' *SQRT?D++/0GE++/0 50 50 :1
CHAPTER 15 E$c% for&'%( in co%'&n H i#)
%ormula &7-( *SQRT?D+4/0GE+4/0 15 20 02
CHAPTER 15 E$c% for&'%( in co%'&n H i#)
%ormula &7-) *D+5,E+5SQRT?D+5/0GE+5/0 4 3 07
CHAPTER 15 E$c% for&'%( in co%'&n H i#) .ne
%ormula &7-* *D+50E+50 1 1500 ::::44
CHAPTER 15 To find c(3(ci"i8 #'#c3"(nc E$c% for&'%( in co%'&n H i#)
%ormula &7-+ *D+52E+52 1 995 :::1
CHAPTER 15 E$c% for&'%( in co%'&n H i#)
%ormula &7- *SQRT?D+5/0GE+5/0 0.000667 0.001 :::10
CHAPTER 15 To find &(9ni"'d of 36(# (n9% E$c% for&'%( in co%'&n H i#)
%ormula &7- *DE.REES?ATAN?D7:1E7:1 1500 995 2477
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-& *SQRT?D7:7/0GE7:7/0 60 80 1::
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-' *SQRT?D7:5/0GE7:5/0 60 80 1::::
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-( *D717E717 80 60 1++
To find A in ( #ri# 0" circ'i" R ?o6&# X " ?o6&#
0 = √ R! # X C
!
To find / T in ( 3(r(%%% 0" circ'i" I
0 ?(&3# I
" ?(&3#
I T = √ I
R! # I
C !
To find A in ( 3(r(%%% 0" circ'i" R ?o6&# X " ?o6&#
0 = R x X C
/√
R! # X C
!
To find 1 in ( 3(r(%%% 0" circ'i" R ?o6&#
G = /R
X c ?o6&#
BC
= / X C or !π f ;
To find B in ( 3(r(%%% 0" circ'i" G ?S B" ?S
1 T = √1 ! # B
C !
R ?o6&# X " ?o6&#
θ
?&(9ni"'d * "(n-1 0 ; "
To find A of ( #ri# 0<" circ'i" R ?o6&# X net
?o6&#
0 = √ R! # X ne'
!
?!6r ; net
* ; <- ;
" if ;
< ;
"
or ; net
* ; " - ;
< if ;
" ;
<
To find 8 T of ( #ri# 0<" circ'i" V
0 ?8o%"# V
$net ?8o%"#
V T =
√
V R
! # V Xne'
!
?!6r 8 xnet
*8 <- 8
" if 8
<8
"
or 8 xnet
*8 " - 8
< if 8
" 8
<6
To find T(nθ knowing X net an+ R X net
?o6&# R ?o6&#
Tang of θ = X ne'
/ R
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-) *D71E71 80 60 1++
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-* *SQRT?D70:/0GE70:/0 2 1 007
CHAPTER 0: To find 3f ;no!in9 36(# (n9% E$c% for&'%( in co%'&n H i#)
%ormula '?-+ *COS?D702,PI?1: 45 ::
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?- *D70,E70 141.5 1 1712
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?- *D7+0/0,E7+0 1 100 1::
To find T(nθ
knowing V X
ne' an+ V R
V X n" ?8o%"# V
0 ?8o%"#
Tang ofθ
= V X
ne' / V R
To find / T of ( 3(r(%%% 0<" circ'i" I
0 ?(&3# I
X n" ?(&3#
I T = √ I
R
! # I X
ne' !
?!6r / x net * /
<- /
" if /
</
"
or / x net * /
" - /
< if /
" /
<
θ
?d9
Power factor ( !"f &) = cos θ
To find (33 3o!r ;no!in9 8 (nd / V ?8o%"# I ?(&3#
"arent ower ( 3 ) = V rms
x I rms
To find "r' 3o!r ;no!in9 / (nd 0 I ?(&3# R ?o6&#
True ower ( P ) = I ! x R
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
8/10/2019 goooood-كل قوانين الكهرباء
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-7 *D7+2,E7+2 141.5 0.707 1::
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-&? *D7+E7+ 100 141.5 ::
CHAPTER 0: E$c% for&'%( in co%'&n H i#)
%ormula '?-&& *SQRT?D771/0GE771/0 100 100 17170
CHAPTER 0: E$c% for&'%(# in co%'&n H (r)
%ormula '?-&' *?D777,COS?E777,PI?1: 45 30 +5
?Sri# circ'i" *?D777,SIN?E777,PI?1: 002
An#!r i#)
CHAPTER 0: E$c% for&'%(# in co%'&n H (r)
%ormula '?-&( *?D72:,COS?E72:,PI?1: 66 60 ++
?Sri# circ'i" *?D72:,SIN?E72:,PI?1: 214
An#!r i#)
CHAPTER 0: E$c% for&'%(# in co%'&n H (r)
%ormula '?-&) *?D724,COS?E724,PI?1: 15 30 1055
?P(r(%%% circ'i" *?D724,SIN?E724,PI?1: 2
An#!r i#)
CHAPTER 0: To find ind'c"i8 #'#c3"(nc E$c% for&'%( in co%'&n H i#)
%ormula '?-&* *1?D740,E740,F740 6.28 60 1 :::042
?P(r(%%% circ'i"
CHAPTER 0: To find c(3(ci"i8 #'#c3"(nc E$c% for&'%( in co%'&n H i#)
%ormula '?-&+ *D744,E744,F744 6.28 60 0.000004 :::121
?P(r(%%% circ'i"
To find "r' 3o!r ;no!in9 S (nd pf 3 ?VA !"f" ?n'&
P = "arent ower x ower factor (&f&)
To find 3f ;no!in9 9 (nd S P "r' ? 3 ?VA
!"f" = True ower ( P )/"& ower ( 3 )
To find S ;no!in9 9 (nd 850 P "r' ? Q ?VAR
3 =√
P ! # Q!
To con8r" A 3o%(r "o rc" d("( 0 ?o6&# θ
?d9
R factor = ( 0 cos θ)
factor =
( 0 sinθ
)
7∠30 =
( 0 cosθ
+
( 0 sinθ
)
72 ∠+: * +5 G 002
To con8r" 8 T 3o%(r "o rc" d("( V
T ?8o%"#
θ ?d9
>eal axis = (V T x cos
θ
)
?mag& axis =
(V T x sin
θ
)
66∠45 = (V T x cos θ + (V
T x sin θ )
44∠72 * ++ G 214
To con8r" / T 3o%(r "o rc" d("( I T ?(&3# θ
?d9
>eal axis = ( I T x cos
θ
)
?mag& axis = ( I T x sin
θ
)
15∠30 = ( I T x cos
θ
+ ( I T x sin
θ
)
12∠30 * 1055 G 2
0π f ?HJ L ?H
B L = /!
π
x f x L
-π f ?HJ C ?F(r(d#
BC = !π x f x C
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 01 E$c% for&'%( in co%'&n H i#)
%ormula '&- *D2:2E2:2 5000 25 0::
To find B ;no!in9 f r (nd @ f
r ?HJ Q ?n'&r
5W = f r /Q
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
504
505
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 01 E$c% for&'%( in co%'&n H i#)
%ormula '&-7 *D2:E2: 5000 200 02
CHAPTER 01 E$c% for&'%( in co%'&n H i#)
%ormula '&-&? *1?D211,E211,F211 6.28 1000 0.0000001 1250+4
3Note: %or hi-pass simple " filter6
CHAPTER 01 E$c% for&'%( in co%'&n H i#)
%ormula '&-&& *1?D212,?E212F212 6.28 0.1 1000 1250+4
3Note: %or lo-pass simple < filter6
CHAPTER 00 To find &($ = of %c"ron# in #6%% n E$c% for&'%( in co%'&n H i#) n
%ormula ''-& *0,D215/0 3 1
CHAPTER 0+ E$c% for&'%( in co%'&n H i#)
%ormula '(-& *?D200-E200F200 10 0.7 150 ::40
CHAPTER 0+ To find diod 3o!r di##i3("ion E$c% for&'%( in co%'&n H i#)
%ormula '(-' *D202,E202 0.01 0.7 :::
CHAPTER 0+ To find Jnr diod 3!r di##i3("ion E$c% for&'%( in co%'&n H i#)
%ormula '(-( *D20,E20 0.05 5.1 :022
CHAPTER 0+ To find r9'%("ion "r(n#i"ion 3oin" E$c% for&'%( in co%'&n H i#)
%ormula '(-) *D2+1,?E2+1GF2+1F2+1 9.1 100 750 1:+1
CHAPTER 0+ E$c% for&'%( in co%'&n H i#)
%ormula '(-* *D2+7,E2+7?E2+7GF2+7 9 750 100 57
CHAPTER 0+ E$c% for&'%( in co%'&n H i#)
%ormula '(-+ *D2+-E2+ 12 1.5 1:2
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-& *:72,D27: 70.7 +1
To find @ ;no!in9 f r (nd B f
r ?HJ B7 ?HJ
Q = f r /5W
To find c'"off for 0" n"!or; -π R ?o6&# C ?F(r(d#
f ) = /!
π
x R x C
To find c'"off for 0< n"!or; -π L ?H R ?o6&#
f ) = /!π x ( L/ R)
Aax 0 of electrons = ! x n!
To find / in circ !#ri# diod (nd 0 V S ?8o%"#
V
. ?8o%"# R ?o6&#
I = (V 3
* V
D 6 / R
I ?(&3# V .
P = I x V D
I J ?(&3# V
J ?8o%"#
P = I 2 x V
2
V JT
R1 ?o6&# R
< ?o6&#
V % = V
2T x ( R
# R
L 6 / R
L
To find o'"3'" 8 !#o'rc "r(n# 3" V % ?8o%"# R
< ?o6&# R
1 ?o6&#
V L = V
% x R
L / ( R
L + R
)
To find 8 "o dro33d < 8 0
V % ?8o%"# V
. ?8o%"#
V R
= V % * V
D
To find 8 dc
o'" of 'nfi%" H rc" V r&#
?8o%"#
V +c
= *&7 x V rms
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
506
507
508
509510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-' *:+1,D27+ 100 +1
To find 8 dc
o'" of 'nfi%" H rc" V P
?8o%"#
V +c
= *&%9 x V PB
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
542
543
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 07 To find PIV of 'nfi%" H rc" E$c% for&'%( in co%'&n H i#)
%ormula ')-( *1717,D274 200 00
CHAPTER 07 To find ri33% fr H rc" E$c% for&'%( in co%'&n H i#)
%ormula ')-) >ile freC& = ac inut freCuency *1,D275 60 4:
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-* *:5,D220 100 5:
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-+ *:72,D222 200 5:
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')- *:4+,D22 141.4 5:1
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')- *:+1,D241 282.8 55
CHAPTER 07 To find PIV of 'nfi%" F rc" E$c% for&'%( in co%'&n H i#)
%ormula ')-7 *1717,D247 200 00
CHAPTER 07 To find ri33% fr F rc" E$c% for&'%( in co%'&n H i#)
%ormula ')-&? >ile freC& = ! x ac inut freCuency *0,D24 60 10:
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-&& *:5,D2: 12.6 11+7
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-&' *:4+,D2+ 17.8 11+7
CHAPTER 07 To find PIV of 'nfi%" rid9 rc" E$c% for&'%( in co%'&n H i#)
%ormula ')-&( *1717,D24 200 00
CHAPTER 07 To find ri33% fr ?rid9 rc" E$c% for&'%( in co%'&n H i#)
%ormula ')-&) *0,D25 60 10:
V r&#
?V
P?4 (1&W&) = & x V rms
#) n!u' f
To find 8 dc
o'" of 'nfi%" F rc" V ?10 #c
V +c
= *& x V rms
of half of secon+ary
To find 8 dc
o'" of 'nfi%" F rc" V ?f'%% #c
V +c
= *&7 x V rms
of full secon+ary
To find 8 dc
o'" of 'nfi%" F rc" V P
?10 #c
V +c
= *&3%. x V PB
of /! secon+ary
To find 8 dc
o'" of 'nfi%" F rc" V P
?f'%% #c
V +c
= *&%9 x V PB
of full secon+ary
V ?F'%% #c
P?4 (F&W&) = & x V rms
full secon+ary
#) n!u' f
To find 8 dc
o'" ?'nfi%" rid9 rc" V r&#
n!u'
V +c
= *& x V rms
of ac inut
To find 8 dc
o'" ?'nfi%" rid9 rc" V 3;
n!u'
V +c
= *&3%. x V PB
of ac inut
V rms
n!u'
P?4 (5ri+ge) = & x V rms
inut
#) n!u' f
>ile freCuency (bri+ge) = ! x ac in f
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
544
545
546
547548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 07 To find 3o!r #'33%< o'" K ri33% E$c% for&'%( in co%'&n H i#) #) r!!le !*! d) u'
%ormula ')-&* >ile = ac(rile ')/+c out x ** *D20E20,1:: 1 48 0:
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
580
581
582
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 07 To find 3o!r #'33%< K r9'%("ion E$c% for&'%( in co%'&n H i#)
%ormula ')-&+ *?D22-E22E22,1:: 12.2 11.8 ++5
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-& *?D2,E2GF2,?E2-.2 0.0044 24 0.15 15 174
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-& *D251?D251GE251,1:: 2.25 1.446 4:
CHAPTER 07 To find r9'%("d dc o'"3'" 8o%"(9 E$c% for&'%( in co%'&n H i#)
%ormula ')-&7 *D257,?1GE257F257 1.25 240 240 02
CHAPTER 07 E$c% for&'%( in co%'&n H i#)
%ormula ')-'? *D25?D25GE25 50 50 :2
CHAPTER 07 E$c% for&'%( in co%'&n H i#) D &#lue
%ormula ')-'& *D4::,E4:: 24 0.5 10
CHAPTER 07 E$c% for&'%( in co%'&n H i#) D &#lue
%ormula ')-'' *D4:+?1-E4:+ 24 0.5 7::
CHAPTER 07 E$c% for&'%( in co%'&n H i#) D &#lue
%ormula ')-'( *-D4:4,E4:4?1-E4:4 24 0.5 -07
CHAPTER 02 To find "r(n#i#"or &i""r c'rrn" E$c% for&'%( in co%'&n H i#)
%ormula '*-& *D4:5GE4:5 18 0.001 1::1
CHAPTER 02 To find dc B"( of "r(n#i#"or E$c% for&'%( in co%'&n H i#)
%ormula '*-' *D410E410 1.2 0.024 2:
CHAPTER 02 To find co%%c"or c'rrn" E$c% for&'%( in co%'&n H i#)
%ormula '*-( *D412,E412 50 0.024 10
CHAPTER 02 To find (# c'rrn" E$c% for&'%( in co%'&n H i#)
%ormula '*-) *D41E41 1.2 50 ::07
V N<
?8o%"# V %<
?8o%"#
>eg& = (V NL
* V FL 6/ V
FL x **
To find 3o!r di## < /" r9'%("or I #
?(&3# V IN
?V I L
?(&3# V OUT
?V
P >E
= I B
x V ?
+ I L
x (V ?
'V 8GT
)
To find fficinc< of /" r9'%("or P o'"
? P r9
?
η = P out
/ ( P out
# P reg
) x **
V rf
?V R0
?o6&# R1 ?o6&#
V out
= V ref
x (# R!/ R
)
To find . f(c"or for @'c;@ r9 T on
?&#c T off
?&#c
D = T on
/ (T on
# T off
)
To find 8 o'"
of ( @'c;@ r9 V in ?8o%"#
V out
= V in x D
To find 8 o'"
of ( @oo#"@ r9 V in ?8o%"#
V out
= V in /(' D6
To find 8 o'"
of ( @f%<(c;@ r9 V in ?8o%"#
V out
= 'V in x D/(' D)
I C ?&A I
# ?&A
I E
= I C # I
B
I " ?&A I
# ?&A
β
+c = I
C /I
B
dc
I #
?&A
I C = β
+c x I
B
I " ?&A
dc
I B
= I C / β
+c
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 02 To find A%36( of "r(n#i#"or E$c% for&'%( in co%'&n H i#)
%ormula '*-* *D401E401 9.8 10 :5
CHAPTER 02 To find (c B"( ?c'rr 9(in of "r(n# E$c% for&'%( in co%'&n H i#)
%ormula '*-+ *D407E407 2 0.04 2:
CHAPTER 04 To find 8o%"(9 9(in of (&3%ifir E$c% for&'%( in co%'&n H i#)
%ormula '+-& *D40E40 1.2 0.05 07
CHAPTER 04 To find c'rrn" 9(in of (&3%ifir E$c% for&'%( in co%'&n H i#)
%ormula '+-' *D4+:E4+: 10 0.5 0:
CHAPTER 04 To find 3o!r 9(in of (n (&3%ifir E$c% for&'%( in co%'&n H i#)
%ormula '+-( *D4++,E4++ 24 20 7:
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
%ormula '+-) *D4+4,F4+4?E4+4GF4+4 12 12000 2000 11
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
%ormula '+-* *?D4+5-E4+5F4+5 1.714 0.7 1000 :::1:17
CHAPTER 04 To find co%%c"or-&i""r 8o%"(9 E$c% for&'%( in co%'&n H i#)
%ormula '+-+ *D470-?E470,?F470G.470 12 1.014 3.9 1 :+
CHAPTER 04 To find d<n(&ic &i""r r#i#"(nc E$c% for&'%( in co%'&n H i#) ?&V
%ormula '+- *D472E472 25 1.014 0742
CHAPTER 04 To find in3'" i&3d(nc E$c% for&'%( in co%'&n H i#) Be'#
%ormula '+- *1?1D47G1E47G?1?F47G1,.47 12000 2000 100 24.65 0+211+
CHAPTER 04 A33ro$i&("ion of o'"3'" i&3d(nc E$c% for&'%( in co%'&n H i#)
%ormula '+-7 *D421 3000 +:::
CHAPTER 04 A33ro$i&("ion of 8o%"(9 9(in E$c% for&'%( in co%'&n H i#)
%ormula '+-&? *-D427E427 3900 24.65 -1200
I " ?&A I
E ?&A
α = I C / I
E
∆ / " ?&A ∆ /
# ?&A
β
ac =
∆
I C /
∆
I B
V o'"
?V33 V in ?V33
AV = V
out / V
in
I o'"
?I33 I in
?I33
A I = I
out / I
in
A8
A/
A P
= AV x A
I
To find (# 8 !i"6 8 di8idr i(# V ""
?8o%"# R1 ?o6&# R
0 ?o6&#
V B≈V
TH = V cc x R
! / ( R
# R
!)
To find &i""r c'rr !i"6 8 di8 i(# V # ?8o%"# V
#E ?8o%"# R
E ?o6&#
I E
= 4V B
* V BE
6 / R E
V ""
?8o%"# I E ?&A R
"?; Ω R
E?; Ω
V CE
= V CC
* I E
x ( RC + R
E )
I E
?&A
re8 = !7 m4 / I E
R1 ?o6&# R
0 ?o6&# re8 ?o6&#
0 IN
= RHH R
-99 (5eta #) x re8
R" ?o6&#
0 .:T
= RC
R" ?o6&# re8 ?o6&#
AV
= *RC / re8
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
619
620
621
622623
624
625
626
627
628
629
630
631632
633
634
635
636
637
638
639
640641
642
643
644
645
646
647
648
649
650
651
652
653
654
C G
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 04 A33ro$i&("ion of c'rrn" 9(in E$c% for&'%( in co%'&n H i#)
%ormula '+-&& *D42,?E42,F42?E42GF42 100 12000 2000 24.65 7:
??E42,F42?E42GF42G?D42G1,.42
β R1 ?o6&# R
0 ?o6&# re8 ?o6&#
Αι β( RHH R
!)/( R
1|| R
!)#(β #)re8
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
655
656
657
658
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 04 A33ro$i&("ion of in3'" i&3d(nc E$c% for&'%( in co%'&n H i#)
%ormula '+-&' *1?1E441G1F441G?1??D441G1,?.441 100 12000 2000 1024.65 144+2
CHAPTER 04 A33ro$i&("ion of o'"3'" i&3d(nc E$c% for&'%( in co%'&n H i#)
%ormula '+-&( *D447 3900 +5::
CHAPTER 04 A33ro$i&("ion of 8o%"(9 9(in E$c% for&'%( in co%'&n H i#)
%ormula '+-&) *-D44?E44GF44 3900 24.65 1000 -+1
CHAPTER 04 A33ro$i&("ion of c'rrn" 9(in E$c% for&'%( in co%'&n H i#)
%ormula '+-&* *D4:,?E4:,F4:?E4:GF4: 100 12000 2000 1024.65 14+
??E4:,F4:?E4:GF4:G?D4:G1,?.4:
CHAPTER 04 A33ro$ 9(in of &'%"i#"(9 (&3%ifir E$c% for&'%( in co%'&n H i#) ---
%ormula '+-&+ *D47,E47,F47 10 50 50 02:::
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
%ormula '+-& *1?1D41G1E41G?1??F41G1,.41 12000 2000 100 1024 144++
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
%ormula '+-& *1?1D47G1E47 500 24.65 0+75
CHAPTER 04 To (33ro$ 8 9(in of CC (&3%ifir E$c% for&'%( in co%'&n H i#)
%ormula '+-&7 *D4?E4GF4 1000 24.65 1000 :5
CHAPTER 04 To (33ro$ c'rr 9(in of CC (&3%ifir E$c% for&'%( in co%'&n H i#) β
%ormula '+-'? *-D451 100 -1::
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
β R1 ?o6&# R
0 ?o6&# 4re8 +R
E; 6
0 IN
= RHH R
-99 (5eta #) x (re8 # R
E;))
R" ?o6&#
0 .:T
= RC
R" ?o6&# re8 ?o6&# R
E& ?o6&#
AV ≈ *R
C / (re8 + R
E;)
β R1 ?o6&# R
0 ?o6&# 4re8 +R
E; 6
Αι
≈β
( RHH R
!)/( R
1|| R
!)#(
β
#)x(re8+R E;
)
A8&
A8'
A8(
AV = A
V; x A
V- x A
V< …
!6r) AV1
= Zin1
/(Zin1
+ Zs)
AV2
is the gain ! !i"st a#$%i!ie"
AV3
= Zin2
/(Zin2
+ Z&t1
)
AV4
is gain ! 2n' a#$
To (33ro$i&(" A /N for CC (&3%ifir R1 ?o6&# R0 ?o6&#β
re G 0 E Ω
0 IN
= R;99R
-99 ((β +1 x (re8 # R
E ))
To (33ro$i&(" A out
for CC (&3%ifir RE ?o6&# re8 ?o6&#
0 .:T
= R E
99 re8
RE ?o6&# re8 ?o6&# R
E ?o6&#
AV = R
E /4re8 + R
E )
No") 58 ≈1
A ≈ *β
To find (33ro$ in of CB (&3%ifir R
E ?o6&# re8 ?o6&#
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
659
660
661
662663
664
665
666
667
668
669
670
671672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
%ormula '+-'& *D457,E457?D457GE457 1000 24.65 07:4
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
%ormula '+-'' *D45 3900 +5::
CHAPTER 04 To (33ro$ 8 9(in of CB (&3%ifir E$c% for&'%( in co%'&n H i#)
%ormula '+-'( *D::E:: 3900 24.65 1200
CHAPTER 04 To (33ro$ c'rrn" 9(in of CB (&3 E$c% for&'%( in co%'&n H i#)
%ormula '+-') *D:+ -1 -1
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
%ormula '+-'* *D:4 12 10
CHAPTER 04 E$c% for&'%( in co%'&n H i#)
%ormula '+-'+ *D:5?E:5GF:5 12 3900 1000 :::072
CHAPTER 0 To find dr(in c'rr FET# > MOSFET#
%ormula '-&
3NOTE: Shocley!s equation, shown here for information onlyF6
CHAPTER 0 To find "r(n#cond'c"(nc of FET E$c% for&'%( in co%'&n H i#)%ormula '-' *D14E14 0.002 3 ::::44
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-( *D15 5 2
3Note: 4sing fixed 2ias6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-) *D0+-?E0+,F0+ 12 0.005 1000
3Note: 4sing fixed 2ias6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-* *-D0,E0 0.004 1000 -7
3Note: 4sing self 2ias6
0 ?
= R E
99 re8
To find (33ro$ A out
of CB (&3%ifir R" ?o6&#
0 8GT
= RC
R" ?o6&# re8 ?o6&#
AV = R
C / re8
A/
A ≈ *
To dfin 8 "E
(" c'"off condi"ion V ""
?8o%"#
V CE
= V CC
To find / " 8(%' (" #("'r("ion V
"" ?8o%"# R
" ?o6&# R
E ?o6&#
I C4%#'6
= V CC
/ ( RC # R
E )
I D
=I D33
('(V G3 /V
G3 (off) ))!
∆ / .
3 (&3# ∆
8 1S
?V
gm = ∆ I
D / ∆ V
G3
To find FET 9(" "o #o'rc 8 V 11
?8o%"#
V G3
= V GG
To find FET dr(in "o #o'rc 8 V ..
?8o%"# I . ?(&3# R
. ?o6&#
V D3
= V DD
* I D
x R D
To find FET 9(" "o #o'rc 8 I . ?(&3# R
S ?o6&#
V G3
= * I D
x R 3
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-+ *D+1-?E+1,F+1-?E+1,.+1 18 0.01 1000 390 71
3Note: 4sing self and 8 div 2ias6
CHAPTER 0 To find FET 9(" 8o%"(9 E$c% for&'%( in co%'&n H i#)
%ormula '- *D+2,F+2?E+2GF+2 12 100000 33000 05
3Note: 4sing voltage div 2ias6
CHAPTER 0 To find FET 9(" "o #o'rc V E$c% for&'%( in co%'&n H i#)
%ormula '- *D+5-?E+5,F+5 2.98 0.0085 470 -1:0
3Note: 4sing 8 divider 2ias6
CHAPTER 0 To find E-MOSFET dr(in c'rr%ormula '-7
3NOTE: Shocley!s equation, shown here for information onlyF6
CHAPTER 0 To find FET 3o!r di##i3("ion E$c% for&'%( in co%'&n H i#)
%ormula '-&? *D7,E7 0.12 1.3 :124
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-& *-D2:,E2: 50000 0.0002 -1:
($en %$) 3Note: /nverting input6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-' *D27,E27 50000 0.0002 1:
($en %$) 3Note: Non-inverting input6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-( *D2,?E2-F2 50000 0.002 0.0015 02
($en %$) 3Note: .ifferential amp circuit config6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-) *D40E40 -15 2 -2
3Note: 5ssuming infinite input 6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
To find FET dr(in "o #o'rc 8 V ..
?8o%"# I . ?(&3# R
. ?o6&# R
S ?o6&#
V D3
= V DD
* I D
x R D
* I D
x R 3
V ..
?8o%"# R1 ?o6&# R
0 ?o6&#
V G = V
DD x R
! / 4R
+ R
!)
V 1 ?8o%"# I
. ?(&3# R
S ?o6&#
V G3
= V G * I
D x R
3
I D
= k x (V G3
* V T )!
V .S
?8o%"# I . ?(&3#
P FET
= V D3
x I D
To find o3-(&3 o'"3'" 8 A486
V in ?8o%"#
V out
= ' A486
x V in
To find o3-(&3 o'"3'" 8 A486
V in ?8o%"#
V out
= A486
x V in
To find o3-(&3 o'"3'" 8 A486
V 1 ?8o%"# V
0 ?8o%"#
V out
= A486
x (V * V
!)
To find in8 o3-(&3 8 9(in V o'"
?8o%"# V in ?8o%"#
AV = V
out / V
in
To find in8 o3-(&3 8 9(in Rf ?o6&# R
i ?o6&#
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751752
753
754
755
756
757
758
759
760
761
762
763
764
765
A B C D E F G H
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
%ormula '-* *-?D44E44 27000 1800 -12
3Note: "losed loop 8 gain6
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-+ *?D:E:G1 13000 1000 17
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '- *?E+D+G1,??.+?.+GF+ 10000 50000 20000 10000 0
AV = *R
f / R
To find non-in8 o3-(&3 8 9(in Rf ?o6&# R
i ?o6&#
AV = ( R f / R ) #
To find 8 9(in of V di8 non-in8 (&3 R& ?o6&# R
' ?o6&# R
( ?o6&# R
) ?o6&#
58 *?0
' >0
& 6H& $ 0
) >30
) H 0
( 6
A B C D E F G H
1
2
3
4
5
6
7
8
9
10
766
767
768
769
770
771
772
773
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 0 To find %o!r "6r#6 3" of Sc6 "ri9 E$c% for&'%( in co%'&n H i#)
%ormula '-& *D10,?E10?E10GF10 -12 10000 100000 -1:5
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-& *?D12,E12SQRT??F12GE12/0G?.12/0, 0.1 2000 8000 723.4 :+5
?0:,D1SQRT?D1/0GE1/0
3Note: 0&5 and 0&# = input signal potentiometer6 8 0.7234
CHAPTER 0 E$c% for&'%( in co%'&n H i#) k
%ormula '-&7 *?D0:-E0:,F0:,?.0:,D00 0.2 0.15 20 0.000486 74
10000
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-'? *D02,E02 0.000486 10000 74
!6r)
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-'& *D+:,E+: -0.000486 10000 -74
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-'' *1?D++,E++,F++ 6.28 1000 0.000001 12507
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-'( *D+4,E+4SQRT?F+4/0GE+4/0, 1 10000 10000 10000 1717
?1G.+4D+
10000
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-') *1?D71,E71,F71 6.28 10000 2.2E-009 0+
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-'* *D77,?E77SQRT?E77/0GF77/0 1 10000 10000 10000 1717
,?1G.77D74
V &in
?8o%"# R1 ?o6&# R
0 ?o6&#
6TP = V min
x I R/( R
# R
!)J
To find o'"3'" 8 of IC ('dio (&3%ifir V in ?8o%"# R
1B ?o6&# R
1A ?o6&# X
C1 ?o6&#
4out
= 4in x I R
5 / ( R
"# R
5'<
;)J
x !* x I R,PB
) / ( R,PB
'<;!
)J RSP
?o6&# X C0
?o6&#
To find 8 o'" of OTA diff (&3%ifir V 1 ?8o%"# V
0 ?8o%"# I
BIAS?(&3#
V out
= (V ' V
!) x k x I
5?", x R
L
R<?o6&#
To find UTP 8 for Sc6 "ri9 co&3 I BIAS
?(&3# R1 ?o6&#
GTP = I 5?",
x R
/ BIAS
* 8 BIAS
- V - - :0 BIAS
To find LTP 8 for Sc6 "ri9 co&3 I BIAS
?(&3# R1 ?o6&#
6TP = ' I 5?",
x R
To find f " of 1#" ordr %o!-3(## fi%"r 0
π R ?o6&# C ?f(r(d#
f c = /(!π x R x C )
To find 8 o'"
of 1#" ordr %o!-3(## fi%" V in ?8o%"# * X
" R ?o6&# R0 ?o6&#
V out
= V in x I' X
;/(>' X
;)J x (# R
!/ R
)
R1 ?o6&#
To find f " of 1#" ordr 6i-3(## fi%"r 0π
R ?o6&# C ?f(r(d# f
c = /(!π x R x C )
To find 8 o'"
of 1#" ordr 6i-3(## fi%" V in ?8o%"# R ?o6&# * X
" R
0 ?o6&#
V out
= V in x I R/( R ' X
C6J x (# R
!/ R
)
R1 ?o6&#
1
2
3
4
5
6
7
8
9
10
810
811
812
813814
815
816
817
818
819
820
821
822823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
10000
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-'+ *1?40,SQRT?D75,E75?D75GE75, 1000 1000 20000 0.00000001 +72
F75,.75,D21
4.7E-009
CHAPTER 0 To find "6 B of (nd3(## fi%"r E$c% for&'%( in co%'&n H i#) Q
%ormula '-' *D27E27 7345 3.16 0+07
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-' *D2-?E20 7345 2324 41+
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-'7 *D4:G?E4:0 7345 2324 2:
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-(? *1?40,SQRT?D4+,E4+,F4+,.4+ 1000 20000 0.00000001 0.00000001 +241
CHAPTER 0 To find di9i" dc 8(%' for ADC circ E$c% for&'%( in co%'&n H i#)
%ormula '-(& *D44,?0222 2 1:0
CHAPTER 0 E$c% for&'%( in co%'&n H i#)
%ormula '-(' *?-D45E45,??F450G?.457G?D1 10 10000 1 0 2+5:402
G?E114G?F1+0G?.147G?D+10
G?E+024,?-F+ 0 0 1 0
1 0 10000
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
%ormula '7-& *1?D4,SQRT?E4,F4 6.28 0.00004 1E-010 021+
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
%ormula '7-' *1?D5,SQRT?E5,F5 6.28 0.00004 1E-010 021+
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
To find cn"r f of (nd3(## fi%"r R1 ?o6&# R
0 ?o6&# R
+ ?o6&# C
1 ?f(r(d#
f o=/!π x√I Rx R
!/( R
# R
!)Jx R
%xC
xC
!)
C 0 ?f(r(d#
f o ?HJ
5W = f o/K
To find %o! c'"off f of (nd3(## fi%"r f o ?HJ 5W ?HJ
f c
= f o ' 5W/!
To find '33r c'"off f of (nd3# fi%" f o ?HJ 5W ?HJ
f c!
= f o # 5W/!
To find cn"r f of (nd#"o3 fi%"r R1 ?o6&# R
0 ?o6&# C
1 ?f(r(d# C
0 ?f(r(d#
f o = /(!π x √ R
x R
!x C
x C
!)
V in1
?8o%"#
D"T" = V in
x (!77/7 4) +ec& re&
To find 8 o'"
for DAC co8r"r V REF
?8o%"# R17
?o6&# D.
D3
V out
= ('V >EF
/ R
) x ID .
/!)#(D3/)#D
7/9)
#(D/3)#(D
%/%!)#(D
!/3)#(D
/!9)# D
7 D
D
% D
!
(D*/!73)J x (' R
)
D
D*
R1 ?o6&#
To find f r of <" "(n; circ'i" 0π L ?H C ?f(r(d#
f r = /!π x √ LC
To find f r of ( H(r"%< O#c circ'i" 0π
L" ?H C ?f(r(d#
f r= /!π x √ L
tC
To find <T in H(r"%< O#c "(n; circ'i" L
1A ?H L
1B ?H
1
2
3
4
5
6
7
8
9
10
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876877
878
879
880
881
CHAPTER BY CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULAS
A B C D E F G H
1
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
%ormula '7-( *D0GE0 0.00002 0.00002 :::::7
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
%ormula '7-) *1?D2,SQRT?E2,F2 6.28 0.0001 3.33E-010 04:4
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
%ormula '7-* *D,E?DGE 0.000000001 5E-010 ::::::::::+++
Lt
= L"
# L5
To find f r of ( Co%3i""# O#c circ'i" 0π L ?H C
T?f(r(d#
f r = /!π x √ L
C
T
To find " T in Co%3i""# O#c "(n; circ C
1 ?f(r(d# C
0 ?f(r(d#
C T = C
x C
!/(C
# C
!)
1
2
3
4
5
6
7
8
9
10
882
883
884
885
886887
888
CHAPTER BY CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULAS
A B C D E F G H
1
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CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
%ormula '7-+ *1?1D51G1E51G1F51 0.000000001 0.0000001 0.0000001 ::::::::::5:
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
%ormula '7- *1??D57,E57,F57,SQRT?4 6.28 3300 0.00000001 15:
3Note: 5ll 0!s = and 5ll "!s = value6
CHAPTER 05 E$c% for&'%( in co%'&n H i#)
%ormula '7- *1?D5,E5,F5 6.28 100000 0.0000001 1250
CHAPTER 05 E#"i&("d "i&in9 for &ono#"(% MV E$c% for&'%( in co%'&n H i#)
%ormula '7-7 *:45,D5:1,E5:1 100000 0.0000001 :::45
CHAPTER 05 E#" "i&in9 for 222 "<3 &ono MV E$c% for&'%( in co%'&n H i#)
%ormula '7-&? *11,D5:7,E5:7 1000000 0.00001 11
CHAPTER 05 E#" "i&in9 in"r8(%# for (#"(% MV E$c% for&'%( in co%'&n H i#)
%ormula '7-&& *:,D5:,E5: 10000 0.00000001 :::::
CHAPTER 05 O3r("in9 fr of (n (#"(% MV E$c% for&'%( in co%'&n H i#)
%ormula '7-&' *1?1+,D51:,E51: 47000 0.00000001 1270
No") If R# * 8(%' (nd C# * 8('#
CHAPTER 05 O3r("in9 fr of (n IC (#"(% MV E$c% for&'%( in co%'&n H i#)
%ormula '7-&( *1?:45,D517,?E517G0,F517 0.000000001 10000 47000 1+5+2
CHAPTER +: Note: No formulas used in this chapter
CHAPTER +1 E$c% for&'%( in co%'&n H i#)
%ormula (&-& 12 1.5 1:2
CHAPTER +1 E$c% for&'%( in co%'&n H i#)
%ormula (&-' *D500E500 7.5 0.015 2::
To find " T in C%(33 O#c "(n; circ'i" C
1 ?f(r(d# C
0 ?f(r(d# C
+ ?f(r(d#
C T = /(/C
# /C
! # /C
%)
To find f rof ( 36(#-#6if" o#ci%%("or 0π R ?o6&# C ?f(r(d#
f r = /!
π
x R x ; x√
3
To find f r of in rid9 o#ci%%("or 0π R ?o6&# C ?f(r(d#
f r = /!
π
x R x ;
R" ?o6&# C ?f(r(d#
' on
= *&3 x RC x ;
R" ?o6&# C ?f(r(d#
' w = & x R
C x ;
R" 1
?o6&# C " 1
?Fd
' = *&. x R x C
R" ?o6&# C ?f(r(d#
f = /&%9 x RC x C
C ?f(r(d# RA ?o6&# R
B ?o6&#
f = /*&3 x C x ( R" + ! x R
5)
To find 8 "o dro33d < 0 in LED circ V S ?8o%"# V
. ?8o%"#
V R
= V 3 * V
D =D515-E515
To find 0 8(%' for 9i8n LED c'rr V 0 ?8o%"# I
. ?(&3#
R = V R
/ I D
3Note: Inowing that 8 0 = 8
S -8
. 6
1
2
3
4
5
67
8
9
10
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULAS
A B C D E F G H
1
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CHAPTER BY CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER +1 E$c% for&'%( in co%'&n H i#)
%ormula (&-( *?D504-E504F504 9 1.5 0.015 2::
To find 0 8(%' for 9i8n LED c'rr V S ?8o%"# V
. ?8o%"# I
. ?(&3#
R = (V 3 * V
D) / I
D
1
2
3
4
5
6
7
8
9
10
925
926
CHAPTER-BY-CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULAS
A B C D E F G H
1
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CHAPTER BY CHAPTER FORMULAS AND SAMPLE EXCEL EQUIVALENT SPREADSHEET FORMULASNOTE: Some of the most-used, more-complex and useful formulas and Excel equivalents are highlighted in yellow
The chapters! text-style formulas in "olumn # are shown in Excel formula format in "olumn "
These same formulas are used as operative formulas in "olumn $, where the formula-computed answers are shown
FORMULAS
./0E"T/ONS: 0eplace sample parameter values shown in columns . through E, %, or 1 with the values for your pro2lem, and your answer appears in "olumn $
CHAPTER = >FORMULA =
EXCEL EQUIVALENT FORMULAS?@CELL ADDRESSES@ APPROACH
PARAMETER HEADIN.SAND THEIR VALUES
ANSERS)Fro& U# of For&'%(#
34se 5pprop 4nits6
CHAPTER +1
%ormula (&-) *D505,E505 100000 (&nn*n) ?Nd 8(%' for E505
3Note: Inowing device spectral response
and amount of received optical power6
CHAPTER +1 To find o3"o-i#o%("or c'rrn" E$c% for&'%( in co%'&n H i#) CTR
%ormula (&-* *D5+7,E5+7 1 0.01 ::1
3Note: "T0 is current transfer ratio6
CHAPTER +1 Po!r 9(in%o## in fir o3"ic c(% E$c% for&'%( in co%'&n H i#)
%ormula (&-+ *1:,LO.?D5+E5+1: 3.33 333 -0:
CHAPTER +1 Find o'"3'" 3o!r of fir o3"ic c% E$c% for&'%( in co%'&n H i#)%ormula (&- *D571,?1:/-0:1: 333 +++E-:15
To find / in 36o"odiod circ'i" R ?o6&# P RCVD
I = R x P >;4D
I . ?(&3#
I C = ;T> x I
D
P o'"
?µ
P in ?
µ
A = * log*
( P out
/ P in)
P in ?µ
P
out = P
in x ( *"/* )
1
2
3
4
5
6
7
8
9
10
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941