Excel Automated Formulas

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 Column B are shown in Excel formula format in Column C. These same formulas are used as operative formulas in Column H, where the formula-computed answers are shown.

FORMULAS

CHAPTER 1 To find force in newtons Excel formula in column H is:

Formula 1-1 =D13*E13*F13/G13^2 1 2 3 2 1.5

CHAPTER 1 To find current in amperes Excel formula in column H is:

Formula 1-2 I=Q/T =D16/E16 5 2 2.5

CHAPTER 2 To find cross-sect. area in circular mils Excel formula in column H is:

Formula 2-1 =D19^2 4 16

CHAPTER 2 To find resistance in ohms Excel formula in column H is:

Formula 2-2 10.4 250 39.75 65.41

CHAPTER 3 To find current in amperes Excel formula in column H is:

Formula 3-1 I = V/R 10 5 2

CHAPTER 3 To find voltage in volts Excel formula in column H is:

Formula 3-2 2 5 10

CHAPTER 3 To find resistance in ohms Excel formula in column H is:

Formula 3-3 R = V/I 10 2 5

CHAPTER 3 To find work in foot pounds Excel formula in column H is:

Formula 3-4 Work (ft lbs)=Force x Distance 100 100 10000

CHAPTER 3 To find power in watts Excel formula in column H is:

Formula 3-5 Power = Energy / Time 100 10 10

CHAPTER 3 To find energy in watthours Excel formula in column H is:

Formula 3-6 Energy (Watthours)= Power x Time 200 3 600


Formula 3-7 10 0.05 0.5


Formula 3-8 0.05 200 0.5

DIRECTIONS: Replace sample parameter values shown in columns D through E, F, or G with the values for your problem, and your answer appears in Column H.

CHAPTER # &FORMULA #

EXCEL EQUIVALENT FORMULAS("CELL ADDRESSES" APPROACH)

PARAMETER HEADINGSAND THEIR VALUES

ANSWERS:From Use of Formulas

(Use Approp. Units)

k (cnstnt) Q1 (coul) Q2 (coul) d (mtr)

F=k x Q1 x Q2/d2

Q (coul) T (sec)

d (mils)

A = d2

r (CM-W/ft) l (feet) A (CM)

R = rl/A =D22*E22/F22

V (volts) R (ohms)

=D25/E25

I (amps) R (ohms)

V = I x R =D28*E28

V (volts) I (amps)

=D31/E31

F (lbs) D (feet)

=D34*E34

E (joules) T (sec)

=D37/E37

P (watts) T (hours)

=D40*E40

V (volts) I (amps)

P = V x I =D43*E43

I (amps) R (ohms)

P = I2x R =D46^2*E46

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FORMULAS






(Use Approp. Units)


Formula 3-9 10 200 0.5

CHAPTER 4 Excel formula in column H is:

Formula 4-1 10 10 10 30


Formula 4-2 =D55/E55 70 2 35


Formula 4-3 0.002 100,000 200


Formula 4-4 4700 17400 50 13.51


Formula 4-5 20 30 10 60


Formula 4-6 40 200 160 400


Formula 5-1 3 1.5 1 5.5


Formula 5-2 22 33 47 0.097


Formula 5-3 10000 27000 20000 5346.53


Formula 5-4 0.1 0.2 0.1 0.4


Formula 5-5 3900 6800 2478.50

V (volts) R (ohms)

P = V2/R =D49^2/E49

To find total R in ohms R1 (ohms) R2 (ohms) R3 (ohms)

RT = R1+R2…+Rn =SUM(D52:F52)

To find total R in ohms VT (volts) IT (amps)

RT = VT / IT

To find V across a specific R IR1 (amps) R1 (ohms)

V1 = IR1 x R1 =D58*E58

To find Vx using V divider rule RX (ohms) RT (ohms) VT (volts)

VX = RX/RT x VT =D61/E61*F61

To find VT in a series circuit V1 (volts) V2 (volts) V3 (volts)

VT = V1 + V2 …+Vn =SUM(D64:F64)

To find PT in a series circuit PR1 (watts) PR2 (watts) PR3 (watts)

PT = P1 + P2 …+ Pn =SUM(D67:F67)

To find IT in a parallel circuit I1 (amps) I2 (amps) I3 (amps)

IT = I1 + I2 + I3 …+In =SUM(D70:F70)

To find GT in a parallel circuit R1 (ohms) R2 (ohms) R3 (ohms)

GT = 1/R1 + 1/R2 …+1/Rn =1/D73+1/E73+1/F73

To find RT in a parallel circuit R1 (ohms) R2 (ohms) R3 (ohms)

RT=1/(1/R1+1/R2+1/R3...1/Rn) =1/(1/D76+1/E76+1/F76)

To find GT in a parallel circuit G1 (S) G2 (S) G3 (S)

GT = G1 + G2 + G3 =SUM(D79:F79)

To find RT in a parallel circuit R1 (ohms) R2 (ohms)

RT = R1 x R2/R1 + R2 =D82*E82/(D82+E82)

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FORMULAS






(Use Approp. Units)


Formula 5-6 10 6 15

To find Ru for a parallel circuit Rk (ohms) Re (ohms)

Ru = Rk x Re/Rk -Re =D85*E85/(D85-E85)

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FORMULAS






(Use Approp. Units)


Formula 5-7 550 1000 0.0055 0.003025


Formula 5-8 10000 11000 0.05 0.02619


Formula 5-9 10000 11000 0.05 0.02381

CHAPTER 6 Ratio expression in column H is:

Formula 6-1 D97*G97=E97*F97 10 20 30 60 Ans. here is 600=600


Formula 6-2 10 20 30 60

CHAPTER 7 To find efficiency of power transfer Excel formula in column H is:

Formula 7-1 8.84 26.6 33.23


Formula 7-2 13 12 100 0.01


Formula 7-3 50 25 25 1


Formula 7-4 25 25 25 50 25


Formula 7-5 25 25 75 2 0.5


Formula 8-1 =((D118*E118)+(E118*F118)+(F118*D118))/D118 3.3 4.7 5.6 18.28

CHAPTER 8 Excel formul in column H is:

Formula 8-2 =((D121*E121)+(E121*F121)+(F121*D121))/E121 3.3 4.7 5.6 12.83

To find IX in a specific branch RT (ohms) RX (ohms) IT (amps)

IX = RT/RX x IT =D88/E88*F88

To find I1 in a parallel circuit R1 (ohms) R2 (ohms) IT (amps)

I1 = R2/R1 + R2 x IT =E91/(D91+E91)*F91

To find I2 in a parallel circuit R1 (ohms) R2 (ohms) IT (amps)

I2 = R1/R1 + R2 x IT =D94/(D94+E94)*F94

To find balanced bridge Rs R1 (ohms) R2 (ohms) R3 (ohms) R4 (ohms)

R1/R2 = R3/R4

To find RX in balanced bridge R1 (ohms) R2 (ohms) R3 (ohms)

RX(R4 here) = R2 x R3/R1 =E100*F100/D100

Pout (watts) Pin (watts)

Efficiency (%) = Pout/Pin x 100 =D103/E103*100

To find internal R of a source V (no-load) V (loaded) I (load A)

rint = V (no-load) - V (loaded)/I (load) =(D106-E106)/F106

To find I load using Thevenin's Th. VTH (volts) RTH (ohms) RL (ohms)

IL = VTH / RTH + RL =D109/(E109+F109)

To find V load using Thevenin's Th. RL (ohms) RL (ohms) RTH (ohms) VTH (v)

VL = RL/RL + RTH x VTH =D112/(E112+F112)*G112

To find I load using Norton's Th. RN (ohms) RN (ohms) RL (ohms) IN (amps)

IL = RN/RN + RL x IN =D115/(E115+F115)*G115

To find RA in delta network R1 (ohms) R2 (ohms) R3 (ohms)

RA= (R1xR2) + (R2xR3) + (R3xR1)/R1

To find RB in delta network R1 (ohms) R2 (ohms) R3 (ohms)

RB = (R1xR2)+(R2xR3)+(R3xR1)/R2

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FORMULAS






(Use Approp. Units)


Formula 8-3 =((D124*E124)+(E124*F124)+(F124*D124))/F124 3.3 4.7 5.6 10.77

To find RC in delta network R1 (ohms) R2 (ohms) R3 (ohms)

RC = (R1xR2)+(R2xR3)+(R3xR1)/R3

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FORMULAS






(Use Approp. Units)


Formula 8-4 =E127*F127/(D127+E127+F127) 18.28 12.83 10.77 3.30


Formula 8-5 =F130*D130/(D130+E130+F130) 18.28 12.83 10.77 4.70


Formula 8-6 =D133*E133/(D133+E133+F133) 18.28 12.83 10.77 5.60

CHAPTER 9 To find force of attract. or repulsion Excel formula in column H is: P1 Strength P2 Strength

Formula 9-1 1 2 0.05 800

CHAPTER 9 To find magnetomotive force Excel formula in column H is:

Formula 9-2 mmf = NI 100 5 500

CHAPTER 9 To find magnetic field intensity Excel formula in column H is: meters

Formula 9-3 5 100 0.1 5000

CHAPTER 9 To find induced voltage per turn Excel formula in column H is:

Formula 9-4 2 1 2

CHAPTER 9 To find induced voltage in coil Excel formula in column H is:

Formula 9-5 100 3 1 300

CHAPTER 10 Note: No formulas used in this chapter

CHAPTER 11 To find time of one period in ac Excel formula in column H is:

Formula 11-1 1000 0.001

CHAPTER 11 To find frequency from time of 1 per. Excel formula in column H is:

Formula 11-2 0.0001 10000

CHAPTER 11 To find effective value from peak Excel formula in column H is:

Formula 11-3 Effective value (rms) = 0.707 x pk. val. 0.707 100 70.7

CHAPTER 11 To find avg. value (1/2 cycle) from pk. Excel formula in column H is:

To find R1 in wye network RA (ohms) RB (ohms) RC (ohms)

R1 = RB x RC/RA + RB + RC


R2 = RC x RA/RA + RB + RC


R3 = RA x RB/RA + RB + RC

d (meters)

Force = Pole 1 Strng. x Pole 2 Strng./d2 =D136*E136/F136^2

N (# of trns) I (amps)

=D139*E139

A (amps) T (turns)

H = AT/meter =D142*E142/F142

Dflux (Wb) Dtime( sec)

Vind = # of lines of flux cut/per unit time =D145/E145

N (# of turns) Dflux (Wb) Dtime( sec)

Vind = N (# of turns) x Dflux/Dtime =D148*E148/F148

f (Hz)

T (sec) = 1/f (Hz) =1/D153

T (time in sec)

f (Hz) = 1/T (sec) =1/D156

V pk. (volts)

=D159*E159

V pk. (volts)

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FORMULAS






(Use Approp. Units)

Formula 11-4 Avg. value (1/2 cycle) = 0.637 x pk. val. 0.637 100 63.7 =D162*E162

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FORMULAS






(Use Approp. Units)

CHAPTER 11 Excel formula in column H is: angle

Formula 11-5 141 30 0.5 70.5

CHAPTER 11 To find % duty cyc. of non-sine waves Excel formula in column H is:

Formula 11-6 4 20 20

CHAPTER 11 Excel formula in column H is: Baseln value duty cycle pk-pk volts

Formula 11-7 2 0.1 5 2.5



Formula 13-1 =D176*E176/F176 500 2 1 1000


Formula 13-2 =D179*E179/F179 10 5 1 50


Formula 13-3 =D182/(E182/F182) 5 12 6 2.5


Formula 13-4 =0.000001257*D185*E185^2*F185/G185 1 2000 0.001 0.01 0.5028


Formula 13-5 =0.000001257*D188^2*E188/F188 2000 0.001 0.01 0.5028


Formula 13-6 = SUM(D191:F191) 10 5 2.5 17.5


Formula 13-7 =1/D194+1/E194+1/F194 10 5 10 0.4


Formula 13-8 =1/(1/D197+1/E197+1/F197) 10 5 10 2.5


To find instant. V of sine wave V pk. (volts) sin qv inst = Vp x sin of angle value =D165*F165

tw (msec) T (msec)

% duty cycle = tw (pulse wid.)/T (1 per.) x 100 =D168/E168*100

To find Vavg of non-sine waves

Vavg = Baseln val. + (duty cycle x p-p amp.) =D171+(E171*F171)

To find V induced in a coil N (# trns) df (Wb) dt (secs)

Vind = N (# of trns) x df /dt

To find VL value of given L L (H) di (amps) dt (secs)

VL = L x di/dt

To find L from VL and di/dt VL (volts) di (amps) dt (secs)

L = VL / di/dt

To find L from physical parameters. mr N (# trns) A (sq mtrs) l (mtrs)

L=12.57 x 10-7x mr x N2 x A / l

To find L of air-core inductor N (# trns) A (sq mtrs) l (mtrs)

L = 12.57 x 10-7 x N2 x A / l

To find LT in a series circuit L1 (H) L2 (H) L3 (H)

LT = L1 + L2 . . . +Ln

To find par. circuit reciprocal of LT L1 (H) L2 (H) L3 (H)

1/LT = 1/L1 + 1/L2 + 1/L3…+1/Ln

To find LT in a parallel circuit L1 (H) L2 (H) L3 (H)

LT = 1 / 1/L1 + 1/L2 + 1/L3…+1/Ln

To find LT of 2 parallel L's L1 (H) L2 (H)

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FORMULAS






(Use Approp. Units)

Formula 13-9 =D200*E200/(D200+E200) 10 10 5LT = L1 x L2 / L1 + L2

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FORMULAS






(Use Approp. Units)

CHAPTER 13 To find amount of stored energy Excel formula in column H is:

Formula 13-10 =D203*E203*F203^2 0.5 20 5 250


Formula 13-11 =D206/E206 10 12 0.83


Formula 13-12 10 10000 0.001 10 0.001


Formula 13-13 6 2200 0.000068 0.05 0.000137


Formula 14-1 =D215*E215*F215 6.28 60 5 1884


Formula 14-2 =D218/(E218*F218) 2000 6.28 1500000 0.000212


Formula 14-3 =D221/(E221*F221) 4000 6.28 0.00003 21231423


Formula 14-4 =1/(D224)+1/(E224)+1/(F224) 2000 4000 6000 0.000917


Formula 14-5 =1/(1/D227+1/E227) 5000 5000 2500


Formula 14-6 =D230*E230/(D230+E230) 5000 5000 2500


Formula 14-7 =D233/E233 3140 50 62.8

CHAPTER 15 Pythagorean Theorem Excel formula in column H is: a b

Formula 15-1 =D236^2+E236^2 10 10 200

L (H) I (amps)

Energy = 0.5 LI2

To find RL circuit time constant L (H) R (ohms)

One time constant = L/R

To find inst. incr. i in an RL circuit Vs (volts) R (ohms) t (sec) L (H)

i = Vs/R x (1 - e-Rt/L) =D209/E209*((1-2.71828^-(E209*F209/G209)))

To find inst. dec. i in an RL circuit Vs (volts) R (ohms) t (sec) L (H)

i = Vs/R x (e-Rt/L) =D212/E212*((2.71828^-(E212*F212/G212)))

To find value of XL in an ac circuit 2p f (Hz) L (H)

XL = 2pfL

To find L ( XL and f known) XL (ohms) 2p f (Hz)

L= XL/2pf

To find frequency (XL and L known) XL (ohms) 2p L (H)

f = XL/2pL

To find 1/XLT in a parallel ac circuit XL1 (ohms) XL2 (ohms) XL3 (ohms)

1/XLT=1/XL1+1/XL2+1/XL3…

To find XLT in a parallel ac circuit XL1 (ohms) XL2 (ohms)

XLT=1/(1/XL1+1/XL2+…)

To find XLT of 2 parallel L's XL1 (ohms) XL2 (ohms)

XLT = XL1 x XL2/XL1 + XL2

To find Q in an RL ac circuit XL (ohms) R (ohms)

Q = XL/R

c2 = a2 + b2

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FORMULAS






(Use Approp. Units)


Formula 15-2 =SQRT(D239^2+E239^2) 10 10 14.14


Formula 15-3 =SQRT(D242^2+E242^2) 5 8.66 10.00


Formula 15-4 =SQRT(D245^2+E245^2) 3 5 5.83


Formula 15-5 =D248*E248/SQRT(D248^2+E248^2) 50 30 25.72

CHAPTER 15 Excel formula in column H is: One

Formula 15-6 =D251/E251 1 1500 0.000667

CHAPTER 15 To find inductive susceptance Excel formula in column H is:

Formula 15-7 =D254/E254 1 1005 0.000995

CHAPTER 15 To find admittance Excel formula in column H is:

Formula 15-8 =D257/E257 1 835 0.001198


Formula 15-9 =SQRT(D260^2+E260^2) 0.000667 0.000995 0.001198

CHAPTER 15 To find magnitude of phase angle Excel formula in column H is:

Formula 15-10 =DEGREES(ATAN(D263/E263)) 1500 1005 56.178

CHAPTER 16 To find mutual inductance Excel formula in column H is: k

Formula 16-1 =D266*SQRT(E266*F266) 1 3 3 3


Formula 16-2 =D269+E269+2*F269 8 8 4 24


Formula 16-3 =D272+E272-2*F272 8 8 4 8

To find VT in a series RL circuit VR (volts) VL (volts)

VT = Ö VR2 + VL

2

To find Z in a series RL circuit R (ohms) XL (ohms)

Z = Ö R2 + XL2

To find IT in a parallel RL circuit IR (amps) IL (amps)

IT = ÖIR2 + IL

2

To find Z in a parallel RL circuit R (ohms) XL (ohms)

Z = R x XL / Ö R2 + XL2

To find G in a parallel RL circuit R (ohms)

G = 1/R

XL (ohms)

BL = 1/XL

Z (ohms)

Y = 1/Z

To find Y in a parallel RL circuit G (S) BL (S)

YT = ÖG2 + BL2

R (ohms) XL (ohms)

q (magnitude) = tan-1 R / XL

L1 (H) L2 (H)

M = k Ö L1 x L2

To find LT of series L's (aid) L1 (H) L2 (H) M (H)

LT = L1 + L2 + 2M

To find LT of series L's (opp) L1 (H) L2 (H) M (H)

LT = L1 + L2 - 2M

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FORMULAS






(Use Approp. Units)

CHAPTER 16 Excel formula in column H is: (aid) 30

Formula 16-4 =D275+E275±2*F275 10 10 5 (opp) 10


Formula 16-5 =1/((1/(D278+F278)+1/(E278+F278))) 8 8 4 6


Formula 16-6 =1/((1/(D281-F281)+1/(E281-F281))) 8 8 4 2

CHAPTER 16 To find coefficient of coupling Excel formula in column H is:

Formula 16-7 =F284/SQRT(D284*E284) 8 8 4 0.5


Formula 16-8 or = D287*G287=E287*F287 20 280 1 14 1


Formula 16-9 or = D290*G290=E290*F290 20 280 1 14 1


Formula 16-10 or = D293*G293 = E293*F293 5 1 0.5 0.1 1


Formula 16-11 or =D296*G296=E296*F296 5 1 0.5 0.1 1


Formula 16-12 or =(D299/E299)^2=F299/G299 1 4 8 128 1


Formula 16-13 =D302*(E302/F302)^2 2000 2 1 8000


Formula 16-14 =SQRT(D305/E305) 1000 10 10

CHAPTER 16 To find transformer efficiency Excel formula in column H is:

General LT formula (aid or opp) L1 (H) L2 (H) M (H)

LT = L1 + L2 ± 2M

To find LT of 2 parallel L's (aid) L1 (H) L2 (H) M (H)

LT = 1/1/L1 + M + 1/L2 + M

To find LT of 2 parallel L's (opp) L1 (H) L2 (H) M (H)

LT = 1/1/L1 - M + 1/L2 - M

L1 (H) L2 (H) M (H)

k = M/ Ö L1 x L2

V ratio compared to T ratio VP (volts) VS (volts) NP (trns) NS(trns)

VP/VS = NP/NS

T ratio compared to V ratio NP (trns) NS (trns) VP (volts) VS(volts)

NP/NS = VP/VS

T ratio compared to I ratio NP (trns) NS (trns) IS (amps) IP (amps)

NP/NS = IS/IP

V ratio compared to I ratio VP (volts) VS (volts) IS (amps) IP (amps)

VP/VS = IS/IP

N ratio compared to Z ratio NS (trns) NP (trns) ZS (ohms) ZP(ohms)

(NS/NP)2 = ZS/ZP

To find ZP from ZS and T ratio ZS (ohms) NP (trns) NS (trns)

ZP = ZS(NP/NS)2

To find T ratio from Z ratio ZP (ohms) ZS (ohms)

NP/NS = Ö ZP/ZS

Pout (watts) Pin (watts)

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290291292

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FORMULAS






(Use Approp. Units)

Formula 16-15 =D308/E308*100 86 100 86


Formula 17-1 =D311/E311 10 2 5


Formula 17-2 =D314*E314 5 2 10


Formula 17-3 V = Q/C =D317/E317 10 5 2

CHAPTER 17 To find energy in joules Excel formula in column H is:

Formula 17-4 =0.5*D320*E320^2 0.000005 250 0.15625

CHAPTER 17 To find dielectric constant Excel formula in column H is:

Formula 17-5 =D323/E323 6 1 6


Formula 17-6 =8.85*D326/(10^12*E326) 0.01 0.001 8.85E-11


Formula 17-7 =8.85*D329*E329/(10^12*F329) 3 0.01 0.001 2.655E-10


Formula 17-8 =2.25*D332*E332/10^7*F332*(G332-1) 100 2 0.005 2 0.009


Formula 17-9 =D335*E335/(D335+E335) 3 6 2


Formula 17-10 =D338/G338 10 10 10 3 3.33


Formula 17-11 =1/(1/D341+1/E341+1/F341) 10 5 10 2.5


Formula 17-12 =D344*E344/F344 60 7.5 15 30

Efficiency % = Pout/Pin x 100

To find C value (Q and V known) Q (coul) V (volts)

C = Q/V

To find Q value (C and V known) C (farads) V (volts)

Q = C x V

To find V value (Q and C known) Q (coul) C (farads)

C (farads) V (volts)

Energy = 0.5 x CV2

eo (abs) ev (vac)

k = eo/ev

To find C (from physical factors) A (sq mtrs) s (mtrs)

C = 8.85 x A/1012s

To find C (from physical factors) k (number) A (sq mtrs) s (mtrs)

C = 8.85 x k x A/1012 x s

To find C in mF (from phys. factors) k (number) A (sq in.) s (in.) n(# plates)

C = 2.25*k*A/107 x s x (n-1)

To find CT of 2 series caps C1 (mF) C2 (mF)

CT = C1 x C2 / C1 + C2

To find CT of = value series C's C1 (mF) C2 (mF) C3 (mF) n(# plates)

CT = C/N

To find CT of any value series C's C1 (mF) C2 (mF) C3 (mF)

CT = 1/1/C1+1/C2+1/C3...+1/Cn

To find VCx in cap V divider circuit VS (volts) CT (uF) CX (mF)

VX = VS x CT/CX

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FORMULAS






(Use Approp. Units)


Formula 17-13 =D347+E347+F347+G347 15 10 10 3 38


Formula 17-14 =D350*E350 1000 0.000001 0.001

CHAPTER 17 Excel formula in column H is: e

Formula 17-15 =D353*((E353^-(F353/G353))) 50 2.71828 10000 10000 18.39

CHAPTER 17 Excel formula in column H is: e

Formula 17-16 =D356*(((1-(E356^-(F356/G356))))) 50 2.71828 18000 10000 41.74


Formula 18-1 =(D359*10^-12)*E359/(F359*10^-6) 100 100 100 0.0001

CHAPTER 18 Excel formula in column H is: 2p

Formula 18-2 =1/(D362*E362*F362) 6.28 120 0.000002 663.48


Formula 18-3 =1/(D365*E365*F365) 6.28 5E-10 1000 318471


Formula 18-4 =1/(D368*E368*F368) 6.28 2000 3180 0.000000025


Formula 18-5 =1/(1/D371+1/E371+1/F371) 1000 2000 3000 545.45


Formula 18-6 =D374*E374/(D374+E374) 1000 2000 666.67


Formula 18-7 =D377/E377 1000 5 200


Formula 19-1 =SQRT(D380^2+E380^2) 50 50 70.71

To find CT of parallel capacitors C1 (mF) C2 (mF) C3 (mF) C4 (mF)

CT = C1 + C2 + C3…+Cn

To find 1 time const. in an RC circuit R (ohms) C (farads)

1 TC (T) = R x C

To find inst. vR in a dc RC circuit VS (volts) t (msec) t (msec)

vR = VS x (e-t/T)

To find inst. vC in a dc RC circuit VS (volts) t (msec) t (msec)

vC = VS x (1 - e-t/T)

To find iC knowing C and dv/dt C (value) dv (volts) dt (sec)

iC = C x dv/dt

To find XC knowing f and C f (Hz) C (farads)

XC = 1/2p x f x C

To find f knowing C and XC C (farads) XC (ohms)

f = 1/2p x C x XC

To find C knowing f and XC f (Hz) XC (ohms)

C = 1/2p x f x XC

To find XCT of parallel C's XC1 (ohms) XC2 (ohms) XC3 (ohms)

XCT = 1/1/XC1 + 1/XC2 + 1/XC3…1/XCn

To find XCT of 2 parallel C's XC1 (ohms) XC2 (ohms)

XCT = XC1 x XC2 / XC1 + XC2

To find XCT of = val. parallel C's XC1 (ohms) N (number)

XCT = XC1 / N

To find VT in a series RC circuit VR (volts) VC (volts)

VT = Ö VR2 + VC

2

A B C D E F G H

1

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345346

347348349350351352

353

354355

356

357358

359360361

362363364

365366367

368369370

371372373

374375376

377378379

380



FORMULAS






(Use Approp. Units)


Formula 19-2 =SQRT(D383^2+E383^2) 50 50 70.71


Formula 19-3 =SQRT(D386^2+E386^2) 15 20 25


Formula 19-4 =D389*E389/SQRT(D389^2+E389^2) 4 3 2.4

CHAPTER 19 Excel formula in column H is: One

Formula 19-5 =D392/E392 1 1500 0.000667

CHAPTER 19 To find capacitive susceptance Excel formula in column H is:

Formula 19-6 =D395/E395 1 995 0.001


Formula 19-7 =SQRT(D398^2+E398^2) 0.000667 0.001 0.0012

CHAPTER 19 To find magnitude of phase angle Excel formula in column H is:

Formula 19-8 =DEGREES(ATAN(D401/E401)) 1500 995 56.44


Formula 20-1 =SQRT(D404^2+E404^2) 60 80 100


Formula 20-2 =SQRT(D409^2+E409^2) 60 80 100.00


Formula 20-3 =D414/E414 80 60 1.33


To find Z in a series RC circuit R (ohms) XC (ohms)

Z = Ö R2 + XC2

To find IT in a parallel RC circuit IR (amps) IC (amps)

IT = Ö IR2 + IC

2

To find Z in a parallel RC circuit R (ohms) XC (ohms)

Z = R x XC / Ö R2 + XC2

To find G in a parallel RC circuit R (ohms)

G = 1/R

Xc (ohms)

BC = 1/XC or 2pfC

To find Y in a parallel RC circuit G (S) BC (S)

YT = ÖG2 + BC2

R (ohms) XC (ohms)

q (magnitude) = tan-1 R / XC

To find Z of a series RLC circuit R (ohms) Xnet (ohms)

Z = Ö R2 + Xnet2

(where Xnet = XL- XC if XL>XC

or Xnet = XC- XL if XC>XL)

To find VT of a series RLC circuit VR (volts) Vxnet(volts)

VT = Ö VR2 + VXnet

2

(where Vxnet=VL- VC if VL>VC

or Vxnet=VC- VL if VC>VL)

To find Tanq knowing Xnet and R Xnet (ohms) R (ohms)

Tang of q = Xnet/R

To find Tanq knowing VXnet and VR VXnet (volts) VR (volts)

A B C D E F G H

1

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381382

383

384385

386

387388

389

390391392393394

395396397

398

399400401402403

404

405406407408

409

410411412413

414415416



FORMULAS






(Use Approp. Units)

Formula 20-4 =D417/E417 80 60 1.33


Formula 20-5 =SQRT(D420^2+E420^2) 2 1 2.24

CHAPTER 20 To find p.f. knowing phase angle Excel formula in column H is:

Formula 20-6 =COS(D425*PI()/180) 45 0.707


Formula 20-7 =D428*E428 141.5 1 141.5


Formula 20-8 =D432^2*E432 1 100 100

Tang of q = VXnet / VR

To find IT of a parallel RLC circuit IR (amps) IXnet (amps)

IT = Ö IR2 + IXnet2

(where Ixnet = IL- IC if IL>IC

or Ixnet = IC- IL if IC>IL)

q (deg)

Power factor (p.f.) = cos q

To find app. power knowing V and I V (volts) I (amps)

Apparent power (S) = Vrms x Irms

To find true power knowing I and R I (amps) R (ohms)

True power (P) = I2 x R

A B C D E F G H

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420

421422423424425426427428429430431432



FORMULAS






(Use Approp. Units)


Formula 20-9 =D435*E435 141.5 0.707 100


Formula 20-10 =D438/E438 100 141.5 0.707


Formula 20-11 =SQRT(D441^2+E441^2) 100 100 141.42

CHAPTER 20 Excel formulas in column H are:

Formula 20-12 =(D444*COS(E444*PI()/180)) 45 30 38.97

(Series circuit) =(D444*SIN(E444*PI()/180)) 22.5

Answer is:


Formula 20-13 =(D450*COS(E450*PI()/180)) 66 60 33

(Series circuit) =(D450*SIN(E450*PI()/180)) 57.16

Answer is:


Formula 20-14 =(D456*COS(E456*PI()/180)) 15 30 12.99

(Parallel circuit) =(D456*SIN(E456*PI()/180)) 7.5

Answer is:

CHAPTER 20 To find inductive susceptance Excel formula in column H is:

Formula 20-15 =1/(D462*E462*F462) 6.28 60 1 0.00265

(Parallel circuit)

CHAPTER 20 To find capacitive susceptance Excel formula in column H is:

Formula 20-16 =D466*E466*F466 6.28 60 0.000004 0.00151

(Parallel circuit)

To find true power knowing S and p.f. S (VA) p.f. (numb.)

P = Apparent power x power factor (p.f.)

To find p.f. knowing P and S Ptrue (W) S (VA)

p.f. = True power (P)/App. power (S)

To find S knowing P and VAR Ptrue (W) Q (VAR)

S = ÖP2 + Q2

To convert Z polar to rect. data Z (ohms) q (deg)

R factor = (Z cos q)

j factor = (Z sin q)

45 Ð30 = (Z cos q) + (jZ sin q)

45 Ð30 = 38.97 + j22.5

To convert VT polar to rect. data VT (volts) q (deg)

Real axis = (VT x cos q)

Imag. axis = (jVT x sin q)

66Ð45 = (VT x cos q) + (jVT x sin q)

66Ð45 = 33 + j57.16

To convert IT polar to rect. data IT (amps) q (deg)

Real axis = (IT x cos q)

Imag. axis = (jIT x sin q)

15Ð30 = (IT x cos q) + (jIT x sin q)

15Ð30 = 12.99 + j7.5

2p f (Hz) L (H)

BL = 1/2p x f x L

2p f (Hz) C (Farads)

BC = 2p x f x C

A B C D E F G H

1

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433434435436437438439440441442443444445446447448449

450

451

452453454455

456

457

458459460461462463464465466467



FORMULAS






(Use Approp. Units)

CHAPTER 20 To find admittance Excel formulas in column H are:

Formula 20-17 =SQRT(D470^2+E470^2) 0.002 0.00114 0.0023

(Parallel circuit) =E470/D470 0.57

=ATAN(H471)*180/pi() 29.7

Answer for Y is:


Formula 21-1 =1/(D477*SQRT(E477*F477)) 6.28 0.0002 4E-10 562983

(Where: L=H; C=Fd; f=Hz)


Formula 21-2 =0.02533/(D481^2*E481) 1000000 2.533E-10 0.0001



Formula 21-3 =0.02533/(D485^2*E485) 1000000 0.0001 2.533E-10



Formula 21-4 =25330/(D489^2*E489) 1 253.3 100


Formula 21-5 =25330/(D493^2*E493) 1 100 253.3

CHAPTER 21 Information only!

Formula 21-6 No computations for this formula are required in text!

CHAPTER 21 To find bandwidth of res. circuit Excel formula in column H is:

Formula 21-7 =D500 - E500 1010000 990000 20000


G (S) Bnet (S)

Y = Ö G2 + jBnet2

(Note: tan of q = B/G)

(Note: q of Y = arctan B/G)

Y = 0.0023 Ð-29.7°S

To find fr when L and C are known 2p L (H) C (Fd)

fr = 1/2p x Ö L x C

To find L when fr and C are known fr (Hz) C (Fd)

L = 0.02533/fr2 x C

To find C when fr and L are known fr (Hz) L (H)

C = 0.02533/fr2 x L

To find L when fr and C are known fr (MHz) C (pF)

L = 25,330/fr2 x C

Where: L=mH; C=pF;f=MHz

To find C when fr and L are known fr (MHz) L (mH)

C = 25,330/fr2 x L

Where: L=mH; C=pF;f=MHz

f2 (Hz) f1 (Hz)

BW = f2 - f1

(Where f2= higher f 0.707 pt

and f1 = lower f 0.707 pt)

To find BW knowing fr and Q fr (Hz) Q (number)

A B C D E F G H

1

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10

468469

470471472473474475476

477478479480

481

482483484

485

486487488

489

490491492

493

494495496497498499500501502503504



FORMULAS






(Use Approp. Units)

Formula 21-8 =D505/E505 5000 25 200BW = fr/Q

A B C D E F G H

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505



FORMULAS






(Use Approp. Units)


Formula 21-9 =D508/E508 5000 200 25


Formula 21-10 =1/(D511*E511*F511) 6.28 1000 0.0000001 1592.36

(Note: For hi-pass simple C filter)


Formula 21-11 =1/(D515*(E515/F515)) 6.28 0.1 1000 1592.36

(Note: For lo-pass simple L filter)

CHAPTER 22 To find max # of electrons in shell n Excel formula in column H is: n

Formula 22-1 =2*D519^2 3 18


Formula 23-1 =(D522-E522)/F522 10 0.7 150 0.062

CHAPTER 23 To find diode power dissipation Excel formula in column H is:

Formula 23-2 =D525*E525 0.01 0.7 0.007

CHAPTER 23 To find zener diode pwr. dissipation Excel formula in column H is:

Formula 23-3 =D528*E528 0.05 5.1 0.255

CHAPTER 23 To find regulation transition point Excel formula in column H is:

Formula 23-4 =D531*(E531+F531)/F531 9.1 100 750 10.31


Formula 23-5 =D534*E534/(E534+F534) 9 750 100 7.94


Formula 23-6 =D537-E537 12 1.5 10.5


Formula 24-1 =0.45*D540 70.7 31.8

To find Q knowing fr and BW fr (Hz) BW (Hz)

Q = fr/BW

To find cutoff for RC network 2p R (ohms) C (Farads)

fc = 1/2p x R x C

To find cutoff for RL network 2p L (H) R (ohms)

fc = 1/2p x (L/R)

Max # of electrons = 2 x n2

To find I in circ. w/series diode and R VS (volts) VD (volts) R (ohms)

I = (VS - VD) / R

I (amps) VD

P = I x VD

Iz (amps) Vz (volts)

P = Iz x Vz

VzT R1 (ohms) RL (ohms)

Vs = VzT x (R1 + RL) / RL

To find output V w/source <trans. pt. Vs (volts) RL (ohms) R1 (ohms)

VL = Vs x RL / (RL + R1)

To find V to be dropped by VR Vs (volts) VD (volts)

VR = Vs - VD

To find Vdc out of unfilt. H.W. rect. Vrms (volts)

Vdc = 0.45 x Vrms

A B C D E F G H

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506507

508509510511512513514515516517518519520521

522523524

525526527528529530

531532533

534535536

537538539540541



FORMULAS






(Use Approp. Units)


Formula 24-2 =0.318*D543 100 31.8

To find Vdc out of unfilt. H.W. rect. VPK (volts)

Vdc = 0.318 x VPK

A B C D E F G H

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FORMULAS






(Use Approp. Units)

CHAPTER 24 To find PIV of unfilt. H.W. rect. Excel formula in column H is:

Formula 24-3 =1.414*D546 200 282.8

CHAPTER 24 To find ripple freq. H.W. rect. Excel formula in column H is:

Formula 24-4 Ripple freq. = ac input frequency =1*D549 60 60


Formula 24-5 =0.9*D552 100 90


Formula 24-6 =0.45*D555 200 90


Formula 24-7 =0.637*D558 141.4 90.1


Formula 24-8 =0.318*D561 282.8 89.9

CHAPTER 24 To find PIV of unfilt. F.W. rect. Excel formula in column H is:

Formula 24-9 =1.414*D564 200 282.8

CHAPTER 24 To find ripple freq. F.W. rect. Excel formula in column H is:

Formula 24-10 Ripple freq. = 2 x ac input frequency =2*D567 60 120


Formula 24-11 =0.9*D570 12.6 11.34


Formula 24-12 =0.637*D573 17.8 11.34

CHAPTER 24 To find PIV of unfilt. bridge rect. Excel formula in column H is:

Formula 24-13 =1.414*D576 200 282.8

CHAPTER 24 To find ripple freq. (bridge rect.) Excel formula in column H is:

Formula 24-14 =2*D579 60 120

Vrms (V)

PIV (H.W.) = 1.414 x Vrms

ac input f

To find Vdc out of unfilt. F.W. rect. V (1/2 sec.)

Vdc = 0.9 x Vrms of half of secondary

To find Vdc out of unfilt. F.W. rect. V (full sec.)

Vdc = 0.45 x Vrms of full secondary

To find Vdc out of unfilt. F.W. rect. VPK (1/2 sec.)

Vdc = 0.637 x VPK of 1/2 secondary

To find Vdc out of unfilt. F.W. rect. VPK (full sec.)

Vdc = 0.318 x VPK of full secondary

V (Full sec.)

PIV (F.W.) = 1.414 x Vrms full secondary

ac input f

To find Vdc out (unfilt. bridge rect.) Vrms input

Vdc = 0.9 x Vrms of ac input

To find Vdc out (unfilt. bridge rect.) Vpk input

Vdc = 0.637 x VPK of ac input

Vrms input

PIV (Bridge) = 1.414 x Vrms input

ac input f

Ripple frequency (bridge) = 2 x ac in f

A B C D E F G H

1

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544545546547548549550551552553554555556557

558559560561562563564565566567568569570571572573574575576577578579580



FORMULAS






(Use Approp. Units)

CHAPTER 24 To find power supply out % ripple Excel formula in column H is: ac ripple p-p dc out

Formula 24-15 % Ripple = ac(ripple p-p)/dc out x 100 =D582/E582*100 1 48 2.08

A B C D E F G H

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FORMULAS






(Use Approp. Units)

CHAPTER 24 To find power supply % regulation Excel formula in column H is:

Formula 24-16 =(D585-E585)/E585*100 12.2 11.8 3.39


Formula 24-17 =(D588*E588)+F588*(E588-G588) 0.0044 24 0.15 15 1.46


Formula 24-18 =D591/(D591+E591)*100 2.25 1.446 60.88

CHAPTER 24 To find regulated dc output voltage Excel formula in column H is:

Formula 24-19 =D594*(1+E594/F594) 1.25 240 240 2.5


Formula 24-20 =D597/(D597+E597) 50 50 0.5

CHAPTER 24 Excel formula in column H is: D value

Formula 24-21 =D600*E600 24 0.5 12


Formula 24-22 =D603/(1-E603) 24 0.5 48.00


Formula 24-23 =-D606*E606/(1-E606) 24 0.5 -24

CHAPTER 25 To find transistor emitter current Excel formula in column H is:

Formula 25-1 =D609+E609 18 0.001 18.001

CHAPTER 25 To find dc Beta of transistor Excel formula in column H is:

Formula 25-2 =D612/E612 1.2 0.024 50

CHAPTER 25 To find collector current Excel formula in column H is:

Formula 25-3 =D615*E615 50 0.024 1.2

CHAPTER 25 To find base current Excel formula in column H is:

Formula 25-4 =D618/E618 1.2 50 0.024

VNL(volts) VFL(volts)

% Reg. = (VNL- VFL)/ VFL x 100%

To find power diss. by IC regulator IB (amps) VIN (V) IL (amps) VOUT (V)

PREG = IB x VIN + IL x (VIN -VOUT )

To find efficiency of IC regulator Pout (W) Preg (W)

h = Pout / (Pout + Preg) x 100%

Vref (V) R2 (ohms) R1 (ohms)

Vout = Vref x (1+R2 / R1 )

To find D factor for "buck" reg. Ton (msec) Toff (msec)

D = Ton / (Ton + Toff)

To find Vout of a "buck" reg. Vin (volts)

Vout = Vin x D

To find Vout of a "boost" reg. Vin (volts)

Vout = Vin /(1-D)

To find Vout of a "flyback" reg. Vin (volts)

Vout = -Vin x D/(1-D)

IC (mA) IB (mA)

IE = IC + IB

IC (mA) IB (mA)

bdc = IC/IB

βdc IB (mA)

IC = bdc x IB

IC (mA) βdc

IB = IC / bdc

A B C D E F G H

1

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583584

585586587

588589590591592593594595596597598599600601602603604605606607608

609610611

612613614

615616617

618



FORMULAS






(Use Approp. Units)

CHAPTER 25 To find Alpha of transistor Excel formula in column H is:

Formula 25-5 =D621/E621 9.8 10 0.98

CHAPTER 25 To find ac Beta (curr. gain) of trans. Excel formula in column H is:

Formula 25-6 =D624/E624 2 0.04 50

CHAPTER 26 To find voltage gain of amplifier Excel formula in column H is:

Formula 26-1 =D627/E627 1.2 0.05 24

CHAPTER 26 To find current gain of amplifier Excel formula in column H is:

Formula 26-2 =D630/E630 10 0.5 20

CHAPTER 26 To find power gain of an amplifier Excel formula in column H is:

Formula 26-3 =D633*E633 24 20 480


Formula 26-4 =D636*F636/(E636+F636) 12 12000 2000 1.71


Formula 26-5 =(D639-E639)/F639 1.714 0.7 1000 0.001014

CHAPTER 26 To find collector-emitter voltage Excel formula in column H is:

Formula 26-6 =D642-(E642*(F642+G642)) 12 1.014 3.9 1 7.03

CHAPTER 26 To find dynamic emitter resistance Excel formula in column H is: (mV)

Formula 26-7 =D645/E645 25 1.014 24.65

CHAPTER 26 To find input impedance Excel formula in column H is: Beta

Formula 26-8 =1/(1/D648+1/E648+(1/(F648+1)))*G648 12000 2000 100 24.65 2351.13

CHAPTER 26 Approximation of output impedance Excel formula in column H is:

Formula 26-9 =D651 3000 3000

CHAPTER 26 Approximation of voltage gain Excel formula in column H is:

Formula 26-10 =-D654/E654 3900 24.65 -158.22

IC (mA) IE (mA)

a = IC / IE

D IC (mA) D IB (mA)

bac = DIC / DIB

Vout (Vpp) Vin (Vpp)

AV = Vout / Vin

Iout (Ipp) Iin (Ipp)

AI = Iout / Iin

AV AI

AP = AV x AI

To find base V with V divider bias VCC (volts) R1 (ohms) R2 (ohms)

VB»VTH = Vcc x R2 / (R1 + R2)

To find emitter curr. with V div. bias VB (volts) VBE (volts) RE (ohms)

IE = (VB - VBE) / RE

VCC (volts) IE (mA) RC (k W) RE (k W)

VCE = VCC - IE x (RC + RE)

IE (mA)

re' = 25 mV / IE

R1 (ohms) R2 (ohms) re' (ohms)

ZIN = R1|| R2|| (Beta +1) x re'

RC (ohms)

ZOUT = RC

RC (ohms) re' (ohms)

AV = -RC / re'

A B C D E F G H

1

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619620

621622623

624625626

627628629

630631632

633634635

636637638

639640641

642643644

645646647

648649650

651652653

654



FORMULAS






(Use Approp. Units)

CHAPTER 26 Approximation of current gain Excel formula in column H is:

Formula 26-11 =D657*(E657*F657/(E657+F657))/ 100 12000 2000 24.65 40.78

((E657*F657/(E657+F657))+(D657+1)*G657

b R1 (ohms) R2 (ohms) re' (ohms)

Ai=b(R1||R2)/(R1||R2)+(b +1)re'

A B C D E F G H

1

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655656657658



FORMULAS






(Use Approp. Units)

CHAPTER 26 Approximation of input impedance Excel formula in column H is:

Formula 26-12 =1/(1/E661+1/F661+(1/((D661+1)*(G661)))) 100 12000 2000 1024.65 1686.35

CHAPTER 26 Approximation of output impedance Excel formula in column H is:

Formula 26-13 =D664 3900 3900

CHAPTER 26 Approximation of voltage gain Excel formula in column H is:

Formula 26-14 =-D667/(E667+F667) 3900 24.65 1000 -3.81

CHAPTER 26 Approximation of current gain Excel formula in column H is:

Formula 26-15 =D670*(E670*F670/(E670+F670))/ 100 12000 2000 1024.65 1.63

((E670*F670/(E670+F670))+(D670+1)*(G670))

CHAPTER 26 Approx. gain of multistage amplifier Excel formula in column H is: ---

Formula 26-16 =D674*E674*F674 10 50 50 25000


Formula 26-17 =1/(1/D681+1/E681+(1/((F681+1)*G681))) 12000 2000 100 1024 1686.33


Formula 26-18 =1/(1/D684+1/E684) 500 24.65 23.49

CHAPTER 26 To approx. v. gain of CC amplifier Excel formula in column H is:

Formula 26-19 =D687/(E687+F687) 1000 24.65 1000 0.98

CHAPTER 26 To approx. curr. gain of CC amplifier Excel formula in column H is: b

Formula 26-20 =-D691 100 -100


Formula 26-21 =D694*E694/(D694+E694) 1000 24.65 24.06

b R1 (ohms) R2 (ohms) (re' +RE1)

ZIN = R1|| R2|| (Beta +1) x (re'+RE1))

RC (ohms)

ZOUT = RC

RC (ohms) re' (ohms) RE1 (ohms)

AV » -RC / (re' + RE1 )

b R1 (ohms) R2 (ohms) (re' +RE1)

Ai»b(R1||R2)/(R1||R2)+(b +1)x(re'+RE1)

AV1 AV2 AV3

AV = AV1 x AV2 x AV3 …

where: AV1 = Zin1/(Zin1 + Zs)

AV2 is the gain of first amplifier

AV3 = Zin2/(Zin2 + Zout1)

AV4 is gain of 2nd amp…

To approximate ZIN for CC amplifier R1 (ohms) R2 (ohms) b re' + RE W

ZIN = R1||R2|| ((b +1) x (re' +RE))

To approximate Zout for CC amplifier RE (ohms) re' (ohms)

ZOUT = RE || re'

RE (ohms) re' (ohms) RE (ohms)

AV = RE/(re' + RE)

Note: AV»1

Ai » -b

To find approx Zin of CB amplifier RE (ohms) re' (ohms)

ZIN = RE || re'

A B C D E F G H

1

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659660

661662663

664665666

667668669

670671672673

674

675676677678679680

681682683

684685686

687

688689690691692693

694



FORMULAS






(Use Approp. Units)


Formula 26-22 =D697 3900 3900

CHAPTER 26 To approx. v. gain of CB amplifier Excel formula in column H is:

Formula 26-23 =D700/E700 3900 24.65 158.22

CHAPTER 26 To approx. current gain of CB amp Excel formula in column H is:

Formula 26-24 =D703 -1 -1


Formula 26-25 =D706 12 12


Formula 26-26 =D709/(E709+F709) 12 3900 1000 0.00245

CHAPTER 27 To find drain curr JFETs & MOSFETs

Formula 27-1

(NOTE: Shockley's equation, shown here for information only!)

CHAPTER 27 To find transconductance of FET Excel formula in column H is:

Formula 27-2 =D716/E716 0.002 3 0.000667


Formula 27-3 =D719 5 5

(Note: Using fixed bias)


Formula 27-4 =D723-(E723*F723) 12 0.005 1000 7

(Note: Using fixed bias)


Formula 27-5 =-D727*E727 0.004 1000 -4

(Note: Using self bias)


To find approx Zout of CB amplifier RC (ohms)

ZOUT = RC

RC (ohms) re' (ohms)

AV = RC / re'

AI

Ai » -1

To define VCE at cutoff condition VCC (volts)

VCE = VCC

To find IC value at saturation VCC (volts) RC (ohms) RE (ohms)

IC(sat) = VCC/(RC + RE)

ID=IDSS(1-(VGS/VGS(off) ))2

D ID (amps) D VGS(V)

gm = D ID / D VGS

To find JFET gate to source V VGG (volts)

VGS = VGG

To find JFET drain to source V VDD (volts) ID (amps) RD (ohms)

VDS = VDD - ID x RD

To find JFET gate to source V ID (amps) RS (ohms)

VGS = - ID x RS

To find JFET drain to source V VDD (volts) ID (amps) RD (ohms) RS (ohms)

A B C D E F G H

1

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10

695696

697698699

700701702

703704705

706707708

709710711

712

713714715

716717718

719720721722

723724725726

727728729730



FORMULAS






(Use Approp. Units)

Formula 27-6 =D731-(E731*F731)-(E731*G731) 18 0.01 1000 390 4.1

(Note: Using self and V div. bias)

CHAPTER 27 To find JFET gate voltage Excel formula in column H is:

Formula 27-7 =D735*F735/(E735+F735) 12 100000 33000 2.98

(Note: Using voltage div. bias)

CHAPTER 27 To find JFET gate to source V Excel formula in column H is:

Formula 27-8 =D739-(E739*F739) 2.98 0.0085 470 -1.02

(Note: Using V divider bias)

CHAPTER 27 To find E-MOSFET drain curr.

Formula 27-9

(NOTE: Shockley's equation, shown here for information only!)

CHAPTER 27 To find FET power dissipation Excel formula in column H is:

Formula 27-10 =D747*E747 0.12 1.3 0.156


Formula 28-1 =-D750*E750 50000 0.0002 -10

(open loop) (Note: Inverting input)


Formula 28-2 =D754*E754 50000 0.0002 10

(open loop) (Note: Non-inverting input)


Formula 28-3 =D758*(E758-F758) 50000 0.002 0.0015 25

(open loop) (Note: Differential amp circuit config.)


Formula 28-4 =D762/E762 -15 2 -7.5

(Note: Assuming infinite input z)


Formula 28-5 =-(D766/E766) 27000 1800 -15

(Note: Closed loop V gain)

VDS = VDD - ID x RD - ID x RS

VDD (volts) R1 (ohms) R2 (ohms)

VG = VDD x R2 / (R1 + R2)

VG (volts) ID (amps) RS (ohms)

VGS = VG - ID x RS

ID = k x (VGS - VT)2

VDS (volts) ID (amps)

PFET = VDS x ID

To find op-amp output V AVOL Vin (volts)

Vout = - AVOL x Vin

To find op-amp output V AVOL Vin (volts)

Vout = AVOL x Vin

To find op-amp output V AVOL V1 (volts) V2 (volts)

Vout = AVOL x (V1 - V2)

To find inv. op-amp V gain Vout (volts) Vin (volts)

AV = Vout / Vin

To find inv. op-amp V gain Rf (ohms) Ri (ohms)

AV = -Rf / Ri

A B C D E F G H

1

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10

731732733734

735736737738

739740741742

743

744745746

747748749750751752753754755756757758759760761

762763764765

766767



FORMULAS






(Use Approp. Units)


Formula 28-6 =(D770/E770)+1 13000 1000 14


Formula 28-7 =(E773/D773+1)*((G773/(G773+F773))) 10000 50000 20000 10000 2

To find non-inv. op-amp V gain Rf (ohms) Ri (ohms)

AV = (Rf / Ri) + 1

To find V gain of V div. non-inv. amp. R1 (ohms) R2 (ohms) R3 (ohms) R4 (ohms)

AV=[(R2/R1)+1] x [R4/(R4 + R3)]

A B C D E F G H

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768769

770771772773



FORMULAS






(Use Approp. Units)


Formula 28-8 =D776*(F776/E776+1)*(E778/(E778+D778))+ 6 10000 10000 2 4

G776*(-F776/E776)

5000 5000


Formula 28-9 =D781-E781 -5 2 -7

(Note: Simplified formula when


Formula 28-10 =D786*(-E786/E786)+F786*(-E786/E786) 2 10000 3 -5

(Note: For inverting amplifier with all R's equal value)


Formula 28-11 D790*(-F792/G790)+(E790)*(-F792/D792)+(F790)* 5 5 5 5000 -2.5

(-F792/E792)

10000 5000 1000


Formula 28-12 =(1+E795/D795)*(D797*(G795/(F795+G795))+ 10000 20000 10000 20000 5.5

E797*F795/(F795+G795))

1.5 2.5

CHAPTER 28 Excel formula in column H is: - V in

Formula 28-13 =D800/(E800*F800)*G800 -3 1000 0.01 5 -1.5


Formula 28-14 =(D803*E803)*(F803/G803) -1000 0.01 0.5 1 -5


Formula 28-15 =(1+2*D806/E806)*(F806-G806) 10000 5000 2 0.5 7.5

CHAPTER 28 To find upper thresh. pt. of Sch. trig. Excel formula in column H is:

Formula 28-16 =D809*(E809/(E809+F809)) 12 10000 100000 1.09

To find V out of subtractor circuit Vin+ (volts) R1 (ohms) R2 (ohms) Vin- (volts)

Vout=Vin+x((R2/R1)+1)x(R4/(R4+R3))+

Vin- x (-R2/R1) R3 (ohms) R4 (ohms)

To find V out of subtractor circuit Vin+ (volts) Vin- (volts)

Vout = Vin+ - Vin-

R1=R2=R3=R4)

To find V out of summing amplifier Vin1 (volts) Rf&R1&R2 Vin2 (volts)

Vout=Vin1 x (-Rf/R1)+Vin2 x (-Rf/R2)

To find V out of summing amplifier Vin1 (volts) Vin2 (volts) Vin3 (volts) R1 (ohms)

Vout=Vin1 x (-Rf/R1)+Vin2 x (-Rf/R2) +

Vin3 x (-Rf/R3) R2 (ohms) R3 (ohms) Rf (ohms)

(Note: 3-input inverting amp with R1 and R3 of equal value)

To find V out of summing amplifier R1 (ohms) R2 (ohms) R3 (ohms) R4 (ohms)

Vout = (1+R2/R1) x [Vin1xR4/(R3+R4)] +

Vin2 x R3/(R3 + R4)] Vin1 (volts) Vin2 (volts)

To find V out. change for integ. circ. R (ohms) C (mF) D t (msec)

DVout = [-Vin / (R x C)] x Dt

To find V out. for differentiator circ. R (ohms) C (mF) D Vin (V) D t (msec)

Vout = (-R x C) x (DVin/Dt)

To find V output of instrum. amp. R (ohms) RG (ohms) V2 (volts) V1 (volts)

Vout = (1 + 2 x R/RG) x (V2 - V1)

Vmax (volts) R1 (ohms) R2 (ohms)

UTP = Vmax x [R1/(R1 + R2)]

A B C D E F G H

1

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10

774775776777778779780781782783784785

786787788789

790

791

792793794795796797798799800801802803804805

806807808809810



FORMULAS






(Use Approp. Units)

CHAPTER 28 To find lower thresh. pt. of Sch. trig. Excel formula in column H is:

Formula 28-17 =D812*(E812/(E812+F812)) -12 10000 100000 -1.09


Formula 28-18 =(D815*E815)/SQRT((F815+E815)^2+(G815)^2)* 0.1 2000 8000 723.4 0.397

(20*D817)/SQRT(D817^2+E817^2)

(Note: R1A and R1B = input signal potentiometer) 8 0.7234

CHAPTER 28 Excel formula in column H is: k

Formula 28-19 =(D820-E820)*F820*(G820*D822) 0.2 0.15 20 0.000486 4.86

10000


Formula 28-20 =D825*E825 0.000486 10000 4.86

where:


Formula 28-21 =D830*E830 -0.000486 10000 -4.86


Formula 28-22 =1/(D833*E833*F833) 6.28 1000 0.000001 159.24


Formula 28-23 =D836*E836/SQRT(F836^2+E836^2)* 1 10000 10000 10000 1.414

(1+G836/D838)

10000


Formula 28-24 =1/(D841*E841*F841) 6.28 10000 2.2E-09 7238


Formula 28-25 =D844*(E844/SQRT(E844^2+F844^2)) 1 10000 10000 10000 1.414

*(1+G844/D846))

10000

Vmin (volts) R1 (ohms) R2 (ohms)

LTP = Vmin x [R1/(R1 + R2)]

To find output V of IC audio amplifier Vin (volts) R1B (ohms) R1A (ohms) jXC1 (ohms)

Vout = Vin x [R1B / (R1A+R1B-jXC1)]

x 20 x [RSPK) / (RSPK-jXC2 )] RSPK (ohms) jXC2 (ohms)

To find Vout of OTA diff. amplifier V1 (volts) V2 (volts) IBIAS (amps)

Vout = (V1 - V2) x k x IBIAS x RL

RL(ohms)

To find UTP V for Sch. trig. comp. IBIAS (amps) R1 (ohms)

UTP = IBIAS x R1

IBIAS = VBIAS - V - - 0.7/RBIAS

To find LTP V for Sch. trig. comp. IBIAS (amps) R1 (ohms)

LTP = -IBIAS x R1

To find fC of 1st order low-pass filter 2 p R (ohms) C (farads)

fc = 1/(2p x R x C)

To find Vout of 1st order low-pass filt. Vin (volts) - j XC R (ohms) R2 (ohms)

Vout = Vin x [-jXC/(R-jXC)] x (1+R2/R1)

R1 (ohms)

To find fC of 1st order hi-pass filter 2 p R (ohms) C (farads)

fc = 1/(2p x R x C)

To find Vout of 1st order hi-pass filt. Vin (volts) R (ohms) - j XC R2 (ohms)

Vout = Vin x [R/(R - jXC)] x (1+R2/R1)

R1 (ohms)

A B C D E F G H

1

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10

811812813814815816817818819

820

821822823824825826827828829830831832833834835836837838839840841842843

844

845846847



FORMULAS






(Use Approp. Units)


Formula 28-26 =1/(6.28*SQRT(D849*E849/(D849+E849)* 1000 1000 20000 0.00000001 7345

F849*G849*D851))

4.7E-09

CHAPTER 28 To find the BW of bandpass filter Excel formula in column H is: Q

Formula 28-27 =D854/E854 7345 3.16 2324


Formula 28-28 =D857-(E857/2) 7345 2324 6183


Formula 28-29 =D860+(E860/2) 7345 2324 8507


Formula 28-30 =1/(6.28*SQRT(D863*E863*F863*G863)) 1000 20000 0.00000001 0.00000001 3561

CHAPTER 28 To find digit. dec. value for ADC circ. Excel formula in column H is:

Formula 28-31 =D866*(255/5) 2 102


Formula 28-32 =(-D869/E869)*((F869/2)+(G869/4)+(D871/8) 10 10000 1 0 5.390625

+(E871/16)+(F871/32)+(G871/64)+(D873/128)

+(E873/256))*(-F873) 0 0 1 0

1 0 10000






Formula 29-3 =D882+E882 0.00002 0.00002 0.00004


To find center f of bandpass filter R1 (ohms) R2 (ohms) R3 (ohms) C1 (farads)

fo=1/2p xÖ[R1xR2/(R1+R2)]xR3xC1xC2)

C2 (farads)

fo (Hz)

BW = fo/Q

To find low cutoff f of bandpass filter fo (Hz) BW (Hz)

fc1 = fo - BW/2

To find upper cutoff f of bandps. filt. fo (Hz) BW (Hz)

fc2 = fo + BW/2

To find center f of bandstop filter R1 (ohms) R2 (ohms) C1 (farads) C2 (farads)

fo = 1/(2p x Ö R1 x R2 x C1 x C2 )

Vin1 (volts)

DATA = Vin1 x (255/5 V) dec. rep.

To find Vout for DAC coverter VREF (volts) R14 (ohms) D7 D6

Vout = (-VREF/R14) x [D 7 /2)+(D6/4)+D5/8)

+(D4/16)+(D3/32)+(D2/64)+(D1/128)+ D5 D4 D3 D2

(D0/256)] x (- R1)

D1 D0 R1 (ohms)

To find fr of LC tank circuit 2p L (H) C (farads)

fr = 1/2p x Ö LC

To find fr of a Hartley Osc. circuit 2p Lt (H) C (farads)

fr = 1/2p x Ö LtC

To find LT in Hartley Osc. tank circuit L1A (H) L1B (H)

Lt = L1A + L1B

To find fr of a Colpitts Osc. circuit 2p L (H) CT (farads)

A B C D E F G H

1

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10

848849850851852853854855856857858859860861862863864865866867868869870871872873874875

876877878

879880881882883884



FORMULAS






(Use Approp. Units)

Formula 29-4 =1/(D885*SQRT(E885*F885)) 6.28 0.0001 3.33E-10 872606


Formula 29-5 =D888*E888/(D888+E888) 0.000000001 5E-10 0.000000000333

fr = 1/2p x Ö L1CT

To find CT in Colpitts Osc. tank circ. C1 (farads) C2 (farads)

CT = C1 x C2/(C1 + C2)

A B C D E F G H

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885886887888



FORMULAS






(Use Approp. Units)


Formula 29-6 =1/(1/D891+1/E891+1/F891) 0.000000001 0.0000001 0.0000001 0.000000000980


Formula 29-7 =1/((D894*E894*F894*SQRT(6))) 6.28 3300 0.00000001 1970

(Note: All R's = and All C's = value)


Formula 29-8 =1/(D898*E898*F898) 6.28 100000 0.0000001 15.92

CHAPTER 29 Estimated timing for monostable MV Excel formula in column H is:

Formula 29-9 =0.69*D901*E901 100000 0.0000001 0.0069

CHAPTER 29 Est. timing for 555 type mono. MV Excel formula in column H is:

Formula 29-10 =1.1*D904*E904 1000000 0.00001 11

CHAPTER 29 Est. timing intervals for astable MV Excel formula in column H is:

Formula 29-11 =0.7*D907*E907 10000 0.00000001 0.00007

CHAPTER 29 Operating freq. of an astable MV Excel formula in column H is:

Formula 29-12 =1/(1.38*D910*E910) 47000 0.00000001 1542

Note: If R's = value and C's = vaues

CHAPTER 29 Operating freq. of an IC astable MV Excel formula in column H is:

Formula 29-13 =1/(0.69*D914*(E914+2*F914)) 0.000000001 10000 47000 13935



Formula 31-1 12 1.5 10.5


Formula 31-2 =D922/E922 7.5 0.015 500


To find CT in Clapp Osc. tank circuit C1 (farads) C2 (farads) C3 (farads)

CT = 1/(1/C1 + 1/C2 + 1/C3)

To find fr of a phase-shift oscillator 2p R (ohms) C (farads)

fr = 1/2p x R x C x Ö 6

To find fr of Wien bridge oscillator 2p R (ohms) C (farads)

fr = 1/2p x R x C

RC (ohms) C (farads)

ton = 0.69 x RC x C


tw = 1.1 x RC x C

RC1 (ohms) CC1 (Fd)

t = 0.7 x R x C


f = 1/1.38 x RC x C

C (farads) RA (ohms) RB (ohms)

f = 1/0.69 x C x (RA + 2 x RB)

To find V to be dropped by R in LED circ. VS (volts) VD (volts)

VR = VS - VD =D919-E919

To find R value for given LED curr. VR (volts) ID (amps)

R = VR / ID

(Note: Knowing that VR = VS-VD)

To find R value for given LED curr. VS (volts) VD (volts) ID (amps)

A B C D E F G H

1

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10

889890891892893

894895896897898899900

901902903

904905906907908909

910911912913914915916917918

919920921

922

923924925



FORMULAS






(Use Approp. Units)

Formula 31-3 =(D926-E926)/F926 9 1.5 0.015 500R = (VS - VD) / ID

A B C D E F G H

1

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926



FORMULAS






(Use Approp. Units)

CHAPTER 31

Formula 31-4 =D929*E929 100000 (unknown) (Need value for E929)

(Note: Knowing device spectral response

and amount of received optical power)

CHAPTER 31 To find opto-isolator current Excel formula in column H is: CTR

Formula 31-5 =D934*E934 1 0.01 0.01

(Note: CTR is current transfer ratio)

CHAPTER 31 Power gain/loss in fiber optic cable Excel formula in column H is:

Formula 31-6 =10*LOG(D938/E938,10) 3.33 333 -20

CHAPTER 31 Find output power of fiber optic cbl. Excel formula in column H is:

Formula 31-7 =D941*(10^-20/10) 333 3.33E-19

To find I in photodiode circuit R (ohms) PRCVD

I = R x PRCVD

ID (amps)

IC = CTR x ID

Pout (mW) Pin (mW)

A = 10 log10 (Pout / Pin)

Pin (mW)

Pout = Pin x ( 10A/10 )

A B C D E F G H

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934935936937938939940941

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