All Electrical Engineering Formulas

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CHAPTER 1 To find force in newtons Excel formula in column H is: k (cnstnt) Q1 (coul) Q2 (coul) d (mtr)

Formula 1-1 F=k x Q1 x Q2/d2

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

CHAPTER 1 To find current in amperes Excel formula in column H is: Q (coul) T (sec)

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: d (mils)

Formula 2-1 A = d2

=D19^2 4 16

CHAPTER 2 To find resistance in ohms Excel formula in column H is: r (CM-W/ft) l (feet) A (CM)

Formula 2-2 R = rl /A =D22*E22/F22 10.4 250 39.75 65.41

CHAPTER 3 To find current in amperes Excel formula in column H is: V (volts) R (ohms)

Formula 3-1 I = V/R =D25/E25 10 5 2

CHAPTER 3 To find voltage in volts Excel formula in column H is: I (amps) R (ohms)

Formula 3-2 V = I x R =D28*E28 2 5 10

CHAPTER 3 To find resistance in ohms Excel formula in column H is: V (volts) I (amps)

Formula 3-3 R = V/I =D31/E31 10 2 5

CHAPTER 3 To find work in foot pounds Excel formula in column H is: F (lbs) D (feet)

Formula 3-4 Work (ft lbs)=Force x Distance =D34*E34 100 100 10000

CHAPTER 3 To find power in watts Excel formula in column H is: E (joules) T (sec)

Formula 3-5 Power = Energy / Time =D37/E37 100 10 10

CHAPTER 3 To find energy in watthours Excel formula in column H is: P (watts) T (hours)

Formula 3-6 Energy (Watthours)= Power x Time =D40*E40 200 3 600

CHAPTER 3 To find power in watts Excel formula in column H is: V (volts) I (amps)

Formula 3-7 P = V x I =D43*E43 10 0.05 0.5

CHAPTER 3 To find power in watts Excel formula in column H is: I (amps) R (ohms)

Formula 3-8 P = I2x

R =D46^2*E46 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 # FORMULAS

EXCEL EQUIVALENT FORMULAS

("CELL ADDRESSES" APPROACH)

PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:

From Use of Formulas

(Use Approp. Units)

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.

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CHAPTER 3 To find power in watts Excel formula in column H is: V (volts) R (ohms)

Formula 3-9 P = V2/R =D49^2/E49 10 200 0.5

CHAPTER 4 To find total R in ohms Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 4-1 RT = R1+R2…+Rn =SUM(D52:F52) 10 10 10 30

CHAPTER 4 To find total R in ohms Excel formula in column H is: V T (volts) I T (amps)

Formula 4-2 R T = V T / I T =D55/E55 70 2 35

CHAPTER 4 To find V across a specific R Excel formula in column H is: IR1 (amps) R1 (ohms)

Formula 4-3 V1 = IR1 x R1 =D58*E58 0.002 100,000 200

CHAPTER 4 To find V x using V divider rule Excel formula in column H is: R X (ohms) R T (ohms) V T (volts)

Formula 4-4 V X = R X /R T x V T =D61/E61*F61 4700 17400 50 13.51

CHAPTER 4 To find V T in a series circuit Excel formula in column H is: V1 (volts) V2 (volts) V3 (volts)

Formula 4-5 VT = V1 + V2 …+Vn =SUM(D64:F64) 20 30 10 60

CHAPTER 4 To find P T in a series circuit Excel formula in column H is: PR1 (watts) PR2 (watts) PR3 (watts)

Formula 4-6 PT = P1 + P2 …+ Pn =SUM(D67:F67) 40 200 160 400

CHAPTER 5 To find I T in a parallel circuit Excel formula in column H is: I1 (amps) I2 (amps) I3 (amps)

Formula 5-1 IT = I1 + I2 + I3 …+In =SUM(D70:F70) 3 1.5 1 5.5

CHAPTER 5 To find G T in a parallel circuit Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 5-2 GT = 1/R1 + 1/R2 …+1/Rn =1/D73+1/E73+1/F73 22 33 47 0.097

CHAPTER 5 To find R T in a parallel circuit Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 5-3 RT=1/(1/R1+1/R2+1/R3...1/Rn) =1/(1/D76+1/E76+1/F76) 10000 27000 20000 5346.53

CHAPTER 5 To find G T in a parallel circuit Excel formula in column H is: G1 (S) G2 (S) G3 (S)

Formula 5-4 GT = G1 + G2 + G3 =SUM(D79:F79) 0.1 0.2 0.1 0.4

CHAPTER 5 To find R T in a parallel circuit Excel formula in column H is: R1 (ohms) R2 (ohms)

Formula 5-5 RT = R1 x R2/R1 + R2 =D82*E82/(D82+E82) 3900 6800 2478.50

CHAPTER 5 To find R u for a parallel circuit Excel formula in column H is: R k (ohms) R e (ohms)

Formula 5-6 R u = R k x R e /R k -R e =D85*E85/(D85-E85) 10 6 15

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CHAPTER 5 To find I X in a specific branch Excel formula in column H is: R T (ohms) R X (ohms) I T (amps)

Formula 5-7 I X = R T /R X x I T =D88/E88*F88 550 1000 0.0055 0.003025

CHAPTER 5 To find I1 in a parallel circuit Excel formula in column H is: R1 (ohms) R2 (ohms) I T (amps)

Formula 5-8 I1 = R2/R1 + R2 x IT =E91/(D91+E91)*F91 10000 11000 0.05 0.02619

CHAPTER 5 To find I2 in a parallel circuit Excel formula in column H is: R1 (ohms) R2 (ohms) I T (amps)

Formula 5-9 I2 = R1/R1 + R2 x IT =D94/(D94+E94)*F94 10000 11000 0.05 0.02381

CHAPTER 6 To find balanced bridge R s Ratio expression in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 6-1 R1/R2 = R3/R4 D97*G97=E97*F97 10 20 30 60 Ans. here is 600=600

CHAPTER 6 To find R X in balanced bridge Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 6-2 RX(R4 here) = R2 x R3/R1 =E100*F100/D100 10 20 30 60

CHAPTER 7 To find efficiency of power transfer Excel formula in column H is: P out (watts) P in (watts)

Formula 7-1 Efficiency (%) = Pout/Pin x 100 =D103/E103*100 8.84 26.6 33.23

CHAPTER 7 To find internal R of a source Excel formula in column H is: V (no-load) V (loaded) I (load A)

Formula 7-2 r int = V (no-load) - V (loaded)/I (load) =(D106-E106)/F106 13 12 100 0.01

CHAPTER 7 To find I load using Thevenin's Th. Excel formula in column H is: V TH (volts) R TH (ohms) R L (ohms)

Formula 7-3 I L = V TH / R TH + R L =D109/(E109+F109) 50 25 25 1

CHAPTER 7 To find V load using Thevenin's Th. Excel formula in column H is: R L (ohms) R L (ohms) R TH (ohms) V TH (v)

Formula 7-4 V L = R L /R L + R TH x V TH =D112/(E112+F112)*G112 25 25 25 50 25

CHAPTER 7 To find I load using Norton's Th. Excel formula in column H is: R N (ohms) R N (ohms) R L (ohms)

Formula 7-5 I L = R N /R N + R L x I N =D115/(E115+F115)*G115 25 25 75 2 0.5

CHAPTER 8 To find R A in delta network Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 8-1 RA= (R1xR2) + (R2xR3) + (R3xR1)/R1 =((D118*E118)+(E118*F118)+(F118*D118))/D118 3.3 4.7 5.6 18.28

CHAPTER 8 To find R B in delta network Excel formul in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 8-2 RB = (R1xR2)+(R2xR3)+(R3xR1)/R2 =((D121*E121)+(E121*F121)+(F121*D121))/E121 3.3 4.7 5.6 12.83

CHAPTER 8 To find R C in delta network Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 8-3 RC = (R1xR2)+(R2xR3)+(R3xR1)/R3 =((D124*E124)+(E124*F124)+(F124*D124))/F124 3.3 4.7 5.6 10.77

R4 (ohms)

I N (amps)

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CHAPTER 8 To find R1 in wye network Excel formula in column H is: R A (ohms) R B (ohms) R C (ohms)

Formula 8-4 R1 = RB x RC/RA + RB + RC =E127*F127/(D127+E127+F127) 18.28 12.83 10.77 3.30


Formula 8-5 R2 = RC x RA/RA + RB + RC =F130*D130/(D130+E130+F130) 18.28 12.83 10.77 4.70


Formula 8-6 R3 = RA x RB/RA + RB + RC =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 d (meters)

Formula 9-1 Force = Pole 1 Strng. x Pole 2 Strng./d2

=D136*E136/F136^2 1 2 0.05 800

CHAPTER 9 To find magnetomotive force Excel formula in column H is: N (# of trns) I (amps)

Formula 9-2 mmf = NI =D139*E139 100 5 500

CHAPTER 9 To find magnetic field intensity Excel formula in column H is: A (amps) T (turns) meters

Formula 9-3 H = AT /meter =D142*E142/F142 5 100 0.1 5000

CHAPTER 9 To find induced voltage per turn Excel formula in column H is: Dflux (Wb) Dtime( sec)

Formula 9-4 V ind = # of lines of flux cut/per unit time =D145/E145 2 1 2

CHAPTER 9 To find induced voltage in coil Excel formula in column H is: N (# of turns) Dflux (Wb) Dtime( sec)

Formula 9-5 V ind = N (# of turns) x Dflux/Dtime =D148*E148/F148 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: f (Hz)

Formula 11-1 T (sec) = 1/f (Hz) =1/D153 1000 0.001

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

Formula 11-2 f (Hz) = 1/T (sec) =1/D156 0.0001 10000

CHAPTER 11 To find effective value from peak Excel formula in column H is: V pk. (volts)

Formula 11-3 Effective value (rms) = 0.707 x pk. val. =D159*E159 0.707 100 70.7

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

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

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CHAPTER 11 To find instant. V of sine wave Excel formula in column H is: V pk. (volts) angle sin q

Formula 11-5 v inst = V p x sin of angle value =D165*F165 141 30 0.5 70.5

CHAPTER 11 To find % duty cyc. of non-sine waves Excel formula in column H is: t w (msec) T (msec)

Formula 11-6 % duty cycle = tw (pulse wid.)/T (1 per.) x 100 =D168/E168*100 4 20 20

CHAPTER 11 To find V avg of non-sine waves Excel formula in column H is: Baseln value duty cycle pk-pk volts

Formula 11-7 Vavg = Baseln val. + (duty cycle x p-p amp.) =D171+(E171*F171) 2 0.1 5 2.5


CHAPTER 13 To find V induced in a coil Excel formula in column H is: N (# trns) d f (Wb) d t (secs)

Formula 13-1 V ind = N (# of trns) x df /dt =D176*E176/F176 500 2 1 1000

CHAPTER 13 To find V L value of given L Excel formula in column H is: L (H) di (amps) dt (secs)

Formula 13-2 V L = L x di /dt =D179*E179/F179 10 5 1 50

CHAPTER 13 To find L from V L and di/dt Excel formula in column H is: V L (volts) di (amps) dt (secs)

Formula 13-3 L = V L / di/dt =D182/(E182/F182) 5 12 6 2.5

CHAPTER 13 To find L from physical parameters. Excel formula in column H is: m r N (# trns) A (sq mtrs) l (mtrs)

Formula 13-4 L=12.57 x 10-7

x mr x N2

x A / l =0.000001257*D185*E185^2*F185/G185 1 2000 0.001 0.01 0.5028

CHAPTER 13 To find L of air-core inductor Excel formula in column H is: N (# trns) A (sq mtrs) l (mtrs)

Formula 13-5 L = 12.57 x 10-7

x N2 x A / l =0.000001257*D188^2*E188/F188 2000 0.001 0.01 0.5028

CHAPTER 13 To find L T in a series circuit Excel formula in column H is: L1 (H) L2 (H) L3 (H)

Formula 13-6 LT = L1 + L2 . . . +Ln = SUM(D191:F191) 10 5 2.5 17.5

CHAPTER 13 To find par. circuit reciprocal of L T Excel formula in column H is: L1 (H) L2 (H) L3 (H)

Formula 13-7 1/LT = 1/L1 + 1/L2 + 1/L3…+1/Ln =1/D194+1/E194+1/F194 10 5 10 0.4

CHAPTER 13 To find L T in a parallel circuit Excel formula in column H is: L1 (H) L2 (H) L3 (H)

Formula 13-8 LT = 1 / 1/L1 + 1/L2 + 1/L3…+1/Ln =1/(1/D197+1/E197+1/F197) 10 5 10 2.5

CHAPTER 13 To find LT of 2 parallel L's Excel formula in column H is: L1 (H) L2 (H)

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

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CHAPTER 13 To find amount of stored energy Excel formula in column H is: L (H) I (amps)

Formula 13-10 Energy = 0.5 LI2

=D203*E203*F203^2 0.5 20 5 250

CHAPTER 13 To find R L circuit time constant Excel formula in column H is: L (H) R (ohms)

Formula 13-11 One time constant = L /R =D206/E206 10 12 0.83

CHAPTER 13 To find inst. incr. i in an R L circuit Excel formula in column H is: V s (volts) R (ohms) t (sec) L (H)

Formula 13-12 i = Vs/R x (1 - -Rt/L

) =D209/E209*((1-2.71828^-(E209*F209/G209))) 10 10000 0.001 10 0.001

CHAPTER 13 To find inst. dec. i in an R L circuit Excel formula in column H is: V s (volts) R (ohms) t (sec) L (H)

Formula 13-13 i = V s/R x (-Rt /L

) =D212/E212*((2.71828^-(E212*F212/G212))) 6 2200 0.000068 0.05 0.000137

CHAPTER 14 To find value of X L in an ac circuit Excel formula in column H is: 2 f (Hz) L (H)

Formula 14-1 XL = 2fL =D215*E215*F215 6.28 60 5 1884

CHAPTER 14 To find L ( X L and f known) Excel formula in column H is: X L (ohms) 2 f (Hz)

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

CHAPTER 14 To find frequency (X L and L known) Excel formula in column H is: X L (ohms) 2 L (H)

Formula 14-3 f = XL/2L =D221/(E221*F221) 4000 6.28 0.00003 21231423

CHAPTER 14 To find 1/XLT in a parallel ac circuit Excel formula in column H is: XL1 (ohms) XL2 (ohms) XL3 (ohms)

Formula 14-4 1/XLT=1/XL1+1/XL2+1/XL3… =1/(D224)+1/(E224)+1/(F224) 2000 4000 6000 0.000917

CHAPTER 14 To find X LT in a parallel ac circuit Excel formula in column H is: XL1 (ohms) XL2 (ohms)

Formula 14-5 XLT=1/(1/XL1+1/XL2+…) =1/(1/D227+1/E227) 5000 5000 2500

CHAPTER 14 To find XLT of 2 parallel L's Excel formula in column H is: XL1 (ohms) XL2 (ohms)

Formula 14-6 XLT = XL1 x XL2/XL1 + XL2 =D230*E230/(D230+E230) 5000 5000 2500

CHAPTER 14 To find Q in an RL ac circuit Excel formula in column H is: X L (ohms) R (ohms)

Formula 14-7 Q = X L /R =D233/E233 3140 50 62.8

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

Formula 15-1 c2 = a

2 + b

2 =D236^2+E236^2 10 10 200

CHAPTER 15 To find V T in a series RL circuit Excel formula in column H is: V R (volts) V L (volts)

Formula 15-2 VT = VR2 + VL

2=SQRT(D239^2+E239^2) 10 10 14.14

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CHAPTER 15 To find Z in a series RL circuit Excel formula in column H is: R (ohms) X L (ohms)

Formula 15-3 Z = R2 + XL

2=SQRT(D242^2+E242^2) 5 8.66 10.00

CHAPTER 15 To find I T in a parallel RL circuit Excel formula in column H is: I R (amps) I L (amps)

Formula 15-4 IT = R2 + IL

2=SQRT(D245^2+E245^2) 3 5 5.83

CHAPTER 15 To find Z in a parallel RL circuit Excel formula in column H is: R (ohms) X L (ohms)

Formula 15-5 Z = R x XL / R2 + XL

2=D248*E248/SQRT(D248^2+E248^2) 50 30 25.72

CHAPTER 15 To find G in a parallel RL circuit Excel formula in column H is: One R (ohms)

Formula 15-6 G = 1/R =D251/E251 1 1500 0.000667

CHAPTER 15 To find inductive susceptance Excel formula in column H is: X L (ohms)

Formula 15-7 BL = 1/XL =D254/E254 1 1005 0.000995

CHAPTER 15 To find admittance Excel formula in column H is: Z (ohms)

Formula 15-8 Y = 1/Z =D257/E257 1 835 0.001198

CHAPTER 15 To find Y in a parallel RL circuit Excel formula in column H is: G (S) B L (S)

Formula 15-9 YT = G2 + BL

2=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: R (ohms) X L (ohms)

Formula 15-10 q (magnitude) = tan-1

R / XL =DEGREES(ATAN(D263/E263)) 1500 1005 56.178

CHAPTER 16 To find mutual inductance Excel formula in column H is: k L1 (H) L2 (H)

Formula 16-1 M = k L1 x L2 =D266*SQRT(E266*F266) 1 3 3 3

CHAPTER 16 To find L T of series L's (aid) Excel formula in column H is: L1 (H) L2 (H) M (H)

Formula 16-2 LT = L1 + L2 + 2M =D269+E269+2*F269 8 8 4 24

CHAPTER 16 To find L T of series L 's (opp) Excel formula in column H is: L1 (H) L2 (H) M (H)

Formula 16-3 LT = L1 + L2 - 2M =D272+E272-2*F272 8 8 4 8

CHAPTER 16 General L T formula (aid or opp) Excel formula in column H is: L1 (H) L2 (H) M (H) (aid) 30

Formula 16-4 LT = L1 + L2 2M =D275+E275±2*F275 10 10 5 (opp) 10

CHAPTER 16 To find LT of 2 parallel L's (aid) Excel formula in column H is: L1 (H) L2 (H) M (H)

Formula 16-5 LT = 1/1/L1 + M + 1/L2 + M =1/((1/(D278+F278)+1/(E278+F278))) 8 8 4 6

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CHAPTER 16 To find LT of 2 parallel L's (opp) Excel formula in column H is: L1 (H) L2 (H) M (H)

Formula 16-6 LT = 1/1/L1 - M + 1/L2 - M =1/((1/(D281-F281)+1/(E281-F281))) 8 8 4 2

CHAPTER 16 To find coefficient of coupling Excel formula in column H is: L1 (H) L2 (H) M (H)

Formula 16-7 k = M/ L1 x L2 =F284/SQRT(D284*E284) 8 8 4 0.5

CHAPTER 16 V ratio compared to T ratio Excel formula in column H is: V P (volts) V S (volts) N P (trns) N S (trns)

Formula 16-8 V P /V S = N P /N S or = D287*G287=E287*F287 20 280 1 14 TRUE

CHAPTER 16 T ratio compared to V ratio Excel formula in column H is: N P (trns) N S (trns) V P (volts) V S (volts)

Formula 16-9 N P /N S = V P /V S or = D290*G290=E290*F290 20 280 1 14 TRUE

CHAPTER 16 T ratio compared to I ratio Excel formula in column H is: N P (trns) N S (trns) I S (amps)

Formula 16-10 N P /N S = I S /I P or = D293*G293 = E293*F293 5 1 0.5 0.1 TRUE

CHAPTER 16 V ratio compared to I ratio Excel formula in column H is: V P (volts) V S (volts) I S (amps)

Formula 16-11 V P /V S = I S /I P or =D296*G296=E296*F296 5 1 0.5 0.1 TRUE

CHAPTER 16 N ratio compared to Z ratio Excel formula in column H is: N S (trns) N P (trns) Z S (ohms)

Formula 16-12 (NS/NP)2 = ZS/ZP or =(D299/E299)^2=F299/G299 1 4 8 128 TRUE

CHAPTER 16 To find Z P from Z S and T ratio Excel formula in column H is: Z S (ohms) N P (trns) N S (trns)

Formula 16-13 ZP = ZS(NP/NS)2

=D302*(E302/F302)^2 2000 2 1 8000

CHAPTER 16 To find T ratio from Z ratio Excel formula in column H is: Z P (ohms) Z S (ohms)

Formula 16-14 N P /N S = Z P /Z S =SQRT(D305/E305) 1000 10 10

CHAPTER 16 To find transformer efficiency Excel formula in column H is: P out (watts) P in (watts)

Formula 16-15 Efficiency % = Pout/Pin x 100 =D308/E308*100 86 100 86

CHAPTER 17 To find C value (Q and V known) Excel formula in column H is: Q (coul) V (volts)

Formula 17-1 C = Q /V =D311/E311 10 2 5

CHAPTER 17 To find Q value (C and V known) Excel formula in column H is: C (farads) V (volts)

Formula 17-2 Q = C x V =D314*E314 5 2 10

CHAPTER 17 To find V value (Q and C known) Excel formula in column H is: Q (coul) C (farads)

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

I P (amps)

I P (amps)

Z P (ohms)

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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

345

346

347

348

349

350

351

352

353

354

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356

357

358

CHAPTER 17 To find energy in joules Excel formula in column H is: C (farads) V (volts)

Formula 17-4 Energy = 0.5 x CV2

=0.5*D320*E320^2 0.000005 250 0.15625

CHAPTER 17 To find dielectric constant Excel formula in column H is: o (abs) v (vac)

Formula 17-5 k = o/v =D323/E323 6 1 6

CHAPTER 17 To find C (from physical factors) Excel formula in column H is: A (sq mtrs) s (mtrs)

Formula 17-6 C = 8.85 x A/1012

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

CHAPTER 17 To find C (from physical factors) Excel formula in column H is: k (number) A (sq mtrs) s (mtrs)

Formula 17-7 C = 8.85 x k x A/1012

x s =8.85*D329*E329/(10^12*F329) 3 0.01 0.001 2.655E-10

CHAPTER 17 To find C in m F (from phys. factors) Excel formula in column H is: k (number) A (sq in.) s (in.) n (# plates)

Formula 17-8 C = 2.25*k*A/107

x s x (n-1) =2.25*D332*E332/10^7*F332*(G332-1) 100 2 0.005 2 0.009

CHAPTER 17 To find CT of 2 series caps Excel formula in column H is: C1 (mF) C2 (mF)

Formula 17-9 CT = C1 x C2 / C1 + C2 =D335*E335/(D335+E335) 3 6 2

CHAPTER 17 To find C T of = value series C 's Excel formula in column H is: C1 (mF) C2 (mF) C3 (mF) n (# plates)

Formula 17-10 C T = C /N =D338/G338 10 10 10 3 3.33

CHAPTER 17 To find C T of any value series C 's Excel formula in column H is: C1 (mF) C2 (mF) C3 (mF)

Formula 17-11 CT = 1/1/C1+1/C2+1/C3...+1/Cn =1/(1/D341+1/E341+1/F341) 10 5 10 2.5

CHAPTER 17 To find V C x in cap V divider circuit Excel formula in column H is: V S (volts) C T (uF) C X (mF)

Formula 17-12 V X = V S x C T /C X =D344*E344/F344 60 7.5 15 30

CHAPTER 17 To find C T of parallel capacitors Excel formula in column H is: C1 (mF) C2 (mF) C3 (mF) C4 (mF)

Formula 17-13 CT = C1 + C2 + C3…+Cn =D347+E347+F347+G347 15 10 10 3 38

CHAPTER 17 To find 1 time const. in an RC circuit Excel formula in column H is: R (ohms) C (farads)

Formula 17-14 1 TC (T) = R x C =D350*E350 1000 0.000001 0.001

CHAPTER 17 To find inst. v R in a dc RC circuit Excel formula in column H is: V S (volts) t (msec) t (msec)

Formula 17-15 v R = V S x (-t/T

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

CHAPTER 17 To find inst. v C in a dc RC circuit Excel formula in column H is: V S (volts) t (msec) t (msec)

Formula 17-16 vC = VS x (1 - -t/T)

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

CHAPTER 18 To find i C knowing C and dv/dt Excel formula in column H is: C (value) dv (volts) dt (sec)

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359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

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378

379

380

381

382

383

384

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386

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390

391

392

393

394

395

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397

Formula 18-1 i C = C x dv /dt =(D359*10^-12)*E359/(F359*10^-6) 100 100 100 0.0001

CHAPTER 18 To find X C knowing f and C Excel formula in column H is: 2 f (Hz) C (farads)

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

CHAPTER 18 To find f knowing C and X C Excel formula in column H is: 2 C (farads) X C (ohms)

Formula 18-3 f = 1/2 x C x XC =1/(D365*E365*F365) 6.28 5E-10 1000 318471

CHAPTER 18 To find C knowing f and X C Excel formula in column H is: 2 f (Hz) X C (ohms)

Formula 18-4 C = 1/2 x f x XC =1/(D368*E368*F368) 6.28 2000 3180 0.000000025

CHAPTER 18 To find X CT of parallel C 's Excel formula in column H is: XC1 (ohms) XC2 (ohms) XC3 (ohms)

Formula 18-5 XCT = 1/1/XC1 + 1/XC2 + 1/XC3…1/XCn =1/(1/D371+1/E371+1/F371) 1000 2000 3000 545.45

CHAPTER 18 To find XCT of 2 parallel C's Excel formula in column H is: XC1 (ohms) XC2 (ohms)

Formula 18-6 XCT = XC1 x XC2 / XC1 + XC2 =D374*E374/(D374+E374) 1000 2000 666.67

CHAPTER 18 To find X CT of = val. parallel C 's Excel formula in column H is: XC1 (ohms) N (number)

Formula 18-7 XCT = XC1 / N =D377/E377 1000 5 200

CHAPTER 19 To find V T in a series RC circuit Excel formula in column H is: V R (volts) V C (volts)

Formula 19-1 VT = VR2 + VC

2=SQRT(D380^2+E380^2) 50 50 70.71

CHAPTER 19 To find Z in a series RC circuit Excel formula in column H is: R (ohms) X C (ohms)

Formula 19-2 Z = R2 + XC

2=SQRT(D383^2+E383^2) 50 50 70.71

CHAPTER 19 To find I T in a parallel RC circuit Excel formula in column H is: I R (amps) I C (amps)

Formula 19-3 IT = IR2 + IC

2=SQRT(D386^2+E386^2) 15 20 25

CHAPTER 19 To find Z in a parallel RC circuit Excel formula in column H is: R (ohms) X C (ohms)

Formula 19-4 Z = R x XC / R2 + XC

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

CHAPTER 19 To find G in a parallel RC circuit Excel formula in column H is: One R (ohms)

Formula 19-5 G = 1/R =D392/E392 1 1500 0.000667

CHAPTER 19 To find capacitive susceptance Excel formula in column H is: X c (ohms)

Formula 19-6 BC = 1/XC or 2fC =D395/E395 1 995 0.001

CHAPTER 19 To find Y in a parallel RC circuit Excel formula in column H is: G (S) B C (S)

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398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

Formula 19-7 YT = G2 + BC

2=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: R (ohms) X C (ohms)

Formula 19-8 q (magnitude) = tan-1

R / XC =DEGREES(ATAN(D401/E401)) 1500 995 56.44

CHAPTER 20 To find Z of a series RLC circuit Excel formula in column H is: R (ohms) X net (ohms)

Formula 20-1 Z = R2 + Xnet

2=SQRT(D404^2+E404^2) 60 80 100

(where X net = X L - X C if X L >X C

or X net = X C - X L if X C >X L )

CHAPTER 20 To find V T of a series RLC circuit Excel formula in column H is: V R (volts) V xnet (volts)

Formula 20-2 VT = VR2 + VXnet

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

(where V xnet =V L - V C if V L >V C

or V xnet =V C - V L if V C >V L)

CHAPTER 20 To find Tanq knowing X net and R Excel formula in column H is: X net (ohms) R (ohms)

Formula 20-3 Tang of q = X net /R =D414/E414 80 60 1.33

CHAPTER 20 To find Tanq knowing V X net and V R Excel formula in column H is: V X net (volts) V R (volts)

Formula 20-4 Tang of q = V X net / V R =D417/E417 80 60 1.33

CHAPTER 20 To find I T of a parallel RLC circuit Excel formula in column H is: I R (amps)

Formula 20-5 IT = IR2 + IXnet

2=SQRT(D420^2+E420^2) 2 1 2.24

(where I x net = I L - I C if I L >I C

or I x net = I C - I L if I C >I L )

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

Formula 20-6 Power factor (p.f .) = cos q =COS(D425*PI()/180) 45 0.707

CHAPTER 20 To find app. power knowing V and I Excel formula in column H is: V (volts) I (amps)

Formula 20-7 Apparent power (S ) = V rms x I rms =D428*E428 141.5 1 141.5

CHAPTER 20 To find true power knowing I and R Excel formula in column H is: I (amps) R (ohms)

Formula 20-8 True power (P) = I2 x R =D432^2*E432 1 100 100

I X net (amps)

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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

CHAPTER 20 To find true power knowing S and p.f. Excel formula in column H is: S (VA) p.f. (numb.)

Formula 20-9 P = Apparent power x power factor (p.f.) =D435*E435 141.5 0.707 100

CHAPTER 20 To find p.f. knowing P and S Excel formula in column H is: P true (W) S (VA)

Formula 20-10 p.f. = True power (P )/App. power (S ) =D438/E438 100 141.5 0.707

CHAPTER 20 To find S knowing P and VAR Excel formula in column H is: P true (W) Q (VAR)

Formula 20-11 S = P2 + Q

2=SQRT(D441^2+E441^2) 100 100 141.42

CHAPTER 20 To convert Z polar to rect. data Excel formulas in column H are: Z (ohms) q (deg)

Formula 20-12 R factor = (Z cos q ) =(D444*COS(E444*PI()/180)) 45 30 38.97

(Series circuit) j factor = (Z sin q ) =(D444*SIN(E444*PI()/180)) 22.5

45 = (Z cos q (jZ sin q) Answer is:

45 30 = 38.97 + j22.5

CHAPTER 20 To convert V T polar to rect. data Excel formulas in column H are: V T (volts) q (deg)

Formula 20-13 Real axis = (V T x cos q ) =(D450*COS(E450*PI()/180)) 66 60 33

(Series circuit) Imag. axis = (jV T x sin q ) =(D450*SIN(E450*PI()/180)) 57.16

= (VT x cos q (jVT x sin q) Answer is:

6645 = 33 + j57.16

CHAPTER 20 To convert I T polar to rect. data Excel formulas in column H are: I T (amps) q (deg)

Formula 20-14 Real axis = (I T x cos q ) =(D456*COS(E456*PI()/180)) 15 30 12.99

(Parallel circuit) Imag. axis = (jI T x sin q ) =(D456*SIN(E456*PI()/180)) 7.5

= (IT x cos q (jIT x sin q) Answer is:

15 = 12.99 + j7.5

CHAPTER 20 To find inductive susceptance Excel formula in column H is: 2 f (Hz) L (H)

Formula 20-15 BL = 1/2 x f x L =1/(D462*E462*F462) 6.28 60 1 0.00265

(Parallel circuit)

CHAPTER 20 To find capacitive susceptance Excel formula in column H is: 2 f (Hz) C (Farads)

Formula 20-16 BC = 2 x f x C =D466*E466*F466 6.28 60 0.000004 0.00151

(Parallel circuit)

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(Use Approp. Units)




468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

CHAPTER 20 To find admittance Excel formulas in column H are: G (S) B net (S)

Formula 20-17 Y = G2 + jBnet

2=SQRT(D470^2+E470^2) 0.002 0.00114 0.0023

(Parallel circuit) (Note: tan of q = B/G) =E470/D470 0.57

(Note: q of Y = arctan B/G) =ATAN(H471)*180/pi() 29.7

Answer for Y is:

Y = 0.0023 29.7S

CHAPTER 21 To find f r when L and C are known Excel formula in column H is: 2 L (H) C (Fd)

Formula 21-1 fr = 1/2 x L x C =1/(D477*SQRT(E477*F477)) 6.28 0.0002 4E-10 562983

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

CHAPTER 21 To find L when f r and C are known Excel formula in column H is: f r (Hz) C (Fd)

Formula 21-2 L = 0.02533/fr2 x C =0.02533/(D481^2*E481) 1000000 2.533E-10 0.0001


CHAPTER 21 To find C when f r and L are known Excel formula in column H is: f r (Hz) L (H)

Formula 21-3 C = 0.02533/fr2 x L =0.02533/(D485^2*E485) 1000000 0.0001 2.533E-10


CHAPTER 21 To find L when f r and C are known Excel formula in column H is: f r (MHz) C (pF )

Formula 21-4 L = 25,330/fr2 x C =25330/(D489^2*E489) 1 253.3 100

Where: L= m H; C=pF;f=MHz

CHAPTER 21 To find C when f r and L are known Excel formula in column H is: f r (MHz) L (m H)

Formula 21-5 C = 25,330/fr2 x L =25330/(D493^2*E493) 1 100 253.3

Where: L= m H; C=pF;f=MHz

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: f2 (Hz) f1 (Hz)

Formula 21-7 BW = f2 - f1 =D500 - E500 1010000 990000 20000

(Where f2= higher f 0.707 pt

and f1 = lower f 0.707 pt)

CHAPTER 21 To find BW knowing f r and Q Excel formula in column H is: f r (Hz) Q (number)

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

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ANSWERS:


(Use Approp. Units)




506

507

508

509

510

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

542

543

CHAPTER 21 To find Q knowing f r and BW Excel formula in column H is: f r (Hz) BW (Hz)

Formula 21-9 Q = f r /BW =D508/E508 5000 200 25

CHAPTER 21 To find cutoff for RC network Excel formula in column H is: 2 R (ohms) C (Farads)

Formula 21-10 fc = 1/2 x R x C =1/(D511*E511*F511) 6.28 1000 0.0000001 1592.36

(Note: For hi-pass simple C filter)

CHAPTER 21 To find cutoff for RL network Excel formula in column H is: 2 L (H) R (ohms)

Formula 21-11 fc = 1/2 x (L/R) =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 Max # of electrons = 2 x n2

=2*D519^2 3 18

CHAPTER 23 To find I in circ. w/series diode and R Excel formula in column H is: V S (volts) V D (volts) R (ohms)

Formula 23-1 I = (V S - V D ) / R =(D522-E522)/F522 10 0.7 150 0.062

CHAPTER 23 To find diode power dissipation Excel formula in column H is: I (amps) V D

Formula 23-2 P = I x V D =D525*E525 0.01 0.7 0.007

CHAPTER 23 To find zener diode pwr. dissipation Excel formula in column H is: I z (amps) V z (volts)

Formula 23-3 P = I z x V z =D528*E528 0.05 5.1 0.255

CHAPTER 23 To find regulation transition point Excel formula in column H is: V zT R1 (ohms) R L (ohms)

Formula 23-4 Vs = VzT x (R1 + RL) / RL =D531*(E531+F531)/F531 9.1 100 750 10.31

CHAPTER 23 To find output V w/source <trans. pt. Excel formula in column H is: V s (volts) R L (ohms) R1 (ohms)

Formula 23-5 VL = Vs x RL / (RL + R1) =D534*E534/(E534+F534) 9 750 100 7.94

CHAPTER 23 To find V to be dropped by V R Excel formula in column H is: V s (volts) V D (volts)

Formula 23-6 V R = V s - V D =D537-E537 12 1.5 10.5

CHAPTER 24 To find V dc out of unfilt. H.W. rect. Excel formula in column H is: V rms (volts)

Formula 24-1 Vdc = 0.45 x Vrms =0.45*D540 70.7 31.8

CHAPTER 24 To find V dc out of unfilt. H.W. rect. Excel formula in column H is: V PK (volts)

Formula 24-2 Vdc = 0.318 x VPK =0.318*D543 100 31.8

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ANSWERS:


(Use Approp. Units)




544

545

546

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

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566

567

568

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570

571

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573

574

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576

577

578

579

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

Formula 24-3 PIV (H.W.) = 1.414 x Vrms =1.414*D546 200 282.8

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

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

CHAPTER 24 To find V dc out of unfilt. F.W. rect. Excel formula in column H is: V (1/2 sec.)

Formula 24-5 Vdc = 0.9 x Vrms of half of secondary =0.9*D552 100 90

CHAPTER 24 To find V dc out of unfilt. F.W. rect. Excel formula in column H is: V (full sec.)

Formula 24-6 Vdc = 0.45 x Vrms of full secondary =0.45*D555 200 90

CHAPTER 24 To find V dc out of unfilt. F.W. rect. Excel formula in column H is: VPK (1/2 sec.)

Formula 24-7 Vdc = 0.637 x VPK of 1/2 secondary =0.637*D558 141.4 90.1

CHAPTER 24 To find V dc out of unfilt. F.W. rect. Excel formula in column H is: V PK (full sec.)

Formula 24-8 Vdc = 0.318 x VPK of full secondary =0.318*D561 282.8 89.9

CHAPTER 24 To find PIV of unfilt. F.W. rect. Excel formula in column H is: V (Full sec.)

Formula 24-9 PIV (F.W.) = 1.414 x Vrms full secondary =1.414*D564 200 282.8

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

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

CHAPTER 24 To find V dc out (unfilt. bridge rect.) Excel formula in column H is: V rms input

Formula 24-11 Vdc = 0.9 x Vrms of ac input =0.9*D570 12.6 11.34

CHAPTER 24 To find V dc out (unfilt. bridge rect.) Excel formula in column H is: V pk input

Formula 24-12 Vdc = 0.637 x VPK of ac input =0.637*D573 17.8 11.34

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

Formula 24-13 PIV (Bridge) = 1.414 x Vrms input =1.414*D576 200 282.8

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

Formula 24-14 Ripple frequency (bridge) = 2 x ac in f =2*D579 60 120

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

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ANSWERS:


(Use Approp. Units)




583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

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CHAPTER 24 To find power supply % regulation Excel formula in column H is: V NL (volts) V FL (volts)

Formula 24-16 % Reg. = (VNL- VFL)/ VFL x 100% =(D585-E585)/E585*100 12.2 11.8 3.39

CHAPTER 24 To find power diss. by IC regulator Excel formula in column H is: I B (amps) V IN (V) I L (amps) V OUT (V)

Formula 24-17 P REG = I B x V IN + I L x (V IN -V OUT ) =(D588*E588)+F588*(E588-G588) 0.0044 24 0.15 15 1.46

CHAPTER 24 To find efficiency of IC regulator Excel formula in column H is: P out (W) P reg (W)

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

CHAPTER 24 To find regulated dc output voltage Excel formula in column H is: V ref (V) R2 (ohms) R1 (ohms)

Formula 24-19 Vout = Vref x (1+R2 / R1 ) =D594*(1+E594/F594) 1.25 240 240 2.5

CHAPTER 24 To find D factor for "buck" reg. Excel formula in column H is: T on (msec) T off (msec)

Formula 24-20 D = T on / (T on + T off) =D597/(D597+E597) 50 50 0.5

CHAPTER 24 To find V out of a "buck" reg. Excel formula in column H is: V in (volts) D value

Formula 24-21 V out = V in x D =D600*E600 24 0.5 12

CHAPTER 24 To find V out of a "boost" reg. Excel formula in column H is: V in (volts) D value

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

CHAPTER 24 To find V out of a "flyback" reg. Excel formula in column H is: V in (volts) D value

Formula 24-23 Vout = -Vin x D/(1-D) =-D606*E606/(1-E606) 24 0.5 -24

CHAPTER 25 To find transistor emitter current Excel formula in column H is: I C (mA) I B (mA)

Formula 25-1 I E = I C + I B =D609+E609 18 0.001 18.001

CHAPTER 25 To find dc Beta of transistor Excel formula in column H is: I C (mA) I B (mA)

Formula 25-2 bdc = I C /I B =D612/E612 1.2 0.024 50

CHAPTER 25 To find collector current Excel formula in column H is: βdc I B (mA)

Formula 25-3 I C = bdc x I B =D615*E615 50 0.024 1.2

CHAPTER 25 To find base current Excel formula in column H is: I C (mA) βdc

Formula 25-4 I B = I C / bdc =D618/E618 1.2 50 0.024

CHAPTER 25 To find Alpha of transistor Excel formula in column H is: I C (mA) I E (mA)

Formula 25-5 a = I C / I E =D621/E621 9.8 10 0.98

1

2

3

4

5

6

7

8

9

10

A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652

653

654

655

656

657

658

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

Formula 25-6 bac = DI C / DI B =D624/E624 2 0.04 50

CHAPTER 26 To find voltage gain of amplifier Excel formula in column H is: V out (Vpp) V in (Vpp)

Formula 26-1 A V = V out / V in =D627/E627 1.2 0.05 24

CHAPTER 26 To find current gain of amplifier Excel formula in column H is: I out (Ipp) I in (Ipp)

Formula 26-2 A I = I out / I in =D630/E630 10 0.5 20

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

Formula 26-3 A P = A V x A I =D633*E633 24 20 480

CHAPTER 26 To find base V with V divider bias Excel formula in column H is: V CC (volts) R1 (ohms) R2 (ohms)

Formula 26-4 VBVTH = Vcc x R2 / (R1 + R2) =D636*F636/(E636+F636) 12 12000 2000 1.71

CHAPTER 26 To find emitter curr. with V div. bias Excel formula in column H is: V B (volts) V BE (volts) R E (ohms)

Formula 26-5 I E = (V B - V BE ) / R E =(D639-E639)/F639 1.714 0.7 1000 0.001014

CHAPTER 26 To find collector-emitter voltage Excel formula in column H is: V CC (volts) I E (mA) R C (k W) R E (k W)

Formula 26-6 V CE = V CC - I E x (R C + R E ) =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) I E (mA)

Formula 26-7 re' = 25 mV / IE =D645/E645 25 1.014 24.65

CHAPTER 26 To find input impedance Excel formula in column H is: R1 (ohms) R2 (ohms) Beta

Formula 26-8 ZIN = R1|| R2|| (Beta +1) x re' =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: R C (ohms)

Formula 26-9 Z OUT = R C =D651 3000 3000

CHAPTER 26 Approximation of voltage gain Excel formula in column H is: R C (ohms) re' (ohms)

Formula 26-10 A V = -R C / re' =-D654/E654 3900 24.65 -158.22

CHAPTER 26 Approximation of current gain Excel formula in column H is: b R1 (ohms) R2 (ohms)

Formula 26-11 =b(R1||R2)/(R1||R2)+(b +1)re' =D657*(E657*F657/(E657+F657))/ 100 12000 2000 24.65 40.78

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

re' (ohms)

re' (ohms)

1

2

3

4

5

6

7

8

9

10

A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697

CHAPTER 26 Approximation of input impedance Excel formula in column H is: b R1 (ohms) R2 (ohms)

Formula 26-12 ZIN = R1|| R2|| (Beta +1) x (re'+RE1)) =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: R C (ohms)

Formula 26-13 Z OUT = R C =D664 3900 3900

CHAPTER 26 Approximation of voltage gain Excel formula in column H is: R C (ohms) re' (ohms) RE1 (ohms)

Formula 26-14 AV -RC / (re' + RE1 ) =-D667/(E667+F667) 3900 24.65 1000 -3.81

CHAPTER 26 Approximation of current gain Excel formula in column H is: b R1 (ohms) R2 (ohms)

Formula 26-15 b(R1||R2)/(R1||R2)+(b +1)x(re'+RE1) =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: AV1 AV2 AV3 ---

Formula 26-16 AV = AV1 x AV2 x AV3 … =D674*E674*F674 10 50 50 25000

where: AV1 = Zin1/(Zin1 + Zs)

AV2 is the gain of first amplifier

AV3 = Zin2/(Zin2 + Zout1)

AV4 is gain of 2nd amp…

CHAPTER 26 To approximate Z IN for CC amplifier Excel formula in column H is: R1 (ohms) R2 (ohms) b

Formula 26-17 ZIN = R1||R2|| ((b x (re' +RE)) =1/(1/D681+1/E681+(1/((F681+1)*G681))) 12000 2000 100 1024 1686.33

CHAPTER 26 To approximate Z out for CC amplifier Excel formula in column H is: R E (ohms) re' (ohms)

Formula 26-18 Z OUT = R E || re' =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: R E (ohms) re' (ohms) R E (ohms)

Formula 26-19 A V = R E /(re' + R E ) =D687/(E687+F687) 1000 24.65 1000 0.98

Note: AV1

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

Formula 26-20 A i - b =-D691 100 -100

CHAPTER 26 To find approx Zin of CB amplifier Excel formula in column H is: R E (ohms) re' (ohms)

Formula 26-21 Z IN = R E || re' =D694*E694/(D694+E694) 1000 24.65 24.06

CHAPTER 26 To find approx Z out of CB amplifier Excel formula in column H is: R C (ohms)

Formula 26-22 Z OUT = R C =D697 3900 3900

(re' +RE1)

(re' +RE1)

re ' + R E W

1

2

3

4

5

6

7

8

9

10

A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




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

730

731

732

733

734

735

736

737

CHAPTER 26 To approx. v. gain of CB amplifier Excel formula in column H is: R C (ohms) re' (ohms)

Formula 26-23 A V = R C / re' =D700/E700 3900 24.65 158.22

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

Formula 26-24 Ai -1 =D703 -1 -1

CHAPTER 26 To define V CE at cutoff condition Excel formula in column H is: V CC (volts)

Formula 26-25 V CE = V CC =D706 12 12

CHAPTER 26 To find I C value at saturation Excel formula in column H is: V CC (volts) R C (ohms) R E (ohms)

Formula 26-26 I C(sat) = V CC / (R C + R E ) =D709/(E709+F709) 12 3900 1000 0.00245

CHAPTER 27 To find drain curr JFETs & MOSFETs

Formula 27-1 ID=IDSS(1-(VGS/VGS(off) ))2

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

CHAPTER 27 To find transconductance of FET Excel formula in column H is: D I D ( amps) D V GS (V)

Formula 27-2 gm = D I D / D V GS =D716/E716 0.002 3 0.000667

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

Formula 27-3 V GS = V GG =D719 5 5

(Note: Using fixed bias)

CHAPTER 27 To find JFET drain to source V Excel formula in column H is: V DD (volts) I D (amps) R D (ohms)

Formula 27-4 V DS = V DD - I D x R D =D723-(E723*F723) 12 0.005 1000 7

(Note: Using fixed bias)

CHAPTER 27 To find JFET gate to source V Excel formula in column H is: I D (amps) R S (ohms)

Formula 27-5 V GS = - I D x R S =-D727*E727 0.004 1000 -4

(Note: Using self bias)

CHAPTER 27 To find JFET drain to source V Excel formula in column H is: V DD (volts) I D (amps) R D (ohms)

Formula 27-6 V DS = V DD - I D x R D - I D x R S =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: V DD (volts) R1 (ohms) R2 (ohms)

Formula 27-7 VG = VDD x R2 / (R1 + R2) =D735*F735/(E735+F735) 12 100000 33000 2.98

(Note: Using voltage div. bias)

R S (ohms)

1

2

3

4

5

6

7

8

9

10

A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




738

739

740

741

742

743

744

745

746

747

748

749

750

751

752

753

754

755

756

757

758

759

760

761

762

763

764

765

766

767

768

769

770

771

772

773

CHAPTER 27 To find JFET gate to source V Excel formula in column H is: V G (volts) I D (amps) R S (ohms)

Formula 27-8 V GS = V G - I D x R S =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 ID = k x (VGS - VT)2

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

CHAPTER 27 To find FET power dissipation Excel formula in column H is: V DS (volts) I D (amps)

Formula 27-10 P FET = V DS x I D =D747*E747 0.12 1.3 0.156

CHAPTER 28 To find op-amp output V Excel formula in column H is: A VOL V in (volts)

Formula 28-1 V out = - A VOL x V in =-D750*E750 50000 0.0002 -10

(open loop) (Note: Inverting input)

CHAPTER 28 To find op-amp output V Excel formula in column H is: A VOL V in (volts)

Formula 28-2 V out = A VOL x V in =D754*E754 50000 0.0002 10

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

CHAPTER 28 To find op-amp output V Excel formula in column H is: A VOL V1 (volts) V2 (volts)

Formula 28-3 Vout = AVOL x (V1 - V2) =D758*(E758-F758) 50000 0.002 0.0015 25

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

CHAPTER 28 To find inv. op-amp V gain Excel formula in column H is: V out (volts) V in (volts)

Formula 28-4 A V = V out / V in =D762/E762 -15 2 -7.5

(Note: Assuming infinite input z)

CHAPTER 28 To find inv. op-amp V gain Excel formula in column H is: R f (ohms) R i (ohms)

Formula 28-5 A V = -R f / R i =-(D766/E766) 27000 1800 -15

(Note: Closed loop V gain)

CHAPTER 28 To find non-inv. op-amp V gain Excel formula in column H is: R f (ohms) R i (ohms)

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

CHAPTER 28 To find V gain of V div. non-inv. amp. Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 28-7 AV=[(R2/R1)+1] x [R4/(R4 + R3)] =(E773/D773+1)*((G773/(G773+F773))) 10000 50000 20000 10000 2

R4 (ohms)

1

2

3

4

5

6

7

8

9

10

A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




774

775

776

777

778

779

780

781

782

783

784

785

786

787

788

789

790

791

792

793

794

795

796

797

798

799

800

801

802

803

804

805

806

807

808

809

810

811

812

813

CHAPTER 28 To find V out of subtractor circuit Excel formula in column H is: V in+ (volts) R1 (ohms) R2 (ohms)

Formula 28-8 Vout=Vin+x((R2/R1)+1)x(R4/(R4+R3))+ =D776*(F776/E776+1)*(E778/(E778+D778))+ 6 10000 10000 2 4

Vin- x (-R2/R1) G776*(-F776/E776) R3 (ohms) R4 (ohms)

5000 5000

CHAPTER 28 To find V out of subtractor circuit Excel formula in column H is: V in+ (volts) V in- (volts)

Formula 28-9 V out = V in+ - V in- =D781-E781 -5 2 -7

(Note: Simplified formula when

R1=R2=R3=R4)

CHAPTER 28 To find V out of summing amplifier Excel formula in column H is: Vin1 (volts) Rf&R1&R2 Vin2 (volts)

Formula 28-10 Vout=Vin1 x (-Rf/R1)+Vin2 x (-Rf/R2) =D786*(-E786/E786)+F786*(-E786/E786) 2 10000 3 -5

CHAPTER 28 To find V out of summing amplifier Excel formula in column H is: Vin1 (volts) Vin2 (volts) Vin3 (volts)

Formula 28-11 Vout=Vin1 x (-Rf/R1)+Vin2 x (-Rf/R2) + D790*(-F792/G790)+(E790)*(-F792/D792)+(F790)* 5 5 5 5000 -2.5

Vin3 x (-Rf/R3) (-F792/E792) R2 (ohms) R3 (ohms) R f (ohms)

10000 5000 1000

CHAPTER 28 To find V out of summing amplifier Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 28-12 Vout = (1+R2/R1) x [Vin1xR4/(R3+R4)] + =(1+E795/D795)*(D797*(G795/(F795+G795))+ 10000 20000 10000 20000 5.5

Vin2 x R3/(R3 + R4)] E797*F795/(F795+G795)) Vin1 (volts) Vin2 (volts)

1.5 2.5

CHAPTER 28 To find V out. change for integ. circ. Excel formula in column H is: - V in R (ohms) C (mF)

Formula 28-13 DV out = [-V in / (R x C)] x Dt =D800/(E800*F800)*G800 -3 1000 0.01 5 -1.5

CHAPTER 28 To find V out. for differentiator circ. Excel formula in column H is: R (ohms) C (mF) D V in (V)

Formula 28-14 V out = (-R x C ) x (DV in/Dt ) =(D803*E803)*(F803/G803) -1000 0.01 0.5 1 -5

CHAPTER 28 To find V output of instrum. amp. Excel formula in column H is: R (ohms) R G (ohms) V2 (volts) V1 (volts)

Formula 28-15 Vout = (1 + 2 x R/RG) x (V2 - V1) =(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: V max (volts) R1 (ohms) R2 (ohms)

Formula 28-16 UTP = Vmax x [R1/(R1 + R2)] =D809*(E809/(E809+F809)) 12 10000 100000 1.09

CHAPTER 28 To find lower thresh. pt. of Sch. trig. Excel formula in column H is: V min (volts) R1 (ohms) R2 (ohms)

Formula 28-17 LTP = Vmin x [R1/(R1 + R2)] =D812*(E812/(E812+F812)) -12 10000 100000 -1.09

D t (msec)

D t (msec)

V in- (volts)

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

R1 (ohms)

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

R4 (ohms)

1

2

3

4

5

6

7

8

9

10

A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




814

815

816

817

818

819

820

821

822

823

824

825

826

827

828

829

830

831

832

833

834

835

836

837

838

839

840

841

842

843

844

845

846

847

848

849

850

851

852

853

CHAPTER 28 To find output V of IC audio amplifier Excel formula in column H is: V in (volts) R1B (ohms) R1A (ohms)

Formula 28-18 Vout = Vin x [R1B / (R1A+R1B-jXC1)] =(D815*E815)/SQRT((F815+E815)^2+(G815)^2)* 0.1 2000 8000 723.4 0.397

x 20 x [RSPK) / (RSPK-jXC2 )] (20*D817)/SQRT(D817^2+E817^2) R SPK (ohms) jXC2 (ohms)

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

CHAPTER 28 To find V out of OTA diff. amplifier Excel formula in column H is: V1 (volts) V2 (volts) k

Formula 28-19 Vout = (V1 - V2) x k x IBIAS x RL =(D820-E820)*F820*(G820*D822) 0.2 0.15 20 0.000486 4.86

R L (ohms)

10000

CHAPTER 28 To find UTP V for Sch. trig. comp. Excel formula in column H is: I BIAS (amps) R1 (ohms)

Formula 28-20 UTP = IBIAS x R1 =D825*E825 0.000486 10000 4.86

where:

IBIAS = VBIAS - V - - 0.7/RBIAS

CHAPTER 28 To find LTP V for Sch. trig. comp. Excel formula in column H is: I BIAS (amps) R1 (ohms)

Formula 28-21 LTP = -IBIAS x R1 =D830*E830 -0.000486 10000 -4.86

CHAPTER 28 To find fC of 1st order low-pass filter Excel formula in column H is: 2 R (ohms) C (farads)

Formula 28-22 fc = 1/(2 x R x C) =1/(D833*E833*F833) 6.28 1000 0.000001 159.24

CHAPTER 28 To find Vout of 1st order low-pass filt. Excel formula in column H is: V in (volts) - j X C R (ohms)

Formula 28-23 Vout = Vin x [-jXC/(R-jXC)] x (1+R2/R1) =D836*E836/SQRT(F836^2+E836^2)* 1 10000 10000 10000 1.414

(1+G836/D838) R1 (ohms)

10000

CHAPTER 28 To find fC of 1st order hi-pass filter Excel formula in column H is: 2 R (ohms) C (farads)

Formula 28-24 fc = 1/(2 x R x C) =1/(D841*E841*F841) 6.28 10000 2.2E-09 7238

CHAPTER 28 To find Vout of 1st order hi-pass filt. Excel formula in column H is: V in (volts) R (ohms) - j X C

Formula 28-25 Vout = Vin x [R/(R - jXC)] x (1+R2/R1) =D844*(E844/SQRT(E844^2+F844^2)) 1 10000 10000 10000 1.414

*(1+G844/D846)) R1 (ohms)

10000

CHAPTER 28 To find center f of bandpass filter Excel formula in column H is: R1 (ohms) R2 (ohms) R3 (ohms)

Formula 28-26 fo=1/2 x[R1xR2/(R1+R2)]xR3xC1xC2) =1/(6.28*SQRT(D849*E849/(D849+E849)* 1000 1000 20000 1E-08 7345

F849*G849*D851)) C2 (farads)

4.7E-09

CHAPTER 28 To find the BW of bandpass filter Excel formula in column H is: f o (Hz) Q

C1 (farads)

jXC1 (ohms)

I BIAS (amps)

R2 (ohms)

R2 (ohms)

1

2

3

4

5

6

7

8

9

10

A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




854

855

856

857

858

859

860

861

862

863

864

865

866

867

868

869

870

871

872

873

874

875

876

877

878

879

880

881

882

883

884

885

886

887

888

Formula 28-27 BW = f o/Q =D854/E854 7345 3.16 2324

CHAPTER 28 To find low cutoff f of bandpass filter Excel formula in column H is: f o (Hz) BW (Hz)

Formula 28-28 fc1 = fo - BW/2 =D857-(E857/2) 7345 2324 6183

CHAPTER 28 To find upper cutoff f of bandps. filt. Excel formula in column H is: f o (Hz) BW (Hz)

Formula 28-29 fc2 = fo + BW/2 =D860+(E860/2) 7345 2324 8507

CHAPTER 28 To find center f of bandstop filter Excel formula in column H is: R1 (ohms) R2 (ohms) C1 (farads)

Formula 28-30 fo = 1/(2 x R1 x R2 x C1 x C2 ) =1/(6.28*SQRT(D863*E863*F863*G863)) 1000 20000 0.00000001 1E-08 3561

CHAPTER 28 To find digit. dec. value for ADC circ. Excel formula in column H is: Vin1 (volts)

Formula 28-31 DATA = Vin1 x (255/5 V) dec. rep. =D866*(255/5) 2 102

CHAPTER 28 To find V out for DAC coverter Excel formula in column H is: V REF (volts) R14 (ohms) D7 D6

Formula 28-32 Vout = (-VREF/R14) x [D 7 /2)+(D6/4)+D5/8) =(-D869/E869)*((F869/2)+(G869/4)+(D871/8) 10 10000 1 0 5.390625

+(D4/16)+(D3/32)+(D2/64)+(D1/128)+ +(E871/16)+(F871/32)+(G871/64)+(D873/128) D5 D4 D3 D2

(D0/256)] x (- R1) +(E873/256))*(-F873) 0 0 1 0

D1 D0 R1 (ohms)

1 0 10000

CHAPTER 29 To find f r of LC tank circuit Excel formula in column H is: 2 L (H) C (farads)

Formula 29-1 fr = 1/2 x LC =1/(D876*SQRT(E876*F876)) 6.28 0.00004 1E-10 2517737

CHAPTER 29 To find f r of a Hartley Osc. circuit Excel formula in column H is: 2 L t (H) C (farads)

Formula 29-2 fr = 1/2 x LtC =1/(D879*SQRT(E879*F879)) 6.28 0.00004 1E-10 2517737

CHAPTER 29 To find L T in Hartley Osc. tank circuit Excel formula in column H is: L1A (H) L1B (H)

Formula 29-3 Lt = L1A + L1B =D882+E882 0.00002 0.00002 0.00004

CHAPTER 29 To find f r of a Colpitts Osc. circuit Excel formula in column H is: 2 L (H) C T (farads)

Formula 29-4 fr = 1/2 x L1CT =1/(D885*SQRT(E885*F885)) 6.28 0.0001 3.33E-10 872606

CHAPTER 29 To find C T in Colpitts Osc. tank circ. Excel formula in column H is: C1 (farads) C2 (farads)

Formula 29-5 CT = C1 x C2/(C1 + C2) =D888*E888/(D888+E888) 0.000000001 5E-10 0.000000000333

C2 (farads)

1

2

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A B C D E F G H


CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




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

925

926

CHAPTER 29 To find C T in Clapp Osc. tank circuit Excel formula in column H is: C1 (farads) C2 (farads) C3 (farads)

Formula 29-6 CT = 1/(1/C1 + 1/C2 + 1/C3) =1/(1/D891+1/E891+1/F891) 0.000000001 0.0000001 0.0000001 0.000000000980

CHAPTER 29 To find f r of a phase-shift oscillator Excel formula in column H is: 2 R (ohms) C (farads)

Formula 29-7 fr = 1/2 x R x C x 6 =1/((D894*E894*F894*SQRT(6))) 6.28 3300 0.00000001 1970

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

CHAPTER 29 To find f r of Wien bridge oscillator Excel formula in column H is: 2 R (ohms) C (farads)

Formula 29-8 fr = 1/2 x R x C =1/(D898*E898*F898) 6.28 100000 0.0000001 15.92

CHAPTER 29 Estimated timing for monostable MV Excel formula in column H is: R C (ohms) C (farads)

Formula 29-9 ton = 0.69 x RC x C =0.69*D901*E901 100000 0.0000001 0.0069

CHAPTER 29 Est. timing for 555 type mono. MV Excel formula in column H is: R C (ohms) C (farads)

Formula 29-10 tw = 1.1 x RC x C =1.1*D904*E904 1000000 0.00001 11

CHAPTER 29 Est. timing intervals for astable MV Excel formula in column H is: RC1 (ohms) CC1 (Fd)

Formula 29-11 t = 0.7 x R x C =0.7*D907*E907 10000 0.00000001 0.00007

CHAPTER 29 Operating freq. of an astable MV Excel formula in column H is: R C (ohms) C (farads)

Formula 29-12 f = 1/1.38 x RC x C =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: C (farads) R A (ohms) R B (ohms)

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


CHAPTER 31 To find V to be dropped by R in LED circ. Excel formula in column H is: V S (volts) V D (volts)

Formula 31-1 V R = V S - V D =D919-E919 12 1.5 10.5

CHAPTER 31 To find R value for given LED curr. Excel formula in column H is: V R (volts) I D (amps)

Formula 31-2 R = V R / I D =D922/E922 7.5 0.015 500

(Note: Knowing that V R = V S -V D )

CHAPTER 31 To find R value for given LED curr. Excel formula in column H is: V S (volts) V D (volts) I D (amps)

Formula 31-3 R = (V S - V D ) / I D =(D926-E926)/F926 9 1.5 0.015 500

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CHAPTER # &

FORMULA # FORMULAS



PARAMETER HEADINGS

AND THEIR VALUES

ANSWERS:


(Use Approp. Units)




927

928

929

930

931

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933

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941

CHAPTER 31 To find I in photodiode circuit R (ohms) P RCVD

Formula 31-4 I = R x P RCVD =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 I D (amps)

Formula 31-5 I C = CTR x I D =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: P out (mW) P in (mW)

Formula 31-6 A = 10 log10 (Pout / Pin) =10*LOG(D938/E938,10) 3.33 333 -20

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

Formula 31-7 Pout = Pin x ( 10A/10

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

All Electrical Engineering Formulas

Engineering

Transcript of All Electrical Engineering Formulas