Engineering Circuit Analysis

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The Resistor Color Code
Band color Black Brown Red Orange Yellow Green Blue Violet Gray White
Numeric value 0123 456789
1st number
2nd number Tolerance band (e.g. gold = 5%
silver = 10%, none = 20%)
Multiplier
1. Write down the numeric value corresponding to the first band on the left.
2. Write down the numeric value corresponding to the second band from the left.
3. Write down the number of zeros indicated by the multiplier band, which represents a power of 10
(black =no extra zeros, brown =1 zero, etc.). A gold multiplier band indicates that the decimal
is shifted one place to the left; a silver multiplier band indicates that the decimal is shifted
two places to the left.
4. The tolerance band represents the precision. So, for example, we would not be surprised to find a 100 
5 percent tolerance resistor that measures anywhere in the range of 95 to 105 .
Example
Red Red Orange Gold =22,000 or 22 ×103=22 k, 5% tolerance
Blue Gray Gold =6.8 or 68 ×10−1=6.8 , 20% tolerance
Standard 5 Percent Tolerance Resistor Values
1.0 1.1 1.2 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1 
10. 11. 12. 13. 15. 16. 18. 20. 22. 24. 27. 30. 33. 36. 39. 43. 47. 51. 56. 62. 68. 75. 82. 91. 
100 110 120 130 150 160 180 200 220 240 270 300 330 360 390 430 470 510 560 620 680 750 820 910 
1.0 1.1 1.2 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1 k
10. 11. 12. 13. 15. 16. 18. 20. 22. 24. 27. 30. 33. 36. 39. 43. 47. 51. 56. 62. 68. 75. 82. 91. k
100 110 120 130 150 160 180 200 220 240 270 300 330 360 390 430 470 510 560 620 680 750 820 910 k
1.0 1.1 1.2 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1 M
TABLE ●14.1 Laplace Transform Pairs
f(t)=−1{F(s)} F(s)={f(t)} f(t)=−1{F(s)} F(s) ={f(t)}
δ(t)11
β−α(e−αt−e−βt)u(t)1 (s+α)(s+β)
u(t)1
ssin ωtu(t)ω s2+ω2
tu(t)1
s2cos ωtu(t)s s2+ω2
tn−1
(n−1)!u(t),n=1,2,... 1
snsin(ωt+θ)u(t)ssin θ+ωcos θ s2+ω2
e−αtu(t)1
s+αcos(ωt+θ)u(t)scos θ−ωsin θ s2+ω2
te−αtu(t)1
(s+α)2e−αtsin ωtu(t)ω (s+α)2+ω2
tn−1
(n−1)!e−αtu(t), n=1,2,... 1
(s+α)ne−αtcos ωtu(t)s+α (s+α)2+ω2

TABLE ●6.1 Summary of Basic Op Amp Circuits
Name Circuit Schematic Input-Output Relation
Inverting Amplifier vout =−Rf
R1vin
Noninverting Amplifier vout =1+Rf
R1vin
Voltage Follower vout =vin
(also known as a
Unity Gain Amplifier)
Summing Amplifier vout =−Rf
R(v1+v2+v3)
Difference Amplifier vout =v2−v1
Rf
R1
–
+
i
i
+
–
vin vout
+
–
Rf
R1
–
+
+
–
vin
vout
+
–
–
+
vin +
–
vout
+
–
–
+
i
vout
+
–
R
RRL
R
v1
va
vb
Rf
i3
i2
i1
+
–
v2+
–
v3+
–
–
+
i
vou
t
+
–
R
RL
R
R
v1
va
vb
R
i2
i1
+
–v2+
–

ENGINEERING
CIRCUIT
ANALYSIS