Analog Engineer’s
Pocket Reference
Art Kay and Tim Green, Editors
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Analog Engineer’s Pocket Reference
Fourth Edition
Edited by:
Art Kay and Tim Green
Special thanks for technical contribution and review:
Kevin Duke
Rafael Ordonez
John Caldwell
Collin Wells
Ian Williams
Thomas Kuehl
© Copyright 2014, 2015 Texas Instruments Incorporated. All rights reserved.
Texas Instruments Analog Engineer's Pocket Reference
3
Message from the editors:
This pocket reference is intended as a valuable quick guide for often used board- and systemlevel design formulae. This collection of formulae is based on a combined 50 years of analog
board- and system-level expertise. Much of the material herein was referred to over the years
via a folder stuffed full of printouts. Those worn pages have been organized and the information is now available via this guide in a bound and hard-to-lose format!
Here is a brief overview of the key areas included:
• Key constants and conversions
• Discrete components
• AC and DC analog equations
• Op amp basic configurations
• OP amp bandwidth and stability
• Overview of sensors
• PCB trace R, L, C
• Wire L, R, C
• Binary, hex and decimal formats
• A/D and D/A conversions
We hope you find this collection of formulae as useful as we have. Please send any comments
and/or ideas you have for the next edition of the Analog Engineer's Pocket Reference to
artkay_timgreen@list.ti.com
Additional resources:
• Browse TI Precision Labs (www.ti.com/precisionlabs), a comprehensive online training
curriculum for analog engineers, which applies theory to real-world, hands-on examples.
• Search for complete board-and-system level circuits in the TI Designs – Precision
reference design library (www.ti.com/precisiondesigns).
• Read how-to blogs from TI precision analog experts at the Precision Hub
(www.ti.com/thehub).
• Find solutions, get help, share knowledge and solve problems with fellow engineers and
TI experts in the TI E2E™ Community (www.ti.com/e2e).
4
Texas Instruments Analog Engineer's Pocket Reference
Contents
Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Standard decimal prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Metric conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Temperature conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Error conversions (ppm and percentage) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Discrete components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Resistor color code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Standard resistor values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Practical capacitor model and specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Practical capacitors vs frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Capacitor type overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Standard capacitance values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Capacitance marking and tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diodes and LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
13
14
15
16
17
17
18
Analog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Capacitor equations (series, parallel, charge, energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inductor equations (series, parallel, energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Capacitor charge and discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
RMS and mean voltage definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
RMS and mean voltage examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Logarithmic mathematical definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
dB definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Log scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pole and zero definitions and examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time to phase shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
21
23
24
24
27
28
29
30
34
Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Basic op amp configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Op amp bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Full power bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Small signal step response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Noise equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Phase margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stability open loop SPICE analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Instrumentation Amp filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
41
42
43
44
48
50
53
PCB and wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
PCB conductor spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Self-heating of PCB traces on inside layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PCB trace resistance for 1oz and 2oz Cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Package types and dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PCB parallel plate capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PCB microstrip capacitance and inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PCB adjacent copper trace capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PCB via capacitance and inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Common coaxial cable specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coaxial cable equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resistance per length for different wire types (AWG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maximum current for wire types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
57
58
60
61
62
63
64
65
66
67
68
Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Temperature sensor overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resistive temperature detector (RTD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diode temperature characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermocouple (J and K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
71
72
74
76
A/D conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Binary/hex conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A/D and D/A transfer function (LSB, Data formats, FSR) . . . . . . . . . . . . . . . . . . . . . . . . . .
Quantization error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal-to-noise ratio (SNR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Total harmonic distortion (THD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal-to-noise and distortion (SINAD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Effective number of bits (ENOB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Noise free resolution and effective resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Setting time and conversion accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Texas Instruments Analog Engineer's Pocket Reference
83
84
90
91
92
94
94
95
96
5
6
Texas Instruments Analog Engineer's Pocket Reference
Standard decimal prefixes •
Metric conversions •
Temperature scale conversions •
Error conversions (ppm and percentage) •
Texas Instruments Analog Engineer's Pocket Reference
7
Conversions
Conversions
Conversions
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Conversions
Conversions
ti.com/precisionlabs
Table 1: Physical constants
Constant
Speed of light in a vacuum
Symbol
Value
c
2.997 924 58 x 108
Units
m/s
-12
εo
8.854 187 817 620 x 10
F/m
Permeability of free space
µo
1.256 637 0614 x 10-6
H/m
Plank’s constant
h
6.626 069 57 x 10-34
J•s
Permittivity of vacuum
-23
Boltzmann’s constant
k
1.380 648 8 x 10
Faraday’s constant
F
9.648 533 99 x 104
C/mol
Avogadro’s constant
NA
6.022 141 29 x 1023
1/mol
mu
1.660 538 921 x 10-27
kg
-19
C
Unified atomic mass unit
Electronic charge
q
J/K
1.602 176 565 x 10
-31
Rest mass of electron
me
9.109 382 15 x 10
kg
Mass of proton
mp
1.672 621 777 x 10-27
kg
-11
Nm2/kg2
Gravitational constant
G
Standard gravity
gn
9.806 65
m/s2
Ice point
Tice
273.15
K
Maximum density of water
Density of mercury (0°C)
Gas constant
Speed of sound in air (at 273°K)
6.673 84 x 10
3
ρ
1.00 x 10
kg/m3
ρHg
1.362 8 x 104
kg/m3
R
8.314 462 1
J/(K•mol)
2
cair
3.312 x 10
m/s
Table 2: Standard decimal prefixes
Multiplier
Abbreviation
10
tera
T
109
giga
G
106
mega
M
103
kilo
k
10–3
milli
m
10–6
micro
µ
10–9
nano
n
10–12
pico
p
10–15
femto
f
atto
a
–18
10
8
Prefix
12
Texas Instruments Analog Texas Instruments Analog Engineer's Pocket Reference
Engineer's Pocket Reference
Conversions
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Table 3: Imperial to metric conversions
Unit
Symbol
Equivalent
Unit
Symbol
inches
in
25.4 mm/in
millimeter
mm
mil
mil
0.0254 mm/mil
millimeter
mm
feet
ft
0.3048 m/ft
meters
m
yards
yd
0.9144 m/yd
meters
m
miles
mi
1.6093 km/mi
kilometers
km
circular mil
cir mil
5.067x10-4 mm2/cir mil
square millimeters
mm2
2
2
square yards
yd
0.8361 m
square meters
m2
pints
pt
0.5682 L/pt
liters
L
ounces
oz
28.35 g/oz
grams
g
pounds
lb
0.4536 kg/lb
kilograms
kg
calories
cal
4.184 J/cal
joules
J
horsepower
hp
745.7 W/hp
watts
W
Symbol
Table 4: Metric to imperial conversions
Unit
Symbol
Conversion
Unit
millimeter
mm
0.0394 in/mm
inch
in
millimeter
mm
39.4 mil/mm
mil
mil
meters
m
3.2808 ft/m
feet
ft
meters
m
1.0936 yd/m
yard
yd
kilometers
km
0.6214 mi/km
miles
mi
square millimeters
mm2
1974 cir mil/mm2
circular mil
cir mil
square meters
m2
1.1960 yd2/ m2
square yards
yd2
liters
L
1.7600 pt/L
pints
pt
grams
g
0.0353 oz/g
ounces
oz
kilograms
kg
2.2046 lb/kg
pounds
lb
joules
J
0.239 cal/J
calories
cal
watts
W
1.341x10-3 hp/W
horsepower
hp
Example
Convert 10 mm to mil.
Answer
10 mm x 39.4
mil
= 394 mil
mm
Texas Instruments Analog Engineer's Pocket Reference
9
Conversions
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Table 5: Temperature conversions
Table 5: Temperature conversions
Table 5:
5 Temperature conversions
Fahrenheit
�� � ��F � �2�
FahrenheittotoCelsius
Celsius
9 5
Fahrenheit to Celsius
��9� ��F � �2�
9
Celsius
CelsiustotoFahrenheit
Fahrenheit
�F � ���� � �2
5 9
Celsius to Fahrenheit
�F � ���� � �2
CelsiustotoKelvin
Kelvin
Celsius
� � �� �52��.15
Celsius to Kelvin
� � �� � 2��.15
KelvintotoCelsius
Celsius
Kelvin
�� � � � 2��.15
Kelvin to Celsius
�� � � � 2��.15
Table 6: Error conversions
Table 6: Error conversions
Table 6: Error
conversions
�easured
� Ideal
Error�%� �
� 100
Ideal � Ideal
�easured
Error�%� � �easured � Ideal� 100
Ideal
Error�% FSR� �
� 100
Full‐scale
range
�easured
� Ideal
Error�% FSR� � ppm
� 100
Full‐scale range
%�
� 100
�
10 ppm
%�
� 100
ppm
10�
� 100 � 1000
m% �
10�ppm
� 100 � 1000
m% �
10�
ppm � % � 10�
ppm � % � 10�
ppm � m% � 10
ppm � m% � 10
Error in measured value
Errorin
inmeasured
measuredvalue
value
Error
Error in percent of full-scale range
Error
Errorin
inpercent
percent of
of full-scale
full-scale range
range
Part per million to percent
Part
Part per
per million
million to
to percent
Part per million to milli-percent
Part per
per million
million to
to milli-percent
Part
Percent to part per million
Percent to
to part
part per
per million
Percent
Milli-percent to part per million
Milli-percent to part per million
Milli-percent
million
Example
Example
Compute the error for a measured value of 0.12V when the ideal value is 0.1V and
theCompute
range
is 5V.
Example
the error for a measured value of 0.12V when the ideal value is 0.1V and
Compute
the
range isthe
5V.error for a measured value of 0.12V when the ideal value is 0.1V
and the range is 5V.
Answer
Answer 0.12V � 0.1V
Error�%�
�
� 100 � 20%
Answer
0.1V � 0.1V
0.12V
V
Error�%� � 0.12V
0.12
� 0.1V � 100 � 20%
Error %
0.1V
� 100 � 0.�%
Error�% FSR� �
0.1V
5V � 0.1V
0.12
V� 100 � 0.�%
Error�% FSR� �
Error % FSR
5V
5V
Example
Error in measured value
Error in measured value
Error in measured value
Percent FSR
Percent FSR
Percent FSR
Example
Example
Convert
10 ppm to percent and milli-percent.
Convert
Convert10
10ppm
ppmtotopercent
percentand
andmilli-percent.
milli-percent.
Answer
Answer
10 ppm
Answer
Part per million to percent
� 100 � 0.001%
�
10
10
ppm
10
ppm
Part
Partper
permillion
milliontotopercent
percent
�
100
�
0.001%
10 ppm
10
10�� 100 � 1000 � 1 m%
Part per million to milli-percent
�
10
10
10ppm
ppm
Part
Partper
permillion
milliontotomilli-percent
milli-percent
� 100 � 1000 � 1 m%
10
10�
10
Texas
Texas Instruments Analog Engineer's Pocket Reference
10
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Discrete
Components
Resistor color code •
Standard resistor values •
Capacitance specifications •
Capacitance type overview •
Standard capacitance values •
Capacitance marking and tolerance •
11
Texas
Texas Instruments Analog Engineer's Pocket Reference
Discrete
Discrete Components
Discrete Components
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Discrete
Table 7: Resistor color code
Color
Digit
Additional
Zeros
Black
0
0
Tolerance
Temperature
Coefficient
Failure
Rate
250
Brown
1
1
1%
100
1
Red
2
2
2%
50
0.1
Orange
3
3
15
0.01
Yellow
4
4
25
0.001
Green
5
5
0.5%
20
Blue
6
6
0.25%
10
Violet
7
7
0.1%
5
0.05%
1
Grey
8
8
White
9
9
Gold
-na-
-1
5%
Silver
-na-
-2
10%
No Band
-na-
-na-
20%
4 Band example: yellow violet orange silver indicate 4, 7, and 3 zeros.
i.e. a 47kΩ, 10% resistor.
Figure 1: Resistor color code
12
Texas
Texas Instruments Analog Engineer's Pocket Reference
10.0
10.1
10.2
10.4
10.5
10.6
10.7
10.9
11.0
11.1
11.3
11.4
11.5
11.7
11.8
12.0
12.1
12.3
12.4
12.6
12.7
12.9
13.0
13.2
13.3
13.5
13.7
13.8
14.0
14.2
14.3
14.5
0.1%
0.25%
0.5%
Texas Instruments Analog Engineer's Pocket Reference
14.3
14.0
13.7
13.3
13.0
12.7
12.4
12.1
11.8
11.5
11.3
11.0
10.7
10.5
10.2
10.0
1%
13
12
11
10
2%
5%
10%
14.7
14.9
15.0
15.2
15.4
15.6
15.8
16.0
16.2
16.4
16.5
16.7
16.9
17.2
17.4
17.6
17.8
18.0
18.2
18.4
18.7
18.9
19.1
19.3
19.6
19.8
20.0
20.3
20.5
20.8
21.0
21.3
0.1%
0.25%
0.5%
21.0
20.5
20.0
19.6
19.1
18.7
18.2
17.8
17.4
16.9
16.5
16.2
15.8
15.4
15.0
14.7
1%
20
18
16
15
2%
5%
10%
21.5
21.8
22.1
22.3
22.6
22.9
23.2
23.4
23.7
24.0
24.3
24.6
24.9
25.2
25.5
25.8
26.1
26.4
26.7
27.1
27.4
27.7
28.0
28.4
28.7
29.1
29.4
29.8
30.1
30.5
30.9
31.2
0.1%
0.25%
0.5%
30.9
30.1
29.4
28.7
28.0
27.4
26.7
26.1
25.5
24.9
24.3
23.7
23.2
22.6
22.1
21.5
1%
30
27
24
22
2%
5%
10%
31.6
32.0
32.4
32.8
33.2
33.6
34.0
34.4
34.8
35.2
35.7
36.1
36.5
37.0
37.4
37.9
38.3
38.8
39.2
39.7
40.2
40.7
41.2
41.7
42.2
42.7
43.2
43.7
44.2
44.8
45.3
45.9
0.1%
0.25%
0.5%
45.3
44.2
43.2
42.2
41.2
40.2
39.2
38.3
37.4
36.5
35.7
34.8
34.0
33.2
32.4
31.6
1%
43
39
36
33
2%
5%
10%
46.4
47.0
47.5
48.1
48.7
49.3
49.9
50.5
51.1
51.7
52.3
53.0
53.6
54.2
54.9
55.6
56.2
56.9
57.6
58.3
59.0
59.7
60.4
61.2
61.9
62.6
63.4
64.2
64.9
65.7
66.5
67.3
0.1%
0.25%
0.5%
Standard resistance values for the 10 to 100 decade
66.5
64.9
63.4
61.9
60.4
59.0
57.6
56.2
54.9
53.6
52.3
51.1
49.9
48.7
47.5
46.4
1%
62
56
51
47
2%
5%
10%
68.1
69.0
69.8
70.6
71.5
72.3
73.2
74.1
75.0
75.9
76.8
77.7
78.7
79.6
80.6
81.6
82.5
83.5
84.5
85.6
86.6
87.6
88.7
89.8
90.9
92.0
93.1
94.2
95.3
96.5
97.6
98.8
0.1%
0.25%
0.5%
97.6
95.3
93.1
90.9
88.7
86.6
84.5
82.5
80.6
78.7
76.8
75.0
73.2
71.5
69.8
68.1
1%
91
82
75
68
2%
5%
10%
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Discrete Components
Table 8: Standard resistor values
13
Discrete Components
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Practical capacitor model and specifications
Rp
ESR
C
ESL
Figure 2: Model of a practical capacitor
Table 9: Capacitor specifications
Parameter
Description
C
The nominal value of the capacitance
Table 11 lists standard capacitance values
ESR
Equivalent series resistance
Ideally this is zero
Ceramic capacitors have the best ESR (typically in milliohms). Tantalum Electrolytic have ESR in the hundreds of milliohms and Aluminum Electrolytic have ESR
in the ohms
ESL
Equivalent series inductance
Ideally this is zero
ESL ranges from 100 pH to 10 nH
Rp
Rp is a parallel leakage resistance (or insulation resistance)
Ideally this is infinite
This can range from tens of megaohms for some electrolytic capacitors to tens of
gigohms for ceramic
Voltage rating
The maximum voltage that can be applied to the capacitor
Exceeding this rating damages the capacitor
Voltage
coefficient
The change in capacitance with applied voltage in ppm/V
A high-voltage coefficient can introduce distortion
C0G capacitors have the lowest coefficient
The voltage coefficient is most important in applications that use capacitors in
signal processing such as filtering
Temperature
coefficient
The change in capacitance with across temperature in ppm/°C
Ideally, the temperature coefficient is zero
The maximum specified drift generally ranges from 10 to 100ppm/°C or greater
depending on the capacitor type (See Table 10 for details)
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Discrete Components
Practical capacitors vs. frequency
Impedance (ohms)
Practical capacitors vs. frequency
of ESR
ESL on capacitor
frequency
Figure 3:Figure
Effect 3:
of Effect
ESR and
ESL and
on capacitor
frequency
responseresponse
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Table 10: Capacitor type overview
Capacitor type
Description
C0G/NP0
(Type 1 ceramic)
Use in signal path, filtering, low distortion, audio, and precision
Limited capacitance range: 0.1 pF to 0.47 µF
Lowest temperature coefficient: ±30 ppm/°C
Low-voltage coefficient
Minimal piezoelectric effect
Good tolerance: ±1% to ±10%
Temperature range: –55°C to 125°C (150°C and higher)
Voltage range may be limited for larger capacitance values
X7R
(Type 2 ceramic)
Use for decoupling and other applications where accuracy and
low distortion are not required
X7R is an example of a type 2 ceramic capacitor
See EIA capacitor tolerance table for details on other types
Capacitance range: 10 pF to 47 µF
Temperature coefficient: ±833 ppm/°C (±15% across temp range)
Substantial voltage coefficient
Tolerance: ±5% to –20%/+80%
Temperature range: –55°C to 125°C
Voltage range may be limited for larger capacitance values
Y5V
(Type 2 ceramic)
Use for decoupling and other applications where accuracy and
low distortion are not required
Y5V is an example of a type 2 ceramic capacitor
See EIA capacitor tolerance table for details on other types
Temperature coefficient: –20%/+80% across temp range
Temperature range: –30°C to 85°C
Other characteristics are similar to X7R and other type 2 ceramic
Aluminum oxide
electrolytic
Use for bulk decoupling and other applications where large
capacitance is required
Note that electrolytic capacitors are polarized and will be damaged, if a
reverse polarity connection is made
Capacitance range: 1 µF to 68,000 µF
Temperature coefficient: ±30 ppm/°C
Substantial voltage coefficient Tolerance: ±20%
Temperature range: –55°C to 125°C (150°C and higher)
Higher ESR than other types
Tantalum
electrolytic
Capacitance range: 1 µF to 150 µF
Similar to aluminum oxide but smaller size
Polypropylene
film
Capacitance range: 100 pF to 10 µF
Very low voltage coefficient (low distortion)
Higher cost than other types
Larger size per capacitance than other types
Temperature coefficient: 2% across temp range
Temperature range: –55°C to 100°C
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Table 11: Standard capacitance table
Standard capacitance table
1
1.1
1.2
1.3
1.5
1.6
1.8
2
2.2
2.4
2.7
3
3.3
3.6
3.9
4.3
4.7
5.1
5.6
6.2
6.8
7.5
8.2
9.1
CK06
223K
Figure 4: Capacitor
marking code
Example
Translate the capacitor marking
2 2 3 K "K" = ±10%
22 000 pF
= 22nF = 0.022µF
Table 12: Ceramic capacitor tolerance markings
Code
Tolerance
Code
Tolerance
B
± 0.1 pF
J
± 5%
C
± 0.25 pF
K
± 10%
D
± 0.5 pF
M
± 20%
F
± 1%
Z
+ 80%, –20%
G
± 2%
Table 13: EIA capacitor tolerance markings (Type 2 capacitors)
First letter
symbol
Low temp
limit
Second
number
symbol
High temp
limit
Second
letter
symbol
Max. capacitance
change over
temperature rating
Z
+10°C
2
+45°C
A
±1.0%
Y
–30°C
4
+65°C
B
±1.5%
X
–55°C
5
+85°C
C
±2.2%
6
+105°C
D
±3.3%
7
+125°C
E
±4.7%
F
±7.5%
P
±10.0%
R
±15.0%
S
±22.0%
T
±22% ~ 33%
U
±22% ~ 56%
V
±22% ~ 82%
Example
X7R: –55°C to +125°C, ±15.0%
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Diodes and LEDs
Anode (+)
Cathode (-)
Anode (+)
Cathode (-)
Anode (+)
Anode (+)
Long Lead
Cathode (-)
Anode (+)
Cathode (-)
Anode (+)
Long Lead
Cathode (-)
Short Lead, Flat
Cathode (-)
Figure 5: Diode and LED pin names
Color
Wavelength (nm)
Voltage (approximate range)
Infrared
940-850
1.4 to 1.7
Red
660-620
1.7 to 1.9
Orange / Yellow
620-605
2 to 2.2
Green
570-525
2.1 to 3.0
Blue/White
470-430
3.4 to 3.8
Table 14: LED forward voltage drop by color
Note: The voltages given are approximate, and are intended to show the general trend for
forward voltage drop of LED diodes. Consult the manufacturer’s data sheet for more precise
values.
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Analog
Analog
Analog
Capacitor equations (series, parallel, charge, energy) •
Inductor equations (series, parallel, energy) •
Capacitor charge and discharge •
RMS and mean voltage definition •
RMS for common signals •
Logarithm laws •
dB definitions •
Pole and zero definition with examples •
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Capacitor equations
Capacitor
equations
C
C
C
1
C
C
C C
1
C
1
1
C
(1) Series capacitors
(2) Two series capacitors
(3) Parallel capacitors
Analog
Where
Ct = equivalent total capacitance
C1, C2, C3…CN = component capacitors
V
(4) Charge storage
(5) Charge defined
Where
Q = charge in coulombs (C)
C = capacitance in farads (F)
V = voltage in volts (V)
I = current in amps (A)
t = time in seconds (s)
dv
dt
(6) Instantaneous current through a capacitor
Where
i = instantaneous current through the capacitor
C = capacitance in farads (F)
dv = the instantaneous rate of voltage change
dt
1
CV
2
(7) Energy stored in a capacitor
Where
E = energy stored in an capacitor in Joules (J)
V = voltage in volts
C = capacitance in farads (F)
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Inductor
equations
Inductor equations
L� � L� � L� � � � L�
L� �
L� �
1
1
1
1
� � ��
L�
L� L�
L� L�
L� � L�
Series
inductors
(8)Series
(8)
inductors
Parallel
inductors
(9)Parallel
(9)
inductors
Two
parallel
inductors
(10)
parallel
inductors
(10)Two
Where
Where
total inductance
inductance
LLtt = equivalent total
LL11,, L
L33…L
…LNN == component
componentinductance
inductance
L22,, L
v�L
di
dt
Instantaneousvoltage
voltageacross
acrossananinductor
inductor
(11)Instantaneous
(11)
Where
Where
v = instantaneous voltage across the inductor
v = instantaneous voltage across the inductor
L = inductance in Henries (H)
L = inductance in Henries (H)
di
� = instantaneous rate of current change
dt = the instantaneous rate of voltage change
��
1
� � LI�
2
Energystored
storedininananinductor
Inductor
(12)Energy
(12)
Where
Where
EE == energy
energy stored
stored in
in an
an inductor
inductorininJoules
Joules(J)
(J)
II ==current
currentininamps
amps
L = inductance in Henries (H)
L = inductance in Henries (H)
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Equation for
for charging
capacitor
Equation
chargingaan
RC circuit
��
V� � V� �� � �� � � �
General
relationship
(13)
(13)
General
relationship
Equation for charging a capacitor
Where
��
Where
relationship
V�C =�voltage
V� �� �
�� � �the
� capacitor(13)
V
across
at anyGeneral
instant in
time (t)
across
the capacitor
VCV ==voltage
the source
voltage
charging at
theany
RCinstant
circuit in time (t)
S
VSt ==time
the source
voltage charging the RC circuit
in seconds
Where
t = =
time
seconds
RC,inthe
time constant for charging and discharging capacitors
VC = voltage across the capacitor at any instant in time (t)
τ = RC, the time constant for charging and discharging capacitors
VS = the source voltage charging the RC circuit
Graphing equation 13 produces the capacitor charging curve below. Note that the
t = time in seconds
capacitor is 99.3% charged at five time constants. It is common practice to consider
 = RC, the time constant for charging and discharging capacitors
this fully charged.
Graphing
equation 13 produces the capacitor charging curve below. Note
that
the capacitor is 99.3% charged at five time constants. It is common
Graphing equation 13 produces the capacitor charging curve below. Note that the
practice
to consider this fully charged.
capacitor is 99.3% charged at five time constants. It is common practice to consider
this fully charged.
Figure 7: RC charge curve
Figure 7: RC charge curve
22
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Figure 6: RC charge curve
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Equation for discharging a capacitor
Equation for discharging an RC circuit
��
V� � V� ��� � � �
(14) General Relationship
(14) General
relationship
Equation for discharging a capacitor
Where
Where
V� � V� ��� � � �
(14) General relationship
==
voltage
across
the capacitor
at any instant
time (t) in time (t)
VV
voltage
across
the capacitor
at anyininstant
CC
==
thethe
initial
voltage
of
the
capacitor
at
t=0s
VV
i Where
initial voltage of the capacitor at t=0s
I
t =VCtime
in seconds
= voltage
across the capacitor at any instant in time (t)
time intime
seconds
τ t=V=IRC,
constant
charging
and discharging capacitors
= thethe
initial voltage
of thefor
capacitor
at t=0s
��
t == time
RC,in the
time constant for charging and discharging capacitors
seconds
 = RC, the time constant for charging and discharging capacitors
Graphing equation 14 produces the capacitor discharge curve below. Note
Graphing
equation
14 produces
capacitor
discharge
curve belo
that
the capacitor
is discharged
to 0.7%the
at five
time constants.
It is comGraphing equation 14 produces the capacitor discharge curve below. Note that the
mon
practice
to
consider
this
fully
discharged.
capacitor is 0.7% charged at five time constants. It is common prac
capacitor is 0.7% charged at five time constants. It is common practice to consider
this fully
this
fullydischarged.
discharged.
Percentage Discharged vs. Number of Time Constants
100
Percentage Discharged vs. Number of Time Consta
100
90
80
PercentagePercentage
Charged Charged
90
70
80
60
70
50
40
60
30
50
20
10
40
0
30 0
1
2
3
4
5
Number of time Constants (τ = RC)
20
Figure
Figure 7: RC discharge curve
10 8: RC discharge curve
0
0
1
2
3
4
Number of time Constants (τ = RC)
Figure 8: RC discharge curve
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RMS voltage
RMS
voltage
RMS voltage
��
RMS voltage1
(15)
General
relationship
(15)
General
relationship
V��� � �
� �V�t��� dt
��� � �� � ��
��
1
��
(15) General relationship
� �V�t��� dt
V��� � � 1
(15) General relationship
V���
��
� ���V�t��� dt
� � ���
Where ����
� � �� � ��
Where
V(t) = continuous function of time
V(t) = continuous function of time
Where
t=
time in seconds
Where
t =V(t)
time continuous
in seconds function of time
T
≤continuous
T2 = the time
interval
that the function is defined over
1 ≤ t=
V(t)
=
function
of time
t
≤
T
the time
interval
that the function is defined over
T1t ≤
= time 2in=seconds
t = time in seconds
T1 ≤ tvoltage
≤ T2 = the time interval that the function is defined over
Mean
T1 ≤ t ≤ T2 = the time interval that the function is defined over
Mean
voltage
Mean voltage
1
��
Mean
(16) General relationship
� V�t�dt
V���� voltage
�
��� � �� � ��
��
1
��
(16)(16)
General
relationship
General
relationship
V���� � 1
� V�t�dt
(16) General relationship
V
� ��V�t�dt
���� � ��� � ���
Where
��� � �� � ��
V(t) = continuous function of time
Where
t=
time in seconds
Where
Where
V(t)
= continuous
function
ofthat
time
T
T2 = the time
interval
1 ≤=t continuous
V(t)
function
of
V(t) = ≤continuous
function
of time
time the function is defined over
t =time
time inseconds
seconds
tt ==
time in
in seconds
T1 ≤ t ≤ T2 = the time interval that the function is defined over
TT11 ≤≤
t ≤ T22 == the
the time
time interval
interval that
that the
the function
functionisisdefined
definedover
over
V����
RMS for full wave rectified
V��� �
(17)
sine wave
√2
V����
RMS for full wave rectified
RMS
for fullsine
wave
rectified
V��� �V����
(17)
(17) RMS for full
wave
rectified
wave
V���
� 2 √2
(17)
sine
wave
Mean
for full wave
rectified
� V����
(18) sine wave
V���� � √2
sine wave
π
Mean for full wave rectified
2 � V����
for full wave rectified
(18) Mean
V���� �2 � V����
(18) Mean for full
rectified
(18)wave
sine
wave sine wave
V����
�
π
sine
wave
π
Figure 9: Full wave rectified sine wave
Figure
8: Fullsine
wave
rectified sine wave
Figure 9: Full wave
rectified
wave
Figure 9: Full wave rectified sine wave
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RMS voltage
andand
mean
voltage
RMS
voltage
mean
voltage
V
τ
2T
V
V
π
V
RMS for a half-wave
(19)
(19) RMS for
a half-wave
sine wave
rectified rectified
sine wave
τ
T
Mean for a half-wave
(20)
(20) Mean for
a half-wave rectified sine wave
rectified sine wave
9: sine
Half-wave
Figure 10: Half-wave Figure
rectified
wave rectified sine wave
V
V
V
V
τ
T
(21)
a square
wave
(21)
RMSRMS
for afor
square
wave
τ
T
Figure 11: Square wave
(22) Mean for a square wave
Figure 10: Square wave
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RMS voltage and mean voltage
RMS voltage and mean voltage
V
V
(V
τ
V
2T
V V
3
V
V
(( T (
τ
(23)
RMS
for afortrapezoid
(23)
RMS
a trapezoid
(24)
Mean
for afortrapezoid
(24)
Mean
a trapezoid
Figure 12: Trapezoidal wave
Figure 11: Trapezoidal wave
V
V
V
τ
V
2T
τ
3T
Figure 13: Triangle wave
26
Texas
(25) RMS
a triangle
wave wave
(25) for
RMS
for a triangle
(26) Mean
for a triangle
(26) Mean
for a triangle
wave wave
Figure 12: Triangle wave
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Logarithmic
mathematical
definitions
Logarithmic mathematical
definitions
A
B
A
log AB
log A
log
log
ln X
A
log
log
A
log
log
B
B
(27)ofLog
of dividend
(27) Log
dividend
(28) Log
product
(28)ofLog
of product
(29)ofLog
of exponent
(29) Log
exponent
(30) Changing
the of
base
log function
(30) Changing
the base
logof
function
(31) Example
changing
to logtobase
2
(31) Example
changing
log base
2
(32) Natural
log is log
log is
base
e
(32) Natural
log base
e
(33) Exponential
function
to 6 digits.
(33) Exponential
function
to 6 digits
Alternative
Alternative notations
notations
exp x
Different
notation
for exponential
(34) Different
notation
for exponential
function
(34)
function
Different notation for scientific
(35) Different notation for scientific notation,
(35) notation, sometimes confused with
sometimes confused with
exponential function
exponential function
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dB definitions
Bode
plot basics
dB definitions
The frequency response for the magnitude or gain plot is the change in
voltage
gain
as frequency changes. This change is specified on a Bode plot,
Bode plot
basics
a plot of frequency versus voltage gain in dB (decibels). Bode plots are
The frequency
for theplots
magnitude
or gain ploton
is the
the change
voltage
usually
plottedresponse
as semi-log
with frequency
x-axis, inlog
scale,gain
as frequency
changes.
This
change
is specified
on half
a Bode
plot,frequency
a plot of frequency
and
gain on the
y-axis,
linear
scale.
The other
of the
versus voltage gain in dB (decibels). Bode plots are usually plotted as semi-log plots
response is the phase shift versus frequency and is plotted as frequency
with frequency on the x-axis, log scale, and gain on the y-axis, linear scale. The other
versus
degrees
phase
shift. Phase
plotsshift
are versus
usuallyfrequency
plotted as
half of the
frequency
response
is the phase
andsemi-log
is plotted as
plots
with
frequency
on
the
x-axis,
log
scale,
and
phase
shift
onasthe
frequency versus degrees phase shift. Phase plots are usually plotted
semi-log
y-axis,
linear
scale.on the x-axis, log scale, and phase shift on the y-axis, linear
plots with
frequency
scale.
Definitions
V
V
Measured
P
P
((36)
36) Voltage
Voltagegain
gaininindecibels
decibels
((37)
37) Power
Power gain
gain in
in decibels
decibels
Power Measured (W)
1 mW
(38) Used
input
or
Powerfor
gain
in decibel
(38) output power
milliwatt
Table 15: Examples of common gain
A (V/V)
A (dB)
Table 14: Examples of common
gain
and dB equivalent
values and
dBvalues
equivalent
0.001
–60
A (V/V)
A (dB)
0.01
–40–60
0.001
Roll-off rate is the decrease in gain with frequency
0.010.1
–20–40
0.1
–20 Decade is a tenfold increase or decrease in
0 0
frequency (from 10 Hz to 100 Hz is one decade)
1 1
20 20
10 10
Octave is the doubling or halving of frequency
100100
40 40
(from 10 Hz to 20 Hz is one octave)
1,000
60
1,000
60
10,000
80
100,000
10,000
80 100
1,000,000
120
100,000
100
10,000,000
140
1,000,000
120
Roll-off rate is the decrease in gain with frequency
10,000,000
140
Decade is a tenfold increase or decrease in frequency.(from 10 Hz to 100 Hz is one
decade)
Octave is the doubling or halving of frequency (from 10 Hz to 20 Hz is one octave)
28
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Analog
Figure 13 illustrates a method to graphically determine values on a
logarithmic axis that are not directly on an axis grid line.
Figure 14 illustrates a method to graphically determine values on a logarithmic axis
that areLnot
directly
an axis
grid line. with a ruler.
1. Given
= 1cm;
D on
= 2cm,
measured
2. L/D = log10(fp)
1. (L/D)
Given L =(1cm/2cm)
1 cm; D = 2cm, measured with a ruler.
3. fP = 10
= 10
= 3.16
2. L/D = log10(fP)
(L/D)
(1CM/2CM) (for this example, f = 31.6 Hz)
4. Adjust
p
3. for
fP =the
10 decade
= 10 range
= 3.16
A (dB)
4. Adjust for the decade range (for example, 31.6 Hz)
Figure14:
13:Finding
Findingvalues
valueson
onlogarithmic
logarithmic axis
axis not
not directly
directly on
on aa grid
grid line
line
Figure
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Analog
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Bode plots:
Poles
Bode plots:
Poles
fP
100
0.707*GV/V = –3 dB
Actual
function
G (dB)
80
Straight-line
approximation
–20 dB/decade
60
40
20
0
1
10
100
(degrees)
+90
+45
1k
10k
100k
1M
10M
100k
1M
10M
Frequency (Hz)
0°
10
100
1k
10k
0
–45
–5.7° at
fP
10
–45° at fP
–90
–45°/decade
–84.3° at fP x 10
–90°
Figure
14: Pole gain and phase
Figure 15: Pole gain
and phase
Pole Location
fP (cutoff freq)
Pole=Location
= fP (cutoff freq)
Magnitude (f < fP) = Gdc (for example, 100 dB)
Magnitude (f < fP) = GDC (for example, 100 dB)
Magnitude (f = fP) = –3 dB
(f dB/decade
= fP) = –3 dB
MagnitudeMagnitude
(f > fP) = –20
Phase (f =Magnitude
fP) = –45° (f > fP) = –20 dB/decade
Phase (0.1
fP < f <(f10
Phase
= ffPP) == –45°/decade
–45°
Phase (f > 10 fP) = –90°
Phase (0.1 f < f < 10 fP) = –45°/decade
Phase (f < 0.1 fP) = 0° P
Phase (f > 10 fP) = –90°
Phase (f < 0.1 fP) = 0°
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Pole (equations)
Pole (equations)
G
V
V
G
V
V
G
G
j f
f
(39) As (39)
a complex
number number
As a complex
G
f
f
(40) Magnitude
(40) Magnitude
f
f
(41)shift
Phase shift
(41) Phase
(42) Magnitude
(42) Magnitude
in dB in dB
Where
Gv = voltage gain in V/V
Where
GdB = voltage gain in decibels
GG
voltage gain in V/V
v=
dc = the dc or low frequency voltage gain
Hz in decibels
GfdB= frequency
= voltageingain
frequency
which
the pole occurs
P ==
GfDC
the dc oratlow
frequency
voltage gain
θ = phase shift of the signal from input to output
f = frequency in Hz
fP = frequency at which the pole occurs
θ = phase shift of the signal from input to output
j = indicates imaginary number or √ –1
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Analog
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BodeBode
plotsplots
(zeros)
(zeros)
80
Straight-line
approximation
+20 dB/decade
G (dB)
60
40
Actual
function
20
+3 dB
0
1
10
100
+90
1k
10k
100k
1M
10M
+90°
+45° at fZ
(degrees)
84.3° at fZ x 10
+45
0°
f
5.7° at Z
10
+45°/decade
0
10
100
1k
10k
100k
1M
10M
Frequency (Hz)
–45
–90
Figure
15: Zero gain and phase
Figure 16: Zero gain
and phase
Zero location
fZ
Zero =location
= fZ
Magnitude (f < fZ) = 0 dB
Magnitude (f < fZ) = 0 dB
Magnitude (f = fZ) = +3 dB
Magnitude (f = fZ) = +3 dB
Magnitude (f > fZ) = +20 dB/decade
Phase (f Magnitude
= fZ) = +45°(f > fZ) = +20 dB/decade
Phase
fZ)fZ=) +45°
= +45°/decade
Phase (0.1
fZ < f(f<=10
Phase
(0.1
fZ < f < 10 fZ) = +45°/decade
Phase (f > 10 fZ) = +90°
Phase (f Phase
< 0.1 fZ(f) =
> 0°
10 fZ) = +90°
Phase (f < 0.1 fZ) = 0°
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Zero (equations)
Zero (equations)
G� �
V���
f
� G�� �j � � � ��
V��
f�
G� �
f �
V���
� G�� �� � � �
f�
V��
f
� � ����� � �
f�
G�� � �������G� �
As a complex
(43) As(43)
a complex
number number
(44) Magnitude
(44) Magnitude
(45) shift
Phase shift
(45) Phase
(46) Magnitude
in dB in dB
(46) Magnitude
Where
GV = voltage gain in V/V
Where
voltage
gain
decibels
GG
==
voltage
gain
in in
V/V
V dB
the dc or
lowinfrequency
voltage gain
DC==voltage
GG
gain
decibels
dB
f = frequency in Hz
GDC = the dc or low frequency voltage gain
fZ = frequency at which the zero occurs
f = frequency in Hz
θ = phase shift of the signal from input to output
fZ = frequency at which the zero occurs
θ = phase shift of the signal from input to output
j = indicates imaginary number or √ –1
Texas Instruments Analog Engineer's Pocket Reference
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Time to phase shift
P
S
Figure 17: Time to phaseFigure
shift 16: Time to phase shift
θ
(47) Phase
fromshift
timefrom time
(47) shift
Phase
• 360°
Where
Where
T
S = time shift from input to output signal
TPS==period
time shift
from input to output signal
of signal
T
θTP= =
phase
shiftofofsignal
the signal from input to output
period
θ = phase shift of the signal from input to output
Example
Calculate the phase shift in degrees for Figure 17.
Example
Answer
Calculate the phase shift in degrees for Figure 16.
T
Answer
θ=
34
T Ts
Tp
0.225
1
• 360° =
(
Texas
ms
0.225ms
ms
1 ms
) • 360° = 81°
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Texas Instruments Analog Engineer's Pocket Reference
Amplifier
Amplifier
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Amplifier
Basic op amp configurations •
Op amp bandwidth •
Full power bandwidth •
Small signal step response •
Noise equations •
Stability equations •
Stability open loop SPICE analysis •
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Basic op amp configurations
Basic op amp configurations
Basic op amp configurations
G�� � �
Gain
for buffer
(48) Gain (48)
for buffer
configuration
configuration
(48) Gain for buffer configuration
G�� � �
VCC
VOUT
VIN
+
+
VEE
Figure 17: Buffer configuration
Figure 18: Buffer configuration
Amplifier
FigureR18: Buffer configuration
�
(49)
forfor
non-inverting
configuration
Gain
non-inverting
configuration
G�� �
��
(49)Gain
R�
G�� �
R�
��
R�
R1
Rf
(49) Gain for non-inverting configuration
VCC
VOUT
+
VIN
VEE
+
Figure 18: Non-inverting configuration
Figure 19: Non-inverting configuration
Figure 19: Non-inverting configuration
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Basic op amp configurations (cont.)
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R�
G�� � �
Amplifier
Gain for inverting configuration
(50)
R�
Basic op amp configurations (cont.)
Basic op amp configurations (cont.)
+
G�� � �
R�
R�
Gain
for inverting
(50) Gain(50)
for inverting
configuration
R1
configura
Rf
VCC
VIN
+
VOUT
VEE
Figure
19: Inverting configuration
Figure 20: Inverting
configuration
V� V�
V�
Transfer function for i
V��� � �R � � �
� � � � (51) Transfer function
(51) for inverting
R
R
R
Figure 20:
configuration
summing amplifier summing amplifier
� Inverting
�
�
Transfer function for i
R�
VV� �V�
Transfer
function
� �V � V
� Transfer function forsumming
V��� V
� � � �V
�
amplifier,
as
(52)
(52)
�
�
�
�
� �� �
(51)inverting summing
��� R �R � �
�
summing
R� R �
R � amplifier, assuming R
R
=
…=R
R1 =
2 = …=R
N amplifi
1 = R
2
N
V��� � �
VN
RN
R�
�V� � V� � � � V� �
R�
RN
R
2
V2
VN
VN
(52)
R2
V1
V2
V2
V1
R1
R
RN1
Transfer function
summing amplifi
R1 = R2 = …=RN
Rf
VCC
Rf
R2
VOUT
Vcc
R1
- + VEE
Rf
+
Vcc
Vee
-+
Vout
V1 Inverting summing configuration
Figure 20:
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Figure 21: Inverting summing configuration
Vout
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Amplifier
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Basic op amp configurations (cont.)
Basic op amp configurations (cont.)
V��� � �
R�
V� V�
V�
� �� � � � � � �
R ��
N N
N
Transfer
function
(53) Transfer
function
forfor noninverting summing
amplifier
(53)noninverting
summing
amplifier
equalinput
inputresistors
resistors
forforequal
Where
R1 = R2 = … = RN
Where
of input resistors
R1N==Rnumber
2 = … = RN
N = number of input resistors
Rin
R1
V1
Rf
VCC
VOUT
R2
V2
RN
VEE
VN
Figure 22: Non-inverting summing configuration
Figure 21: Non-inverting summing configuration
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Simple
amp
Cf filter
Simplenon-inverting
non-inverting amp
withwith
Cf filter
R � non-inverting amp with Cf filter
Simple
Gain for non-inverting configuration
G�� �
�1
(54) Gain(54)
for non-inverting configuration for f < fc
for f < fc
R�
R�
Gain
non-inverting
configuration
Gain
forfor
non-inverting
configuration
G��
�1
(54)
(55) Gain(55)
for
non-inverting
configuration
for f >> fc
��
1
G��
f <fcfc
R�
forfor
f >>
Gain frequency
for non-inverting
configuration
for non-inverting
(55) Cut off for
(56) Cut off
configuration
(56)frequency
for f >> fnon-inverting
c
configuration
Cut off frequency for non-inverting
(56)
Cf configuration
G �11
f� ���
2π R � C�
1
f� �
2π R � C�
R1
Rf
VCC
VOUT
VIN
VEE
Figure 23: Non-inverting amplifier with Cf filter
Figure 22: Non-inverting amplifier with Cf filter
Figure 23: Non-inverting amplifier with Cf filter
Figure 24: Frequency response for non-inverting op amp with Cf filter
Figure 23:
24: Frequency
Frequency response
response for
for non-inverting
non-inverting op
op amp
amp with
with C
Cff filter
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Simple inverting amp with Cf filter
SimpleRinverting amp with Cf filter
(57) Gain for inverting configuration for f < fC
G
R
R
Gain for inverting configuration
(57)
−20dB/decade after f C
GG
< fC
R
(58) Gainfor
forf inverting
configuration for f > fC
f
G
f
until op amp bandwidth
limitation
−20dB/decade after fC
1until op amp bandwidth (59) Cutoff frequency for inverting configuration
2π Rlimitation
C
1
frequency for inverting configuration
(59) Cutoff
Cf
2π R C
Cf
R1
R1
Rf
VIN
Rf
VCC
Vcc
Vin
VOUT
-+
+
Vout
VEE
Vee
Figure 24: Inverting amplifier with Cf filter
Figure 25: Inverting amplifier with Cf filter
Figure
25: Frequency
response
for inverting
op amp
with
Cf filter
Figure
26: Frequency
response
for inverting
op amp
with C
f filter
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Op amp
bandwidth
Op amp bandwidth
GBW
= Gain
• BW
GBW
� Gain���BW
(60) Gain
product
defined
Gain bandwidth
product
defined
(60) bandwidth
Where
Where
= bandwidth
gain bandwidth
product,
op amp
sheet specification table
GBWGBW
= gain
product,
listedlisted
in opinamp
datadata
sheet
Gain
= closed loop
gain, set by op amp gain configuration
specification
table
= the loop
bandwidth
limitation
of thegain
amplifier
Gain BW
= closed
gain, set
by op amp
configuration
BW = the bandwidth limitation of the amplifier
Example
Determine bandwidth using equation 60
Example
Gain � �100
Determine
bandwidth using equation 60(from amplifier configuration)
Gain = 100 (from amplifier configuration)
(from data sheet)
GBW � �22MHz
GBW = 22MHz (from data sheet)
GBW 22MHz
22MHz
GBW
= 220�Hz
220 kHz
BW BW
= � Gain=� � 100 �
100
Gain
Note that the same result can be graphically determined using the AOL curve as
Note shown
that thebelow.
same result can be graphically determined using the AOL curve
as shown below.
Open-loop gain and phase vs. frequency
Open-loop gain and phase vs. frequency
Figure 27: Using AOL to find closed-loop bandwidth
Figure 26: Using AOL to find closed-loop bandwidth
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Full power
Full
powerbandwidth
bandwidth
Full power bandwidth
SR
Maximum output without slew-rate induced
(61) Maximum
(61) output without slew-rate induced distortion
V� �
distortion
2πfSR
Maximum output without slew-rate induced
(61)
V� �
distortion
2πf
Where
VP = maximum peak output voltage before slew induced distortion occurs
Where
Where
= slew ratepeak output voltage before slew induced distortion occurs
VSR
P=
= maximum peak output voltage before slew induced distortion occurs
VPmaximum
f = =frequency
of applied signal
SR
raterate
SRslew
= slew
f = ffrequency
of applied
signal
= frequency
of applied
signal
Maximum output voltage vs. frequency
Maximum output voltage vs. frequency
Maximum output voltage vs. frequency
�. ��/��
��
� �. ����� �� �. �����
�
��� ���������
��
�. ��/��
�� �
�
� �. ����� �� �. �����
��� ���������
�� �
Figure 28: Maximum output without slew-rate induced distortion
Figure 27: Maximum output without slew-rate induced distortion
Figure
output
withoutusing
slew-rate
induced
Notice
that28:
theMaximum
above figure
is graphed
equation
61 for distortion
the OPA188. The
example
calculation
shows
the
peak
voltage
for
the
OPA277
at
40kHz.
This can be
Notice
thatthat
thethe
above
figure
is graphed
using
equation
6161
forfor
thethe
OPA277.
Notice
above
figure
is graphed
using
equation
OPA188. The
determined
graphically
or
with the
equation.
The
example
calculation
shows
the
peak
voltage
for
the
OPA277
at
40kHz.
example calculation shows the peak voltage for the OPA277 at 40kHz. This can be
Thisdetermined
can be determined
graphically
with the equation.
graphically
or with theorequation.
Example
Example
SR
Example
V� �
�
0.8V/μs
� 3.�8Vpk or 6.37Vpp
2πfSR 2π��0k���
0.8V/μs
V� �
�
SR
0.8V/µs � 3.�8Vpk or 6.37Vpp
VP = 2πf= 2π��0k��� = 3.18Vpk or 6.37Vpp
2πf
2π(40kHz)
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Small signal
signal step
response
Small
step
response
τ� �
0.35
f�
a small
signal
(62)
(62)
RiseRise
timetime
for afor
small
signal
stepstep
Small signal step response
Where
0.35
τ� �of a small signal step response
(62) Rise time for a small signal step
R = the rise time
f�
Where
C = the closed-loop bandwidth of the op amp circuit
t f=
the rise time of a small signal step response
R
Wherebandwidth of the op amp circuit
fC = the closed-loop
Small signal step
response waveform
R = the rise time of a small signal step response
fC = the closed-loop bandwidth of the op amp circuit
Small signal step response waveform
Small signal step response waveform
Figure 29: Small signal step response
Figure
29: Small
signal
step response
Figure 28:
Maximum
output
without
slew-rate induced distortion
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Op amp noise model
Op amp noise model
Figure 30: Op amp noiseFigure
model29: Op amp noise model
Op amp intrinsic noise includes:
 Noise caused by op amp (current noise + voltage noise)
Op amp intrinsic noise includes:
 Resistor noise
• Noise caused by op amp (current noise + voltage noise)
• Resistor noise
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Noise bandwidth calculation
Noise
bandwidth
calculation
Noise bandwidth
calculation
(63) Noise bandwidth
NoiseBW
bandwidth
� � � � f� calculation
Noise
bandwidth
BW� � � � f�
(63)Noise
(63)
bandwidth
BW Where
�� f
(63) Noise bandwidth
Where� BW � =� noise bandwidth of the system
N
Where
BWN = noise
of the
systemfactor for different filter order
KN = bandwidth
the brick wall
correction
Where
BW
noise
bandwidth
of the factor
system
KNN==the
brick
wall
correction
for
different filter order
–3 dB
bandwidth
system
noise
bandwidth
of of
thethe
system
BWN f=C =
brick
wall correction
factor for different filter order
KNfC == the
–3 dB
bandwidth
of the system
KN = the brick wall correction factor for different filter order
fC = –3 dB bandwidth of the system
fC = –3 dB bandwidth of the system
Figure 31: Op amp bandwidth for three different filters orders
Figure 31: Op amp bandwidth for three different filters orders
Figure 30: Op amp bandwidth for three different filters orders
Figure 31: Op amp bandwidth for three different filters orders
Table 15: Brick wall correction factors for noise bandwidth
Table 15: Brick wall correction factors for noise bandwidth
wall for noise bandwidth
KN brickfactors
16:ofBrick
wall correction
Number
poles
Table Table
15:
Brick
wall
correction
factors for noise
bandwidth
wall
KN brick
correction
factor
Number of poles
correction factorKN brick wall correction factor
Number
of
poles
KN brick wall
1
1.57
Number
1 of poles1
1.57
correction
factor
1.57
2
1.22
2 1
1.221.57
2
1.22
3
1.13
3 2
1.13
1.22
3
1.13
4
1.12
4 3
1.121.13
4
1.12
4
1.12
Broadband
total
noise
calculation
Broadband
totalcalculation
noise calculation
Broadband
total noise
Broadband
total
noise
calculation
Totalfrom
rmsbroadband
noise from broadband
E� � ���
(64) noise
�BW
(64) Total rms
�
E� � ��� �BW�
(64) Total rms noise from broadband
��� �BW�
E� � Where
(64) Total rms noise from broadband
Where Where
EN = total rms noise from broadband noise
ENrms
= total
rms
noise
from broadband
noise
EN = total
noise
from
broadband
noise
eBB = broadband
noise spectral
density (nV/rtHz)
Where
eBB = broadband
noise
spectral
density
(nV/rtHz)
e
=
broadband
noise
spectral
density
BB
= noise
bandwidth
(Hz)
EN = BW
totalN rms
noise
from broadband
noise (nV/rtHz)
BWN = noise
bandwidth
(Hz)
bandwidth
(Hz)
N = noisenoise
eBB =BW
broadband
spectral
density (nV/rtHz)
BWN = noise bandwidth (Hz)
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1/f total
noise
calculation
1/f
total
noise
calculation
1/f total noise calculation
Normalized1/f
1/fnoise
noiseatat1 1Hz
Hz
(65) Normalized
E�_������ � � ��� �f�
(65)
E�_������ � � ��� �f�
(65) Normalized 1/f noise at 1 Hz
Where
Where
E Where = 1/f noise normalized to 1 Hz
ENN_NORMAL
_NORMAL = 1/f noise normalized to 1 Hz
EN_NORMAL
= 1/f noise
normalized
to 1 in
Hzthe 1/f region
eBF
= noise spectral
density
measured
= =noise
spectral
density measured
in the
eBF
noise
spectral
the1/f
1/fregion
region
frequency
thatdensity
the 1/f measured
noise eBF isinmeasured
at
fOe=BFthe
fOfO= =the
frequency
that
the
1/f
noise
e
is
measured
BF
the frequency that the 1/f noise eBF is measuredat
at
f�
E�_������� � � E�_������ ��� � f�
f �
E�_������� � � E�_������ ��� �� �
f�
1/f total noise calculation
(66)
1/fnoise
total noise
calculation
(66)
(66) 1/f total
calculation
Where
Where = total rms noise from flicker
EN_FLICKER
rmsnormalized
noise fromtoflicker
EN_FLICKER= =1/ftotal
noise
1 Hz
EN_NORMAL
Where
1/f frequency
noise
normalized
tobandwidth
1 Hz
E
E
==total
rms noise
flicker
fHN_FLICKER
=N_NORMAL
upper cutoff
orfrom
noise
f=H =
upper
frequency
or noise
bandwidth
fLN_NORMAL
lower
cutoff
normally
to 0.1 Hz
E
=cutoff
1/f frequency,
noise
normalized
to set
1Hz
f
=
lower
cutoff
frequency,
normally
set to 0.1 Hz
L
f = upper cutoff frequency or noise bandwidth
H
fL = lower cutoff frequency, normally set to 0.1Hz
Table 16: Peak-to-peak conversion
Table 16: Peak-to-peak conversion
Number of
Percent chance
Table
17:Number
Peak-to-peak
conversion
standard
deviations
reading
is inchance
range
of
Percent
reading
is in range
2σstandard
(same
as deviations
±1σ)
68.3%
Number
of standard deviations
Percent chance reading is in range
2σ (same as ±1σ)
3σ (same as 2σ
±1.5σ)
(same as ±1σ)
3σ (same as ±1.5σ)
(same as ±1.5σ)
4σ (same as3σ
±2σ)
4σ (same as
±2σ)
4σ
(same as ±2σ)
5σ (same as ±2.5σ)
5σ (same as
±2.5σ)
5σ (same as ±2.5σ)
6σ (same as ±3σ)
6σ (same as ±3σ)
6σ
(same
as
6.6σ (same as ±3σ)
±3.3σ)
6.6σ (same
as(same
±3.3σ)
6.6σ
as ±3.3σ)
68.3%
86.6%
86.6%
95.4%
95.4%
98.8%
98.8%
99.7%
99.7%
99.9%
99.9%
68.3%
86.6%
95.4%
98.8%
99.7%
99.9%
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Thermal noise calculation
En_R =
√ 4kTR�f
√ 4kTR
Thermal noise calculation
en_R =
(67) Total rms Thermal Noise
(68) Thermal Noise Spectral Density
(67)
E�_� � √4 kTRΔf
Total rms thermal nois
Where
En_R = Total rms noise from resistance, also called thermal noise (V rms)
Where
en_R = Noise spectral density from resistance, also called thermal noise (V/√Hz )
EkN_R
= total rms noise from resistance, also called thermal noise
= Boltzmann’s constant 1.38 x 10-23J/K -23
kT== Boltzmann’s
constant 1.38 x 10 J/K
Temperature in Kelvin
T∆f==temperature
ininKelvin
Noise bandwidth
Hz
∆f = noise bandwidth in Hz
Noise Spectral Density (nV/rtHz)
1000
100
10
‐55C
25C
1
0.1
1.E+01
125C
1.E+02
1.E+03 1.E+04 1.E+05
Resistance (Ω)
1.E+06
1.E+07
Figure
32:
Noise
spectral
vs. resistance
Figure 31:
Noise
spectral
densitydensity
vs. resistance
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Ac response
frequency (Dominant 2-Pole System)
Ac responseversus
versus frequency
Ac response versus frequency
Figure
32 illustrates
a bode
four different
differentexamples
examples
of peaking.
ac peaking.
Figure
33 illustrates
a bodeplot
plotwith
with four
of ac
Figure 33 illustrates a bode plot with four different examples of ac peaking.
Figure
32: Stability
– ac peaking
relationship
Figure 33:
Stability
– ac peaking
relationship
exampleexample
Figure 33: Stability – ac peaking relationship example
Phase margin versus ac peaking
Phase
marginversus
versus ac
Phase
margin
acpeaking
peaking
This graph illustrates the phase margin for any given level of ac peaking.
graph
illustrates
thephase
phasemargin
margin for
of of
ac ac
peaking.
This This
graph
illustrates
the
for any
anygiven
givenlevel
level
peaking.
Note that 45° of phase margin or greater is required for stable operation.
NoteNote
thatthat
45°45°
of phase
isrequired
requiredforfor
stable
operation.
of phasemargin
marginor
or greater
greater is
stable
operation.
Figure 34: Stability – phase margin vs. peaking for a two-pole system
Figure 34: Stability – phase margin vs. peaking for a two-pole system
Figure 33: Stability – phase margin vs. peaking for a two-pole system
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Transient overshoot (Dominant 2-Pole System)
Transient overshoot
Figure
34 35
illustrates
withtwo
two
different
examples of
Figure
illustratesa atransient
transient response
response with
different
examples
percentage
overshoot.
of
percentage
overshoot.
Transient overshoot
Figure 35 illustrates a transient response with two different examples
of percentage overshoot.
Figure 35:Figure
Stability
transient
overshootovershoot
example example
34:–Stability
– transient
Phase margin versus percentage overshoot
Figure 35: Stability – transient overshoot example
Phase
margin
versus
overshoot
This graph
illustrates
the percentage
phase margin for
any given level of
transient
overshoot.
Note
that 45° of overshoot
phase margin or greater is required
Phase margin
versus
percentage
Thisforgraph
stableillustrates
operation. the phase margin for any given level of transient
This graph
illustrates
theof
phase
margin
for any
given level
of
overshoot.
Note
that 45°
phase
margin
or greater
is required
for
transient overshoot. Note that 45° of phase margin or greater is required
stable
operation.
for stable operation.
Figure 36: Stability – phase margin vs. percentage overshoot
Note:
assume
a two-pole
system.
Figure
35:
Stability
––phase
margin
FigureThe
36:curves
Stability
phase
marginvs.
vs.percentage
percentageovershoot
overshoot
Note: The curves assume a two-pole system.
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VFB
R1
C1 1T
RF
L1 1T
VIN
V+
VO
Riso
VOUT
CL
V–
Figure 36: Common spice test circuit used for stability
Figure 37: Common spice test circuit used for stability
A��_������ � �
β � � V��
V�
V��
1
1
��
β
V��
Loaded
open-loop gain
(68)
(69) Loaded
open-loop
gain
(70) Feedback
Feedback factor
(69) factor
(71) Closed-loop
gain noise gain
Closed-loop
(70) noise
A��_������ � β � � V�
(72) Loop gain
(71)
Loop gain
Where
VO = the voltage at the output of the op amp.
Where
= the
voltage
delivered
the
load, which may be important to the
VVOOUT
= the
voltage
at output
the output
of thetoop
amp.
application
but
is
not
considered
in
stability
analysis.
VOUT = the voltage output delivered to the load,
which may be important to
VFB =the
feedback
voltage
application
but is not considered in stability analysis.
RF , R1, RISO and CL = the op amp feedback network and load. Other op amp
VFB = feedback voltage
topologies will have different feedback networks; however, the test circuit will be the
Rsame
, RiS0
andcases.
CL = the
op amp
feedback
network and
load.
most
Figure
38 shows
the exception
to the
rule (multiple feedback).
F , R1for
Other
op components
amp topologies
have different
feedbackThey
networks;
C1 and
L1 are
thatwill
facilitate
SPICE analysis.
are large (1TF, 1TH)
however,
the test
circuit will
the
same
most
to make
the circuit
closed-loop
forbe
dc,
but
openfor
loop
for cases.
ac frequencies. SPICE
Figure
37 showsoperation
the exception
rule (multiple feedback).
requires
closed-loop
at dc to
forthe
convergence.
C1 and L1 are components that facilitate SPICE analysis. They are large
(1TF, 1TH) to make the circuit closed-loop for dc, but open loop for ac
frequencies. SPICE requires closed-loop operation at dc
for convergence.
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R1
R1
VFB
CIN
CF
V-
VIN
Vin
C1 1T
C1 1T
RF
RF
L1 1T
Cin
VFB
CF
V+
-
Riso
+
+
+
V+
V–
Vo
Riso
VO
Vout
C
CL
VOUT
L
Figure 37: Alternative (multiple feedback) SPICE test circuit used for stability
Figure 38: Alternative (multiple feedback) SPICE test circuit used for stability
A��_������ � V�
β�
V��
V�
V�
1
�
V��
β
A��_������ � β � V��
open
loop gain
(73) (72)
LoadedLoaded
open loop
gain
Feedback
(74) (73)
Feedback
factor factor
Closed-loop
noise gain
(75) (74)
Closed-loop
noise gain
Loop gain
(76) (75)
Loop gain
Where
Where
VO = the voltage at the output of the op amp.
VO = the voltage at the output of the op amp.
VOUT = the voltage output delivered to the load. This may be important to the
V
output
delivered
to the load.
This may be important to
application
but is not
considered
in stability
analysis.
OUT = the voltage
application
but is not considered in stability analysis.
VFB =the
feedback
voltage
, RISO and voltage
CF = the op amp feedback network. Because there are two paths for
RFB
F, R
V
=1feedback
feedback, the loop is broken at the input.
RF, R1, Riso and CF = the op amp feedback network. Because there are two
C1 and L1 are components that facilitate SPICE analysis. They are large (1TF, 1TH)
paths for feedback, the loop is broken at the input.
to make the circuit closed loop for dc, but open loop for ac frequencies. SPICE
C
are components
thatatfacilitate
SPICE analysis. They are large
1 and L1
requires
closed-loop
operation
dc for convergence.
1TH) to make
circuit closed
loop
forthe
dc,op
but
open
loop for This
the equivalent
inputthe
capacitance
taken
from
amp
datasheet.
CIN =(1TF,
ac frequencies. SPICE requires closed-loop operation at dc for
capacitance normally does not need to be added because the model includes it.
convergence.
However, when using this simulation method the capacitance is isolated by
C
= theinductor.
equivalent input capacitance taken from the op amp datasheet.
IN 1TH
the
This capacitance normally does not need to be added because the
model includes it. However, when using this simulation method the
capacitance is isolated by the 1TH inductor.
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R1
RF
+Vs
VOUT
+
Voffset
+
-Vs
VIN
Volts
VOUT
Voffset
50mVpp
Figure 38: Transient real world stability test
Test tips
• Choose test frequency << fcl
• Small signal (Vpp ≤ 50 mV) ac output square wave (for example, 1 kHz)
• Adjust VIN amplitude to yield output ≤ 50 mVpp
• Worst cases is usually when Voffset = 0 (Largest RO, for IOUT = 0A).
• Use Voffset as desired to check all output operating points for stability
• Set scope = ac couple and expand vertical scope scale to look for
amount of overshoot, undershoot, and ringing on VOUT
• Use 1x attenuation scope probe on VOUT for best resolution
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+15V
RIN1
VIN-
CCM1
1nF
CDIF
10nF
1kΩ
RIN2
VIN+
Rg
1kΩ
RG
RG
Ref
Out
VOUT
U1 INA333
1kΩ
CCM2
1nF
-15V
Figure
filter for instrumentation
amplifier
Figure 40:
40: Input
Input
filter39:
forInput
instrumentation
amplifier
Figure
filter
for
instrumentation
amplifier
Figure 40: Input filter for instrumentation amplifier
Differential
filter
is sized
sized
10
(77) Differential
filter
is sized
10 is
times
the
filter
10
(76) Differential
Select C
C��� �
� 1�C
1�C���
(76)
Select
times
the
common-mode
filter
���
���
common-mode
filter
Differential
filter is sized 10
times
the common-mode
filter
(76) Input resistors must be equal
Select
� 1�C���
(77)
R
�CR
R���
��� �
���
times
the
common-mode
filter
(77)
Input
resistors
must
be
equal
R
���
���
(78) Input resistors
must be equal
Common-mode
capacitors
(77)
Input
resistors
must
be
equal
R���
RC���
Common-mode
capacitors
��� �
(78)
C
�
���
(78) must be equal
C��� � C���
Common-mode
must
be equal capacitors
(79) Common-mode
capacitors must be equal
(78)
C��� � C���1
1
must be equal
ff �� �
�
(79)
Differential
filter cutoff
cutoff
(79) Differential filter
��
2πR ���
1 C���
2πR
��� C���
f�� �
(79)
Differential
filter
cutoff
(80) Differential filter cutoff
2πR ��� C���
1
1
�
��� �
(80) Common-mode
Common-mode filter
filter cutoff
cutoff
ff���
1
(80)
��C1��� �
�1C
C�����
2π�2R �����C
2
f��� � 2π�2R ���
���
���
(81)
Common-mode
filter
cutoff
(80) Common-mode filter cutoff
21
2π�2R ��� ��C��� � C��� �
2
Where
Where
fWhere
DIF = differential cutoff frequency
f
DIF = differential cutoff frequency
Where
ff CM =
= common-mode
common-mode
cutoff
frequency
differentialcutoff
cutoff
frequency
cutoff
frequency
DIF==differential
CM
frequency
fDIF
= common-mode
input
resistance
R
IN =
fRCM
cutoff
frequency
input resistance
IN
fCM
==common-mode
cutoff
frequency
C
common-mode
filter capacitance
capacitance
CM
resistance filter
RCM
C
=input
common-mode
IN =
C
=
differential
filter
capacitance
DIF
RC = =input
resistance
common-mode
capacitance
differential
filter filter
capacitance
CM
INDIF
= common-mode
differential filter filter
capacitance
DIF=
CCCM
capacitance
Note: Selecting
Selecting C
CDIF ≥
≥ 10
10 C
CCM sets
sets the
the differential
differential mode
mode cutoff
cutoff frequency
frequency 10
10 times
times
Note:
DIF
CM
Clower
= differential
filter capacitance
than
the
common-mode
cutoff
frequency.
This
prevents
common-mode
noise
DIF
Note: than
Selecting
CDIF ≥ 10 CCM sets
differential
mode
cutoff common-mode
frequency 10 times
lower
the common-mode
cutoffthe
frequency.
This
prevents
noise
from
being
converted
into differential
differential
noise due
due to
to
component
tolerances.
lowerbeing
than the
common-mode
cutoff frequency.
This
prevents tolerances.
common-mode noise
from
converted
into
noise
component
10 Cdifferential
differential
cutoff tolerances.
frequency 10 times
Note:
CDIF ≥ into
from Selecting
being converted
due to mode
component
CM sets thenoise
lower than the common-mode cutoff frequency. This prevents common-mode noise
from being converted into differential noise due to component tolerances.
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Notes
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PCB
andWire
Wire
PCB
and
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PCB and wire
PCB trace resistance for 1oz and 2oz Cu •
Conductor spacing in a PCB for safe operation •
Current carrying capacity of copper conductors •
Package types and dimensions •
PCB trace capacitance and inductance •
PCB via capacitance and inductance •
Common coaxial cable specifications •
Coaxial cable equations •
Resistance per length for wire types •
Maximum current for wire types •
Texas Instruments Analog Engineer's Pocket Reference
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PCB and Wire
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Table 18: Printed circuit board conductor spacing
Minimum spacing
PCB and wire
Voltage between
conductors
(dc or ac peaks)
Bare board
Assembly
B1
B2
B3
B4
A5
A6
A7
0-15
0.05 mm
[0.00197 in]
0.1 mm
[0.0039 in]
0.1 mm
[0.0039 in]
0.05 mm
[0.00197 in]
0.13 mm
[0.00512 in]
0.13 mm
[0.00512 in]
0.13 mm
[0.00512 in]
16-30
0.05 mm
[0.00197 in]
0.1 mm
[0.0039 in]
0.1 mm
[0.0039 in]
0.05 mm
[0.00197 in]
0.13 mm
[0.00512 in]
0.25 mm
[0.00984 in]
0.13 mm
[0.00512 in]
31-50
0.1 mm
[0.0039 in]
0.6 mm
[0.024 in]
0.6 mm
[0.024 in]
0.13 mm
[0.00512 in]
0.13 mm
[0.00512 in]
0.4 mm
[0.016 in]
0.13 mm
[0.00512 in]
51-100
0.1 mm
[0.0039 in]
0.6 mm
[0.024 in]
1.5 mm
[0.0591 in]
0.13 mm
[0.00512 in]
0.13 mm
[0.00512 in]
0.5 mm
[0.020 in]
0.13 mm
[0.00512 in]
101-150
0.2 mm
[0.0079 in]
0.6 mm
[0.024 in]
3.2 mm
[0.126 in]
0.4 mm
[0.016 in]
0.4 mm
[0.016 in]
0.8 mm
[0.031 in]
0.4 mm
[0.016 in]
151-170
0.2 mm
[0.0079 in]
1.25 mm
[0.0492 in]
3.2 mm
[0.126 in]
0.4 mm
[0.016 in]
0.4 mm
[0.016 in]
0.8 mm
[0.031 in]
0.4 mm
[0.016 in]
171-250
0.2 mm
[0.0079 in]
1.25 mm
[0.0492 in]
6.4 mm
[0.252 in]
0.4 mm
[0.016 in]
0.4 mm
[0.016 in]
0.8 mm
[0.031 in]
0.4 mm
[0.016 in]
251-300
0.2 mm
[0.0079 in]
1.25 mm
[0.0492 in]
12.5 mm
[0.492 in]
0.4 mm
[0.016 in]
0.4 mm
[0.016 in]
0.8 mm
[0.031 in]
0.8 mm
[0.031 in]
301-500
0.25 mm
[0.00984 in]
2.5 mm
[0.0984 in]
12.5 mm
[0.492 in]
0.8 mm
[0.031 in]
0.8 mm
[0.031 in]
1.5 mm
[0.0591 in]
0.8 mm
[0.031 in]
B1 Internal conductors
B2 External conductors uncoated sea level to 3050m
B3 External conductors uncoated above 3050m
B4 External conductors coated with permanent polymer coating (any elevation)
A5 External conductors with conformal coating over assembly (any elevation)
A6 External component lead/termination, uncoated, sea level to 3050m
A7 External component lead termination, with conformal coating (any elevation)
Extracted with permission from IPC-2221B, Table 6-1.
For additional information, the entire specification can be downloaded at
www.ipc.org
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Texas
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PCB and Wire
Figure
Self of
heating
of PCB
on inside layer
Figure 41:
Self 40:
heating
PCB traces
on traces
inside layer
Example
cause a 20Ԩ temperature rise in a PCB trace that is 0.1 inch
Example Find the current that will
2
wide and
useswill
2 oz/ft
copper.
(Assume
traces on outside
Find the current
that
cause
a 20°C
temperature
rise in of
a PCB.)
PCB trace
2
that is 0.1 Answer
inch wide and uses 2 oz/ft copper. (Assume traces on
outside of PCB.)
First translate 0.1 inch to 250 sq. mils. using bottom chart. Next find the current
Answer associated with 10Ԩ and 250 sq. mils. using top chart (Answer = 5A).
First translate 0.1 inch to 250 sq. mils. using bottom chart. Next find
with permission from IPC-2152, Figure 5-1.
the currentExtracted
associated
with 10°C and 250 sq. mils. using top chart
For additional information the entire specification can be downloaded at www.ipc.org
(Answer = 5A).
Extracted with permission from IPC-2152, Figure 5-1.
For additional information the entire specification can
be downloaded at www.ipc.org
57
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PCB and Wire
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PCBtrace
trace resistance
for 1
PCB
PCB traceresistance
resistancefor
for11oz
ozCu
Cu
oz-Cu
5mil
5mil
10mil
10mil
25mil
25mil
50mil
50mil
100mil
100mil
11
100m
100m
10m
10m
1m
1m
100µ
100µ
10µ
10µ
1µ
1µ
11
10
10
100
1000
100
1000
Trace
Tracelength
length(mils)
(mils)
10000
10000
Figure
42:
trace
resistance
vs.
and
width
for
oz-Cu,
25°C
Figure
41:
trace
resistance
vs. length
width
for
1 oz-Cu,
25°C
Figure
42:PCB
PCBPCB
trace
resistance
vs.length
length
andand
width
for11
oz-Cu,
25°C
Figure
43:
PCB
trace
resistance
vs.
and
width
for
11oz-Cu,
125°C
Figure
PCB
trace
resistance
vs.
length
width
1 oz-Cu,
125°C
Figure
43:42:
PCB
trace
resistance
vs.length
length
andand
width
forfor
oz-Cu,
125°C
Example
Example
What
Example
Whatisisthe
theresistance
resistanceof
ofaa20
20mil
millong,
long,55mil
milwide
widetrace
tracefor
foraa11oz-Cu
oz-Cuthickness
thicknessat
at
25°C
and
125°C?
What
is
the
resistance
of
a
20
mil
long,
5
mil
wide
trace
for
a
25°C and 125°C?
1 oz-Cu thickness at 25°C and 125°C?
Answer
Answer
Answer
R25C
==33mΩ.
The
points
are
on
curves.
R25C==222mΩ,
mΩ,
R125C
TheThe
points
arecircled
circled
onthe
theon
curves.
R25C
mΩ,R125C
R125C
= mΩ.
3 mΩ.
points
are circled
the curves.
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Texas
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PCB and Wire
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PCB trace resistance for 2 oz Cu
PCB trace
1 resistance for 2 oz-Cu
PCB trace resistance for 2 oz Cu
1
100m
100m
10m
10m
1m
5mil
10mil
25mil
5mil
10mil
50mil
25mil
100mil
50mil
100mil
1m
100µ
100µ
10µ
10µ
1µ
1µ 1
1
10
100
1000
10000
Trace length
100 (mils) 1000
10000
Trace length (mils)
Figure 44: PCB trace resistance vs. length and width for 2 oz-Cu, 25°C
10
Figure
PCB
trace
resistance
length
and
width
2 oz-Cu,
25°C
Figure
44:43:
PCB
trace
resistance
vs.vs.
length
and
width
forfor
2 oz-Cu,
25°C
Figure
44:
PCBtrace
traceresistance
resistancevs.
vs.length
length and
and width
width for
for 2
2 oz-Cu,
Figure
45:
PCB
oz-Cu, 125°C
125°C
Figure 45: PCB trace resistance vs. length and width for 2 oz-Cu, 125°C
Example
Example
What is the resistance of a 200 mil long, 25 mil wide trace for a 2 oz-Cu thickness at
Example
What is the resistance of a 200 mil long, 25 mil wide trace for a 2 oz-Cu thickness at
25°Cisand
What
the125°C?
resistance of a 200 mil long, 25 mil wide trace for a
25°C and 125°C?
2 oz-Cu thickness at 25°C and 125°C?
Answer
Answer
Answer
R25C
22mΩ,
== 3
mΩ. The
Thepoints
pointsare
arecircled
circled
on
R25C= =
mΩ,R125C
R125C =
mΩ.
thecurves.
curves.
=2
mΩ,
R125C
33 mΩ.
The points
are circled
ononthe
theR25C
curves.
Texas Instruments Analog Engineer's Pocket Reference
59
PCB and Wire
ti.com/precisionlabs
Common package
typetype
and dimensions
Common
package
and dimensions
120.2mil
3.05mm
60
Texas
Texas Instruments Analog Engineer's Pocket Reference
60
PCB and Wire
ti.com/precisionlabs
PCB
parallel
plate
capacitance
PCB parallel
plate
capacitance
Capacitance for parallel copper
(82) Capacitance
for parallel copper planes
(81)
planes
k ∙ ℓ ∙ w ∙ εr
PCB parallel plate capacitance
Where
Where
of free space.
kk ==Permittivity
Permittivity
of free space.
Both the metric and imperial
Capacitance for parallel copper
k ∙ ℓ version
∙ w ∙ εofr the constant are given.
k = Both
8.854·10-3
pF/mm,
or 2.247·10-4
pF/mil
the
metric
and imperial
version of (81)
the constant
are given.
planes
ℓ =PCB
length (metric
in
mm,
or
imperial
in mil)
parallel plate capacitance
-4
w = width
(metric
in mm, or-3
imperial in mil)
k
=
8.854∙10
pF/mm,
or
2.247∙10
pF/mil
h = separation between planes (metric in mm, or imperial in mil)
PCB relative dielectric constant (εr ≈ 4.5 for FR-4)
Where
Capacitance for parallel copper
ℓε ==
length (metric
k ∙ in
ℓ ∙ mm,
w ∙ εr or imperial in mil)
(81)
planes
k = Permittivity of free space.
w = width (metric in mm, or imperial in mil)
r
Both the metric and imperial version of the constant are given.
k = 8.854·10-3 pF/mm, or 2.247·10-4 pF/mil
w
h=
between
(metric in mm, or imperial
in mil)
ℓ = separation
length (metric in mm,
or imperial inplanes
mil)
Where
w = width (metric in mm, or imperial in mil)
εrhk === Permittivity
PCB relative
dielectric
constant
≈
4.5
for
FR-4)
separation
between planes
(metric in mm,
or imperial in(ε
mil)
r
of free space.
εr = PCB relative dielectric constant (εr ≈ 4.5 for FR-4)
Both the metric and imperial version of the constant are given.
k = 8.854·10-3 pF/mm, or 2.247·10-4 pF/mil
ℓ = length (metric in mm, or imperial in mil)
l or imperial in mil)
w = width (metric in mm,
h = separation between planes (metric in mm, or imperial in mil)
εr = PCB relative dielectric constant (εr ≈ 4.5 for FR-4)
h
A
w
w
A
l
εr
A
Figure 45: PCBl parallel plate capacitance
h
Example Calculate the total capacitance for ℓ=5.08mm,
w=12.7mm,
h=1.575mm,
h
Figure
45: PCB
parallel plate
capacitance
εr = 4.5
εr
εr
(8.854
∙ 10–3 pF⁄mm)
∙ (5.08mm)
∙ (12.7mm)
∙ (4.5)
Example
Calculate
the total
capacitance
for ℓ=5.08mm,
C(pF)
= 45: PCB parallel plate capacitance
= 1.63pF
Figure
1.575mm
w=12.7mm, h=1.575mm, ε = 4.5
r
Example Calculate
–3 the total capacitance for ℓ=5.08mm,
(8.854 ∙ 10
pF⁄mm) ∙ (5.08mm) ∙ (12.7mm) ∙ (4.5)
C(pF) = Calculate
= 1.63pF
w=12.7mm,
h=1.575mm,
εr = 4.5
Example
the1.575mm
total capacitance
for ℓ=200mil,
w=500mil, h=62mil, εr = 4.5
(8.854 ∙ 10–3 pF⁄mm) ∙ (5.08mm) ∙ (12.7mm) ∙ (4.5)
C(pF) =
= 1.63pF
–4
C(pF)
= (2.247
∙ 10 pF⁄mil)
∙ (200mil)
∙ (500mil)
(4.5)
Example
Calculate
the1.575mm
total
capacitance
for ∙ℓ=200mil,
= 1.63pF
62mil ε = 4.5
w=500mil, h=62mil,
r
Example
C(pF)
= (2.247 ∙ 10
–4
Calculate
the total
capacitance
for∙ (4.5)
ℓ=200mil,
pF⁄mil)
∙ (200mil)
∙ (500mil)
= 1.63pF
w=500mil, h=62mil,
62mil εr = 4.5
–4
C(pF) = (2.247 ∙ 10
pF⁄mil) ∙ (200mil) ∙ (500mil) ∙ (4.5)
62mil
Texas Instruments Analog Engineer's Pocket Reference
61
= 1.63pF
61
PCB and Wire
ti.com/precisionlabs
Microstrip capacitance and inductance
L(nH) = kL ∙ ℓ ∙ ln
C(pF) =
( 0.85.98∙ w∙ +h t (
kC ∙ ℓ ∙ (εr + 1.41)
ln
5.98 ∙ h
( 0.8
∙w+t (
(83) Inductance for microstrip
(84) Capacitance for microstrip
Where
kL = PCB inductance per unit length.
Both the metric and imperial version of the constant are given.
kL = 2nH/cm, or 5.071nH/in
kC = PCB capacitance per unit length.
Both the metric and imperial version of the constant are given.
kC = 0.264pF/cm, or 0.67056pF/in
ℓ = length of microstrip (metric in cm, or imperial in inches)
w = width of microstrip (metric in mm, or imperial in mil)
t = thickness of copper (metric in mm, or imperial in mil)
h = separation between planes (metric in mm, or imperial in mil)
εr = relative permittivity, approximately 4.5 for FR-4 PCB
For imperial:
Copper thickness (mils) =
1.37 • (number of ounces)
i.e. 1oz Cu = 1.37mils
i.e. ½oz Cu = 0.684mils
ℓ
t
W
h
Figure 46: PCB Microstrip capacitance and inductance
Example
Calculate the total inductance and capacitance for ℓ=2.54cm, w=0.254mm,
t=0.0356mm, h=0.8mm, εr = 4.5 for FR-4
L(pF) = (2 nH⁄cm) ∙ (2.54cm) ∙ ln
(
5.98 ∙ 0.8mm
0.8 ∙ 0.254mm + 0.0356mm
C(pF) = (0.264pF/cm) ∙ (2.54cm)(4.5 + 1.41) = 1.3pF
5.98 ∙ 0.8mm
ln (
)
0.8 ∙ 0.254mm + 0.0356mm
) = 15.2nH
Example Calculate the total inductance and capacitance for ℓ=1in, w=10mil,
t=1.4mil, h=31.5mil, εr = 4.5 for FR-4
L = 15.2nH, C=1.3pF. Note: this is the same problem as above with imperial units.
62
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Texas Instruments Analog Engineer's Pocket Reference
Where
l = length of copper trace (mils)
t = thickness of copper trace (mils)
copper thickness (mils) = 1.37 * (number of ounces)
PCB
ti.com/precisionlabs
ex: 1 oz. copper thickness = 1.37 mils
ex: ½ oz. copper thickness = 0.685 mils
d = distance
Adjacent
copperbetween
tracestraces (mils)
and Wire
r =∙ tPCB
r ≈ 4.2 for FR-4)
k
∙ ℓ dielectric constant ((85)
Same layer
C(pF) ≈ w = width of copper trace (mils)
d
h = separation between planes (mils)
εr ∙ w ∙ ℓ
C(pF) ≈ Example
h
k∙
(86) Different layers
l = 100 mils
Where t = 1.37 mils (1 oz. copper)
ℓ = length
themils
copper trace (mil, or mm)
d of
= 10
-3
εr = 4.2
k = 8.854*10
pF/mm, or k=2.247*10-4 pF/mil
w = 25
t = thickness
of mils
trace (in mil, or mm)
h = 63 mils
d = distance between traces if on same layer (mil, or mm)
For imperial:
Copper thickness (mils) =
1.37 • (number of ounces)
w = widthAnswer
of trace. (mil, or mm)
h = separation between planes. (mil, or mm)
C (same layer) = 0.003 pF
i.e. 1oz Cu = 1.37mils
i.e. ½oz Cu = 0.684mils
εr = PCBCdielectric
constant (εr = 4.5 for FR-4)
(different layers) = 0.037
pF
Figure 47: Capacitance for adjacent copper traces
Figure 48: Capacitance for adjacent copper traces
Example: Calculate the total capacitance for both cases: ℓ=2.54mm,
t=0.0348mm, d=0.254mm, w=0.635mm, h=1.6mm, εr = 4.5 for FR-4
C(pF) ≈
(8.854 ∙ 10–3 pF/mm) (0.0348mm) (2.54mm)
63
0.254mm
= 0.0031pF Same
layer
(8.854 ∙ 10–3 pF/mm) (4.5mm) (0.635mm) (2.54mm)
= 0.04pF
1.6mm
Adjacent
layers
Example: Calculate the total capacitance for both cases: ℓ=100mil,
t=1.37mil, d=10mil, w=25mil, h=63mil, εr = 4.5 for FR-4
C(pF) ≈
C = 0.0031pF (Same layer), C=0.4pF (Adjacent layers). Note: this is the
same problem as above with imperial units.
Texas Instruments Analog Engineer's Pocket Reference
63
PCB and Wire
ti.com/precisionlabs
PCB via capacitance and inductance
[
L(nH) ≈ kL ∙ h 1 + ln
C(pF) ≈
(4hd )]
(87) Inductance for via
kC ∙ εr ∙ h ∙ d1
d2 — d1
(88) Capacitance for via
Where
kL = PCB inductance per unit length.
Both the metric and imperial version of the constant are given.
kL = 0.2nH/mm, or 5.076∙10-3nH/mil
kC = PCB capacitance per unit length.
Both the metric and imperial version of the constant are given.
kC = 0.0555pF/mm, or 1.41∙10-3pF/mil
h=
separation between planes
d=
diameter of via hole
d1 = diameter of the pad surrounding the via
d2 = distance to inner layer ground plane.
εr =
PCB dielectric constant (εr = 4.5 for FR-4)
d1
d
Top Layer
Trace
Middle Layer
GND
Plane
h
d2
Bottom Layer
Trace
Figure 48: Inductance and capacitance of via
Example: Calculate the total inductance and capacitance for h=1.6mm,
d=0.4mm, d1=0.8mm, d2=1.5mm
[
L(nH) ≈ (0.2 nH⁄mm) ∙ (1.6mm) 1 + ln
C(pF) ≈
∙ 1.6mm
(40.4mm
)] = 1.2nH
(0.0555pF/mm) ∙ (4.5) ∙ (1.6mm) ∙ (0.8mm)
1.5mm — 0.8mm
= 0.46pF
Example: Calculate the total inductance and capacitance for h=63mil,
d=15.8mil, d1=31.5mil, d2=59mil
L=1.2nH, C=0.46pF. Note: this is the same problem as above with imperial units.
64
Texas
Texas Instruments Analog Engineer's Pocket Reference
PCB and Wire
ti.com/precisionlabs
Type
ZO
Capacitance / length (pF/feet)
Outside diameter (inches)
dB attenuation /100 ft at 750 MHz
Dielectric type
Table 19: Coaxial cable information
RG-58
53.5Ω
28.8
0.195
13.1
PE
Application
Test equipment and RF power to a few
hundred watts, and a couple hundred MHz
RG-8
52Ω
29.6
0.405
5.96
PE
RG-214/U
50Ω
30.8
0.425
6.7
PE
9914
50Ω
26.0
0.405
4.0
PE
RG-6
75Ω
20
0.270
5.6
PF
RG-59/U
73Ω
29
0.242
9.7
PE
RG-11/U
75Ω
17
0.412
3.65
PE
RF power to a few kW, up to several
hundred MHz
RG-62/U
93Ω
13.5
0.242
7.1
ASP
Used in some test equipment and 100Ω
video applications
RG-174
50Ω
31
0.100
23.5
PE
RG-178/U
50Ω
29
0.071
42.7
ST
Texas Instruments Analog Engineer's Pocket Reference
RF power to a few kW, up to several
hundred MHz
Video and CATV applications. RF to a few
hundred watts, up to a few hundred MHz,
sometimes to higher frequencies if losses
can be tolerated
Miniature coax used primarily for test
equipment interconnection. Usually short
runs due to higher loss.
65
PCB and Wire
ti.com/precisionlabs
Coaxial
cable
equations
Coaxial cable
equations
C
ℓ
L
ℓ
2πε
D
Coaxial
cable equations
d
μC
ℓ
2π
D2πε
d D
d
LL μ1 μD
2π εd
ℓ C 2π
Capacitance
per length
(89)
per length
(84)Capacitance
per length
(90)
per
length
(85)Inductance
Capacitance
per length
(84) Inductance
impedance
(91)
impedance
(86)Characteristic
Inductance
per length
(85) Characteristic
L
1 μ
Characteristic impedance
(86)
Where
Where
C 2π ε
inductance in
in henries
henries (H)
(H)
LL==inductance
C = capacitance in farads (F)
C = capacitance in farads (F)
Z = impedance in ohms (Ω)
Where
Zd == impedance
ohms
(Ω)
diameter of in
inner
conductor
L = inductance in henries (H)
D
=
inside
diameter
of
shield,
or diameter of dielectric insulator
d = diameter of inner conductor
C = capacitance in farads (F)
ε = dielectric constant of insulator (ε = εr εo )
D = inside
diameter ofinshield,
Z = impedance
ohms or
(Ω)diameter of dielectric insulator
µ = magnetic permeability (µ = µr µo )
d = diameter of inner conductor
εl = length
dielectric
constant
of the
cable of insulator (ε = εr εo )
D = inside diameter of shield, or diameter
of dielectric insulator
μ = magnetic
permeability
(μof
= insulator
μr μo ) (ε = εr εo )
ε = dielectric
constant
µ = magnetic
permeability (µ = µr µo )
ℓ = length
of the cable
l = length of the cable
Insulation
Figure 49: Coaxial cable cutaway
Figure 49: Coaxial cable cutaway
Figure 49: Coaxial cable cutaway
66
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Texas Instruments Analog Engineer's Pocket Reference
65
PCB and Wire
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Table 20: Resistance per length for different wire types (AWG)
AWG
Stds
36
36
Outside diameter
Area
dc resistance
in
mm
circular mils
mm2
Ω / 1000 ft
Ω / km
Solid
0.005
0.127
25
0.013
445
1460
7/44
0.006
0.152
28
0.014
371
1271
34
Solid
0.0063
0.160
39.7
0.020
280
918
34
7/42
0.0075
0.192
43.8
0.022
237
777
32
Solid
0.008
0.203
67.3
0.032
174
571
32
7/40
0.008
0.203
67.3
0.034
164
538
30
Solid
0.010
0.254
100
0.051
113
365
30
7/38
0.012
0.305
112
0.057
103
339
28
Solid
0.013
0.330
159
0.080
70.8
232
28
7/36
0.015
0.381
175
0.090
64.9
213
26
Solid
0.016
0.409
256
0.128
43.6
143
26
10/36
0.021
0.533
250
0.128
41.5
137
24
Solid
0.020
0.511
404
0.205
27.3
89.4
24
7/32
0.024
0.610
448
0.229
23.3
76.4
22
Solid
0.025
0.643
640
0.324
16.8
55.3
22
7/30
0.030
0.762
700
0.357
14.7
48.4
20
Solid
0.032
0.813
1020
0.519
10.5
34.6
20
7/28
0.038
0.965
1111
0.562
10.3
33.8
18
Solid
0.040
1.020
1620
0.823
6.6
21.8
18
7/26
0.048
1.219
1770
0.902
5.9
19.2
16
Solid
0.051
1.290
2580
1.310
4.2
13.7
16
7/24
0.060
1.524
2828
1.442
3.7
12.0
14
Solid
0.064
1.630
4110
2.080
2.6
8.6
14
7/22
0.073
1.854
4480
2.285
2.3
7.6
Texas Instruments Analog Engineer's Pocket Reference
67
PCB and Wire
ti.com/precisionlabs
Polypropylene
Polyethylene
(high density) at 90°C
Polyvinylchloride Nylon
at 105°C
Imax (A)
Imax (A)
Imax (A)
Imax (A)
Kapton
Teflon
Silicon at 200°C
Polyethylene
Neoprene
Polyvinylchloride
(semi-ridged) at 80°C
AWG
Kynar
Polyethylene
Thermoplastic at 125°C
Wire gauge
Table 21: Maximum current vs. AWG
Imax (A)
30
2
3
3
3
4
28
3
4
4
5
6
26
4
5
5
6
7
24
6
7
7
8
10
22
8
9
10
11
13
20
10
12
13
14
17
18
15
17
18
20
24
16
19
22
24
26
32
14
27
30
33
40
45
12
36
40
45
50
55
10
47
55
58
70
75
Note: Wire is in free air at 25°C
Example
What is the maximum current that can be applied to a
30 gauge Teflon wire in a room temperature environment?
What will the self-heating be?
Answer
Imax = 4A
Wire temperature = 200°C
68
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Texas Instruments Analog Engineer's Pocket Reference
Sensor
Sensor
ti.com/precisionlabs
Sensor
Thermistor •
Resistive temperature detector (RTD) •
Diode temperature characteristics•
Thermocouple (J and K) •
69
Texas Instruments Analog Engineer's Pocket Reference
70
–55°C < T < 150°C
Low
LowLow
Low
High
Low
Less rugged
Very nonlinear. Follows reciprocal
|of logarithmic function
General
Applications
General
General
General
General
Requires excitation
General
purpose
Requires
excitation
Requires
excitation
Requires
excitation
Requires
excitation
Very
wide
variation
in resistance
Applications
General
purpose
General
purpose
Applications
General
purpose
Applications
General
purpose
Applications
range
180 to 3.9 kΩ for PT1000
Requires excitation
Scientific
and industrial
Requires
excitation
Requires
excitation
Requires
excitation
Requires
excitation
Scientific
industrial
Scientific
andindustrial
industrial
Scientific
and and
industrial
Scientific
and
Industrial temperature
Requires excitation
Self-powered
Requires cold junction comp
Requires
Self-powered
Requires
excitation
Self-powered
Requires
excitation
Requires
excitation
Self-powered
Lowexcitation
cost
linear response Self-powered
measurement
Requires
junction
comp
Requires
cold
junction
comp
Requires
coldcold
junction
comp
Requires
cold
junction
comp
Low cost temperature monitor
10s of millivolts
0.4 to 0.8V
cost
temperature
monitor
Industrial
temperature
Low
cost
temperature
monitor Industrial
Industrial
temperature
LowLow
cost
temperature
monitor
temperature
Low
cost
temperature
monitor
Industrial
temperature
cost
linear
response
measurement
Low
cost
linear
response
measurement
LowLow
cost
linear
response
measurement
Low
cost
linear
response
measurement
of
millivolts
10s
millivolts
10s 10s
of millivolts
10s
ofofmillivolts
Most rugged
0.40.8V
to0.4
0.8V
0.8V
0.4 to
0.4
toto0.8V
Complex 10th order polynomial
rugged
Most
rugged
MostMost
rugged
Most
rugged
Rugged
diode processing
Rugged
Rugged
Rugged
Rugged
Depends on Type (can be rugged)
Typically
to
100s
of full
kΩ
full
to18
390
Ω
for
PT100
Output
range
Typically
10s
to100s
100s
kΩfull
fullto18390
390
forPT100
PT100
Output
range
18
Ωtofor
PT100
Typically
10s 10s
to 100s
kΩ
Output
range
Typically
10s
toof
ofofkΩ
18
to
390
ΩΩfor
Output
range
Typically
10s
toVery
100s
ofvariation
kΩ
scale.
Very
wide
variation
to
3.9
kΩ
for
PT1000
180
to3.9
3.9
kΩfor
forPT1000
PT1000
scale.
wide
variation
scale.
Very
wide
variation
in in inin180 180
to 180
3.9
kΩ
for
PT1000
to
kΩ
scale.
Very
wide
Output
18
to
390
Ω
for
PT100
resistance.
resistance.
resistance.
resistance.
full scale
Construction
Linearity
Relatively simple quadratic function
Good accuracy with
polynomial correction
Depends
on on
Type
(can
be bebe
Depends
on
Type
(can
Depends
on Type
(can
be(can
Depends
Type
rugged)
rugged)
rugged)
rugged)
Poor accuracy without calibration
rugged
Construction
Less
rugged
Construction
LessLess
rugged
Construction
Less
rugged
Construction
Less accurate over full range
Low
LowLow
Low
accuracy
without
calibration.
Good
accuracy
polynomial
Poor
accuracy
without
calibration.
Good
accuracy
with
polynomial
PoorPoor
accuracy
without
calibration.
Good
accuracy
withwith
polynomial
Poor
accuracy
without
calibration.
Good
accuracy
with
polynomial
correction.
correction.
correction.
correction.
Low
–250°C
T< <1800°C
–250°C
<–250°C
T<T
1800°C
–250°C
<<<T1800°C
–250°C
<1800°C
T < 1800°C
Thermocouple
Thermocouple
Thermocouple
Thermocouple
Thermocouple
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Fairly
linear
Nonlinearity
< 4.5%
of scale.
full
scale.
Slope
≈ -2mV/C
Nonlinearity
< 10%
of scale
full
scale
Slope
-2mV/C
Nonlinearity
10%
fullscale
scale
Nonlinearity
4.5%
fullscale.
scale.
Slope
≈Slope
-2mV/C
< 10%
full
Nonlinearity
< 4.5%
full
Nonlinearity
<of<4.5%
ofoffull
≈ ≈linear
-2mV/C
Nonlinearity
<of<10%
ofoffull
Fairly
Slope ≈ -2mV/CNonlinearity
Fairly
linear
Fairly
linear
Relatively
simple
quadratic
Slope
varies
according
to current
Complex
order
polynomial
Slope
varies
according
tocurrent
current
Complex
10th
order
polynomial
Relatively
simple
quadratic Slope
varies
according
to current
Complex
10th10th
order
polynomial
Relatively
simple
quadratic
Relatively
simple
quadratic
Slope
varies
according
to
Complex
10th
order
polynomial
Slope
varies
according
to
current
function.
excitation,
diode
type,
and
diode
function.< 4.5% of full scaleexcitation,
excitation,
diode
type,
anddiode
diode
diode
type,
and
diode
function.
function.
excitation,
diode
type,
and
Nonlinearity < 10% of full scale
Nonlinearity
excitation, diode type, and
processing.
processing.
processing.
processing.
Accuracy
Low
LowLow
Low
Diode
–55°C
T< <150°C
–55°C
< –55°C
T<T
150°C
–55°C
<<<T150°C
–55°C
<150°C
T < 150°C
Diode
Diode
Diode
Diode
TableTable
22: Temperature
sensor overview
21: Temperature sensor overview
Table 21: Temperature sensor overview
Table 21: Temperature sensor overview
Table 21: Temperature sensor overview
nonlinear.
Follows
Linearity
Very
nonlinear.
Follows
Linearity VeryVery
nonlinear.
Follows
Linearity
Very
nonlinear.
Follows
Linearity
reciprocal
of logarithmic
reciprocal
logarithmic
reciprocal
of logarithmic
reciprocal
ofoflogarithmic
function.
function.
function.
function.
Accuracy
High
HighHigh
High
RTD
–200°C
850°C
–200°C
<–200°C
T<T
850°C
–200°C
<<<T850°C
–200°C
<T<T<850°C
<
850°C
RTD
RTDRTD
RTD
Excellent
accuracy
Excellent
accuracy
Excellent
accuracy
Excellent
accuracy
Good accuracy at one
temperature.
temperature.
temperature.
Goodtemperature.
accuracy
at
one
temperature
accurate
full full
range.
Less
accurate
over
fullrange.
range.
LessLess
accurate
overover
fullover
range.
Less
accurate
Excellent accuracy
CostAccuracy
Low
Good
accuracy
at one
Accuracy
Good
accuracy
at one
AccuracyGood
accuracy
at one
Cost
CostCost
Cost
<150°C
150°C
Temprange
range
–55°C –55°C
< –55°C
T < 150°C
Temp range
T T<150°C
Temp
Temp
range
–55°C
< T< <<
Temp range
Thermistor
Thermistor
Thermistor
Thermistor
Thermistor
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Thermistor:
Resistance to temperature, Steinhart-Hart equation
Thermistor: Resistance to temperature, Steinhart-Hart equation
1
Convert resistance to
(87)
R to temperature,
(92) Convert Steinhart-Hart
resistance
to temperature
a thermistor
Thermistor: RResistance
equation
temperature
for for
a thermistor
T
1
Convert resistance to
Where
(87)
R
R
Where
temperature for a thermistor
T
T = temperature in Kelvin
T = temperature in Kelvin
a, b, c = Steinhart-Hart equation constants
a,Where
b, c = Steinhart-Hart equation constants
R = resistance in ohms
temperature
in Kelvin
RT==resistance
in ohms
a,
b,
c
=
Steinhart-Hart
equation
constants Steinhart-Hart equation
Thermistor: Temperature
to resistance,
R = resistance in ohms
[
[
[
[
Thermistor:x Temperature
to resistance, Steinhart-Hart
equation
Convert temperature
to
x
(88)
y Temperature
y+
Thermistor:
to resistance, Steinhart-Hart
equation
resistance
for a thermistor
2
2
x
x
y
y
c
1y
T
1
T
cb
3c
b
3c
x
2
y+
x
4
x
4
x
2
Convert temperature to
(88)
(93) Convert
to resistance
resistance
forinaEquation
thermistor
Factor
used
88
(89)temperature
for a thermistor
Factor
used93
in Equation 88
(94) Factor(89)
used in
Equation
Factor used in Equation 88
(90)
(95) Factor(90)
used in
Equation
Factor
used93
in Equation 88
Where
R = resistance in ohms
T = temperature in Kelvin
Where
Where
a,
b, c = Steinhart-Hart equation constants
R==
resistance
Rx,
ininΩohms
yresistance
=
Steinhart-Hart
factors used in temperature to resistance equation
T
=
temperature
Kelvin
T = temperature ininKelvin
a, b, c = Steinhart-Hart equation constants
a, b, c = Steinhart-Hart equation constants
x, y = Steinhart-Hart factors used in temperature to resistance equation
x, y = Steinhart-Hart factors used in temperature to resistance equation
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RTD equation
temperature
to resistance
RTD
equation
temperature
to resistance
T
R
0
0
0T
0
RTD equation
temperature
to
resistance
R
0
0
0T
0
T
RTD resistance for
(96) RTD resistance
for T<0°C
(91)
T<0°C
RTD resistance for
(97) RTD resistance
for T>0°C
(92)
(91)
T>0°C
T<0°C
Where
RTD resistance for
Where
R
0
0 of RTD
0 T over temperature range of (–200°C (92)
Rrtd = resistance
< T < 850°C)
T>0°C
Rrtd = resistance of RTD over temperature range of (–200°C < T < 850°C)
Ro = 100 Ω for PT-100, 1000Ω for PT-1000
RWhere
for PT-100, 1000Ω for PT-1000
A0O=
, B100Ω
O, CO = Callendar-Van Dusen coefficients
Rrtd = resistance of RTD over temperature range of (–200°C < T < 850°C)
in degreesDusen
Celsius
( )
AT0,=Btemperature
coefficients
0, C0 = Callendar-Van
Ro = 100 Ω for PT-100, 1000Ω for PT-1000
TA=O,temperature
in
degrees
Celsius
(°C)
BO, CO = Callendar-Van Dusen coefficients
RTD equation
resistance to temperature (T>0°C)
T = temperature in degrees Celsius ( )
R
RTD resistance
A
RTD
equation
resistance
to temperature
RTD equation
resistance
toRtemperature
(T>0°C) (T>0°C)
(93)
0
for T>0°C
2B
R
RTD
A
(98) RTD resistance
for resistance
T>0°C
Where
R0
(93)
for T>0°C
RRTD = resistance2B
of RTD over temperature range of (–200°C < T < 850°C)
Ro = 100 Ω
Where
AO, BO, CO = Callendar-Van Dusen coefficients
Where
RRTD = resistance of RTD over temperature range of (–200°C < T < 850°C)
= temperature
Celsius
( )
RTRTD
= resistanceinofdegrees
RTD over
temperature
range of (–200°C < T < 850°C)
Ro = 100 Ω
RA0O=
, B100Ω
, C = Callendar-Van Dusen coefficients
TableO22:OCallendar-Van Dusen coefficients for different RTD standards
T
=
temperature
in degreesDusen
Celsius
( )
A0, B0, C0 = Callendar-Van
coefficients
IEC-751
T = temperature
in degrees Celsius (°C) US Industrial
43760
Table 22: DIN
Callendar-Van
Dusen coefficients for different RTD standards
US Industrial
Standard
BS 1904
IEC-751
Standard
D-100
ASTM-E1137
US Industrial
Table 23: Callendar-Van
Dusen
coefficients
for different
RTD standardsITS-90
DIN
43760
American
EN-60751
JISC 1604
American
US Industrial
Standard
BS 1904
A0
+3.9083E-3
+3.9787E-3
IEC-751
DIN 43760 +3.9739E-3
US Industrial +3.9692E-3
US Industrial +3.9888E-3
Standard
D-100
ASTM-E1137
1904 ASTM-E1137 –5.870E-7
Standard –5.8495E-7
Standard –5.915E-7
B0 BS –5.775E-7
–5.8686E-7
American
EN-60751
JISC 1604
American
ITS-90
EN-60751
JISC 1604
D-100 American
American
ITS-90
C0
–4.183E-12
–4.4E-12
–4.167E-12
–4.233E-12
–3.85E-12
A0
+3.9083E-3
+3.9739E-3
+3.9787E-3
+3.9692E-3
+3.9888E-3
+3.9083E-3
+3.9739E-3
+3.9787E-3
+3.9692E-3
+3.9888E-3
A0
B0
–5.775E-7
–5.870E-7
–5.8686E-7
–5.8495E-7
–5.915E-7
–5.775E-7
–5.870E-7
–5.8686E-7
–5.8495E-7
–5.915E-7
B0
C0
–4.183E-12
–4.4E-12
–4.167E-12
–4.233E-12
–3.85E-12
Example
–4.183E-12
–4.4E-12
–4.167E-12
–4.233E-12
–3.85E-12
C
0
What is the temperature given an ITS-90 PT100 resistance of 120 Ω?
Example
Answer
What is the temperature given an ITS-90 PT100 resistance of 120 Ω?
Example
120
What is the temperature3.9888
given∙ an
10 ITS-90 PT100 resistance of 120Ω?
100
Answer
Answer
3.9888 ∙ 10
72
120
120
100
100
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RTD
equation
resistance
to temperature
RTD equation
resistance
to temperature
(T<0°C) (T<0°C)
�
� � � �� �� ��� ��
(99) RTD resistance for T<0°C
(94)
���
RTD resistance
for T<0�
Where
Where
(�)
T = temperature in degrees Celsius (°C)
RRTD = resistance of RTD over temperature range of (T<0�)
RRTD
= resistance of RTD over temperature range of (T<0°C)
αI = polynomial coefficients for converting RTD resistance to temperature for T<0�
αi = polynomial coefficients for converting RTD resistance to temperature for T<0°C
th
Table 23: Coefficients for 5 order RTD resistance to temperature
IEC-751
Table 24:DIN
Coefficients
for 5th orderUS
RTD
resistance to temperature
Industrial
43760
US Industrial
Standard
BS 1904
IEC-751
Standard
D-100
ASTM-E1137
DIN 43760
American
EN-60751
JISC
1604
American
ITS-90
BS 1904
US Industrial
α0 –2.4202E+02
–2.3864E+02
ASTM-E1137 –2.3820E+02 –2.3818E+02
Standard
US Industrial –2.3791E+02
EN-60751
JISC 1604
D-100
American Standard
American
ITS-90
α1
2.2228E+00
2.1898E+00
2.1956E+00
2.1973E+00
2.2011E+00
αα2
0
–2.4202E+02
2.5857E-03 –2.3820E+02
2.5226E-03
–2.3818E+02
2.4413E-03
–2.3864E+02 2.3223E-03
–2.3791E+02
2.4802E-03
αα3
1
–4.8266E-06
–4.7825E-06
2.2228E+00
2.1898E+00
–4.7517E-06
2.1956E+00
–4.7791E-06
2.1973E+00 –4.6280E-06
2.2011E+00
αα4
2
αα5
–2.8152E-08
–2.7009E-08
2.5857E-03
2.5226E-03
1.5224E-10
1.4719E-10
–4.8266E-06 –4.7825E-06
–2.3831E-08
2.4413E-03
1.3492E-10
–4.7517E-06
–2.5157E-08
2.4802E-03 –1.9702E-08
2.3223E-03
1.4020E-10
1.1831E-10
–4.7791E-06
–4.6280E-06
α4
–2.8152E-08
–2.7009E-08
–2.3831E-08
–2.5157E-08
–1.9702E-08
1.5224E-10
α5
Example
1.4719E-10
1.3492E-10
1.4020E-10
1.1831E-10
3
Find the temperature given an ITS-90 PT100 resistance of 60 Ω.
Answer
Example
�
� ��������� � 0�� ∗ �60�� � ����0��� � 00� ∗ �60�� � �������� � 0�� ∗ �60�� � �
�
Find the temperature
given an
ITS-90
resistance of 60 Ω.
� ��������
� 0��
∗ �60�PT100
� ����6�
Answer
•
60
•
•
60
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Diode equation vs. temperature
Diode equation vs. temperature
V� �
nkT
I
nkT
I
�n � � �� �
�n � �
q
I�
q
I�
(100) Diode(95)
voltage
Diode voltage
Diode equation vs. temperature
Where
Where
vs. nkT
temperature
and current
VD = diode
nkT voltage
I
I
VV
diode�n
voltage
vs.�temperature
and1 current
� � ��
�n � �from
D�=
n
=�diode
factor
(ranges
to 2)
q ideality
I-23
q
I
�
�
1.38 xideality
10 J/K,
Boltzmann’s
constant
n k==diode
factor
(ranges from
1 to 2)
T = temperature
in Kelvin
k Where
= 1.38 x 10-23
-19 J/K, Boltzmann’s constant
q
x 10
C, charge
of an electron
diode
voltage
vs. temperature
and current
VD= =1.60
TI==temperature
in current
Kelvin in amps
forward
diode
n = diode ideality factor (ranges from 1 to 2)
-19
-23 C, charge of an electron
saturation
qkIS===1.60
xx10
1.38
10 current
J/K, Boltzmann’s constant
(95)
Diode voltage
T forward
= temperature
in Kelvinin amps
I=
diode current
qV�
-19
⁄��
��x
q
=�1.60
10
C, charge
� of an electron
(96) Saturation current
�T
���
��
I
�
IS = saturation current
nkT
I = forward diode current in amps
IS = saturation current
Where
IS = saturation current
qV�
Saturation current
�T ��⁄�� ���
�� to�the cross sectional area
(96) current
I� =�constant
α
related
of the
junction
(101)
Saturation
nkT
VG = diode voltage vs. temperature and current
n = diode ideality factor (ranges from 1 to 2)
Where
-23
x 10 current
J/K, Boltzmann’s constant
IkS == 1.38
saturation
Where
T=
= constant
temperature
in Kelvin
α
related
IS = saturation-19
currentto the cross sectional area of the junction
q = =1.60
x 10
C, charge
of an electron
V
diode
voltage
vs. temperature
and current
G
α = constant related to the cross sectional area of the junction
n = diode ideality factor (ranges from 1 to 2)
-23
VkG == 1.38
diodex voltage
vs.Boltzmann’s
temperatureconstant
and current
10 J/K,
temperature
in Kelvin
n T= =diode
ideality factor
(ranges from 1 to 2)
-19
q = 1.60 x 10-23 C, charge of an electron
k = 1.38 x 10 J/K, Boltzmann’s constant
T = temperature in Kelvin
q = 1.60 x 10-19 C, charge of an electron
74
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Diode voltage versus temperature
Figure 50 shows an example of the temperature drift for a diode.
Depending on the characteristics of the diode and the forward current
versus temperature
the Diode
slopevoltage
and offset
of this curve will change. However, typical diode drift
is about
–2mV/°C.
A forward drop of about 0.6V is typical for
Figure 50 shows an example of the temperature drift for a diode. Depending on the
room
temperature.
characteristics
of the diode and the forward current the slope and offset of this curve
will change. However, typical diode drift is about –2mV/°C. A forward drop of about
0.6V is typical for room temperature.
Figure 50: Diode voltage
vs. temperature
Figuredrop
50: Diode
voltage drop vs. temperature
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Type J thermocouples translating temperature to voltage
(ITS-90 standard)
Type J thermocouples translating temperature to voltage (ITS-90 standard)
�
V� � � �� ����
(102) Thermoelectric voltage
(97)
���
Thermoelectric
voltage
Where
Where
T = thermoelectric voltage
VV
T = thermoelectric voltage
T = temperature in degrees Celsius
T = temperature in degrees Celsius
ci = translation coefficients
ci = translation coefficients
Table 24: Type J thermocouple temperature to voltage coefficients
Type J thermocouple temperature to voltage
Table 25: Type J thermocouple temperature to voltage coefficients
–219� to 760�
760�temperature
to 1,200�to voltage
Type J thermocouple
c0
c1
c0
c2
c
1
c3
c2
c4
c3
c5
c4
c6
c
c75
c6
c8
c7
c8
76
0.0000000000E+00
–219°C to 760°C2.9645625681E+05
5.0381187815E+01
–1.4976127786E+03
0.0000000000E+00
760°C to 1,200°C
2.9645625681E+05
3.0475836930E-02
3.1787103924E+00 –1.4976127786E+03
5.0381187815E+01
–8.5681065720E-05
–3.1847686701E-03
3.0475836930E-02
3.1787103924E+00
1.3228195295E-07
1.5720819004E-06
–8.5681065720E-05
–3.1847686701E-03
–1.7052958337E-10
–3.0691369056E-10
1.3228195295E-07
1.5720819004E-06
2.0948090697E-13
-–1.7052958337E-10
–3.0691369056E-10
–1.2538395336E-16
-2.0948090697E-13
—
1.5631725697E-20
--
–1.2538395336E-16
—
1.5631725697E-20
—
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Type J thermocouples translating voltage to temperature
(ITS-90 standard)
Type J thermocouples translating voltage to temperature (ITS-90 standard)
�
� � � �� �V� ��
(103) Temperature
(98)
Temperature
���
Table 25: Type J thermocouple voltage to temperature coefficients
Table 26: Type J thermocouple voltage to temperature coefficients
Type J thermocouple voltage to temperature
Type J thermocouple temperature to voltage
–219°C to 0°C
0°C to 760°C
760°C to 1,200°C
–219°C to 0°C
0°C to 760°C
760°C to 1,200°C
c0
0.000000000E+00
0.000000000E+00
–3.113581870E+03
0.000000000E+00
0.000000000E+00
–3.113581870E+03
c0
c1
1.952826800E-02
1.978425000E-02
3.005436840E-01
c1
1.952826800E-02
1.978425000E-02
3.005436840E-01
c2
–1.228618500E-06
–2.001204000E-07
–9.947732300E-06
–1.228618500E-06
–2.001204000E-07
–9.947732300E-06
c2
c3
–1.075217800E-09
1.036969000E-11
1.702766300E-10
–1.075217800E-09
1.036969000E-11
1.702766300E-10
c3
c4
–5.908693300E-13
–2.549687000E-16
–1.430334680E-15
–5.908693300E-13
–2.549687000E-16
–1.430334680E-15
cc5
4
–1.725671300E-16
3.585153000E-21
4.738860840E-21
cc6
5
cc7
6
–1.725671300E-16
–2.813151300E-20
–2.813151300E-20
–2.396337000E-24
3.585153000E-21
–5.344285000E-26
–5.344285000E-26
5.099890000E-31
cc8
7
–8.382332100E-29
–2.396337000E-24
-5.099890000E-31
c8
–8.382332100E-29
Texas Instruments Analog Engineer's Pocket Reference
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4.738860840E-21
--- —
--
—
—
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Type K thermocouples translating temperature to voltage
(ITS-90
standard) translating temperature to voltage (ITS-90 standard)
Type K thermocouples
�
Thermoelectric
voltage
(99)
(104) Thermoelectric
voltage for
T<0°C
for T<0�
V� � � �� ����
���
�
�
V� � �� �� ���� � � �� e��� �������������
���
(105) Thermoelectric
voltage forT>0°C
voltage
(100) Thermoelectric
forT>0�
Where
VT = thermoelectric voltage
Where
in degrees
VTT==temperature
thermoelectric
voltage Celsius
translation coefficients
Tci == temperature
in degrees Celsius
α0, α1 = translation coefficients
ci = translation coefficients
26: Type K thermocouple temperature to voltage coefficients
αTable
0, α1 = translation coefficients
–219°C to 760°C
760°C to 1,200°C
0.0000000000E+00
–1.7600413686E+01
c0 27: Type
Table
K thermocouple temperature
to voltage coefficients
3.9450128025E+01
3.8921204975E+01
c1
–219°C to 760°C
760°C to 1,200°C
2.3622373598E-02
1.8558770032E-02
c2
0.0000000000E+00
–1.7600413686E+01
c0
–3.2858906784E-04
–9.9457592874E-05
c
3
cc41
3.9450128025E+01 3.1840945719E-07 3.8921204975E+01
–4.9904828777E-06
2.3622373598E-02 –5.6072844889E-10 1.8558770032E-02
–6.7509059173E-08
cc6
–5.7410327428E-10
–3.2858906784E-04 5.6075059059E-13 –9.9457592874E-05
–3.1088872894E-12
–3.2020720003E-16
–4.9904828777E-06
3.1840945719E-07
–1.0451609365E-14
9.7151147152E-20
–6.7509059173E-08
–5.6072844889E-10
–1.9889266878E-17
–1.2104721275E-23
–5.7410327428E-10
5.6075059059E-13
–1.6322697486E-20
--
cc52
3
c7
c4
c8
c
c9 5
cc
106
αc07
αc1
8
78
–3.1088872894E-12
-1.1859760000E+02 –3.2020720003E-16
-–1.1834320000E-04 9.7151147152E-20
–1.0451609365E-14
c9
–1.9889266878E-17
–1.2104721275E-23
c10
–1.6322697486E-20
—
α0
—
1.1859760000E+02
α1
—
–1.1834320000E-04
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78
Sensor
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Type K thermocouples translating voltage to temperature
(ITS-90 standard)
Type K thermocouples translating voltage to temperature (ITS-90 standard)
�
(106) Temperature
� � � �� �V� ��
(101)
Temperature
���
Table 27: Type K thermocouple voltage to temperature coefficients
Table 28: Type K thermocouple voltage to temperature coefficients
–219°C to 0°C
–219°C to 0°C
0°C to 760°C
760°C to 1,200°C
0°C to 760°C
760°C to 1,200°C
0.0000000E+00
0.0000000E+00
–1.3180580E+02
2.5173462E-02
2.5083550E-02
4.8302220E-02
7.8601060E-08
–1.6460310E-06
–1.0833638E-09
–8.9773540E-13
–2.5031310E-10
8.3152700E-14
5.4647310E-11
–9.6507150E-16
–8.9773540E-13
–3.7342377E-16
8.3152700E-14
–1.2280340E-17
–9.6507150E-16
8.8021930E-21
c5c6
–3.7342377E-16
–8.6632643E-20
–1.2280340E-17
9.8040360E-22
8.8021930E-21
–3.1108100E-26
c6c7
–1.0450598E-23
–8.6632643E-20
–4.4130300E-26
9.8040360E-22
-–3.1108100E-26
–5.1920577E-28
–1.0450598E-23
1.0577340E-30
–4.4130300E-26
— --
–1.0527550E-35
1.0577340E-30
—
–1.0527550E-35
—
c0
0.0000000E+00
c1
2.5173462E-02
c2
–1.1662878E-06
c0
c1
c2c3
c3c4
c4c5
c7c8
c9
–1.1662878E-06
–1.0833638E-09
c8
-–5.1920577E-28
c9
—
0.0000000E+00
2.5083550E-02
7.8601060E-08
–2.5031310E-10
Texas Instruments Analog Engineer's Pocket Reference
–1.3180580E+02
4.8302220E-02
–1.6460310E-06
5.4647310E-11
--
79
Sensor
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Table 29: Seebeck coefficients for different material
Material
Seebeck
coefficient
Material
Seebeck
coefficient
Material
Seebeck
coefficient
Aluminum
4
Gold
6.5
Rhodium
6
Antimony
47
Iron
19
Selenium
900
Bismuth
–72
Lead
4
Silicon
440
Cadmium
7.5
Mercury
0.6
Silver
6.5
Carbon
3
Nichrome
25
Sodium
–2.0
Constantan
–35
Nickel
–15
Tantalum
4.5
Copper
6.5
Platinum
0
Tellurium
500
Germanium
300
Potassium
–9.0
Tungsten
7.5
Note: Units are μV/°C. All data at temperature of 0°C
80
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A/D Conversion
A/D conversion
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A/D conversion
Binary/hex conversions •
A/D and D/A transfer function •
Quantization error •
Signal-to-noise ratio (SNR) •
Signal-to-noise and distortion (SINAD) •
Total harmonic distortion (THD) •
Effective number of bits (ENOB) •
Noise-free resolution and effective resolution •
A/D Conversion
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Numbering systems: Binary, decimal, and hexadecimal
Numbering systems: Binary, decimal, and hexadecimal
Numbering systems: Binary, decimal, and hexadecimal
Binary (Base-2)
0
1
0 1 2 3 4 5 6 7 8 9
01 2 3 4 5 6 7 8 9 A B C D E F
Decimal (Base-10)
Hexadecimal (Base-16)
2(1000) + 3(100) + 4(10) + 1(1) = 2,341
MSD
= Most significant digit
2(1000) + 3(100) + 4(10) + 1(1) = 2,341
MSD = Most significant
digit
Example
conversion:
todecimal
decimal
Example
conversion: Binary
Binary to
Example conversion: Binary to decimal
Binary
Decimal
Decimal
Binary
=
=
LSD
LSD
8 + 4 + 0 + 1
8 + 4 + 0 + 1
Example conversion: Decimal to binary
Example conversion:
Decimal
to binary
Example
conversion:
Decimal
to binary
Decimal
Binary
Binary
Decimal
LSD
=
=
A/D conversion
LSD
128 + 64 + 32 + 8 + 4 = 236
MSD
128 + 64 + 32 + 8 + 4 = 236
LSD = Least Significant Digit
MSD = Most Significant Digit
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Example conversion:
Binary
to hexadecimal
Example
conversion:
Binary to hexadecimal
Binary
Example conversion: Binary
MSD to hexadecimal
LSD
128 + 64 + 16 + 8 + 1 = 217
Hexadecimal
Conversion
128 + 64 + 16 + 8 + 1 = 217
8 + 4 + 1 = 13 (D)
8 8++14=+91 = 13 (D)
161 160
161 160
Hexadecimal
8+1=9
D 9
D 9
MSD LSD
MSD
208 + 9 = 217
208 + 9 = 217
Example Conversion: Hexadecimal to decimal
Example Conversion:
Hexadecimal
binary
and
decimal totohexadecimal
Decimal (Base-10)
Hexadecimal (Base-16)
0
1
2
3
4
5
6
8
9 10 11 12 13 14 15
0 1 2 3 4 5 6 7 8 9 A BCDE F
Decimal
Hexadecimal
x16 3 x16 2 x16 1 x16 0
16 9903 R = 15 (F)
=
2 6 A F
MSD
7
LSD
LSD
16 618 R = 10 (A)
16 38 R = 6 (6)
16 38 R = 2 (2)
LSD
MSD
2(4096) + 6(256) + 10(16) + 16(1) = 9903
LSD = Least Significant Digit
MSD = Most Significant Digit83
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A/D Converter with PGA
5V
FSR
0 to 2.5V
VREF
PGA
x2
ADC
12 bits
ADC in
0 to 5V
Digital
I/O
Figure 51: ADC full-scale range (FSR) unipolar
Full Scale Range (FSR) Unipolar
VREF
FSR =
PGA
1LSB =
FSR
2n
Example calculation for the circuit above.
FSR =
VREF
1LSB =
PGA
FSR
2n
=
=
5V
= 2.5V
2
2.5V
= 610.35µV
212
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A/D Converter with PGA
2.5V
FSR
0 to ±1.25V
VREF
PGA
x2
ADC
12 bits
ADC in
0 to ± 2.5V
Digital
I/O
Figure 52: ADC full-scale range (FSR) Bipolar
Full Scale Range (FSR) Bipolar
FSR =
VREF
PGA
1LSB =
FSR
2n
Example calculation for the circuit above.
FSR =
±VREF
±2.5V
=
= ±1.25V ⇒ 2.5V
PGA
2
1LSB =
FSR
2n
=
2.5V
= 610.35µV
212
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Table 30: Different data formats
Code
Straight binary
Offset binary
2’s complement
Decimal value
Binary
Decimal value
Decimal value
11111111
255
127
11000000
Code
192
Straight binary
Table 29: Different data formats
Binary
10000000
128Decimal value
Table
29: Different data formats
11111111
255
127
11000000
192
Code
Straight
binary
01000000
64Decimal
10000000
128value
Binary
01111111
127
11111111
255
00000000
0
01000000
64
11000000
192
00000000
0
10000000
128
01111111
01111111
–1
64
Offset binary
–64
2’s complement
Decimal
0 value
127
–1
Offset 64
binary
–640value
Decimal
–1
127
–128
–64
64
–128
0
Decimal –128
value
–1
127
–64
2’s complement
64
–128
Decimal
value
127 0
–1
64
–64
0
–128
–1
127
64
0
127
Converting two’s complement to decimal:
01000000
64
–64
Converting
two’s complement
to decimal:
Negative
number example
00000000
0
–128
Negative number example
Converting two’s complement
to decimal:
SIGN x4
x2 x1
Negative number example
Step 1: Check sign bit
This case is negative
Step 1: Check sign bit
This case is negative
Step 2: Invert all bits
1 x40
SIGN
MSD
1 x11
x2
LSD
1 0 1 1
MSD
0 1 0 0
Step 2: Invert all bits
Step 3: Add 1
0 1 0 0
0 1 0 1
Step
: Add 1
Final3result
0–(4+1)
1 =0 –51
Converting two’s complement to decimal:
–(4+1) = –5
Positive number example
Converting two’s complement to decimal:
Converting
two’s complement to decimal:
Positive
number example
Positive number exampleSIGN x4 x2 x1
Final result
Just add bit weights
SIGN
0 x41
x2
0 x11
MSD
Just add bit weights
Final result
Final result
0 4+1
1 = 50 1
LSD
MSD
4+1 = 5
84
86
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Table 31: LSB voltage vs. resolution and reference voltage
voltage
FSR Reference
(Full-Scale
Range)
1.024V
1.25V
2.048V
2.5V
4 mV
4.88 mV
8 mV
9.76 mV
10
1 mV
1.22 mV
2 mV
2.44 mV
12
250 µV
305 µV
500 µV
610 µV
14
52.5 µV
76.3 µV
125 µV
152.5 µV
16
15.6 µV
19.1 µV
31.2 µV
38.14 µV
18
3.91 µV
4.77 µV
7.81 µV
9.53 µV
20
0.98 µV
1.19 µV
1.95 µV
2.384 µV
22
244 nV
299 nV
488 nV
596 nV
24
61 nV
74.5 nV
122 nV
149 nV
Resolution
8
Table 32: LSB voltage vs. resolution and reference voltage
voltage
FSR Reference
(Full-Scale
Range)
Resolution
3V
3.3V
4.096V
5V
8
11.7 mV
12.9 mV
16 mV
19.5 mV
10
2.93 mV
3.222 mV
4 mV
4.882 mV
1.221 mV
12
732 µV
806 µV
1 mV
14
183 µV
201 µV
250 µV
305 µV
16
45.77 µV
50.35 µV
62.5 µV
76.29 µV
18
11.44 µV
12.58 µV
15.6 µV
19.07 µV
20
2.861 µV
3.147 µV
3.91 µV
4.768 µV
22
715 nV
787 nV
976 nV
1.192 µV
24
179 nV
196 nV
244 nV
298 nV
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DAC definitions
DAC definitions
Resolution = n
The number of bits used to quantify the output
n
Resolution
The number
of bits used
quantify the output
The
number
of input
codetocombinations
Codes == 2n
Number of Codes = 2n
The number of input code combinations
Sets the LSB voltage or current size and
Reference voltage = V
Full-Scale Range output = FSRREF
Sets the converter output range and the LSB voltage
converter
rangestep size of each LSB
n
The voltage
LSB = FSR / 2
n
2
The output
voltage
or current
LSB = V
REF / voltage
Full-scale
output voltage
of thestep
DAC size of each
Full-scale
output
= (2n – 1) • 1LSB
code Largest code that can be written
Full-scale input code = 2n – 1
n
n
) largest
Relationship
between
output
and input code
Transfer
Function:
Vout==2Number
Full-scale
code
– 1 of Codes • (FSR/2
The
code
that can
bevoltage
written
Full-scale voltage = VREF – 1LSB
Full-scale output voltage of the DAC
n
Transfer function = VREF x (code/ 2 ) Relationship between input code and output
voltage or current
FSR = 5V
Output voltage (V)
Full-scale
voltage = 4.98V
Resolution
1LSB = 19mV
Full-scale
code = 255
Number of codes = 2n
Resolution
= 8bits
Figure
53: DAC transfer function
Figure 51: DAC transfer
function
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ADC definitions
Resolution = n
The number of bits used to quantify the output
n
ADC
Codesdefinitions
=2
The number of input code combinations
Sets theThe
LSB
voltage
current
sizethe
and
Reference
Resolution
= nvoltage = VREF
number
of bitsorused
to quantify
input
converter
Therange
number of output code combinations
Number of Codes = 2n
n
Full-Scale
input
= FSR
Sets the
converter
input
rangecode.
and the
LSB voltage
– 1)
LSB = VRange
The voltage
step
size of
each
Note
that
REF / (2
n
n
The voltage step
of 2
each
LSB = FSR / 2
some topologies
maysize
use
asLSB
opposed to
input voltage of the ADC
Full-scale input voltage = (2n – 1) • 1LSB 2n – 1 inFull-scale
the denominator.
n
Largest code that can be read
Full-scale output code =
n 2 –1
The largest code that can be written.
Full-scale code = 2 – 1
Transfer Function: Number of Codes = Vin / (FSR/2n) Relationship between input voltage and output code
Full-scale output voltage of the DAC. Note that
Full-scale voltage = VREF
the full-scale voltage will differ if the alternative
definition for resolution is used.
n
Transfer function = VREF x (code/ 2 ) Relationship between input code and output
voltage or current
Full-scale
code=255
Input voltage (V)
Figure
54: ADC transfer function
Figure 52: ADC transfer
function
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Full-scale
Range
FSR = 5V
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Quantization error of ADC
Quantization error of ADC
Quantization error
Figure 53: Quantization error of an A/D converter
Figure 55: Quantization error of an A/D converter
Quantization error
The error introduced as a result of the quantization process. The amount of this error
is a function of the resolution of the converter. The quantization error of an A/D
Quantization
error
converter is ½ LSB. The quantization error signal the difference between the actual
The error
introduced
result
of the
quantization
The amount
voltage
applied andas
theaADC
output
(Figure
53). The rmsprocess.
of the quantization
signal of
is
this error
is
a
function
of
the
resolution
of
the
converter.
The
quantization
1LSB⁄√12
error of an A/D converter is ½ LSB. The quantization error signal is the
difference between the actual voltage applied and the ADC output
(Figure 55). The rms of the quantization signal is 1LSB ⁄√12
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Signal-to-noise
ratio
(SNR)
from quantization
Signal-to-noise ratio
(SNR)
from quantization
noise only noise only
MaxRMSSignal �
RMSNoise �
SNR �
FSR/2
1LSB
√12
√2
�
1LSB � 2���
(102)
(107)
√2
(103)
(108)
from quantization only
MaxRMSSignal 1LSB � 2��� /√2
�
� 2��� √6
RMSNoise
1LSB⁄√12
SNR�dB� � 2�log�SNR� � �2� log�2��N � 2�log �
SNR�dB� � 6��2N � 1��6
√6
�
2
(109)
(104)
(110)
(105)
(111)
(106)
Where
FSR = full-scale range of the A/D converter
Where
n
1LSB = the voltage of 1LSB, VREF/2
FSR = full-scale range of the A/D
converter
N = the resolution of the A/D converter
MaxRMSSignal
= the
rms equivalent
1LSB
= the voltage
of 1LSB,
VREF/2n of the ADC’s full-scale input
RMSNoise = the rms noise from quantization
NSNR
= the= resolution
thesignal
A/D converter
the ratio ofofrms
to rms noise
MaxRMSSignal = the rms equivalent of the ADC’s full-scale input
RMSNoise = the rms noise from quantization
Example
SNR = the ratio of rms signal to rms noise
What is the SNR for an 8-bit A/D converter with 5V reference, assuming only
quantization noise?
Answer
Example
��
SNR �is2���
� 2�for
√6
314 A/D converter with 5V reference,
What
the√6
SNR
an�8-bit
assuming only quantization noise?
SNR�dB� � 2�log�314� � 4��� dB
Answer
SNR�dB�
� 6��2�8�
� 1��6
4��� dB
SNR
= 2N-1
√6 = 28-1
√6 =�314
SNR(dB) = 20log(314) = 49.9 dB
SNR(dB) = 6.02(8) + 1.76 = 49.9 dB
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Total harmonic distortion (Vrms)
Total harmonic distortion (Vrms)
%
THD dB
RMSDistortion
MaxRMSSignal
•
100
RMSDistortion
MaxRMSSignal
V
V
V
V
V
•
100
(112)
(107)
(113)
(108)
Total harmonic distortion (Vrms)
Where
RMSDistortion
V
V
V
V
• 100rms(107)
%
THD = total harmonic
distortion, the• 100
ratio of the rmsVdistortion to the
signal
MaxRMSSignal
Where
RMSDistortion = the rms sum of all harmonic components
THD
= total harmonic
the
ratio
of the
rms distortion to the rms signal
RMSDistortion
MaxRMSSignal
= thedistortion,
rms value
of the
input
signal
THD dB
(108)
MaxRMSSignal
generally
input signal
V1 = the fundamental,
RMSDistortion
= the rms
sum
of the
all harmonic
components
V2, V3, V4, …Vn = harmonics of the fundamental
MaxRMSSignal
= the rms value of the input signal
Where
THD = total harmonic distortion, the ratio of the rms distortion to the rms signal
V1 = the fundamental,
generally
signal components
RMSDistortion
= the rmsthe
suminput
of all harmonic
MaxRMSSignal = the rms value of the input signal
V2, V3, V4, …V
= harmonics of the fundamental
V n= the fundamental, generally the input signal
1
V2, V3, V4, …Vn = harmonics of the fundamental
Figure 56:and
Fundamental
harmonics in Vrms
Figure 54: Fundamental
harmonicsand
in Vrms
Figure 54: Fundamental and harmonics in Vrms
92
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Total
harmonic distortion (dBc)
Total harmonic distortion (dBc)
Total harmonic distortion (dBc)
ୈమ
ୈయ
ୈర
ୈ౤
THD(dBc)
ൌ ͳͲŽ‘‰ ൤ͳͲቀ ଵ଴ ቁ ൅ ͳͲቀ ଵ଴ ቁ ൅ ͳͲቀ ଵ଴ ቁ ൅ ‫ ڮ‬൅ ͳͲቀ ଵ଴ ቁ ൨
ൌ
ୈమ
ͳͲŽ‘‰ ൤ͳͲቀ ଵ଴ ቁ
൅
ୈయ
ͳͲቀ ଵ଴ ቁ
൅
ୈర
ͳͲቀ ଵ଴ ቁ
൅‫ڮ‬൅
(114)
ୈ౤
ͳͲቀ ଵ଴ ቁ ൨
(109)
(109)
Where
Where
THDWhere
= total harmonic distortion. The ratio of the rms distortion to the rms signal
THD D
= total
harmonic distortion. The ratio of the rms distortion to the rms signal
1 = the fundamental, generally the input signal. This is normalized to 0 dBc
THD = total harmonic distortion. The ratio of the rms distortion to the rms signal
D
,
D
,
D
of the
fundamental
relative
the
2
3
4, …Dn = harmonics
D1 = the D
fundamental,
generally the
input
signal. Thismeasured
is normalized
to 0to
dBc
1 = the fundamental, generally the input signal. This is normalized to 0 dBc
fundamental
D
2, D3, D4, …Dn = harmonics of the fundamental measured relative to the
D2, D3, D4, …Dn = harmonics of the fundamental measured relative to
fundamental
the fundamental
Figure 57: Fundamental
andin
harmonics
in dBc
Figure
55: 55:
Fundamental
andand
harmonics
dBc
Figure
Fundamental
harmonics
in
dBc
Example
Example
Determine
THDTHD
for the
example
above.
Determine
for the
example
above.
Example
Answer
Answer
Determine THD for the example above.
ିଽଶ ିଽଶ
ି଻ହ ି଻ହ
ିଽହିଽହ
ିଵଵ଴
ିଵଵ଴
ቀ
ቁ ቀ
ቀ
ቁ
ቀ
ቁ
ቀ ଵ଴
ቀ ଵ଴
ቁ ቁ
ଵ଴ ቁ ଵ଴
ଵ଴ ቁଵ଴
ଵ଴ ቁଵ଴൅ ‫ڮ‬
ൌ ͳͲŽ‘‰
൅ ͳͲ
൅ ቀͳͲ
൅൅
‫Ͳͳ ڮ‬
൅ ͳͲ
ൌ ͳͲŽ‘‰
൤ͳͲቀ൤ͳͲ
൅ ͳͲ
൅ ͳͲ
൨ ൨
-75
)
)
)
-95
)
-92
)
-110
)
)
Answer
10
10
10
ൌ െ͹ͶǤ͹͸†10
ൌ THD(dBc)
=െ͹ͶǤ͹͸†
10 log 10 +10
+10 + ... +10
)
THD(dBc) = -74.76 dB
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Ac
signals
Ac signals
Signal-to-noise and distortion (SINAD) and effective number of bits (ENOB)
SINAD�dB� � 20 log �
SINAD�dB� � �20log ��10
�N�B �
MaxRMSSignal
√RMSNoise� � RMSDis�or�ion�
��������
�
�
��
� 10
�
�������
�
�
��
�
SINAD�dB� � 1.76dB
6.02
(115)
(110)
(116)
(111)
(117)
(112)
Where
MaxRMSSignal = the rms equivalent of the ADC’s full-scale input
Where
RMSNoise = the=rms
integratedofacross
the A/D
converters
MaxRMSSignal
the noise
rms equivalent
the ADC’s
full-scale
input
RMSDistortion = the rms sum of all harmonic components
RMSNoise
= the
noise
integrated
across the A/D
SINAD = the
ratiorms
of the
full-scale
signal-to-noise
ratioconverters
and distortion
THD = total harmonic
distortion.
ratio of the
rms distortion to the rms signal.
RMSDistortion
= the rms
sum of The
all harmonic
components
SNR = the ratio of rms signal to rms noise
SINAD = the ratio of the full-scale signal-to-noise ratio and distortion
THD = total harmonic distortion. The ratio of the rms distortion to the rms signal.
SNR = the ratio of rms signal to rms noise
Example
Calculate the SNR, THD, SINAD and ENOB given the following information:
MaxRMSSignal = 1.76 Vrms
Example
RMSDistortion
50 µVrms
Calculate
the =
SNR,
THD, SINAD and ENOB given the following
RMSNoise = 100 µVrms
information:
MaxRMSSignal = 1.76 Vrms
Answer
RMSDistortion
= 50 μVrms
RMSNoise = 100 1.76
μVrms
Vrms
SNR�dB� � 20 log �
� � ��.� dB
100 μVrms
Answer
THD�dB�
SNR dB � 20 log �
50
μVrms
1.76
Vrms
� � � �0.� dB
1.76 Vrms
1.76V rms
SINAD�dB�
� � ��.� dB
THD dB � 20 log �
μVrms�� � �50 μVrms��
��100
1.76
Vrms
���.�1.76V
��
���.� ��
� rms� �� �
��
� 10
�
SINAD dB � �20 log ��10�
SINAD�dB�
��.�dB � 1.76dB
�N�B
� 1�.65
SINAD�dB
10
6.02
6.02
94
� ��.� dB
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A/D Conversion
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Dcsignals
signals
Dc
Noise free resolution and effective resolution
Noise�ree�eso��tion � �o� � �
2�
�
PeaktoPeakNoiseinLSB
2�
���e�ti�e�eso��tion � �o� � �
�
rmsNoiseinLSB
PeaktoPeakNoiseinLSB � 6.6 � rmsNoiseinLSB
���e�ti�e�eso��tion � Noise�ree�eso��tion � 2.7
(118)(113)
(119)(114)
(120)(115)
(121)(116)
Note: The maximum effective resolution is never greater than the ADC resolution.
Note:
The maximum
resolution
is never
greater than
the ADC
resolution.
For
example,
a 24-biteffective
converter
cannot have
an effective
resolution
greater
than
Forbits.
example, a 24-bit converter cannot have an effective resolution greater
24
than 24 bits.
Example
Example
What
is the noise-free resolution and effective resolution for a 24-bit converter
What is the
resolution
effective resolution for a
assuming
the noise-free
peak-to-peak
noise is 7and
LSBs?
24-bit converter assuming the peak-to-peak noise is 7 LSBs?
Answer
��
2
Answer
Noise�ree�eso��tion
� �o� � � � � 2�.2
72
7
2��
���e�ti�e�eso��tion � �o� � �
� � 2�.�
7
2
6.6
7
6.6
���e�ti�e�eso��tion � 2�.2 � 2.7 � 2�.�
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A/D Conversion
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Time Constant
R
VIN A/D
VIN
C
Figure 58: Settling time for RC circuit-related to A/D converters
Figure 56: Settling time for RC circuit-related to A/D converters
Table 33: Conversion accuracy achieved after a specified time
Table 32: Conversion accuracy achieved after a specified time
Settling time in time
Settling time in time
Settling time
time in (NTC)
Accuracy in bits (N)Settling constants
Accuracy in bits
constants
(NTC)in
time constants
Accuracy in
time constants
Accuracy in
1 )
1.44
10
14.43
(N
bits
(NTC)
bits
TC
21
2.89
11
15.87
10
14.43
1.44
11
15.87
2.89
32
4.33
12
17.31
3
12
17.31
4.33
4
5.77
13
18.76
4
13
18.76
5.77
55
7.21
14
20.20
14
20.20
7.21
66
8.66
15
21.64
15
21.64
8.66
77
88
9
9
ൌ Ž‘‰ ଶ ሺ‡ି୒౐ి ሻ
16
17
18
10.10
10.10
11.54
11.54
12.98
12.98
(122)
16
17
18
23.08
24.53
25.97
23.08
24.53
25.97
(117)
Where
Where
N = the number of bits of accuracy the RC circuit has settled to after NTC number of
N = the number of bits of accuracy the RC circuit has settled to after NTC number of
time constants.
time constants.
NTC = the number of RC time constants
NTC = the number of RC time constants
Note: For a FSR step. For single-ended input ADC with no PGA front end
FSR (Full Scale Range) = VREF
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Table 34: Time required to settle to a specified conversion accuracy
Table in
33:
Time required
to settle
accuracy
Accuracyconversion
in bits
Settling
time in time
Accuracy
bits
Settling time
in timeto a specified
)
(N)
(NTC)
(N)
constants
(N
Settling timeconstants
in
Settling time inTC
Accuracy
8
in bits (N)
9
8
10 9
11 10
11
12
12
13 13
14 14
15 15
16
16
time constants
5.5
(NTC)
6.24
5.55
6.93
6.24
6.93
7.62
7.62
8.32
8.32
9.01
9.01
9.70
9.70
10.40
10.40
11.09
11.04
N�� � ����� �
Accuracy
in bits (N)
17
18
19
20
21
22
23
24
25
17 time constants
(NTC)
18
11.78
19
12.48
13.17
20
13.86
21
14.56
22
15.25
23
15.94
16.64
24
17.33
25
11.78
12.48
13.17
13.86
14.56
15.25
15.94
16.64
17.33
(118)
(123)
Where
NTC = the number of time constants required to achieve N bits of settling
Where
N the
= the
number
bitsconstants
of accuracy
NTC =
number
ofof
time
required to achieve N bits of settling
N = the number of bits of accuracy
Note: For a FSR step. For single-ended input ADC with no PGA front end
FSR (Full Scale Range) = VREF
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Notes
6
98
Texas Instruments Analog Engineer's Pocket Reference
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© 2014, 2015 Texas Instruments Incorporated
Printed in U.S.A. by (Printer, City, State)
SLYW038B
IMPORTANT NOTICE
Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, enhancements, improvements and other
changes to its semiconductor products and services per JESD46, latest issue, and to discontinue any product or service per JESD48, latest
issue. Buyers should obtain the latest relevant information before placing orders and should verify that such information is current and
complete. All semiconductor products (also referred to herein as “components”) are sold subject to TI’s terms and conditions of sale
supplied at the time of order acknowledgment.
TI warrants performance of its components to the specifications applicable at the time of sale, in accordance with the warranty in TI’s terms
and conditions of sale of semiconductor products. Testing and other quality control techniques are used to the extent TI deems necessary
to support this warranty. Except where mandated by applicable law, testing of all parameters of each component is not necessarily
performed.
TI assumes no liability for applications assistance or the design of Buyers’ products. Buyers are responsible for their products and
applications using TI components. To minimize the risks associated with Buyers’ products and applications, Buyers should provide
adequate design and operating safeguards.
TI does not warrant or represent that any license, either express or implied, is granted under any patent right, copyright, mask work right, or
other intellectual property right relating to any combination, machine, or process in which TI components or services are used. Information
published by TI regarding third-party products or services does not constitute a license to use such products or services or a warranty or
endorsement thereof. Use of such information may require a license from a third party under the patents or other intellectual property of the
third party, or a license from TI under the patents or other intellectual property of TI.
Reproduction of significant portions of TI information in TI data books or data sheets is permissible only if reproduction is without alteration
and is accompanied by all associated warranties, conditions, limitations, and notices. TI is not responsible or liable for such altered
documentation. Information of third parties may be subject to additional restrictions.
Resale of TI components or services with statements different from or beyond the parameters stated by TI for that component or service
voids all express and any implied warranties for the associated TI component or service and is an unfair and deceptive business practice.
TI is not responsible or liable for any such statements.
Buyer acknowledges and agrees that it is solely responsible for compliance with all legal, regulatory and safety-related requirements
concerning its products, and any use of TI components in its applications, notwithstanding any applications-related information or support
that may be provided by TI. Buyer represents and agrees that it has all the necessary expertise to create and implement safeguards which
anticipate dangerous consequences of failures, monitor failures and their consequences, lessen the likelihood of failures that might cause
harm and take appropriate remedial actions. Buyer will fully indemnify TI and its representatives against any damages arising out of the use
of any TI components in safety-critical applications.
In some cases, TI components may be promoted specifically to facilitate safety-related applications. With such components, TI’s goal is to
help enable customers to design and create their own end-product solutions that meet applicable functional safety standards and
requirements. Nonetheless, such components are subject to these terms.
No TI components are authorized for use in FDA Class III (or similar life-critical medical equipment) unless authorized officers of the parties
have executed a special agreement specifically governing such use.
Only those TI components which TI has specifically designated as military grade or “enhanced plastic” are designed and intended for use in
military/aerospace applications or environments. Buyer acknowledges and agrees that any military or aerospace use of TI components
which have not been so designated is solely at the Buyer's risk, and that Buyer is solely responsible for compliance with all legal and
regulatory requirements in connection with such use.
TI has specifically designated certain components as meeting ISO/TS16949 requirements, mainly for automotive use. In any case of use of
non-designated products, TI will not be responsible for any failure to meet ISO/TS16949.
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