Lecture 8
Resistors
Passive Electronic Components and Circuits (PECC)
V. Bande, Applied Electronics Department
www.ael.utcluj.ro (English version)-> Information for students
1
Resistors
Resistors
History and new trends
Electrical Properties
Classification
Parameters
Marking and Codification
Variable resistors
History and new trends
• 1827 – the first resistor
1W resistors:
Axial leaded
• 1976 – first embedded resistors
• General evolution trends:
 Performance improvement
 Size reducing
 Cost reduction
Chip
6.5
0.6
22.5
6.3
History and new trends
 Miniaturization
History and new trends
 Miniaturization
Resistors
Resistors
History and new trends
Electrical Properties
Classification
Parameters
Marking and Codification
Variable resistors
Electrical properties
l
R
S
• The mathematical relation which
designates the resistance calculation:
l
t
w
R
D
l
tw
[1  (T  20o C)  ]
R
http://www.8886.co.uk/ref/resistivity_values.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/rstiv.html#c1
http://www.istonline.org.uk/Handbook/40.pdf
4 l
o
[
1

(
T

20
C)  ]
2
D
Electrical properties
 The equivalent electrical model
• Due to fabrication particularities,
every each resistor will have besides
its own resistance a parasitic
inductance and as well a parasitic
capacitance.
• The parasitic parameters must be
taken into consideration at high
frequencies.
R
Lp
A
B
Cp
ZR 
R  jL p
1   2 L p C p  jRC p
Electrical properties
 Problem:
• Please consider the following voltage
divider.
R1
1. What is the dividing factor, if:
a) R1=1kΩ and R2=100Ω;
b) R1=100kΩ and R2=10kΩ;
c) R1=100kΩ and R2=1kΩ;
2. How will this dividing factor modify
with the frequency if every resistor has a
parasitic capacitance of 2 pF?
vi
R2
vo
Resistors
Resistors
History and new trends
Electrical Properties
Classification
Parameters
Marking and Codification
Variable resistors
Classification
 Constructive criteria:
• Discrete
 Fixed (constant).
 Variable.
• Integrated
 Resistor arias.
 Resistor networks.
• Embedded (“built in” the structure)




On the PCB level.
On the ceramic substrate level (multichip modules – MCM).
In silicon with the thin film technology.
Inside integrated circuits.
Classification
 Discrete resistors:
• Fixed (R=ct.)
• Variable (R≠ct.)
Classification
 Integrated resistors:
• Networks
• Arias
Classification
 Embedded
• Fabrication cost reduction.
• Thermo-mechanical reliability.
• Dimension reducing.
• Large scale compatibility between
different materials
• Values between 10Ω and 200kΩ
with under 10% tolerances.
Classification
 Linearity criteria:
R  const.
• Linear
• Non-linear
R  R(t ) t  temperature
 Thermistors
t
R  R(v) v  voltage
 Varistors
V
 Photo-resistors
R  R( )   light _ flux
Classification
 Technological criteria:
• Film resistors – are being obtained
by depositing layers of resistive
materials ( agglomerated carbon,
crystalline carbon, metal alloys,
metal oxides) in a thin pellicle (film
– under 10μm) on a insulating
support.
• Winded resistors – are being
obtained by winding a metallic
conductive wire on a insulating
support. This technology is being
used for obtaining high accuracy
resistors or high power resistors.
• Volume resistors – the resistive
element is basically the resistor’s
body.
Resistors
Resistors
History and new trends
Electrical Properties
Classification
Parameters
Marking and Codification
Variable resistors
Parameters
• Mandatory printed parameters
 Nominal resistance.
 Nominal value’s tolerance.
• Parameters printed only for particular resistors:
 The dissipated nominal power.
 The temperature coefficient.
 The upper limit voltage.
• Parameters the are not printed:
 The nominal values domain.
 The nominal temperature domain.
 Noise factor.
Parameters
 Normalized values series:
• In practice, there isn’t a continuous value range for the resistors.
• The solution adopted is to use normalized values series. Every
series is characterized by a certain tolerance.
• The resistance’s nominal values are being obtained from a
normalized series value by multiplication with the powers of 10.
• A certain series covers almost all the resistances possible values
domain, taking into consideration that between two successive
values from a series the following formula must apply:
Ri (t  1)  Ri 1 (t  1)
Parameters
 Normalized values series:
• The number of values from a
series is dependent of the
tolerance by resolving the
adjacent equation and taking
into consideration the first
higher then “n” integer.
1 t 

  10
1 t 
n
R0  1;
• The nominal values from a
series are in a geometrical
progression given by the
adjacent relation:
Ri  R0  r i
r  10
1
n
Parameters
 Normalized values series:
• The most important normalized series are:
E6(20%); E12(10%); E24(5%);
E48(2%); E96(1%); E192(0,5%);
• Values from the first three normalized series:
Serie
E6
E12
E24
Toleranţă
20%
10%
5%
Putere 1/n
0.166667
0.083333
0.041667
Ratie
1.47
1.21
1.1
Valori normalizate
1
2
3
1
1.5 2.2
1
1.2 1.5
1
1.1 1.2
4
3.3
1.8
1.3
5
4.7
2.2
1.5
6
6.8
2.6
1.6
7
8
9
10
11
12
13
3.3
1.8
3.8
2
4.7
2.2
5.6
2.4
6.8
2.6
8.3
2.9 3.3
Parameters
 Choosing a resistor by taking into consideration its tolerance:
• When choosing a resistor for a certain
application you must take into
consideration its tolerance.
• The one circuit’s function variation with
its components tolerances is called
sensitivity.
vO
R2
K

; R1  R 2
vI R 2  R1
1 t
1 t
1 t
K
; K min 
; K max 
1 t 1 t
2
2
R1
v
I
R2
v
O
Parameters
 Nominal power, Pn:
• The nominal power represents the maximum power which can be
dissipated by a resistor in a continuous functionality regime, at an
environment temperature equal with the nominal temperature, Tn
without changing its parameters.
• This parameter is being printed only for the resistors with the
nominal power higher then 2W.
• For this parameter, you will find 24 standardized values:
0,05W; 0,1W; 0,125W; 0,25W; 0,5W; 1W;
2W; 3W; 4W; .... 10W; 16W; ... 500W
Parameters
 Low-power resistors:
• For
the
low-power
resistors (below 2W), the
nominal power can be
deduced watching every
resistor’s
geometrical
dimensions.
Parameters
 Temperature coefficient:
• Is being printed only for high accuracy resistors.
• The temperature coefficient is defined as follows:
1 dR
R  
R dT
• For most of the resistors this parameter can be considered as a
constant.
Parameters
 The upper-limit voltage, Vn:
• Is being printed only for resistors dedicated to function at very
high voltages.
• For a common resistor, the upper-limit voltage can be calculated
as follows:
Vn  Pn  Rn
Parameters
 Noise factor, F:
• The noise factor can be defined as the noise voltage value that
appears at the resistor's terminals when applying a 1V DC
voltage.
• The noise voltage occurs because of the disordered movement of
the electrons through the conductive material:
Resistors
Resistors
History and new trends
Electrical Properties
Classification
Parameters
Marking and Codification
Variable resistors
Marking and Codification
 Resistors marking
• Resistors marking refers at the way the information printed on
the resistors is being encoded:
 Marking using digits and letters – alphanumeric.
 Marking using the resistors color code.
Marking and Codification
 Marking using digits and letters - alphanumeric
• The nominal value marking can be done using digits and letters
as multipliers. The letter’s position marks the decimal point
position in the nominal value.
Multiplicatori: R=1; K=1.000 (kilo);
M=1.000.000 (mega); G=1.000.000.000 (giga)
• Tolerance marking can be done either by clearly printing the
tolerance value (5%, 1%, etc.) or the tolerance can be encoded
using letters.
B0,1%; C0,25%; D0,5%; F1%;
G2%; H2,5%; J5%; K10%; M20%
Marking and Codification
 Marking using digits and letters - alphanumeric
• The avoid confusion between the letters that designate the
positon of the decimal point and the letters that designate the
tolerance there is a space between the tolerance and the other
letters (or event the tolerance is printed in a row below).
2K7
J
Nominal value 2700Ω, 5% tolerance
330K
M
Nominal value 330kΩ, 20% tolerance
R33
K
Nominal value 0.33Ω, 10% tolerance
• Nominal power and temperature coefficient marking can also be
done for the special resistors.
Marking and Codification
 Marking using digits and letters – alphanumeric – for SMD resistors
• For the SMD resistors which are generally smaller then THD
resistors, the encoding of the parameters uses the following
values – EIA-96 code:
Marking and Codification
 Marking using the resistors color code
• This procedure of encoded marking, although is more difficult to
decode, has the advantage that the printing area covers most of
the resistor’s body and is visible indifferently of the position of
the resistor on a PCB.
• The decoding procedure starts with the colored ring (or a group
of colored rings) which is closest from one terminal.
• For resistors with nominal values from E6, E12, E24, E48
normalized series, the color code contains 4 colored rings (bands).
• For resistors with nominal values from E96, E192 normalized
series, that have lower tolerances, the color code contains 5
colored rings (bands).
Marking and Codification
 Marking using the resistors color code
Marking and Codification
 Observations:
• Some colors don’t have a tolerance code (orange, yellow and
white).
• For the 4 band color code, the tolerance is encrypted using only
the following colors: red (2%), gold (5%) or silver (10%).
• When the color ring designating the tolerance is missing, that
means that resistor has a 20% tolerance value. Thus, the color
code will contain only 3 colored rings.
Brown, Black, Red + Gold
=
10*100, 5% tolerance
=
1kΩ, 5% tolerance
Marking and Codification
 Codification:
• Generally, in the electronic
circuits besides the resistor
symbol you will find its
reference (R1, R45, etc.) and its
nominal value (1k, 3k3, etc.).
The dissipated power or its
tolerance are being specified
only for specific applications.
Q1
2N3055
VI
D1
R3
1R5 2W
120
Q3
BD136
1N4001
Q2
BD135
VO
D4
DZ12
R4
• Those information regarding
the codification procedures
are being printed only on the
assembly layers of every PCB
board.
D3
R1
1N4001
R5
5k76
1%
R2
120
D2
PL5V 6
0
1k2
R6
6k34
1%
Resistors
Resistors
History and new trends
Electrical Properties
Classification
Parameters
Marking and Codification
Variable resistors
Variable Resistors
 Classification:
• Divided in 2 major categories:
 Semi-adjustable
 Potentiometers
Variable Resistors
 Use:
• Potentiometer circuit:
vI
R
R2
R2
vO 
vI 
vI
R  R1  R2
R  Rp
• Rheostat circuit:
vI
iO 
R  Rx
R
1
Rp
R2
vI
R
v
O
R
x
iO
Rp
Variable Resistors
 Classification:
• By the resistive element manufacturing technology:
 Metallic film resistors
 Carbon film resistors
 Metal-ceramic (cermet) resistors
 Winded resistors
Variable Resistors
 Classification:
• By the resistive elements number:
 Simple – with only one
resistive element
 Multiple – with more then
one resistive element. Can
work
in
tandem
or
independently.
Variable Resistors
 Classification:
• By destination:
• By the resistance variation
equation dependent with the
cursor position:
 Bulk (commercial use)
 Linear
 Logarithmic
 Accurate (with parameters
tolerances lower and very
high reliability)
 Inverse logarithmical
 Exponential
 Inverse exponentially
Variable Resistors
 Parameters:
• They are being characterized by the same parameters as the fixed
resistors.
• The potentiometers tolerances doesn’t have very low values
because the exact position of the cursor cannot be technologically
set in a very accurate way. To obtain high accuracy
potentiometers, multi-turn potentiometers are being used
Variable Resistors
 Specific parameters:
• The residual resistance, r0 – represents the value of the resistance
measured between the cursor and one of the terminals when the
cursor is positioned at that end of the resistor. Ideally, this
parameter should be zero.
• Contact resistance, rk – represents the value of the resistance
measured between moving cursor and the resistive element.
Again, this parameter should be as low as possible.
• The limit cursor current, In – represents the maximum value that
can pass through the resistive element.
Variable Resistors
 Specific parameters:
• The resistance variation equation:
• Linear
• Logarithmical
• Inverse logarithmical
R  r0    Rn
R  r0  e
 Rn
 r0
 ln 



R
 ln n 

R  r0  Rn 1  e r0 


Variable Resistors
 Mechanical parameters:
• The mechanical endurance – represents the minimum number of
cursor movements during which the potentiometer keeps its
designed parameters. This parameter has values between 10000
and 25000 for the common potentiometers and 100-200 for
trimmers.
• Pressure force – represents the force with witch the cursor
pressures the resistive film.
Resistors
 Problem 1:
• For a 100Ω resistor a tolerance t=10% at the reference temperature
T0=20°C has been determined. The resistor has a temperature
variation
coefficient
αT=20ppm/°C.
The
environment
temperature in which the resistor is designate to work is between
[-30°C;+90°C].
Considering that due to its dissipated power, the resistor’s
body heats up with 50°C, what is the global tolerance in
which the nominal value of the resistor can be found?
Resistors
 The dividing factor for R1=1kΩ and R2=100Ω:
Resistors
 The dividing factor for R1=100kΩ and R2=10kΩ:
Resistors
 The dividing factor for R1=100kΩ and R2=1kΩ: