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by Dr. Michael Randall
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A technical paper discussing chip resistor types and the factors that should be
considered when selecting the best SMT resistor for your application.
Functionality, component design and make-up, circuit design and power
rating are considered as part of a framework for effectively pairing an application
with the best available surface mount resistor for the job.
The Definitive Guide to Surface
Mount Resistor Selection
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Background...........................................................................................................................................................................................................3
Types.............................................................................................................................................................................................................................7
General Purpose
............................................................................................................................................................................................7
High Precision
................................................................................................................................................................................................7
Current Sense
.................................................................................................................................................................................................8
High Voltage
....................................................................................................................................................................................................8
High Power
......................................................................................................................................................................................................8
High Resistance
.............................................................................................................................................................................................8
Trimmable Resistors
....................................................................................................................................................................................8
Environmentally Compliant and Chemically Stable Chip Resistors
........................................................................................8
Applications and Design Considerations ..............................................................................................................................................9
Power Considerations
.................................................................................................................................................................................9
Applications
.................... ..............................................................................................................................................................................11
Frequency Considerations
......................................................................................................................................................................12
Summary..................................................................................................................................................................................................................14
Figure 1. Resistance as a function of device geometry and resistivity..........................................................................................4
Figure 2. Serpentine pattern vs. straight pattern for resistor trace..............................................................................................5
Figure 3. Example power derating graph for chip resistors.......................................................................................................10
Figure 4. Non-inverting Op-Amp circuit Example.......................................................................................................................11
Table of Contents
Figures
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Surface mount chip resistors are ubiquitous. Hundreds of billions of these devices are sold every year into myriad ap-
plications from handheld devices to precision lab test equipment to aerospace electronics and others. Chip resistors
and associated technologies are discussed from the standpoints of types, functionality, device design, and applications
as well as circuit design and power rating considerations. Careful consideration of these important factors should
help lead you to the selection of the proper chip resistor component for your design.
Background
Resistors impede current ow, causing a voltage drop when placed in an electrical circuit. Both alternating and direct
currents are impeded by perfect resistors. e unit for resistance is Ohms (Ω), named aer German physicist Georg
Ohm. An Ohm is dened as the amount of resistance required to create a voltage drop of 1 volt (V), when the cur-
rent ow is 1 Ampere (A). From a dimensional standpoint, an Ohm is dened as:
Chip Resistors
Where:
m is meter
Kg is Kilogram
s is second
C is Coulomb
J is Joule
S is Siemens
F is Farad
W is Watt
It is evident from the above that the Ohm may be described in many dierent terms including time, distance, mass,
charge, energy, capacitance and power and conductance. As illustrated in Figure 1, the resistance to current ow
between two planes (i.e., plane 1 and plane 2 in Figure 1) of cross sectional area within a conductor is found by the
relation:
Where:
ρ is the resistivity of the material through which the current traverses (units, Ω-m)
L is the length that the current traverses between planes 1 and 2 (units, m)
A is the cross-sectional area of the conductor through which the current traverses (the area of either plane
1 or plane 2 (units, m
2
)
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is is bulk resistance, and the above relation can be further simplied if the conductor is broken into square seg-
ments (i.e., if W = L) as shown below. In that case, resistance simplies to:
T is the thickness of the conductor through which the current traverses (units, m)
In the above case, resistance simplies to a value having units of Ohms per square (Ω/h), which is typically called
“sheet resistance.” Sheet resistance is a simplication of resistance that is useful to chip designers as it greatly simpli-
es the process of resistor design.
Figure 1. Resistance as a function of device geometry and resistivity
e chip resistor device designed will typically have at least one resistor element. e element is usually constant
in thickness (T) with a geometry comprised of squares. e width and thickness of the trace helps establish power
rating and the number of squares is utilized to determine the resistance of the device. us, it is important to maxi-
mize the number of squares in the design when it is desirable to maximize resistance within a small case size device.
icker and wider squares typically result in the ability to carry more current and to handle more power, but the
number of squares (and the resulting resistance per unit length) is reduced, limiting the maximum resistance possible
within a given case size device.
During the chip resistor design process, the designer picks a material having a specic Ω/square value in order to
enable the intended nominal resistance within the given package size. e designer will also utilize a serpentine pat-
tern of interconnected squares in order to maximize resistance within the case size if needed, as a serpentine pattern
of squares enables more resistance (i.e., squares) to be packed into a smaller area, thereby making the best of circuit
board “real estate.” An example of this is illustrated in Figure 2. Use of a serpentine pattern of squares, in this case,
enables almost 2X the resistance in the same lineal distance.
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Figure 2. Serpentine pattern vs. straight pattern for resistor trace
e resistor pattern is deposited onto a substrate, that is typically comprised of an alumina-based ceramic (typi-
cally Al2O3 with from 1 w% to 10 w% glass as a sintering aid). However, other materials, such as silicon carbide
(SiC), etc., may be used for high power applications or other application needs. e resistor patterns are typically
deposited, many at a time onto a large substrate that is singulated into individual devices, later in the manufacturing
process, in order to enable cost eective mass manufacture.
e resistor pattern is connected to two terminals that are also deposited on the substrate as well as around the
edges of the substrate in order to form surface mount terminals, typically one on each end of the device, or in mul-
tiple stripes along the long sides of the device in the case of a resistor network. ese exterior terminals or termi-
nations enable connection of the chip resistor device with the circuit board. e resistor trace is trimmed to meet
nominal resistance within the specication range for the device as necessary, and the resistor trace is over-coated
with an electrically insulating material. Aer curing, the over-coat material is marked and each device is tested in
order to create the nished chip resistor product which is then packaged (typically in tape and reel form) for storage,
shipping, delivery, and placing or mounting with proper orientation.
During the circuit assembly process, the resistor device is then removed from the tape and is deposited on the
circuit board (PCB) using a pick and place machine. Each chip resistor is then physically connected to the circuit
within the PCB at the assembly facility using a thermal heat treatment that reows solder in order to physically,
thermally and electrically interconnect the resistor chip and the PCB. e solder is typically applied to the PCB
prior to the chip placement operation by stencil printer deposition of specialized solder paste and the solder reow
process is typically performed in a carefully controlled reow oven.
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e resistor pattern is typically established via one of two methods, either thick lm deposition or thin lm deposi-
tion. Other, much less prominent methods of manufacture are used as well for certain application specic devices.
As a result, chip resistors are typically categorized as either thick lm chip resistors or thin lm chip resistors based
upon the deposition method used in their associated manufacture.
ick lm manufacturing processes usually involve the precision deposition of particle loaded liquids (e.g. inks or
pastes) onto a substrate using some type of printing process (e.g., screen printing, stencil printing, pad printing or
the like). e printed inks or pastes are then dried and red to a dense, conductive, patterned resistor trace. Be-
cause patterning of the resistor is done during the application of the thick lm ink or paste, this is called an additive
process. ick lm resistor technology benets from relatively easy composition modication as modication of
the resistor thick lm “ink” (e.g., chemistry, glass content, dopants for TCR, etc. for the resistor trace) is relatively
easy to accomplish. ick lm resistor materials are generally based upon ruthenium oxide (RuO2) or platinum
(Pt) mixed with specialized glass formulations and other dopants in order to achieved desired properties during
ring.
e thin lm chip resistor manufacturing processes typically involves the precision deposition of an un-patterned
lm or material onto a substrate. e deposited material is usually applied utilizing either thermal deposition in
a relatively “hard” vacuum, or by physical vapor deposition using a sputtering process in a “soer” vacuum (e.g., a
vacuum backlled with Argon or other gas to increase the pressure) in order to create a plasma. in lm deposi-
tion techniques usually result in very thin, uniform lms. While thin lms may be patterned during the deposition
process, they usually are not when manufacturing chip resistors. Aer the precision deposition of the lm, the lm
is typically patterned, post deposition, using photolithography. Because of this, the patterns are formed by remov-
ing material and the process is called a subtractive process.
in lm resistor compositions are generally based upon vapor deposited nickel-chromium metals, called “ni-
chrome.” is is generally done using physical vapor deposition via a sputtering technique. e resulting resistor
elements generally need not be red to achieve desired properties using this technique. It is relatively dicult to
change the composition of the resistor element using thin lm technology. However, thin lm technology typically
benets from better deposit uniformity and more accurate patterning than thick lm technology, so both manufac-
turing methods for chip resistors have their associated advantages and disadvantages.
e general resistor manufacturing process involves designing the device to achieve a specied range around the
resistance nominal while maintaining the power rating in the package size of interest. Next, the resistor material is
deposited onto the substrate, which is selected for mechanical strength as well as for electrical and thermal proper-
ties. e resistor element is patterned either during deposition (additive, thick lm) or aer deposition (subtrac-
tive, thin lm), then adjusted to nominal resistance as needed, then over-coated and the individual resistor chips
are singulated, then terminated, tested and packaged.
In the case of thick lm resistors, the resistor trace chemistry is carefully selected to set Ω/square as well as to adjust
temperature coecient of resistance (TCR) and other key properties, and the material is deposited and patterned in
one step using screen or stencil printing (additive). e thick lm resistor deposit is then thermal treated to achieve
the electrical properties desired. In the case of thin lm resistors, the resistor material is rst deposited to achieve a
highly uniform thin lm, and is then patterned using photolithographic technics.
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In the case of both technologies, the deposit thickness is carefully controlled to achieve the desired Ω/square, and the
pattern is further adjusted, typically via LASER ablation, to achieve the desired resistance (nominal). e resistor
pattern may also be adjusted for high voltage applications, or other specialized applications. e thickness and the
pattern uniformity of thick lm resistor elements is typically much thicker and less uniform for thick lm resistors in
comparison to thin lm resistors, making thin lm resistors more desirable for certain applications (e.g., those involv-
ing, precision tolerances, high frequencies, etc.).
Types
Chip resistors come in many dierent sizes, shapes and congurations. us, it is important to understand how each
chip resistor will be used in your design. Before selecting your chip resistor device, it is prudent to be able to answers
questions regarding your design needs, such as:
• What is the intended purpose and application environment?
• What values, tolerances, temperature stabilities and other specics are required?
• What size can you accommodate and how much power will said resistor have to tolerate in its environment?
• What other environmental factors (e.g., RoHS, high sulfur atmosphere, or the like) are important to your application?
• Other questions depending upon your application and design constraints.
A Myriad of chip resistor types are available to address one’s design and application requirements such as:
• General purpose chip resistors,
• High precision chip resistors,
• Current sense chip resistors,
• High voltage chip resistors,
• High power chip resistors,
• High resistance chip resistors,
• Trimmable chip resistors,
• Environmentally compliant and chemically stable chip resistors.
A discussion of each type of chip resistor follows.
General Purpose
General purpose chip resistors are used in surface mount circuit designs wherever a standard or general resistor such
as for voltage reduction, current control, or the like is needed. ese are typically thick lm resistors, and are avail-
able in case sizes as small as 01005 (EIA). General purpose chip resistors exhibit temperature coecient of resistance
(TCR) values as low as +/-100 ppm/oC, with operating temperature range from -55oC to 150oC+, and have nominal
values from as low as 0 Ω to 20 MΩ+, with power ratings ranging from ~0.01W to 2W+.
High Precision
High precision chip resistors are available in either thick lm or thin lm congurations. ey typically exhibit very
low change in resistance with changing temperature. e corresponding temperature coecient of resistance (TCR)
values for high precision chip resistors may be as low as +/-5 ppm/oC. Resistance tolerances are also very “tight”
relative to standard chip resistors. For example ultra high precision chip resistors may have resistor value tolerances
as tight as +/-0.01%. ey are useful when it is dicult or impossible to trim or calibrate a circuit post assembly, or
in other circumstances where tight tolerances and high levels of resistor value stability with changing temperature are
required.
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Current Sense
Current sensors are circuits that detect and convert current to voltage that is proportional to the amount of current
traversing the circuit. Current sensing resistors are common for this purpose. ey create a voltage drop when
voltage is measured across the resistor. is voltage drop is directly related to the current via Ohm’s law (V=IR). e
resistance is carefully selected so as to cause a voltage drop suitable to the circuit when passing currents in the range
anticipated by the design. Current sense resistors are typically low value (<1 Ω) in order to avoid excessive power
usage. Further current sense resistor information is available via Venkel’s Current Sense Resistors Cheat Sheet.
High Voltage
High voltage circuits are common for lighting, HV instrumentation, HV industrial or other HV applications. For
these applications, it is likely that high voltage chip resistors are needed. ese devices are designed to prevent arcing
or voltage-related failure in circuits that are rated up to 3KV.
High Power
Applications requiring enhanced reliability or requiring high power density may benet from the use of high power
resistors in your design. High power resistors utilize special materials and designs to improve thermal properties in
order to provide better power dissipation capability. High power resistors may be used in place of general purpose
resistors where high power density is needed as they oer higher power ratings (generally a factor of at least 2 or
more) compared to general purpose chip resistor analogs. ey are well-suited for applications subjected to high
current, or where a large de-rating margin is needed such as in high temperature environments or high power den-
sity applications or the like.
High Resistance
High resistance chip resistors are typically used in high impedance instruments, test equipment circuits, temperature
measurement circuits, voltage dividers, circuits for gain setting, or other high impedance amplier circuits or the like.
High resistance chip resistors are typically thick lm resistors ranging in case size from 0402 (EIA) to 2512 (EIA) or
larger. Resistance values for these applications typically range from as low as 1 MΩ to 100GΩ+.
Trimmable Resistors
Some circuit designs require at least one tunable or trimmable resistor as it is very dicult to “design-in” the optimal
value until all of the other variations within the circuit are accounted. Devices using circuits that require calibration
such as certain Op Amps, oscillators, voltage dividers, tuned sensor circuits and the like may benet from use of
trimmable resistors. Trimmable resistors can be LASER trimmed, post mounting, to higher resistance than nominal
as the resistor element and the glass passivation utilized are specially designed to allow in-situ LASER trimming aer
mounting the resistor to the circuit. is enables in-situ tuning of the circuit. In certain cases, trimmable resistors
may even replace more costly and clumsy potentiometers as well.
Environmentally Compliant and Chemically Stable Chip Resistors
RoHS (restriction of hazardous substances) regulations have resulted in the reduction or elimination of lead, mer-
cury, cadmium hexavalent chromium, brominated biphenyls and diphenyl ethers from electronic components and
equipment, chip resistors included. In some cases, Pb is still allowed as a constituent (i.e., RoHS 5 or 5/6), but in
many cases RoHS 6 or 6/6 is required. e demand for the latter is likely to increase in the future as environmental
regulations and requirements further mature. e availability of chip resistors for application in high sulfur environ-
ments can be quite benecial to device reliability as certain materials, such as silver or copper, tend to react with
atmospheric sulfur, creating corrosion that can become a major reliability problem. Care in materials selection and
resistor design can help avoid this problem.
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Anti–sulfuration resistors increase the reliability of chip resistors in sulfuric or otherwise contaminated environments
such as experiences with certain industrial atmospheres, or with in-tire electronics or the like, where reaction with
sulfur at the resistor element-termination interface can result in increased resistance due to formation of silver sulde
at that interface.
is can occur with as little as 1-3 parts per million (ppm) sulfur concentration in the ambient. Anti-sulfuration
resistors have been proven to prevent these types of failures.
us, as with other types of electronic components, it is critical to understand the temperature range and other
environmental factors of your application as well as the voltages, power dissipations, resistance values, tolerances and
other key requirements of the components that you select for your application.
Applications and Design Considerations
Power Considerations
e nature of resistors is to turn the ow of electricity into heat. ey can dissipate considerable power as heat
depending upon the design in which they are utilized. Resistors reduce voltage within a circuit, turning said voltage
reduction into heat via Joule heating following the relation:
Where:
P = power (units, W)
I = current (units, A)
V = Voltage (units, V)
R = Resistance (units, Ω)
is creation of heat via resistive or Joule heating occurs within the resistor element of the device, causing it to heat
up as it passes current. Some of the heat generated escapes from the resistor element to the outer environment,
through the components of the chip resistor. Heat dissipation can only happen so fast however, and the amount of
heat that is retained within the device heats it to higher temperature. e amount that the temperature increases is
typically simplied to a linear value that is specied for the device. is value is typically stated in oC/W (units, de-
grees Celsius per Watt of power dissipated by the resistor element), and the nominal power rating of the chip resistor
is determined from that value, amongst other considerations. e nominal power rating of a chip resistor is given in
Watts. e value is determined by calculation based upon experimentation and is typically veried through reliabil-
ity testing of several batches of qualication devices.
Further, the nominal power rating of the chip resistor decreases once the operating temperature of the device exceeds
a given temperature (typically 70oC). In this case, the nominal power rating of the chip resistor is reduced at a rate of
~-1.2%/oC as the device temperature increases past 70oC, as indicated in the illustration below, and the chip resistor
is completely derated by 155oC (the maximum use temperature). It may also be possible to increase the rating of the
chip resistor selected if the operating temperature of the chip resistor is always kept below 70oC using an extrapola-
tion of the derating line in Figure 3 to temperatures less than 70oC (e.g., ~+1.2%/oC below 70oC), but be sure to get
your supplier’s “blessing” before you do this, as this practice may result in warranty issues regardless of whether or
not it is appropriate.
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Figure 3. Example power derating graph for chip resistors
For proper design, the circuit designer needs to carefully consider the balance between component selection and
thermal management considerations in order to achieve a thermal equilibrium condition in the device that does not
signicantly exceed the operating temperature of the circuit. Heat generated during operation must be removed
from the device in an ecient manner. Heat may be removed via one or more of the mechanisms of conduction,
convection or radiation. However, in this case, radiation and convection are typically only minor contributors to
heat ux as the temperature is too low to emit signicant radiation, and the ambient around the chip resistor device
is typically a poor convective medium. So we must rely on conduction for removal of the large majority of the heat
generated from a chip resistor in its associated circuit.
e primary path for removal of the heat generated is the conduction path of heat through the metal terminals of
the chip resistor, to the conductive traces of the PCB and out into the thermal mass of the PCB. is heat ow can
be maximized in the design of the chip resistor by maximizing the size of the terminals (i.e., using a large case size
chip resistor) or through the use of larger solder connections, or through the use of two sided metallization and/or
thicker metallization on the PCB, or the use of prudently placed thermal vias in the vicinity of the mounting pads.
Each of these methods, especially when used in combination, results in an improved thermal conduction path for
heat from the chip resistor.
Further, material selection is important. For example, the thermal conductivity (symbol, K, units, Watts per meter
degree Kelvin, W/mK) of alumina, the material typically used for chip resistor substrates, is ~24-30 W/mK. Use of
more exotic electrically insulating materials for the chip resistor substrate, such as Silicon Carbide (SiC, K ~350-
500 W/mK) or even diamond (C, K ~900-3,000 W/mK), helps to increase the power rating of the device by pro-
viding a greater dissipation path for heat generated in the resistor element. However, use of these materials can be
highly expensive, and it is important to balance the improvement in thermal performance with the cost of utilizing
exotic materials. In the case of diamond, for instance, the increase in cost is usually prohibitive. e above discus-
sion also applies to the over-coating material and to the terminal materials.
Improper chip resistor selection with respect to power rating may result in aging (embrittlement) or even melting
of solder joints, which will lead to a lack of reliability of the chip’s solder joints. It can also result in a loss in printed
circuit board (PCB) performance, or even failure of the PCB. Improper component selection or circuit design can
also result in poor chip resistor performance, such as high dri in resistance value, or the like. ese eects may not
be reversible without reworking or even replacing the component.
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Additionally, thermally conducting, but electrically insulating materials, such as thermally conductive epoxies or
the like, may be used to underll the chip resistor in order to enhance thermal conduction from the bottom of the
chip resistor into the PCB. ermal vias below said underll can further enhance conduction of heat from the chip
resistor to the PCB as well.
Applications
Resistors are used in numerous applications, such as current sensing, circuit tuning, voltage dividing, gain setting,
high frequency terminations and myriad high voltage and high power applications. Many of these applications
may also be environmentally challenging, such as high temperature, high sulfur or high humidity atmospheres or
the like. us, it is important to understand the potential eects of precision/matching, frequency, temperature and
current in your design as each may be an important factor in your application.
In certain applications, it is highly important to use resistors that are well-matched. For example in the non-invert-
ing amplier circuit (Op-Amp based) illustrated in Figure 4, the gain (G) is established by the ratio of the resistor
values shown through the relation G = 1 + (R2/R1). If a minimum amplier precision of 1% is required, then the
nominal resistance values of resistors R1 and R2 not vary more than +/-0.25%. Further, it is important that the resis-
tors used in this application have well-matched temperature coecient of resistance (TCR).
Figure 4. Example non-inverting Op-Amp circuit
For example, using resistors having TCR of 200 ppm/oC would result in 1% change in gain (G) if Δ temperature
(ΔT) between them is 50oC. is could occur as a result of self heating of R2 for instance, or if one of the resistors is
placed too close to a heat source (e.g., high power actives or the like). For high precision systems (say 10 bit, requir-
ing 0.1% G accuracy or better), matching of R1 and R2, combined with use of low TCR (and similar TCR) resistor
materials becomes important. Additionally, design that minimizes ΔT between R1 and R2 is important. In these
cases, the use of high precision resistors or of matched resistor networks is a common solution. Trimmable resistors
may also be valuable in these applications.
Temperature eects are not only important for resistors that must be matched, but are also important in other appli-
cations requiring stable resistance. Low TCR is generally preferred, but must be balanced with the economic factors
of your design, as low TCR resistors are generally more expensive. e eect of TCR on resistance is calculated
using the relation:
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Where:
R
T
is resistance at the temperature of interest (Ω)
R
0
is the nominal resistance (Ω)
TCR is temperature coecient of resistance (PPM/
o
C)
ΔT is the change in temperature from nominal (
o
C)
Indicating that the use of low TCR materials in the resistors that are used in your design is preferred, and that ΔT
in your circuit’s operating environment should be kept to a minimum in order to avoid resistance changes in your
design.
Additional variation in resistance may result from thermoelectric eects. Chip resistors typically are made from at
least two dierent conductor materials; the resistive element is generally one material and the external terminal ma-
terial, or the termination, is generally at least one dierent conductor material. When dissimilar metals are joined,
a thermocouple may be formed due to the Seebeck eect. is eect results in the generation of a small voltage
between the terminals of the resistor that is based upon the dierence in temperature (T) between the terminals. It
is similar to the phenomenon that results in a thermocouple output voltage that makes thermocouples useful for
measuring temperature. is eect can be signicant in precision circuits, so it is important to design your circuit
such that ΔT between each chip resistor terminal is minimized (e.g., design such that cooling airow traverses each
resistor terminal equally, or design that avoids placement of one terminal near a heat source, or the like).
Random thermal movement of charge carriers in a resistor element also produces noise that is proportional to the
operating temperature, as well as to the use bandwidth, the current and the resistance of the device in a one half
power manner. is can become signicant as one or more of operating temperature, current, use bandwidth or
resistance is increased.
Frequency Considerations
While a resistor is conceptually simple, each has non-ideal characteristics, as no device is perfect. In the case of a
chip resistor, said device will have capacitive and inductive parasitics. e eect of the capacitance can be mod-
eled as a capacitor in parallel with the resistor, and the eect of inductance as an inductor in series with the resistor.
Parasitic capacitance of chip resistors tends to be quite small (<1 pF), leading to low frequency (near DC) impedance
that is generally >100 GΩ, which will have minimal eect on the resistance value of all but the highest resistance
value resistors. is eect is generally compensated during the design process but should be understood as the
compensation likely changes with frequency. With increasing frequency the impedance associated with the parasitic
capacitance is reduced. is eect can be signicant when capacitive parasitic impedance is similar to, or less than,
the nominal resistance value. For example, in the case of a parasitic capacitance of 1 pF, the associated capacitive
impedance at 100 MHz will be about 100 Ω.
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is parasitic could aect the actual impedance by as much as 33% in the case of a 50 Ω termination resistor at 100
MHz. Again, this is usually compensated in the design, but it is important to understand as the eect changes with
frequency and with resistance value. e inductive parasitic may also be important at high frequencies. For exam-
ple, a parasitic inductance as low as 10 nH at 100 MHz will contribute about 50 Ω in to the impedance of the resistor.
Again, this is compensated for during the design process in order to achieve proper performance over a range of
frequencies, and thus is important to the understanding of the frequency range appropriate to the device selected for
your circuit and your situation, as the combined eect of the parasitics upon overall impedance changes with chang-
ing frequency.
Also, as frequency is increased in an AC circuit, current ows more and more toward the periphery of the conduc-
tor through which it ows. is is called the skin eect, and may result in increased impedance as frequency is
increased. e current density in a conductor (or resistor element) decreases from the outside to the inside of the
conductor according to the relation:
Where:
J
d
is the current density at depth d into the conductor (units, A/m
2
)
J
S
is the current density at the surface (s) of the conductor (units, A/m
2
)
d is the depth into the conductor (units, m)
δ is the skin depth of the material comprising the conductor (units, m) as dened by the relation:
Where:
ρ is the resistivity of the conductor or resistor material (units, Ω-m)
f is frequency (units, Hz)
µ
0
is the magnetic permeability of free space (units, 1.257×10
−6
H/m)
µ
r
is the magnetic permeability of the conductor or resistor material (units, H/m)
Skin depth is the depth into a conductor at which the eective conductivity of a material is reduced to 1/e (~37%) of
its full value at the exterior skin. As frequency and/or magnetic permeability are increased, skin depth δ decreases
at a half power rate, and as resistivity increases, δ increases at a half power (square root) rate. is is important
mainly in thick lm resistors where the thickness of the resistor element(s) tends to be considerably greater than for
thin lm analogs, making thick lm resistors generally more susceptible to increased impedance at high frequency,
as compared to thin lm resistors, due to the skin eect. Additionally, perimeter geometries of printed thick lm
resistor traces tend to be less consistent compared to thin lm resistor traces, and as the current is forced toward the
outer portion of the conductor, the current path becomes more tortuous, further increasing apparent impedance at
elevated frequencies in thick lm resistors. Magnetic permeabilities and resistivities of the resistor trace materials are
also important considerations. To minimize the skin eect (i.e., to maximize δ), it is generally preferable to use high
resistivity, low magnetic permeability materials, and to understand these values at the frequencies and elds of your
application as they may change greatly with changing eld or frequency.
Venkel Ltd 800-950-8365 | www.venkel.com | engineering@venkel.com
14 Venkel Ltd
Summary
Resistors have a myriad of applications in electronic circuits. It is important to understand the operating parameters
required for your design when selecting a chip resistor. For example, it is important to consider power rating when
selecting a chip resistor, and while it may be tempting to use the smallest chip resistor possible, that may not be
prudent as it may lead to overheating and associated reliability issues. As the balance between heat generation and
heat dissipation is paramount, it is important to select the appropriate chip resistor as well as to properly design your
PCB, making sure to use the appropriate amount of metal in the traces and lands, as well as thermal vias, etc. where
prudent. e balance between power dissipation and cost is an important consideration as well, since use of high
thermal conductivity materials and specialized designs and cooling schemes, etc. can quickly become prohibitively
expensive.
For gain setting applications, it is important to make sure that precision and TCR are appropriate. Use of a resistor
network, or precision resistors, or trimmable resistors may be most appropriate. In order to avoid temperature-
related resistance change, as well as other signal noise related eects, it is important to design for minimal ΔT both
between resistor terminals and between individual resistors in your circuit, as well as to keep the overall temperature
of the resistors as low as practicable. It is also important to understand how parasitics aect resistor performance as
frequency is changed, and to minimize parasitics in a manner that is cost eective for your application through both
device selection and circuit design. For high frequency applications, skin eect may become important, and the
potential geometric advantages of thin lm resistors over thick lm resistors, as well as the properties of the resistor
materials used in the device selected, should be carefully considered.
High power chip resistors are designed using high thermal conductivity materials, combined with resistor patterns
having better thermal properties, and by utilizing modied construction and processing techniques, all in a cost
eective manner. High power chip resistors may have double the power rating, or better, compared to the same case
size standard chip resistor. Because of this, they are typically an economic option for the designer when it is impor-
tant to maximize power density as well as component density within the circuit design. Additionally, if the designed
circuit is kept below 70oC, it may be possible to increase the power rating of a chip resistor using a slope similar to,
or less than the slope of the derating line extrapolated to the operating temperature below 70oC. Be sure to talk to
your chip resistor supplier, prior to adopting this practice, in order to make sure that this practice does not void any
warranties, however.
15 Venkel Ltd
Venkel Ltd 800-950-8365 | www.venkel.com | engineering@venkel.com
About Venkel
Venkel is a supplier of Surface Mount Passive Components, located in Austin, Texas since 1986. We oer a complete line of sur-
face mount components as well as Supply Chain Management Programs to help manage your supply chain.
Additionally we provide FREE Engineering Support onsite and through our website at venkel.com. We support companies
worldwide, all the way from prototype to high volume production.
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About The Author
Dr. Michael Randall is a technologist with nearly 25 years of experience in R&D, passive components, product development in
the electronics industry including design, materials, processing, testing and business development having a strong track record of
taking ideas to protable products. Recognized as a technical expert in the area of passive electronic components and certied as
a Six Sigma Black Belt (DFSS). An experienced consultant having provided expert services in areas of intellectual property, pro-
cess optimization, market studies, and grants. Award winning author as well as inventor on 19 US Patents, lecturer and technical
consultant. For more informaiton about Dr. Randall, visit www.almegacy.com.
