This is Part 3 of a Three Part Series

• Chip Resistors Part 1: The Basics
• Chip Resistors Part 2: Types
• Chip Resistors Part 3: Applications and Considerations

Greetings designers!  In my last post we discussed several types of chip resistors and applications.  In this post, we will discuss some application factors as well as important considerations. 

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.  This article focuses on the potential effects of precision/matching, frequency, temperature and current as each may be an important factor in your application.

 Precision and Matching

In certain applications, it is highly important to use resistors that are well-matched.  For example in the non-inverting amplifier circuit (Op-Amp based) illustrated below, the gain (G) is established by the ratio of the resistor values shown through the relation G=1+(R₂/R).  If a minimum amplifier 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 resistors used in this application have well-matched temperature coefficient of resistance (TCR).

For example, using resistors having TCR of 200 ppm/C would result in 1% change in gain (G) if ΔT between them is 50C.  This 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, requiring 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 Considerations

As mentioned above, temperature effects are important for resistors that must be matched, but they are also important in other applications 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.  The effect of TCR on resistance is calculated using the relation:

where:

•      R_T is resistance at the temperature of interest (Ω)
•      R₀ is the nominal resistance (Ω)
•      TCR is temperature coefficient of resistance (PPM/C)
•      ΔT is the change in temperature from nominal (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 effects.  Chip resistors typically are made from at least two different conductor materials; the resistive element is generally one material and the external terminal material, or the termination, is generally at least one different conductor material.  When dissimilar metals are joined, a thermocouple may be formed due to the Seebeck effect.  This effect results in the generation of a small voltage between the terminals of the resistor that is based upon the difference 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.  This effect can be significant 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 airflow 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.  This can become significant as one or more of operating temperature, current, use bandwidth or resistance is increased.[1]  

Frequency Considerations

Resistor Parasitics

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.  The effect of the capacitance can be modeled as a capacitor in parallel with the resistor, and the effect 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 effect on the resistance value of all but the highest resistance value resistors.  This effect 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.  This effect can be significant 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.  This parasitic could affect 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 effect changes with frequency and with resistance value.  The inductive parasitic may also be important at high frequencies.  For example, 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 effect of the parasitics upon overall impedance changes with changing frequency.

Skin Effect

As frequency is increased in an AC circuit, current flows more and more toward the periphery of the conductor through which it flows.  This is called the skin effect, and may result in increased impedance as frequency is increased.  The 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 (A/m²)
•      J_S is the current density at the surface (s) of the conductor (A/m²)
•      d is the depth into the conductor (m)

δ is the skin depth of the material comprising the conductor (m) as defined by the relation:

where:

•      ρ is the resistivity of the conductor or resistor material (Ω-m)
•      f is frequency (Hz)
•      µ₀ is the magnetic permeability of free space (1.257×10⁻⁶ H/m)
•      µ_r is the magnetic permeability of the conductor or resistor material (H/m)

Skin depth tells you the depth at which the effective 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 rate.  This is important mainly in thick film resistors where the thickness of the resistor element(s) tends to be considerably greater than for thin film analogs, making thick film resistors generally more susceptible to increased impedance at high frequency as compared to thin film resistors due to the skin effect.  Additionally, perimeter geometries of printed thick film resistor traces tend to be less consistent compared to thin film 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 film resistors.  Magnetic permeabilities and resistivities of the resistor trace materials are also important considerations. To minimize the skin effect (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 fields of your application as they may change greatly with changing field or frequency.

Summary

Resistors have myriad applications in electronic circuits.  For gain setting, it is important to make sure that precision and TCR are appropriate for your application, and using a resistor network, or precision resistors, or trimmable resistors is appropriate.  Additionally, to avoid temperature-related resistance change, as well as other signal noise related effects, 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 affect resistor performance as frequency is changed, and to minimize parasitics in a manner that is cost effective for your application through both device selection and circuit design.  For high frequency applications, skin effect may also become important, and the potential geometric advantages of thin film resistors over thick film resistors, as well as the properties of the resistor materials used in the device selected, should be carefully considered.  Until next time…TTFN!

This is Part 2 of a Three Part Series

• Chip Resistors Part 1: The Basics
• Chip Resistors Part 2: Types
• Chip Resistors Part 3: Applications and Considerations

Greetings designers!  “A resistor by any other name” still resists current, right?  Of course, you know by now that the answer is, “it depends.”  What is the intended purpose and application environment for the resistor you seek?  What values, tolerances, temperature stabilities and other specifics are required?  What size can you accommodate and how much power will said resistor have to tolerate?  What other environmental factors (e.g., RoHS, high sulfur atmosphere, or the like) are important to your application?  To that end let’s talk about some different types of chip resistors.  We’ll discuss general purpose, high precision, current sense, high voltage, high power, high resistance, trimmable and environmentally compliant and chemically stable flavors of resistors.

General Purpose

General purpose chip resistors are used in surface mount circuit designs wherever you need a standard or general resistor such as for voltage reduction, current control, or the like.  These are typically thick film resistors, and are available in case sizes as small as 01005 (EIA).  General purpose chip resistors exhibit temperature coefficient of resistance (TCR) values as low as +/-100 ppm/C, with operating temperature range from -55C to 150C+, 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 film or thin film configurations.  They typically exhibit very low change in resistance with changing temperature.  Temperature coefficient of resistance (TCR) values for high precision chip resistors may be as low as +/-5 ppm/C.  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%.  These resistors are useful when you can’t trim or calibrate your circuit post assembly, or in other circumstances where tight tolerances and high levels of resistor value stability with changing temperature are required.

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.  They create a voltage drop when voltage is measured across the resistor.  This voltage drop is directly related to the current via Ohm’s law (V=IR).  The 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

Got a high voltage circuit for lighting or HV instrumentation or HV industrial or other HV applications?  As with HVMLCCs, high voltage chip resistors are likely needed.  These devices are designed to prevent arcing or voltage related failure in circuits rated up to 2KV.   

High Power

If you have an application requiring enhanced reliability or requiring high power density, you should consider using 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 offer higher power ratings than their general purpose chip resistor analogs in the same case size.  They 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 density 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 amplifier circuits or the like.  High resistance chip resistors are typically thick film 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

As a continuation of the “it depends” mantra, some circuit designs require at least one tunable or trimmable resistor as you just can’t “design-in” the optimal value until you actually test the circuit.  Devices using circuits that require calibration such as certain Op Amps, oscillators, voltage dividers, tuned sensor circuits and the like may benefit from use of trimmable resistors.  Trimmable resistors can be LASER trimmed to higher resistance than nominal as the resistor element and the glass passivation utilized are specially designed to allow in-situ LASER trimming after mounting the resistor to the circuit.  This enables in-situ tuning of the circuit.  In certain cases, trimmable resistors may even replace more costly and clumsy potentiometers as well.

Environmental Issues

We all care about our environment, and to that end RoHS (restriction of hazardous substances) regulations have resulted in the reduction or elimination of lead, mercury, 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.  The demand for the latter is likely to increase in the future as environmental regulations and requirements further mature.

Do you have problems with sulfur in your application atmosphere?  Certain materials, such as silver or copper tend to react with atmospheric sulfur creating corrosion that can become a major problem.  Care in materials selection and resistor design can help avoid this problem.  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 sulfide at that interface.  This can occur with as little as 1-3 ppm sulfur concentration in the ambient.  Anti-sulfuration resistors have been proven to prevent these types of failures.

Wow!…I hope that you agree that there are lots of “flavors” of chip resistors out there and I hope that this article will be helpful to you when selecting chip resistors for your circuit designs.  As with other 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.  My apologies to all of you Shakespeare lovers out there for butchering the prose of “The Master,” whether you be Capulet or Montague!  ;- )   TTFN!

This is Part 1 of a Three Part Series

• Chip Resistors Part 1:  The Basics
• Chip Resistors Part 2:  Types
• Chip Resistors Part 3:  Applications and Considerations

Greetings designers, let’s talk about resistors.  Resistors impede current flow, both alternating and direct currents are impeded equally by perfect resistors.  The unit for resistance is Ohms (Ω), named after German physicist Georg Ohm.  An Ohm is defined as the amount of resistance required to create a voltage drop of 1 volt (V), when the current flow is 1 Ampere (A).  From a dimensional standpoint, an Ohm is defined as 

m is meter 

• Kg is Kilogram
• s is second
• C is Coulomb
• J is Joule
• S is Siemens
• F is Farad
• W is Watt

…whew!  Thanks Wikipedia!   ;-)

This is interesting as the Ohm may be described in many different terms including time, distance, mass, charge, energy, capacitance and power…oh yes and conductance (Siemens-1), quite a versatile unit indeed!

Resistance Defined
Now that we understand what Ohms are, let’s find out how resistance (R) is determined.  As shown in the figure below, the resistance to a current flowing between plane 1 and plane 2 is found by the relation

• This is bulk resistance, and the above relation can be further simplified if the conductor is broken into square segments (i.e., if W = L) as shown below.   In that case, resistance simplifies to 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 m2)
  
  
  
  

• T is the thickness of the conductor through which the current traverses (units m)

In the above case, resistance simplifies to a value having units of Ohms per square (Ω/□), which is typically called “sheet resistance.”  Sheet resistance is a simplification of resistance and is useful to designers as it simplifies the process of resistor design.  

Chip Resistor Design
The device designed will typically have at least one resistor element.  The element is constant in thickness (T) with a geometry that is comprised of squares.  The width and thickness of the trace helps establish power rating as well as the number of squares possible in the trace for a given package size.  Thicker 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.  The designer will pick a material with a specific Ω/□ value in order to enable the design to achieve the intended nominal resistance. Further, in order to maximize the number of squares per unit area, a serpentine pattern of interconnected squares is generally used so that more resistance can be packed into a smaller area, making the best of circuit board “real estate.”  An example is shown below.  In this case, use of a serpentine pattern of squares enables almost 2X the resistance in the same lineal distance.


 The resistor pattern is deposited on to a substrate, typically comprised of an alumina-based ceramic.  However, other materials, such as silicon carbide, etc., may be used for high power applications or other applications.  The resistor pattern is connected to two terminals, typically one on each end of the device, in order to enable connection with the circuit board.  The resistor trace is then trimmed to meet nominal resistance as necessary, and the resistor trace is over-coated, marked and tested to create the finished product.  The resistor device is then connected to the circuit at the assembly facility via surface mount technology (SMT).

Thick and Thin Film Resistors
As mentioned in Chris Gutierrez’s recent blog post, the resistor pattern is typically established via one of two methods, so chip resistors are usually categorized as either thick film or thin film resistors based upon the deposition method used.   Chris’ post is an excellent discussion of the two technologies.  Additionally, thick film resistor technology benefits from relatively easy composition modification as modification of the resistor thick film “ink” (e.g., chemistry, glass content, dopants for TCR, etc. for the resistor trace) is easily accomplished, whereas it is relatively difficult to change the resistor composition using thin film technology.  Thick film resistor materials are generally based upon ruthenium oxide (RuO2) mixed with specialized glass formulations and other dopants to achieved desired properties during firing, while thin film resistors are generally based upon vapor deposited Nichrome and need not fired to achieve desired properties.  In contrast, thin film technology typically benefits from better deposit uniformity and more accurate patterning, so both have their advantages.

How They Are Made
The general resistor manufacturing process involves designing the device to fit resistance nominal and power rating in the package size of interest as described above.  Next, the resistor material is deposited on the substrate which is selected for mechanical strength as well as electrical and thermal properties.  The resistor element deposition is patterned, then adjusted to nominal, then over-coated and the individual resistor chips are singulated, then terminated, tested and packaged.  In the case of thick film resistors, the resistor trace chemistry is carefully selected to set Ω/□ as well as to adjust temperature coefficient of resistance (TCR) and other key properties, and the material is deposited and patterned in one step using screen or stencil printing.  The thick film resistor deposit is then thermal treated to achieve the electrical properties desired.  In the case of thin film resistors, the resistor material is first deposited to achieve a highly uniform thin film, and then patterned using photolithographic technics.  In the case of both technologies, the deposit thickness is carefully controlled to achieve the desired Ω/□, and the pattern is adjusted, typically via LASER ablation, to achieve the desired resistance (nominal).  The resistor pattern may also be adjusted for high voltage applications, or other specialized applications.  The thickness and the pattern uniformity of thick film resistor elements is typically much thicker and less uniform for thick film resistors in comparison to thin film resistors, making thin film resistors more desirable for certain applications (e.g., those involving, precision tolerances, high frequencies or the like).  

I hope that you found this useful…TTFN!