Resistors: A Detailed Educational Resource

electronics, resistor, passive component, resistance, ohm's law

A resistor is a fundamental passive two-terminal electrical component that is designed to implement electrical resistance within a circuit.

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Introduction to Resistors

A resistor is a fundamental passive two-terminal electrical component that is designed to implement electrical resistance within a circuit.

Passive Component: In electronics, a passive component is a component that does not require an external power source to operate and cannot amplify or oscillate an electrical signal. Resistors, capacitors, and inductors are examples of passive components.

Electrical Resistance: Electrical resistance is the opposition that a substance offers to the flow of electric current. It’s analogous to friction in mechanics. The higher the resistance, the less current flows for a given voltage.

In essence, resistors are used to control the flow of electrical current in a circuit. They are ubiquitous in electronics and play a vital role in a wide variety of applications.

Uses of Resistors in Electronic Circuits

Resistors are incredibly versatile components used for a multitude of purposes in electronic circuits, including:

• Current Limiting: Reducing the amount of current flowing in a specific part of a circuit to protect sensitive components or achieve desired functionality. For example, resistors are often used in series with Light Emitting Diodes (LEDs) to prevent them from burning out due to excessive current.
• Signal Level Adjustment: Modifying the voltage or current levels of signals within a circuit. This is essential for ensuring proper signal compatibility between different circuit stages.
• Voltage Division: Creating specific voltage levels from a higher voltage source. This is achieved using voltage dividers, which are configurations of resistors in series.
• Biasing Active Elements: Setting the operating point of active components like transistors and vacuum tubes. Biasing ensures these components operate in their desired linear region for amplification or switching.
• Termination of Transmission Lines: Preventing signal reflections in high-frequency circuits by matching the impedance of the transmission line. This ensures signal integrity and prevents signal distortion.
• Heat Generation: High-power resistors can dissipate significant electrical power as heat. This is utilized in applications like:
  • Motor Controls: Regulating motor speed and torque by controlling current flow.
  • Power Distribution Systems: Balancing loads and managing current in power networks.
  • Test Loads for Generators: Simulating real-world loads to test the performance of electrical generators.

Types of Resistors

Resistors come in two primary categories based on their resistance value:

• Fixed Resistors: These resistors have a resistance value that is set during manufacturing and remains relatively constant under normal operating conditions. While their resistance may slightly change with temperature, time, or voltage, these changes are typically small and predictable within specified tolerances. Most resistors used in electronic circuits are fixed resistors.
• Variable Resistors: Also known as potentiometers or rheostats, these resistors allow their resistance to be adjusted. They can be used for:
  • Circuit Adjustment: Fine-tuning circuit parameters, such as volume control in audio equipment or lamp dimmers.
  • Sensing Devices: Detecting changes in physical quantities like heat (thermistors), light (photoresistors), humidity (humistors), force (strain gauges), or chemical activity (chemiresistors).

Ubiquity of Resistors

Resistors are fundamental components in virtually all electrical networks and electronic circuits. They are ubiquitous, meaning they are found everywhere in electronic equipment, from simple consumer devices to complex industrial systems. They can be implemented as:

• Discrete Components: Individual, packaged resistors that are soldered or connected into circuits. These come in various shapes, sizes, and lead configurations.
• Integrated Components: Resistors fabricated directly onto semiconductor chips as part of integrated circuits (ICs). This allows for miniaturization and complex circuit designs within a single chip.

Integrated Circuit (IC): Also known as a microchip or chip, an integrated circuit is a set of electronic circuits on one small flat piece (or “chip”) of semiconductor material, normally silicon. Large numbers of tiny MOSFETs (metal-oxide-semiconductor field-effect transistors) integrate to form a complete electronic circuit.

Resistance Range and Tolerance

The electrical function of a resistor is defined by its resistance, measured in ohms (Ω). Commercial resistors are manufactured across an extremely wide range of resistance values, spanning more than nine orders of magnitude (from milliohms to gigaohms).

Ohm (Ω): The ohm is the SI unit of electrical resistance, named after Georg Simon Ohm. One ohm is defined as the resistance between two points of a conductor when a potential difference of one volt applied across these points produces in the conductor a current of one ampere, the conductor not being the source of any electromotive force.

Due to this vast range, derived units are commonly used:

• Milliohm (mΩ): 1 mΩ = 10^-3 Ω (one-thousandth of an ohm)
• Kilohm (kΩ): 1 kΩ = 10³ Ω (one thousand ohms)
• Megohm (MΩ): 1 MΩ = 10⁶ Ω (one million ohms)

The nominal value of a resistor, indicated by markings like color codes or numerical codes, represents its intended resistance. However, due to manufacturing variations, the actual resistance of a resistor may deviate slightly from this nominal value. This deviation is known as manufacturing tolerance, usually expressed as a percentage (e.g., ±5%, ±1%). Resistors are manufactured with different tolerance ratings depending on the precision required for the application.

Electronic Symbols and Notation

Resistors are represented in schematic diagrams using specific symbols. Two common symbols are:

• Rectangular Symbol (IEC Standard): A rectangle, often with jagged lines inside, representing the resistor. This symbol is widely used internationally.

• Zig-zag Symbol (ANSI Standard): A zig-zag line, representing the resistive path. This symbol is more common in North America.

(Unfortunately, I cannot directly display images here. Please refer to online resources or textbooks for visual representations of these symbols.)

RKM Code for Resistance Value Notation

To simplify notation and avoid decimal separators, the RKM code (defined in IEC 60062) is frequently used to indicate resistor values, especially in circuit diagrams and Bills of Materials (BOMs). This code utilizes letters associated with SI prefixes to represent multipliers:

• R: Represents the unit ohm (Ω). Used in place of a decimal point when the resistance value is less than 1000 ohms.
• K: Represents kilohm (kΩ) (10³ Ω).
• M: Represents megohm (MΩ) (10⁶ Ω).

Examples of RKM Code:

• 8K2: Indicates 8.2 kΩ (8.2 kilohms or 8200 ohms).
• 15M0: Indicates 15.0 MΩ (15.0 megohms or 15,000,000 ohms). The trailing zero implies tighter tolerance (three significant digits).
• 1R2: Indicates 1.2 Ω (1.2 ohms).
• 18R: Indicates 18 Ω (18 ohms).

This notation system makes it easier to read and write resistor values without ambiguity, particularly in technical documentation and manufacturing settings.

Theory of Operation

The fundamental principle governing the behavior of resistors is Ohm’s Law.

Ohm’s Law

An ideal resistor, which is a theoretical concept representing a pure resistance without any other electrical properties like reactance, perfectly obeys Ohm’s Law.

Reactance: Reactance is the opposition to the flow of alternating current (AC) caused by capacitance and inductance in a circuit. Unlike resistance, reactance is frequency-dependent. Ideal resistors are assumed to have negligible reactance.

Ohm’s Law is mathematically expressed as:

V = I * R

Where:

• V is the voltage (potential difference) across the resistor, measured in volts (V).
• I is the current flowing through the resistor, measured in amperes (A) or amps.
• R is the resistance of the resistor, measured in ohms (Ω).

In words, Ohm’s Law states that the voltage across an ideal resistor is directly proportional to the current flowing through it, with the resistance being the constant of proportionality.

Example:

If a resistor with a resistance of 300 ohms is connected across the terminals of a 12-volt battery, the current flowing through the resistor can be calculated using Ohm’s Law:

I = V / R = 12 V / 300 Ω = 0.04 A

Therefore, a current of 0.04 amperes (or 40 milliamperes) will flow through the 300-ohm resistor.

Series and Parallel Resistors

Resistors can be connected in circuits in two fundamental configurations: series and parallel. Understanding how resistors behave in these configurations is crucial for circuit analysis and design.

Resistors in Series

When resistors are connected in series, they are connected end-to-end, forming a single path for current flow. The same current flows through each resistor in a series circuit.

The total equivalent resistance (R_eq) of resistors connected in series is simply the sum of their individual resistances:

R<sub>eq</sub> = R<sub>1</sub> + R<sub>2</sub> + ... + R<sub>n</sub>

Where R₁, R₂, …, R_n are the resistances of the individual resistors in series.

Explanation: Imagine resistors as obstacles to current flow. In a series connection, the current has to overcome each obstacle sequentially. Therefore, the total opposition to current flow (total resistance) is the sum of individual oppositions.

Example: If you have three resistors with resistances of 100 Ω, 220 Ω, and 470 Ω connected in series, the equivalent resistance is:

R<sub>eq</sub> = 100 Ω + 220 Ω + 470 Ω = 790 Ω

Resistors in Parallel

When resistors are connected in parallel, they are connected side-by-side, providing multiple paths for current flow. The voltage across each resistor in a parallel circuit is the same.

The total equivalent resistance (R_eq) of resistors connected in parallel is calculated using the reciprocal of the sum of the reciprocals of the individual resistances:

1 / R<sub>eq</sub> = (1 / R<sub>1</sub>) + (1 / R<sub>2</sub>) + ... + (1 / R<sub>n</sub>)

Or, equivalently:

R<sub>eq</sub> = 1 / [(1 / R<sub>1</sub>) + (1 / R<sub>2</sub>) + ... + (1 / R<sub>n</sub>)]

Explanation: In a parallel connection, the current has multiple paths to flow. Each resistor provides a path, effectively reducing the overall opposition to current flow. Therefore, the total resistance is less than the smallest individual resistance in the parallel combination.

Example: Consider resistors of 10 Ω, 5 Ω, and 15 Ω connected in parallel. The equivalent resistance is:

1 / R<sub>eq</sub> = (1 / 10 Ω) + (1 / 5 Ω) + (1 / 15 Ω)
1 / R<sub>eq</sub> = (3/30) + (6/30) + (2/30) = 11/30
R<sub>eq</sub> = 30/11 Ω ≈ 2.727 Ω

Resistor Networks:

Many circuits involve combinations of series and parallel resistor connections, forming resistor networks. These networks can often be simplified by breaking them down into smaller series and parallel sections and calculating equivalent resistances step-by-step. However, some complex networks require more advanced circuit analysis techniques like the Y-Δ transform or matrix methods to determine the overall equivalent resistance.

Power Dissipation in Resistors

When current flows through a resistor, electrical energy is converted into heat. This process is known as power dissipation. The power dissipated by a resistor is a crucial parameter, especially in high-power circuits, as excessive power dissipation can damage the resistor and other components.

The power (P) dissipated by a resistor can be calculated using several formulas derived from Ohm’s Law:

P = V * I  (Power = Voltage * Current)
P = I<sup>2</sup> * R (Power = Current Squared * Resistance)
P = V<sup>2</sup> / R (Power = Voltage Squared / Resistance)

Where:

• P is the power dissipated, measured in watts (W).
• V is the voltage across the resistor in volts (V).
• I is the current through the resistor in amperes (A).
• R is the resistance of the resistor in ohms (Ω).

Explanation: These formulas are all equivalent and can be derived from each other using Ohm’s Law (V = I * R). The choice of formula depends on which circuit parameters (voltage, current, resistance) are known.

Resistor Power Rating:

Resistors are manufactured with a power rating, which specifies the maximum power they can safely dissipate continuously without overheating or being damaged. Common power ratings for discrete resistors in solid-state electronics are 1/10 W, 1/8 W, and 1/4 W. These low-power resistors are typically used in signal processing and logic circuits where power dissipation is minimal.

Power Resistors:

For applications requiring significant power dissipation (typically 1 watt or greater), power resistors are used. These are physically larger and designed to handle higher power levels. They are commonly found in power supplies, power conversion circuits, and power amplifiers. Power resistors may have different physical forms and may not adhere to standard color codes or preferred value series.

Consequences of Overpowering:

If the average power dissipated by a resistor exceeds its power rating, several negative consequences can occur:

• Resistance Change: The resistance value may permanently alter, deviating from its intended value and affecting circuit performance.
• Component Damage: Excessive heat can damage the resistor itself, potentially leading to failure (open circuit or short circuit).
• Circuit Board Damage: The heat generated can damage the printed circuit board (PCB) or adjacent components, potentially causing malfunctions or even fires.
• Fire Hazard: In extreme cases, overheating resistors can ignite flammable materials nearby, posing a fire risk.

Flameproof Resistors: To mitigate fire hazards, flameproof resistors are available. These resistors are designed to fail safely under overload conditions without producing flames, even under extreme overloads.

Derating for Safe Operation:

To ensure reliable operation and longevity, resistors are often derated in power applications. This means using resistors with power ratings significantly higher than the expected power dissipation in the circuit. Derating accounts for factors like:

• Poor Air Circulation: Limited airflow can hinder heat dissipation, leading to higher resistor temperatures.
• High Altitude: Reduced air density at higher altitudes decreases cooling efficiency.
• High Operating Temperature: Ambient temperatures above standard room temperature increase resistor operating temperatures.

Maximum Voltage Rating:

In addition to power rating, resistors also have a maximum voltage rating. This specifies the maximum voltage that can be safely applied across the resistor. Exceeding the voltage rating can lead to dielectric breakdown or arcing within the resistor, even if the power dissipation is within the rated limit. This is particularly important for high-resistance values, where even moderate voltages can result in significant voltage stress across the resistor.

Example: A 1/4 watt resistor with a resistance of 100 MΩ might have a maximum voltage rating of 750 V. Even though 750 V across 100 MΩ dissipates only 5.6 mW (well below 1/4 W), exceeding the voltage rating could damage the resistor.

Nonideal Properties of Resistors

While the concept of an ideal resistor is useful for basic circuit analysis, real-world resistors exhibit nonideal properties that can become significant in certain applications, especially at high frequencies or in precision circuits. These nonideal properties include:

• Series Inductance: Practical resistors inherently possess a small amount of series inductance. This is due to the physical construction of the resistor, particularly wirewound types, which resemble coils of wire. At high frequencies, this inductance can become significant, affecting the resistor’s impedance and frequency response.

• Parallel Capacitance: Resistors also exhibit a small amount of parallel capacitance. This arises from the proximity of conductive parts within the resistor structure. Similar to inductance, this capacitance can affect high-frequency performance.

• Johnson Noise: Even an ideal resistor generates Johnson noise (also known as thermal noise or Nyquist noise), which is a fundamental source of electrical noise due to the random thermal motion of charge carriers within the resistor material. This noise is unavoidable and depends on the temperature and resistance value.

• Excess Noise: Practical resistors can exhibit excess noise in addition to Johnson noise. This noise is current-dependent and often frequency-dependent (typically increasing at lower frequencies, known as 1/f noise). The level of excess noise varies depending on the resistor technology and material. Carbon composition and thick-film resistors tend to have higher excess noise compared to metal film and wirewound resistors.

• Temperature Coefficient of Resistance (TCR): The resistance of a resistor is not perfectly constant but varies with temperature. The temperature coefficient of resistance (TCR) quantifies this change, typically expressed in parts per million per degree Celsius (ppm/°C) or ppm/K. A positive TCR means resistance increases with temperature, while a negative TCR means resistance decreases with temperature. In precision applications, a low TCR is desirable to minimize resistance variations due to temperature changes.

• Voltage Coefficient of Resistance (VCR): In some resistor types, particularly certain thick-film resistors, the resistance can also vary slightly with the applied voltage. The voltage coefficient of resistance (VCR) quantifies this effect, usually expressed in ppm/V.

These nonideal properties are primarily determined by the technology used in manufacturing the resistor. For a given family of resistors manufactured using a specific technology, these properties are generally not individually specified but are considered inherent characteristics.

Form Factor:

Another practical aspect of resistors is their form factor, which refers to the physical size and shape of the resistor, including the lead arrangement (axial, radial, surface mount). Form factor is crucial for circuit board layout and assembly.

Power and Voltage Ratings (Revisited):

As discussed earlier, practical resistors have maximum power and voltage ratings that must be considered in circuit design to ensure reliable operation and prevent damage.

Fixed Resistors

Fixed resistors are the most common type of resistor, characterized by a resistance value that is fixed during manufacturing and intended to remain constant. They are available in a wide variety of types, each with its own advantages and disadvantages in terms of performance, cost, and applications.

Lead Arrangements

Fixed resistors are available in various lead arrangements for different mounting techniques:

• Through-Hole Components (Leaded Resistors): These resistors have wire leads that are inserted into holes in a printed circuit board (PCB) and soldered on the opposite side.

  • Axial Leads: Leads extend from the resistor body along its axis (parallel to the longest dimension). Axial-leaded resistors are easy to handle and suitable for breadboarding and prototyping.
  • Radial Leads: Leads extend radially from the resistor body, typically from one end. Radial-leaded resistors can offer a more compact footprint on the PCB.

• Surface Mount Technology (SMT) Components (Surface Mount Resistors): These resistors are designed to be mounted directly onto the surface of a PCB without through-holes. SMT resistors are much smaller than leaded resistors and are essential for miniaturized electronic devices. They have metal pads or terminals for soldering to the PCB.

• High Power Resistors: Some high-power resistors may have specialized lead arrangements, including designs where one lead is integrated with a heat sink to facilitate heat dissipation.

Carbon Composition Resistors (CCR)

Carbon composition resistors (CCRs) were among the earliest types of resistors and were widely used in electronics until the mid-20th century.

Construction: CCRs consist of a solid cylindrical resistive element made from a mixture of finely powdered carbon and an insulating material (usually ceramic). Wire leads or metal end caps are embedded into the element, and lead wires are attached to these caps. The resistor body is typically protected with paint or plastic.

Resistance Determination: The resistance value of a CCR is determined by the ratio of carbon to insulating material in the mixture. Higher carbon concentrations (being a good conductor) result in lower resistances.

Historical Significance and Limitations: CCRs were commonly used in the 1960s and earlier. However, they have several limitations compared to newer resistor types, making them less popular for general-purpose applications today:

• Poor Tolerance and Stability: CCRs have relatively poor tolerance (typically ±5% or worse) and stability over time. Their resistance can drift significantly with temperature, voltage stress, and humidity. They were often factory-sorted to achieve even 5% tolerance.
• Voltage Dependence: CCRs exhibit a noticeable change in resistance when subjected to overvoltages.
• Moisture Sensitivity: Exposure to humid environments can lead to moisture absorption, causing irreversible changes in resistance when soldering heat is applied.

Advantages: Despite their limitations, CCRs have some advantages:

• Non-Inductive: CCRs are essentially non-inductive, making them suitable for high-frequency applications and pulse circuits where inductance is undesirable.
• Overload Capability: CCRs can withstand short-term overloads better than some other resistor types of similar size.

Current Usage: Due to their higher cost and limitations, CCRs are no longer widely used in most modern electronic designs. However, they still find niche applications:

• Power Supplies and Welding Controls: Their overload capability makes them suitable for some power applications.
• Vintage Equipment Repair: CCRs are often used for repairing and restoring vintage electronic equipment where authenticity is a factor.

Carbon Pile Resistors

Carbon pile resistors are a type of variable resistor that utilizes the principle of pressure-dependent resistance.

Construction: A carbon pile resistor consists of a stack of carbon disks compressed between two metal contact plates.

Resistance Adjustment: The resistance between the plates is adjusted by changing the clamping pressure applied to the carbon disks. Increasing the pressure reduces the resistance, and decreasing the pressure increases the resistance.

Applications: Carbon pile resistors are used in applications requiring adjustable loads or variable resistance control:

• Automotive Battery Testing: Providing adjustable loads for testing automotive batteries.
• Radio Transmitter Testing: Simulating variable antenna loads for testing radio transmitters.
• Motor Speed Control: Used as speed controls for small motors in appliances like sewing machines and hand-held mixers (up to a few hundred watts).
• Automatic Voltage Regulators (AVRs): In generator AVRs, carbon piles control the field current to maintain a relatively constant output voltage.
• Carbon Microphones: The principle of pressure-dependent resistance is also utilized in carbon microphones for converting sound waves into electrical signals.

Carbon Film Resistors

Carbon film resistors offer improved performance compared to carbon composition resistors and are widely used in general-purpose applications.

Manufacturing Process: Carbon film resistors are manufactured by depositing a thin film of carbon onto an insulating substrate (typically ceramic). A helical groove (helix) is then cut into the carbon film to create a long, narrow resistive path.

Resistance Value Control: The resistance value is controlled by:

• Film Thickness: Thicker films result in lower resistance.
• Helix Geometry: The length and pitch of the helix determine the resistive path length and thus the resistance.
• Resistivity of Amorphous Carbon: The intrinsic resistivity of the carbon material also influences the resistance. Amorphous carbon has a resistivity range of 500-800 μΩ·m.

Advantages of Carbon Film Resistors:

• Lower Noise: Carbon film resistors exhibit lower noise compared to carbon composition resistors due to the more uniform distribution of pure graphite in the film.
• Wider Resistance Range: Carbon film technology allows for a wider range of resistance values, typically from 1 ohm to 10 megaohms.
• Power Rating: Power ratings typically range from 0.125 W to 5 W at 70 °C.
• Operating Temperature Range: Operating temperature range is typically from -55 °C to +155 °C.
• Working Voltage Range: Maximum working voltage range is typically 200 to 600 volts.
• Pulse Stability: Special carbon film resistors are available for applications requiring high pulse stability, such as surge protection circuits.

Printed Carbon Resistors

Printed carbon resistors are a cost-effective method for creating resistors directly on printed circuit boards (PCBs).

Manufacturing Process: Carbon composition resistive paste is printed directly onto PCB substrates as part of the PCB manufacturing process. This technique is more common in hybrid PCB modules but can also be used on standard fiberglass PCBs.

Characteristics:

• High Tolerances: Printed carbon resistors typically have large tolerances, often around ±30%. This limits their use to non-critical applications.
• Low Cost: The main advantage is their low cost due to the integration into the PCB manufacturing process.

Applications:

• Non-Critical Pull-Up Resistors: Commonly used as pull-up resistors in digital circuits where precise resistance values are not essential.

Thick and Thin Film Resistors

Thick film resistors and thin film resistors are the dominant types of resistors used in modern electronics, especially for surface mount devices (SMDs).

Key Difference: The primary difference lies in the thickness of the resistive film and the method of film deposition. Thick films are significantly thicker (about 1000 times thicker) than thin films.

Thin Film Resistors

Manufacturing Process:

1. Sputtering: A thin film of resistive material is deposited onto an insulating substrate (e.g., ceramic) using sputtering, a vacuum deposition technique.
2. Photolithography and Etching: The film is then patterned using a process similar to the subtractive process for making PCBs:
   • The surface is coated with a photo-sensitive material (photoresist).
   • A pattern mask is applied.
   • UV light is used to expose the photoresist through the mask.
   • The exposed photoresist is developed.
   • The underlying thin film is etched away in the areas where the photoresist was removed, leaving the desired resistor pattern.

Resistive Materials: Thin film resistors typically use cermet (ceramic-metal composite) conductors, including:

• Tantalum nitride (TaN)
• Ruthenium oxide (RuO₂)
• Lead oxide (PbO)
• Bismuth ruthenate (Bi₂Ru₂O₇)
• Nickel chromium (NiCr)
• Bismuth iridate (Bi₂Ir₂O₇)

Characteristics:

• Precise Control of Thickness: Sputtering allows for accurate control of film thickness, leading to better resistance tolerance.
• Tight Tolerances and Low TCR: Thin film resistors are typically specified with tolerances of 1% or 5% and temperature coefficients of 5 to 50 ppm/K.
• Low Noise: They exhibit much lower noise levels (10-100 times less) than thick film resistors.
• Higher Cost: Thin film resistors are generally more expensive than thick film resistors.

Thick Film Resistors

Manufacturing Process:

1. Screen Printing: A thick film paste, consisting of conductive ceramic particles mixed with sintered (powdered) glass and a carrier liquid, is screen-printed onto an insulating substrate.
2. Firing (Baking): The printed film is then fired (baked) in an oven at around 850 °C to fuse the glass and ceramic particles together and bond the film to the substrate.

Resistive Materials: Thick film resistors may use similar conductive ceramics as thin film resistors, but they are in powder form and mixed with glass and a binder.

Characteristics:

• Lower Cost: Thick film resistors are generally less expensive than thin film resistors, making them widely used in cost-sensitive applications.
• Wider Tolerance and Higher TCR: Typical tolerances were initially 5%, but have improved to 2% or 1% in recent decades. Temperature coefficients are typically ±200 or ±250 ppm/K. A 40 K (70 °F) temperature change can cause a 1% resistance change.
• Higher Noise: Thick film resistors generally have higher noise levels compared to thin film resistors.

Cost Comparison: SMD thin film resistors with 0.5% tolerance and 25 ppm/K TCR are typically about twice the cost of 1% tolerance and 250 ppm/K TCR thick film resistors, when purchased in large quantities.

Metal Film Resistors

Metal film resistors are a common type of axial-leaded resistor and are also used in Metal Electrode Leadless Face (MELF) resistors.

Manufacturing Process: A thin metal film is deposited onto an insulating substrate. The resistive material is typically nickel chromium (NiCr) but can also be other cermet materials used in thin film resistors. Unlike thin film resistors, the metal film may be applied using techniques other than sputtering. The resistance value is adjusted by cutting a helical groove through the metal film, similar to carbon film resistors.

Characteristics:

• Good Tolerance and TCR: Metal film resistors offer reasonable tolerances (0.5%, 1%, or 2%) and temperature coefficients generally between 50 and 100 ppm/K.
• Low Noise and Non-Linearity: They exhibit good noise characteristics and low non-linearity due to a low voltage coefficient.
• Long-Term Stability: Metal film resistors offer good long-term stability of resistance value.

Metal Oxide Film Resistors

Metal oxide film resistors are a variation of metal film resistors, using metal oxides as the resistive material.

Advantages:

• Higher Operating Temperature: Metal oxide films allow for higher operating temperatures compared to metal films.
• Greater Stability and Reliability: They offer improved stability and reliability, especially under harsh environmental conditions.

Applications: Metal oxide film resistors are used in applications with high endurance demands, such as automotive and industrial electronics.

Wirewound Resistors

Wirewound resistors are designed for high power handling and precision applications.

Construction: Wirewound resistors are made by winding a metal wire, typically nichrome (nickel-chromium alloy), around a ceramic, plastic, or fiberglass core. The wire ends are soldered or welded to metal caps or rings attached to the core ends. The assembly is then protected with a coating of paint, molded plastic, or high-temperature enamel.

Characteristics:

• High Power Rating: Wirewound resistors are capable of dissipating significant power, ranging from a few watts to thousands of watts.
• High Temperature Capability: They can withstand unusually high temperatures, up to 450 °C.
• Low Resistance Values: Wirewound resistors are well-suited for low resistance values and are often used for current sensing.
• Inductance: Because they are coils of wire, wirewound resistors have higher inductance than other resistor types. This can be a limitation in high-frequency applications.

Inductance Mitigation Techniques: To minimize inductance, wirewound resistors can employ special winding techniques:

• Section Winding with Reversed Direction: Winding the wire in sections with alternating winding directions can partially cancel out inductance.
• Bifilar Winding: Winding two wires in parallel and then connecting them in series but in opposite directions.
• Flat Thin Former: Using a flat, thin core shape reduces the cross-sectional area of the coil and thus inductance.
• Ayrton-Perry Winding: A more complex winding technique for extremely low inductance precision resistors.

Applications:

• High-Power Circuits: Power supplies, motor controls, braking resistors, and other high-power applications.
• Current Sensing: Low-value wirewound resistors are often used as current shunts.
• Precision Resistors: Wirewound resistors can be manufactured with high precision and low TCR.

Cement Resistors and Aluminum-Cased Resistors:

• Cement Resistors: Some wirewound resistors, particularly those with ceramic outer cases, are sometimes called “cement” resistors, although they do not actually contain cement. The ceramic case provides insulation and protection.
• Aluminum-Cased Resistors: High-power wirewound resistors may have an aluminum outer case with an insulating layer underneath. These are designed to be mounted on a heat sink for efficient heat dissipation. The power rating of aluminum-cased resistors is often specified assuming they are used with a suitable heat sink.

Metal Foil Resistors

Metal foil resistors represent the highest level of precision and stability among resistor types.

Development: Developed in the 1960s by Felix Zandman and Sidney J. Stein, metal foil resistors offer exceptional performance characteristics.

Construction: The resistive element is a thin foil (several micrometers thick) of a chromium-nickel alloy (e.g., Chromel A, Nichrome V, Nichrome, Chromel C) bonded to a ceramic substrate. These alloys are chosen for their high resistivity, low TCR, and resistance to oxidation.

Characteristics:

• Highest Precision and Stability: Metal foil resistors offer the best precision and stability of any resistor type.
• Extremely Low TCR: TCR values can be as low as 0.14 ppm/°C.
• Tight Tolerance: Tolerances down to ±0.005% are achievable.
• Excellent Long-Term Stability: Long-term stability (e.g., 25 ppm per year, 50 ppm for 3 years) is exceptional. Hermetic sealing further improves stability.
• Stability Under Load: Resistance change under load is very low (e.g., 0.03% after 2000 hours).
• Low Thermal EMF: Thermal electromotive force (EMF) is very low (e.g., 0.1 μV/°C), minimizing errors in precision measurement circuits.
• Low Noise: Noise performance is excellent (e.g., -42 dB).
• Low Voltage Coefficient: Voltage coefficient is very low (e.g., 0.1 ppm/V).
• Low Inductance and Capacitance: Inductance (e.g., 0.08 μH) and capacitance (e.g., 0.5 pF) are very low, making them suitable for high-frequency applications.

Thermal Stability Mechanism: The exceptional thermal stability of foil resistors arises from the opposing effects of temperature on resistance:

• Increased Resistance with Temperature: The electrical resistance of metals typically increases with temperature.
• Reduced Resistance due to Thermal Expansion: Thermal expansion of the foil leads to an increase in its thickness, which tends to decrease resistance.

By carefully selecting the alloy and substrate materials and controlling the manufacturing process, these opposing effects can be largely compensated, resulting in an extremely low overall TCR.

Applications: Metal foil resistors are used in demanding applications requiring the highest levels of precision, stability, and low noise, such as:

• Precision Measurement Instruments: Calibration standards, high-accuracy measurement equipment.
• Medical Equipment: Critical medical devices requiring high reliability and accuracy.
• Aerospace and Military Applications: High-performance systems operating in harsh environments.
• High-End Audio Equipment: Applications where extremely low noise and distortion are critical.

Ammeter Shunts

Ammeter shunts are specialized low-value resistors used for measuring high currents.

Function: Ammeter shunts allow current-measuring instruments (ammeters) to measure currents that are beyond their direct measurement range. The high current is passed through the shunt, and the voltage drop across the shunt is measured and interpreted as current.

Construction: A typical shunt consists of:

• Metal Blocks: Two solid metal blocks, often made of brass, mounted on an insulating base.
• Resistive Strips: One or more strips of low-TCR manganin alloy (a copper-manganese-nickel alloy known for its low TCR) soldered or brazed between the metal blocks.
• Current Terminals: Large bolts threaded into the metal blocks for making high-current connections.
• Voltage Terminals: Smaller screws for connecting voltmeters to measure the voltage drop across the shunt.

Characteristics:

• Very Low Resistance Values: Shunts have extremely low resistance values, typically in the milliohm (mΩ) or even micro-ohm (µΩ) range.
• Four-Terminal Connection: Shunts are four-terminal devices to minimize the effect of lead resistance on accurate voltage measurement. Two terminals are for current injection, and two are for voltage sensing.
• Rated Current and Voltage Drop: Shunts are rated by their full-scale current and often have a voltage drop of 50 mV at rated current.

Usage with Ammeters: Ammeters used with shunts are calibrated to read the full-scale current based on the 50 mV voltage drop. The ammeter dial face is marked accordingly, and no changes are needed to the internal meter circuitry.

Grid Resistors

Grid resistors are large, heavy-duty resistors used in high-current industrial applications.

Construction: Grid resistors are constructed as a large, convection-cooled lattice of stamped metal alloy strips connected in rows between two electrodes.

Characteristics:

• High Current Handling: Grid resistors can handle very high currents, up to 500 amperes or more in some designs.
• Low Resistance Range: They offer a range of resistances extending down to very low values, less than 0.04 ohms.
• Large Size: Grid resistors can be quite large, sometimes comparable in size to a refrigerator.
• Convection Cooling: They rely on natural air convection for cooling.

Applications: Grid resistors are used in demanding industrial applications:

• Dynamic Braking and Load Banking: For locomotives, trams, and other heavy vehicles to dissipate braking energy and provide load for testing.
• Neutral Grounding: In industrial AC distribution systems to provide a path to ground for fault currents.
• Control Loads for Cranes and Heavy Equipment: Used in motor control circuits for heavy machinery.
• Load Testing of Generators: Providing resistive loads for testing the output capacity of generators.
• Harmonic Filtering for Electric Substations: Used in filter circuits to reduce harmonic distortion in power systems.

“Grid Resistor” in Vacuum Tube Circuits: The term “grid resistor” can also refer to a resistor connected to the control grid of a vacuum tube. This is not a resistor technology type but rather a circuit topology and a different usage of the term.

Special Varieties of Fixed Resistors

In addition to the common types discussed above, there are also specialized fixed resistor varieties:

• Cermet Resistors: A general term referring to resistors using cermet (ceramic-metal composite) resistive films, often referring to thick-film resistors.
• Phenolic Resistors: An older type of resistor using phenolic resin as a binder for carbon particles. Less common today.
• Tantalum Resistors: Resistors using tantalum-based resistive films, known for high reliability and stability.
• Water Resistors: Resistors that use water as the resistive element. These are typically used for very high-power, short-duration pulse applications, such as in radar modulators.

Variable Resistors

Variable resistors are resistors whose resistance value can be adjusted. They are essential components for circuit tuning, control, and sensing applications.

Adjustable Resistors (Tapped Resistors)

Adjustable resistors, also sometimes called tapped resistors, have one or more fixed tapping points along their resistive element. By connecting circuit wires to different terminals, the resistance value can be changed in discrete steps.

Sliding Tap Wirewound Resistors: Some wirewound power resistors have a sliding tapping point that can be moved along the resistance element. This allows for a continuously variable adjustment of the resistance portion used in the circuit.

Rheostats: When a variable resistor with a sliding tap is used with only two terminals (one end terminal and the sliding tap), it functions as a rheostat. Rheostats are used to control current in a circuit by varying the resistance. The sliding tap is typically connected to a knob or lever for operator control.

Potentiometers

A potentiometer (often called a “pot”) is a three-terminal variable resistor with a continuously adjustable tapping point. The tapping point is controlled by rotating a shaft or knob (rotary potentiometer) or by moving a linear slider (linear potentiometer).

Potentiometer: The term “potentiometer” originates from its function as an adjustable voltage divider. By varying the position of the tapping point, it divides the voltage applied across its end terminals into a variable ratio, providing a variable potential (voltage) at the tapping point terminal.

Voltage Divider Application: The primary function of a potentiometer is to act as an adjustable voltage divider. When a voltage is applied across the two end terminals of a potentiometer, the voltage at the wiper terminal (tapping point) is a fraction of the input voltage, determined by the wiper position.

Volume Control Example: A common application of potentiometers is volume control in audio devices. By rotating the potentiometer knob, the user adjusts the voltage level of the audio signal, thereby controlling the volume.

Potentiometer Construction:

• Flat Resistance Element: Typical low-power potentiometers use a flat resistance element (track) made of carbon composition, metal film, or conductive plastic.
• Wiper Contact: A springy phosphor bronze wiper contact moves along the resistance track as the shaft is rotated or the slider is moved. The wiper makes electrical contact with the track at the desired position.

Wirewound Potentiometers: Another type of potentiometer construction uses resistance wire wound on a cylindrical form (mandrel). The wiper slides axially along the coil.

Resolution of Potentiometers:

• Wirewound Potentiometers: Wirewound potentiometers have lower resolution because resistance changes in discrete steps equal to the resistance of a single wire turn.
• Film and Conductive Plastic Potentiometers: Film and conductive plastic potentiometers offer much higher resolution as the resistance change is continuous.

Multiturn Potentiometers

Multiturn potentiometers are designed for high-precision applications requiring fine adjustment.

Construction: Multiturn potentiometers have wirewound resistance elements wound on a helical mandrel. The wiper moves along a helical track as the control is turned, maintaining continuous contact with the wire. Some multiturn potentiometers incorporate a conductive-plastic resistance coating over the wire to further improve resolution.

Characteristics:

• High Resolution: Multiturn potentiometers offer very high resolution, allowing for precise resistance adjustments.
• Multiple Turns: Typically require ten or more turns of the shaft to cover their full resistance range.
• Dials and Readouts: Often used with dials that include turns counters and graduated scales to indicate the wiper position and resistance setting with three-digit or better resolution.

Historical Applications:

• Analog Computers: Multiturn potentiometers were extensively used in electronic analog computers for setting coefficients and parameters.
• Delayed-Sweep Oscilloscopes: Older oscilloscopes often included multiturn potentiometers on their front panels for precise time-base adjustments.

Resistance Decade Boxes

A resistance decade box (or resistor substitution box) is a laboratory instrument containing a set of precision resistors and mechanical switches.

Function: Decade boxes allow users to quickly select and dial in a wide range of discrete resistance values without having to connect individual resistors manually.

Components:

• Resistors: Contains multiple resistors of different values, typically organized in decades (multiples of 10).
• Mechanical Switches: One or more rotary switches are used to select and combine resistors to achieve the desired total resistance.

Accuracy and Precision: Resistance decade boxes are available with varying levels of accuracy:

• Laboratory/Calibration Grade: High-precision boxes with accuracies of 20 parts per million (ppm) or better are used for calibration and metrology applications.
• Field Grade: Boxes with accuracies of around 1% are suitable for general-purpose laboratory and field work.
• Inexpensive Boxes: Lower-accuracy, less expensive boxes are also available for less demanding applications.

Applications: Decade boxes are invaluable tools in:

• Laboratory Work: Quickly setting up and changing resistances in experimental circuits.
• Experimental Design: Prototyping and testing circuit designs.
• Calibration and Measurement: Providing known resistance values for calibration and measurement purposes.
• Troubleshooting: Substituting known resistances to isolate faults in circuits.

Specifications: The key specifications of a resistance decade box include:

• Resistance Range: The total range of resistance values available (e.g., 0 to 100 megohms).
• Maximum Resolution: The smallest increment of resistance that can be selected (e.g., 0.1 ohm).
• Accuracy: The accuracy of the resistance values provided (e.g., 0.1%).

Special Variable Resistors (Sensors)

Certain variable resistors are designed to change their resistance in response to specific physical or chemical quantities, making them useful as sensors.

• Thermistors (Negative Temperature Coefficient - NTC):

  • Resistance decreases as temperature increases.
  • Used for temperature measurement and temperature compensation.
  • Also used as inrush current limiters because their high resistance at low temperatures prevents current surges when equipment is powered on, and their resistance decreases as they heat up due to current flow.

• Humistors (Humidity Sensors):

  • Resistance varies with humidity levels.
  • Used for humidity sensing and control.

• Photoresistors (Light Dependent Resistors - LDRs):

  • Resistance decreases as light intensity increases.
  • Used as light sensors in light-sensitive circuits, automatic lighting controls, and photographic exposure meters.

• Strain Gauges:

  • Invented in 1938 by Edward E. Simmons and Arthur C. Ruge.
  • Resistance changes when subjected to mechanical strain (stress or deformation).
  • Used to measure strain, force, pressure, and acceleration.
  • Can be used individually, in pairs (half-bridge), or in a Wheatstone bridge configuration (full-bridge) for increased sensitivity and temperature compensation.
  • Bonded to an object under test with adhesive.
  • Combined with filters, amplifiers, and analog-to-digital converters to create strain measurement systems.

• Quantum Tunnelling Composite (QTC) Sensors:

  • A more recent invention.
  • Resistance changes dramatically with applied pressure.
  • Current magnitude can vary by a factor of 10¹² in response to pressure changes.
  • Used as pressure sensors and force sensors.

Measurement of Resistance

The resistance of a resistor can be measured using an ohmmeter, which is often a function integrated into a multimeter.

Ohmmeters and Multimeters

• Ohmmeter: A dedicated instrument for measuring resistance.
• Multimeter: A versatile electronic instrument that can measure voltage, current, resistance, and often other parameters like capacitance, frequency, and continuity.

Measurement Procedure:

1. Connection: Probes on the ends of test leads are connected to the two terminals of the resistor being measured.
2. Simple Ohmmeter (Analog):
   • Applies a voltage from an internal battery across the unknown resistor and a known internal resistor in series.
   • Measures the current flowing through the circuit using a meter movement.
   • The current is inversely proportional to the total resistance (unknown resistor + internal resistor).
   • The meter scale is non-linear and calibrated in ohms, ranging from infinity (open circuit) to 0 ohms (short circuit).
3. Digital Multimeter (DMM):
   • Typically uses active electronics for more accurate and linear measurements.
   • May pass a specified current through the test resistor.
   • Measures the voltage drop across the resistor.
   • Resistance is calculated using Ohm’s Law (R = V/I).
   • The measured resistance value is displayed digitally.

Current Levels in Ohmmeters:

• Low Resistance Ranges: Ohmmeters pass a relatively high current through the test leads when measuring low resistances to generate measurable voltage drops.
• High Resistance Ranges: Ohmmeters use much lower currents for high resistance measurements to keep voltage levels within reasonable limits (typically below 10 volts) and prevent excessive power dissipation in the resistor under test.

Four-Terminal Measurement for Low-Value Resistors

Measuring very low resistance values (fractional ohms) with acceptable accuracy requires four-terminal connections (also known as Kelvin connections) to eliminate errors caused by lead resistance.

Problem with Two-Terminal Measurement: In two-terminal resistance measurement, the resistance of the test leads and contact resistances are included in the measurement, which can be significant compared to the low resistance value being measured, leading to inaccurate results.

Four-Terminal Measurement (Kelvin Method):

1. Current Injection Terminals (Force Terminals): One pair of terminals is used to apply a known, calibrated current to the resistor under test.
2. Voltage Sensing Terminals (Sense Terminals): The other pair of terminals is used to sense the voltage drop directly across the resistor. These sensing leads are connected as close as possible to the resistor terminals to minimize the inclusion of lead resistance in the voltage measurement.
3. Kelvin Clips: Specialized test leads called Kelvin clips are often used for four-terminal measurements. Each clip has two insulated jaws. One jaw applies the measuring current, and the other jaw senses the voltage drop, ensuring separate current and voltage paths.

Resistance Calculation: The resistance is calculated using Ohm’s Law:

R = V<sub>measured</sub> / I<sub>applied</sub>

Where:

• V_measured is the voltage drop measured by the voltage sensing terminals.
• I_applied is the calibrated current applied through the current injection terminals.

Instruments:

• Laboratory Ohmmeters and Milliohmmeters: High-precision instruments specifically designed for accurate resistance measurements, often employing four-terminal connections.
• Advanced Digital Multimeters: Some high-quality DMMs also offer four-terminal measurement capabilities for low-resistance measurements.

Standards for Resistors

Resistor characteristics, performance, and testing are governed by various national and international standards.

Production Resistor Standards

MIL-STD-202 (US Military Standard): A comprehensive standard that defines test methods for electronic and electrical component parts, including resistors. Many other resistor standards refer to MIL-STD-202 for test procedures.

IEC 60062 (International Electrotechnical Commission): An international standard that covers resistor color codes, RKM code, date codes, and other marking conventions for resistors. It is also known as IEC 62, DIN 40825, BS 1852, IS 8186, JIS C 5062, and others in different countries.

EIA RS-279 (Electronic Industries Alliance): A standard that specifies the resistor color code used in North America. Also known as DIN 41429.

IEC 60063 (IEC 63): Defines the Standard E series values for preferred resistor values. Also known as JIS C 5063.

Military Performance Specifications (MIL-PRF-): A series of US military performance specifications for resistors, including:

• MIL-PRF-26: General specification for wirewound, power type resistors.
• MIL-PRF-39007: Fixed power, established reliability wirewound resistors.
• MIL-PRF-55342: Surface-mount thick and thin film resistors.
• MIL-PRF-914: General specification for resistors, fixed, film (insulated), high reliability.
• MIL-R-39017: Fixed, general purpose, established reliability resistors.
• MIL-PRF-32159: Zero ohm jumpers (used as circuit links).

UL 1412 (Underwriters Laboratories): Standard for fusing and temperature-limited resistors, focusing on safety aspects.

Obsolete Standards: Some older military standards like MIL-R-11 have been canceled but may still be referenced in older documentation.

Resistance Standards

Primary Standard for Resistance (Historical):

• Mercury Ohm (1884 Definition): Initially defined as the resistance of a column of mercury 106.3 cm long and 1 square millimeter in cross-section at 0 degrees Celsius. However, replicating this standard accurately was challenging due to difficulties in precisely measuring physical constants, leading to variations of up to 30 ppm.

Secondary Standard (Historical):

• Manganin Plate (1900): The mercury ohm was replaced by precision-machined plates made of manganin alloy, which offered better stability and reproducibility.

Modern Primary Standard (Quantum Standard):

• Quantized Hall Effect (1990): Since 1990, the international resistance standard has been based on the quantized Hall effect, a quantum mechanical phenomenon discovered by Klaus von Klitzing (Nobel Prize in Physics, 1985). This standard is based on fundamental physical constants and offers extremely high accuracy and stability.

Precision Resistance Standards for Calibration:

• High-Precision Resistors: Manufactured for calibration laboratories and metrology applications.
• Four-Terminal Design: Often use four terminals to eliminate lead resistance errors, especially for low-value standards (100 Ω to 0.0001 Ω). Current is passed through one pair of terminals, and voltage is sensed across the other pair, ensuring accurate resistance measurement.

Resistor Marking

Resistors are marked to indicate their resistance value, tolerance, and sometimes other characteristics. Common marking methods include color codes and numerical codes.

Color Code for Axial Resistors

Axial-leaded resistors typically use a color code system of colored bands painted around the resistor body to indicate their resistance value and tolerance.

Resistor Body Color: Axial resistor bodies are often tan, brown, blue, or green, but other colors like dark red or dark gray can also be found. The body color itself does not carry any value information in the standard color code.

Color Bands: Resistors typically have three to six color bands:

• Four-Band Resistors:

  • Band 1: First significant digit of the resistance value.
  • Band 2: Second significant digit of the resistance value.
  • Band 3: Multiplier (power of 10).
  • Band 4: Tolerance (if absent, default is ±20%).

• Five-Band Resistors:

  • Band 1: First significant digit.
  • Band 2: Second significant digit.
  • Band 3: Third significant digit.
  • Band 4: Multiplier.
  • Band 5: Tolerance.

• Six-Band Resistors:

  • Bands 1-5: Same as five-band resistors (resistance value and tolerance).
  • Band 6: Temperature coefficient of resistance (TCR).

(Refer to online resistor color code calculators or tables for the color-to-digit and color-to-multiplier mappings.)

Reading Direction: The color bands are read from left to right, starting from the band closest to one end of the resistor. The tolerance band (if present) is usually wider than the other bands and is located at the end.

Power Rating Marking: The power rating of an axial resistor is typically not explicitly marked on the resistor body. It is generally inferred from the physical size of the resistor. Larger resistors generally have higher power ratings.

Early Resistor Color Coding (Body-Tip-Dot):

Early 20th-century resistors, which were uninsulated, used a simpler color-coding system:

• Body Color: Represented the first significant digit.
• Tip Color: Painted on one end, represented the second significant digit.
• Dot Color: A colored dot (or band) in the middle represented the multiplier.
• Rule: “Body, Tip, Dot” – sequence for reading the value.
• Default Tolerance: ±20%.
• Closer Tolerance Markings: Silver paint on the other end indicated ±10% tolerance, and gold paint indicated ±5% tolerance.

Numerical Code for Surface Mount Resistors (SMT)

Surface mount resistors (SMT resistors) are typically marked with numerical codes due to their small size, making color bands impractical.

Standard Tolerance SMT Resistors (Three-Digit Code):

• First Two Digits: First two significant digits of the resistance value.
• Third Digit: Multiplier (power of 10).

Examples (Three-Digit Code):

• 334: 33 × 10⁴ Ω = 330 kΩ
• 222: 22 × 10² Ω = 2.2 kΩ
• 473: 47 × 10³ Ω = 47 kΩ
• 105: 10 × 10⁵ Ω = 1 MΩ

Resistances Less Than 100 Ω (Three-Digit Code):

• Written as: 100, 220, 470.
• The final zero represents 10⁰ (which is 1).

Examples (Three-Digit Code, Less Than 100 Ω):

• 100: 10 × 10⁰ Ω = 10 Ω
• 220: 22 × 10⁰ Ω = 22 Ω

Sometimes, these values are marked as 10 or 22 to avoid misinterpretation.

Resistances Less Than 10 Ω (R-Notation):

• Use the letter ‘R’ to indicate the position of the decimal point (radix point).

Examples (R-Notation):

• 4R7: 4.7 Ω
• R300: 0.30 Ω
• 0R22: 0.22 Ω
• 0R01: 0.01 Ω

Zero-Ohm Links:

• Marked as 000 or 0000 on surface-mount zero-ohm links (jumpers) which have near-zero resistance and are used as circuit connections or jumpers.

Small SMT Resistors: Very small SMT resistors may be too physically small to accommodate any markings.

Precision Resistor Markings (Four-Digit Code)

Precision resistors, including both surface mount and axial-lead types, often use a four-digit code for higher accuracy resistance value indication.

• First Three Digits: Three significant figures of the resistance value.
• Fourth Digit: Multiplier (power of 10).

Examples (Four-Digit Code):

• 1001: 100 × 10¹ Ω = 1.00 kΩ
• 4992: 499 × 10² Ω = 49.9 kΩ
• 1000: 100 × 10⁰ Ω = 100 Ω

Axial-lead precision resistors may use color code bands to represent this four-digit code.

EIA-96 Marking (3-Character Code for 1% SMT Resistors)

EIA-96 marking (now included in IEC 60062:2016) is a compact 3-character marking system for small, high-precision (1%) SMT resistors.

• Two Digits (01-96): A two-digit code (from “01” to “96”) represents one of the 96 “positions” in the standard E96 series of 1% resistor values.
• One Letter (A-Z): An uppercase letter represents a power of ten multiplier.

(Refer to EIA-96 marking tables for the digit-to-value and letter-to-multiplier mappings.)

Examples (EIA-96 Marking):

• 01C: Represents 10 kΩ
• 10C: Represents 12.4 kΩ
• 96C: Represents 97.6 kΩ

Industrial Type Designation (Less Common)

Some older or specialized industrial resistors may use a type designation code with letters and numbers to indicate power dissipation, resistance value, and tolerance.

Code Structure (Example):

1. First Two Letters: Power dissipation capacity (e.g., EB = 1/2 watt, CB = 1/4 watt).
2. Next Three Digits: Resistance value:
   • First two digits are significant digits.
   • Third digit is the multiplier (power of 10).
3. Final Digit: Tolerance (e.g., 1 = ±10%, 2 = ±20%).

Examples (Industrial Type Designation):

• EB1041: 1/2 watt, 10 × 10⁴ Ω ±10% (90 kΩ to 110 kΩ).
• CB3932: 1/4 watt, 39 × 10³ Ω ±20% (31.2 kΩ to 46.8 kΩ).

Preferred Values (E-Series)

Early resistors were manufactured with more or less arbitrary resistance values. However, to optimize resistor selection and availability, preferred value systems, known as E-series, were developed and standardized (IEC 60063).

Geometric Progression: E-series values are based on a geometric progression. Each value in a series is greater than the previous value by a fixed multiplier or percentage. This spacing is chosen to align with the tolerance of the resistor series.

Tolerance and E-Series:

• Wider Spacing (Fewer Values): For wider tolerance resistors, fewer values are needed within each decade (a decade is a range increasing by a factor of 10, e.g., 1-10, 10-100).
• Narrower Spacing (More Values): For tighter tolerance resistors, more values are needed to provide sufficient overlap and minimize gaps in available resistance values.

E-Series Designations and Tolerances:

• E6 Series (±20% Tolerance): 6 values per decade (multiplier ≈ 1.47). Rounded values: 1.5, 2.2, 3.3, 4.7, 6.8, 10 (and their multiples/submultiples).
• E12 Series (±10% Tolerance): 12 values per decade.
• E24 Series (±5% Tolerance): 24 values per decade.
• E48 Series (±2% Tolerance): 48 values per decade.
• E96 Series (±1% Tolerance): 96 values per decade.
• E192 Series (±0.5% or Better Tolerance): 192 values per decade.

(Refer to IEC 60063 standard for the complete lists of preferred values for each E-series.)

Manufacturing and Binning:

Resistors are manufactured in values corresponding to the E-series. Due to manufacturing tolerances, the actual resistance values will vary around the nominal value. Manufacturers often bin resistors based on post-production measurements. This means resistors are sorted into tolerance classes based on their measured resistance.

Example (Binning): A batch of 100 Ω resistors intended for ±10% tolerance may be measured. Resistors that are within ±5% of 100 Ω might be re-classified and sold as ±5% tolerance resistors (higher grade), while those within ±10% but greater than ±5% are sold as ±10% tolerance. This “binning” process ensures that resistors meet their specified tolerance ratings but can result in a non-uniform distribution of actual resistance values within a tolerance class.

Common Usage Patterns of Resistors

Resistors are used in various common circuit configurations to achieve specific functionalities.

Current Limiting

Purpose: Resistors are frequently used to limit the amount of current flowing through a circuit or a specific component.

Applications:

• LED Current Limiting: Essential for protecting LEDs from overcurrent and ensuring proper brightness and lifespan. LEDs themselves have low resistance and require external current limiting.
• Component Protection: Protecting sensitive components (e.g., transistors, ICs) from excessive current that could damage them.
• Power Consumption Reduction: Limiting current to reduce overall power consumption in circuits where full current flow is not needed.

Example: An LED connected directly to a voltage source without a series resistor would draw excessive current and likely burn out. A series resistor is added to limit the current to a safe operating level for the LED.

Voltage Divider

Purpose: Creating specific voltage levels from a higher voltage source. Voltage dividers are used to provide reference voltages for other circuits or to scale down voltage levels.

Configuration: A voltage divider consists of two resistors connected in series between two fixed voltage points (e.g., a voltage source and ground).

Voltage Division Principle: The voltage at the junction between the two resistors is a fraction of the total voltage, determined by the ratio of the resistances.

Voltage Divider Formula:

For two resistors R₁ and R₂ in series, with input voltage V_in and output voltage V_out across R₂:

V<sub>out</sub> = V<sub>in</sub> * (R<sub>2</sub> / (R<sub>1</sub> + R<sub>2</sub>))

Example: A voltage divider using a 200 Ω resistor (R₁) and a 400 Ω resistor (R₂) connected between 6 V (V_in) and 0 V (ground) will produce an output voltage (V_out) of:

V<sub>out</sub> = 6 V * (400 Ω / (200 Ω + 400 Ω)) = 6 V * (400 Ω / 600 Ω) = 4 V

The voltage at the junction is 4 V, which is two-thirds of the input voltage, proportional to the ratio of the resistances.

Applications:

• Reference Voltage Generation: Providing stable reference voltages for voltage comparators, operational amplifiers, and other circuits.
• Voltage Level Shifting: Scaling down higher voltage signals to levels suitable for lower-voltage circuits.
• Sensor Interfacing: Creating appropriate voltage ranges for interfacing with sensors.

Pull-Up and Pull-Down Resistors

Purpose: Providing a defined voltage level to a circuit input when it is otherwise disconnected or in a high-impedance state. Pull-up and pull-down resistors ensure a predictable logic state (high or low) in digital circuits.

Problem: Undefined Voltage State: When a circuit input is not actively driven by a voltage source (e.g., when a switch is open or a transistor is off), its voltage is not necessarily zero but is undefined or floating. The voltage can be influenced by stray charges, previous voltage states, or environmental noise.

Pull-Up Resistor:

• Connects the circuit input to a high positive voltage (VCC or VDD) through a resistor.
• Provides a default high logic state when the input is not actively driven low.
• When the input is actively driven low (e.g., by closing a switch to ground), the voltage is pulled down to low logic state, overcoming the pull-up resistor.

Pull-Down Resistor:

• Connects the circuit input to ground (0 V) through a resistor.
• Provides a default low logic state when the input is not actively driven high.
• When the input is actively driven high, the voltage is pulled up to high logic state, overcoming the pull-down resistor.

Resistor Value Selection:

• High Enough Value: The resistor value must be high enough so that when the input is actively driven (low for pull-up, high for pull-down), the voltage source (VCC or ground) does not significantly interfere with the intended operation of the circuit. The current through the pull-up/pull-down resistor should be small compared to the drive current.
• Low Enough Value: The resistor value must be low enough to:
  • Pull Quickly: Ensure the voltage level transitions quickly to the default state when the input becomes inactive.
  • Maintain Voltage Level: Prevent the voltage from drifting significantly from the intended default value due to leakage currents or noise.

Typical Applications:

• Microcontroller Inputs: Pull-up or pull-down resistors are commonly used with microcontroller input pins to define the logic state when input signals are not actively asserted.
• Button and Switch Inputs: Ensuring a defined logic state when a button or switch is open (not pressed).
• Logic Gate Inputs: Providing a stable input state for logic gates when inputs are not actively driven.

Electrical and Thermal Noise in Resistors

Resistors, being dissipative components, inherently generate electrical noise, even ideal resistors. This noise can be a limiting factor in sensitive electronic circuits, especially in low-signal amplification.

Johnson-Nyquist Noise (Thermal Noise)

Fundamental Noise Source: Johnson-Nyquist noise (or thermal noise) is a fundamental noise source generated by all resistors due to the random thermal motion of charge carriers within the resistive material.

Characteristics:

• Randomly Fluctuating Voltage: It manifests as a randomly fluctuating voltage across the resistor terminals.
• Temperature and Resistance Dependence: The noise power is directly proportional to the absolute temperature (in Kelvin) and the resistance value. Higher temperature and higher resistance lead to more noise.
• Frequency Independent (White Noise): Johnson noise has a flat power spectral density across a wide frequency range, making it “white noise.”
• Fundamental Limit: It represents a fundamental lower limit on noise performance in resistive components, predicted by the fluctuation-dissipation theorem in thermodynamics.

Fluctuation-Dissipation Theorem: A fundamental principle in statistical mechanics that relates the fluctuations in a system at equilibrium to its response to external perturbations (dissipation). In the context of resistors, it relates the random voltage fluctuations (Johnson noise) to the resistor’s ability to dissipate electrical energy.

Noise Voltage and Current:

• Voltage Noise: Larger resistance values produce larger voltage noise at a given temperature.
• Current Noise: Smaller resistance values generate more current noise.

Excess Noise

Practical Resistor Noise: Practical resistors often exhibit excess noise in addition to Johnson noise. Excess noise is observed only when current flows through the resistor.

Characteristics:

• Current Dependent: Excess noise is proportional to the current flowing through the resistor.
• Frequency Dependent (1/f Noise): Excess noise typically increases at lower frequencies, exhibiting a 1/f noise spectrum (also called pink noise or flicker noise). The noise power is inversely proportional to frequency.
• Technology Dependence: The level of excess noise varies significantly depending on the resistor technology and material.
  • High Excess Noise: Thick-film and carbon composition resistors generally have higher excess noise, especially at low frequencies.
  • Low Excess Noise: Wirewound and thin-film resistors typically exhibit better noise characteristics and lower excess noise. Metal foil resistors have exceptionally low excess noise.

Noise Index (dB μV/V/decade): Excess noise is often specified using a noise index, expressed in dB μV/V/decade.

• dB μV/V/decade: Decibels of microvolts of noise (RMS) per volt applied across the resistor per decade of frequency.
• 0 dB Noise Index: Corresponds to 1 μV (RMS) of excess noise per volt per frequency decade.
• Negative Noise Index: Indicates noise levels below 1 μV/V/decade. Metal foil resistors can have noise indices as low as -40 dB, making their excess noise insignificant in many applications.

Resistor Type Comparison (Noise):

• Carbon Composition Resistors: Noise index around 0 dB (relatively high excess noise).
• Metal Foil Resistors: Noise index around -40 dB (extremely low excess noise).
• Thin Film Surface Mount Resistors: Lower noise and better thermal stability than thick film surface mount resistors.
• Thick Film Surface Mount Resistors: Higher noise compared to thin film.

Size Dependence of Excess Noise: Excess noise is generally size-dependent. Larger physical size resistors tend to have lower excess noise than smaller resistors of the same type. This is because the independently fluctuating resistances of smaller components tend to average out when combined in a larger resistor structure or when multiple resistors are used in parallel.

Thermoelectric Effect (Seebeck Effect)

Thermocouple Effect: Resistors can act as thermocouples, generating a small DC voltage differential across their terminals due to the thermoelectric effect (Seebeck effect) if their ends are at different temperatures.

Thermoelectric Effect (Seebeck Effect): A phenomenon where a temperature difference between two dissimilar electrical conductors or semiconductors creates a voltage difference between them.

Origin of Thermoelectric Voltage: Thermoelectric voltages arise at the junctions of:

• Resistor leads with the circuit board traces (dissimilar metals).
• Resistor leads with the resistor body itself (material interfaces).

Impact on Precision Circuits: This induced DC voltage can degrade the precision of instrumentation amplifiers and other sensitive circuits, especially in DC or low-frequency applications.

Magnitude of Thermoelectric Voltage:

• Metal Film Resistors: Typical thermoelectric offset of about 20 μV/°C (microvolts per degree Celsius temperature difference).
• Carbon Composition Resistors: Can exhibit offsets as high as 400 μV/°C.
• Specially Constructed Resistors: Can reduce thermoelectric offsets to as low as 0.05 μV/°C.

Mitigation Strategies:

• Horizontal Mounting: Mount resistors horizontally on the PCB to minimize temperature gradients across the resistor body.
• Airflow Management: Consider airflow over the PCB to ensure uniform temperature distribution and reduce temperature gradients.
• Resistor Selection: Choose resistor types with low thermoelectric coefficients (e.g., metal film, wirewound).

Failure Modes of Resistors

Resistors are generally reliable components, but they can fail under certain conditions. Understanding common failure modes is important for circuit design and troubleshooting.

Overheating and Power Overload

Most Common Failure Mode: Overheating due to excessive power dissipation is the most frequent cause of resistor failure.

Causes of Overheating:

• Power Rating Exceeded: When the average power delivered to a resistor significantly exceeds its power rating, it overheats.
• External Faults: Faults in other circuit components (e.g., shorted transistors) can cause excessive current to flow through resistors, leading to overload.
• Component Failure: Failure of another component in the circuit connected to the resistor can indirectly cause resistor overload.

Consequences of Overheating:

• Resistance Change: Overheating can cause permanent changes in resistance value, often increasing or decreasing depending on the resistor type.
• Open Circuit Failure: Carbon film and composition resistors are prone to failing open (resistance becomes infinitely high) when overheated, especially if operating close to their maximum dissipation rating. Metal film and wirewound resistors are less likely to fail open under overload.
• Fire Hazard (Less Common): In extreme cases, overheating resistors can ignite and cause a fire.

Safe Design Practices:

• Power Derating: Use resistors with power ratings significantly higher than the expected power dissipation to provide a safety margin.
• Thermal Management: Consider heat sinks for high-power resistors and ensure adequate air circulation to facilitate heat dissipation.

Long-Term High-Voltage Stress

Low-Power Thin-Film Resistors: Low-power thin-film resistors can be susceptible to damage from long-term exposure to high voltage stress, even below their maximum specified voltage and power rating.

Startup Resistors in Switched-Mode Power Supplies: This is a common issue with startup resistors used in switched-mode power supply (SMPS) integrated circuits. These resistors may experience prolonged high-voltage stress during startup.

Failure Mechanism: Long-term high-voltage stress can cause gradual degradation of the resistive film, leading to increased resistance over time.

Mechanical Stress and Environmental Factors

• Mechanical Stress: Physical stress or vibration can damage resistor bodies or lead connections, especially in leaded resistors.
• Humidity: Exposure to humid environments can cause corrosion, particularly in wirewound resistors that are not properly enclosed.
• Sulfur Ingress (SMT Resistors): A specific failure mode for some SMT resistors is sulfur ingress. Sulfur from the environment can penetrate the resistor body and chemically react with the silver layer used in some resistor terminations, forming non-conductive silver sulfide (Ag₂S). This leads to an open circuit failure (resistance goes to infinity).

Sulfur-Resistant Resistors: For applications in harsh environments with sulfur contamination (e.g., automotive, industrial, military), sulfur-resistant or anti-corrosive resistors are available.

ASTM B809: An industry standard test method (ASTM B809) is used to evaluate a component’s susceptibility to sulfur corrosion.

Maximum Voltage Rating Exceedance

Large Value Resistors: For very high resistance values (hundreds of kilohms and higher), resistors are not only limited by power dissipation but also by a maximum voltage rating.

Voltage Breakdown: Exceeding the maximum voltage rating can cause dielectric breakdown or arcing within the resistor, even if the power dissipation is well below the rated limit.

Resistance Degradation: Prolonged voltage stress above the maximum rating can lead to gradual degradation of the resistor, typically resulting in a decrease in resistance over time.

Application Consideration: Maximum voltage rating is particularly important in high-voltage circuits, where large value resistors may experience significant voltage drops even at moderate power levels.

Variable Resistor Degradation (Potentiometers and Rheostats)

Contact Degradation: Variable resistors (potentiometers, rheostats) can degrade due to poor contact between the wiper and the resistive element track.

Causes of Poor Contact:

• Dirt and Debris: Accumulation of dust, dirt, and other contaminants on the resistive track.
• Corrosion: Oxidation or corrosion of the wiper contact or resistive track surface.

Symptoms of Degradation:

• Crackling Noise: Fluctuations in contact resistance as the wiper moves, causing “crackling” or “scratchy” noise, especially noticeable when adjusting the potentiometer.
• Intermittent Operation: In severe cases, contact can become intermittent, leading to unreliable operation.

Self-Cleaning Action: Potentiometers have a degree of self-cleaning action. Moving the wiper across the resistive track can sometimes improve contact by wiping away surface contaminants.

Contact Cleaner: If self-cleaning is insufficient, contact cleaner spray (also known as “tuner cleaner”) can be used to clean the wiper and track and improve contact.

DC Voltage and Crackling: Crackling noise in potentiometers, particularly in audio circuits (e.g., volume controls), is often exacerbated by the presence of an undesired DC voltage across the potentiometer. This can indicate a failure of a DC blocking capacitor elsewhere in the circuit.