# Resistor & Resistance

Resistor is a basic design unit for Analog Design. Basically resistor can be defined as 2-port electronic device that can limit the flow of electronic current in a design. Resistor does not have a direction, current can flow in both direction.

On the other hand, resistance is a quantitative term that is used to compare the strength of the resistors. Under certain voltage, the rate of a charge flow determines the  resistance. The following equation relates resistance with Voltage that is applied between terminals of resistors and current that flows over resistors.

V=I x R  (Ohm’s Law)

There are three variables that affect the resistance of a resistor:

1. The conductor material is the most important parameter for resistance. Depending on the crystal lattice structure of a material, resistance may increase or decrease.
2. Length of the resistor affects resistance in a directly proportional way. If length is increased while keeping other parameters same, then resistance will increase as well.
3. Cross-section area of a resistor has affect on resistance in inversely proportional manner. If the cross-section area of resistor is increased then resistance of the device decreases.

Resistance symbol is defined as Ω (Ohm) that comes from the German physicist Georg Simon Ohm (founder of the Ohm’s Law). Depending on the number of digits in resistance, a prefix can be used to make it easier to pronounce. Two of the common resistance prefix terms are given below.

MΩ — 1 millon Ohms
kΩ — 1 thousand Ohms

## Resistor Types

There are different resistor types, some of them have fixed resistance whereas in some ressitors, resistance depends on environmental issues.

• Carbon Compositon Resistors: These resistors are formed by mixing carbon granules with a binder and then this resistor forms into a rod. Disadvantages of this type of resistors are:
• Having a large negative temperature coefficient. This makes it more temperature dependent and it will affect the performance.
• Irreversible changes in resistance due to heat and resistor age. The resistance changes in a irreversible manner.
• High noise
• Carbon Film Resistors: This type of resistors are formed by cracking hydrocarbon on ceramic former. Main application areas of these devices are RF-based applications.
• Metal Oxide Film Resistor: This is the most common resistor that we encounter in real life. These resistors are formed by depositing metal oxide film on a ceramic rod. Temperature coefficient of these resistors are better than carbon based resistors. Additionally, tolerance range of these resistors range from  %5 to %1 and they have better noise performance compared to carbon-based resistors.
• Metal Film Resistor: This resistor types have similarities with Metal Oxide film resistors. In these resistor types, metals such as nickel alloy are utilized instead of metal axide films.
• Surface Mount Resistor: These resistors are similar to the devices that are defined above but the main difference of these resistors is related to their shape. Instead of rod structure, these devices have surface mount structure.
• Wire Wound Resistor: These types of resistors are used in high power circuits due to their ability to handle large power without break-down.
• Photoresistor: As its name implies, the resistance of these type of resistors changes with level of light that falls on the resistor. These types of resistors are utilized in sensor applications that are mainly focusing on imaging.
• Varistor: The resistance of varistor changes with applied voltage. These kind of resistors are used for spike and surge protection applications.

### Resistor Colour Coding

The resistance of rode-type resistors can be evaluated through colour coding that is implmented on package of resistors. There are two different notation for colour coding.

• In first notation, there are 4 different colours on resistor. The resistance of resistor is X.XX EX starting from left.
• In second notation, there are 5 colours on resistor. The resistance of resistor can be calculated as X.XX EX with tolerance X.

The details of resistor colour coding is given in following figure.

## Resistors in CMOS Design

The lumped resistor types are explained in previous chapter. In this chapter, we will be talking about the resistor types that we cannot see by eye but we design using Cadence or other softwares. In CMOS design, unit resistance is defined as resistance per square. Height of the resistor layer is constant due to automated process. Therefore the width and length of the resistor can be changed during design. If length and width are equal, this resistor corresponds to 1 square and sheet resistance of this device should be checked from foundary design documents.

• Diffusion Resistor: This resistor is formed by n or p dopped diffusion area. Since the doping concentration of these regions are lower than conductor, the resistance per square value for these resistors are higher than other types. You can have MΩ range resistor in a small area. Doping concentration of diffusion region willl have great impact on resistance value.
• Poly Resistor: These resistors are formed by using poly-Silicon layer that is used to form gates of transistor. The resistance per square for poly resistors are in mid range and they are most common resistor types that are used in CMOS due to their density and relability.
• Metal Resistor: These resistors are formed by the metal layers and they have lower densities compared to other resistor types. However these resistors are more reliable compared to others.
• Active Resistors: These are formed by biasing transistors in such a way that they operate in linear region. The resistance of these types of resistors are depending on process and temperature. Reliability of these type of resistors is worse than other resistor types but the area consumption of these resistors is much smaller.

### Resistor Design Concerns in CMOS Design

In CMOS design resistors have many application areas ranging from amplifiers to Voltage DACs. In most cases, instead of using a single line, resistors are formed in finger-like structure to optimize the area. The