# Basic Electrical Concepts

## Ohm's Law

First some basic terms:

Term Abbrev. Unit
Voltage V Volts (V)
Current I Amps (A)
Resistance (similar to Impedance) R Ohms (Ω)

Voltage is analogous to mechanical force, and is sometimes called Electro-Motive Force or EMF. It represents potential energy. Like the concept of zero potential energy, the concept of zero volts is an arbitrary designation. Only differences between voltages are significant. Therefore zero volts is only a reference (called Ground) used to measure voltage differences.

Voltage in vehicle systems: The relative nature of zero voltage can be demonstrated by thinking of several cars. The metal frame of each car is considered as zero volts, or ground, for all the electrical devices within each vehicle. But the bodies of the different cars can be at different voltages relative to each other.

Current is analogous to mechanical velocity. In order to transfer power (or even information), some current must flow. Useful current in circuits must always flow through a complete loop, not just one wire.

Current in vehicle systems: If you're thinking about single wires in a car that lead to the headlights or starter motor, remember that the metal body of the car acts as the second wire to return the current back to the negative battery terminal.

Resistance is analogous to mechanical friction or damping. Just as friction resists the motion of an object due to a net force acting on it, resistance resists the tendency of current to flow due to a voltage difference.

In a resistive circuit, voltage and current are related by the most important relationship in electrical engineering, Ohm's Law:

 V = IR

Impedance is a type of resistance to changes in voltage or current. It is defined by differential equations.

## Power

Electrical power can be found as the product of voltage and current, P = VI. This is analogous to mechanical power, which is the product of instantaneous force and velocity, P = Fv.

If you subsitute in for Ohm's Law, it becomes

 P = I²R
 P = V²/R

These equations only apply when computing the power which is converted to heat in a resistor (or another device which acts like a resistor, such as an electric heater). In other devices such as transistors and diodes, power should be computed as P = VI.

## Circuits

A circuit consists of devices that are connected by wires. This usually includes a power source, passive devices, and active devices.

Parallel and Series terms are sometimes used to refer to how two devices are connected to eachother.

### Power Sources

Circuits usually need an external source of power to operate.

Constant Voltage Source: A constant voltage output is maintained by varying the current depending on the circuit resistance (V=IR).

• Series: Veq = V1 + V2
• Parallel: Veq = V1 = V2 (Voltages in parallel must have the same output and the equivalent voltage is the same value as a single source)

Constant Current Source: A constant current output is maintained by varying the voltage as dictated by Ohm's Law.

• Series: ieq = i1 = i2 (Currents in series must have the same output and the equivalent current is the same value as a single source)
• Parallel: ieq = i1 + i2

Direct Current(DC) Source: The controlled variable (Voltage or Current) is kept constant. DC power is generally more dangerous than AC power.

Alternating Current(AC) Source: The controlled variable (Voltage or Current) alternates or changes between positive and negative, usually in a sine wave.

### Passive Devices

The most basic components of a circuit are passive devices. Passive Components are components that do not require a power source other than the signals (wires) to which they are connected.

#### Resistor

• Relation: V = IR

A Resistor provides resistance to current. Higher resistance will decrease the current for a given voltage. Resistance is measured in Ohms (Ω). An equivalent resistance (Req) can be calculated for resistors in series or parallel. Adding Reistors in series increases the resistance; adding reistors in parallel decreases the resistance.

• Series: Req = R1 + R2
• Parallel: Req = (R1*R2)/(R1+R2)

#### Capacitor

• Relation: I = C(dv/dt)
• Series: Ceq = (C1*C2)/(C1+C2)
• Parallel: Ceq = C1 + C2

Measured in Farads(F). A capacitor “tries” to keep the voltage the same. It slows any voltage change. The higher the capacitance, the longer the change takes. Capacitors are often used as simple noise filters, usually on lines carrying power. Capacitors will block DC current and pass AC current. For DC analysis a capacitor can be approximated by an open circuit. For AC analysis they can be approximated by a short ciruit.

Important Parameters:

• Voltage Rating: maximum voltage that can be applied between the leads. Use a rating of at least twice the maximum voltage that will ever be applied to the capacitor.
• Tolerance: Stated as a percent deviation from the nominal capacitance.
• Polarized/Non-Polarized: Non-Polarized capacitors can be connected in any orientation; polarized capacitors have a specific orientation with respect to positive and negative. Electrolitic capacitors usually have a black strip on the side of the negative lead; tantalum capacitors usually have a tiny ”+” sign printed on the positive side. Electrolitic and tantalum capacitors are used when parasitic effects, such as ESR (Equivalent Series Resistance), must be minimized.

Explosive! When electrolytic capacitors are reverse biased (connected backwards) they can act as a short circuit and explode!

#### Inductor

• Relation: v = L(di/dt)

Measured in Henrys(H). Inductors “try” to keep the current the same. This slows any current change. The higher the inductance, the slower the change. Inductors, like capacitors, are also used in noise filters. For analysis, an inductor can be replaced by a short circuit in DC circuits. They can be approximated by an open ciruit in AC circuits.

#### Diode

• When forward biased and the voltage across the diode is greater than Vf (usually 0.7V), then current can pass. Under this condition, a constant 0.7V will be maintained across the diode. Use a resistor in series with the diode to limit the current, as the voltage applied is usually greater than Vf. If no resitor is used, the resulting high current may burn out the diode.
• When reverse biased, the diode blocks current (appears as an open circuit) unless the reverse voltage exceeds the breakdown voltage of the diode.

Important Parameters:

• Vf: The forward biased voltage that appears across the diode, usually 0.7V
• Vr: The maximum reverse biased voltage allowed before the diode breaks down and passes current. Usually >40V.
• If: The maximum forward current the diode can handle before burning up.

#### Zener Diode

This is a special diode whose breakdown voltage is set to a controlled value. Zener diodes are usually used as voltage references. If a zener diode is placed in series with a properly chosen resistor and supplied with a source voltage higher than the breakdown voltage, the voltage across the zener diode will remain at the breakdown voltage.

Zener diodes are sometimes used as simple surge suppressors. Again placed in series with resistors, the zener diode can prevent the voltage input to a FET or integrated circuit from exceeding the diode's breakdown voltage.

#### Light Emitting Diode (LED)

An LED is essentially the same as a diode, but with the added property of giving off light (photons) when forward biased. Always use a resistor in series to limit the current.

Important Parameters:

• Vf: The forward biased voltage that appears across the diode. This voltage varies from about 1.2V for small red or green diodes to 3.3V for high-brightness blue and white LED's.
• Vr: The maximum reverse biased voltage allowed before the diode breaks down and passes current. Usually >40V. This voltage should never be exceeded, because doing so generally destroys the diode.
• If: The maximum forward current the diode can handle before burning up.

High-brightness LED's are becoming useful as light sources at the time of this writing (2006). They are more efficient than conventional light bulbs (though not quite as efficient as modern fluorescent lights), and they last longer than both. White LED's, which are actually made by combining blue LED light sources with yellow-green flourescent materials, are available with power ratings up to about 3-5 watts (and they produce as much light as 10 watt halogen bulbs).

#### Transistor

A transistor's characteristics are relatively complex, allowing the transistor to be used in many different ways. The simplest use of a transistor is as a switch. When used in this way, it can be used to turn on and off a load. This allows a low current carrying signal line to control a higher current device.

• A common simple transistor is a NPN Bipolor Junction Transistor (BJT). A PNP BJT is similiar but switches current which flows in the opposite direction.
• Field-effect transistors are more efficient than bipolar transistors, though they are suceptible to damage by static electricity (never touch them after walking across the carpet in bunny slippers!).

#### Transformer

A transformer operates on AC signals only. It is simply two coils of wire with the two coils having no direct electrical connection. The changing voltage/current in one coil is induced into the second coil. Any DC (constant) component of the input voltage/current is removed from the output signal. The ratio of the number of turns of wire between the two coils determines the scale factor of the input voltage/current to the output voltage/current. The voltage/current can be increased or decreased in this way. If the voltage is increased, then the current is decreased.

#### Bridge Recticfier

Used to convert AC voltage to DC voltage. The rectifier is made from a set of diodes.

• Full Wave Bridge Rectifier: A full wave bridge utilizes both the negative and positive going phases of the AC voltage using four diodes.
• Half Wave Bridge Rectifier: A half wave bridge utilizes only the positve phase of the AC voltage using a single diode, which blocks the negative phase.

After being rectified, the power is usually filtered (or “smoothed”) by a circuit containing capacitors and/or inductors. Learn more

### Active Devices

Active devices require a power source (usually 5V or 3.3V). This includes any digital logic devices.

#### Opamp

An opamp is a very versatile analog active device. When combined with resistors and capacitors, they can be used as voltage adders, integrators, differentiators, as well as anolog amplifiers (aka multipliers). They usually require a symmetric positive and negative dc power source as well a ground reference, although op-amps designed for use with a single voltage supply are available.

 Beginners often forget that no opamp can produce an output voltage which is higher than the positive voltage supply or lower than the negative supply. In fact, if a typical opamp is powered with +15V and -15V supplies, its output is limited to about +13V to -13V.

Opamps are also useful as a type of buffer, called a voltage follower. A voltage follower presents a high impedance connection for the volatage input, and a low impedance output. This basically means that the input voltage can be set and maintained with low current draw, while the ouput can source or sink a much higher current while maintaining the same voltage.

#### Voltage Regulators

Voltage regulators are complex devices containing transistors, resistors, opamps, and capacitors. They usually take a higher voltage that can be noisy (varying), and outputs a fairly constant and usually fixed voltage. An example would be using a battery pack (say 6V, 7.2V, or 9V) to power a circuit that runs at 5V. A regulator would be used in between the battery and the circuit to drop the voltage down to 5V and provide a constant stable ouptut. There are various types of regulators.

• Linear Regulator: The simpleist type of regulator, it essentially drops the excess voltage across a transistor and gives off the excess energy as heat. If high currents are required (>1A), then a heat sink is usually required to help dissipate the heat. Most linear regulators have thermal shutdown circuitry which operates if the device overheats and will output a low voltage (~1V) when in shutdown mode. Linear regulators can only output lower voltages than the input.
• Switching Regulator: A more complex regulator that usually requires many external components (~10), but is much more efficient, giving off less heat, and thus can supply a higher current for a small package size. Switching regulators generally work by switching quickly on and off at a constant frequency. The output is smoothed using a capacitor and inductor. The resulting volatage is approximately Vcc*(High time/switching period) for a step-down converter. The voltage can be decreased (or stepped down) or increased (or stepped up, or boosted), depending on the design. Some switching regulators can invert the voltage; for example, the MAX-232 class of serial interface chips (from Maxim) produce +10V and -10V voltages from a single +5V supply.
• DC-DC Voltage Regulator: In the strict sense, a DC to DC regulator converts the input voltage to AC, decreases or increases the voltage using a transformer, then converts it back to a DC voltage using a bridge rectifier. This provides superior efficiency when large voltage changes are required, with the added benifit that the input and output are electrically isolated. This, for example would allow you to have separate and different ground references.

## Analog Circuits

Analog circuits operate on continously varying voltage or current, ie. voltage that has an infinite number of possible values. Under the right conditions, analog circuits can be more accurate and faster than digital circuits, but analog circuits are more susceptible to noise.

Many sensors give an anolog voltage output proportional to the variable being measured. Usually the analog voltage is fed into a Analog to Digital Converter (ADC) which converts the analog votlage to a binary value (1's and 0's). The ADC may be part of the microcontroller or a separate chip.

To reduce the affect of noise on wires carrying analog voltages, the signal and ground return wires for a given sensor should be twisted together. This is commonly refered to as a twisted pair. Telephone lines are twisted together for this reason.

## Digital Logic

Digital logic generally refers to 0's and 1's, or two well defined states (binary). Digital logic is used because it offers far superior tolerance to noise than analog circuits.

### Output States

Although binary systems have only two possible states, digital circuits/signals can be considered to have 3 output states.

• Output High: A high voltage level (Vcc) usually interpreted as logic 1
• Output Low: A low voltage level (GND) usually interpreted as logic 0
• High Impedance: (abreviated High-Z) Approximately equivalent to an open circuit or disconnected wire, the voltage is not forced to any value, it is left floating. This state allows another device connected to the wire to set the voltage. If all devices connected to the wire are in a High-Z output state, then the voltage is unknown and could be any value between Vcc and GND. To avoid this condition, use a pull-up or pull-down resistor.

A pull-up resistor is a resistor connected between the signal line and Vcc. If the signal is floating, the resistor will ” pull ” the line to Vcc. This essentially sets a default logic value if no devices are controlling the line. A pull-down resistor is connected between the signal and GND, setting the default value to GND.

### Input States

Input pins are always set to a High-Z state to allow another device to control the voltage level and provide the input state.

• Input High: A high voltage level (Vcc).
• Input Low: A low voltage level (GND).
• Floating: A meaningless input state. Nothing is controlling the voltage, so it could be any value.

If two devices try to set the voltage on the same line at the same time, contention could arise. This occurs if one device is trying to ouput high while the other is outputing low. This is essentially a short (Vcc to GND) and can damage the devices. You can put a resistor in series with the signal and each output device to protect against this situation (the resistor will limit the current).

### Basic Binary Logic Functions

Input Output
AB ANDORXOR
00 0 0 0
01 0 1 1
10 0 1 1
11 1 1 0

Binary logic functions are implemented electrically using combinations of transistors and/or diodes. The electrical devices are referred to as gates. The symbols are shown below.

## Determining Component Values

Components such as resistors and capacitors state their values in sometimes crytic methods. Following are some of the ways that are used to label component values.

### Resistor Color Table

Most resistors are labeled using 4 color bands. This uses 2 significant digits, one multiplier, and one tolerance value.

### Capacitor Code

Capacitors are usually labeled using three numbers and optionally a letter to designate tolerance. The first two numbers are significant digits, the third is a multiplier and designates the number of zeros to add to the first two digits to get the value in pico Farads (1pF = 10-12 Farads).