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Introduction to Electrical and Computer Engineering

Basic Circuits and Simulation

Electrical & Computer Engineering Basic Circuits and Simulation (1 of 22)

International System of Units (SI)

• Length: meter (m) • SI Prefixes (power of 10) • Mass: kilogram (kg) – 1012 Tera (T) • Time: second (s) – 109 Giga (G) – 106 Mega (M) • Current: Ampere (A) – 103 kilo (k) • : Volt (V) – 10-3 milli (m) • Temperature: Degrees – 10-6 micro (µ) Kelvin (ºK) – 10-9 nano (n) – 10-12 pico (p)

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1 SI Examples

• A few examples: • 1 Gbit = 109 bits, or 103106 bits, or one thousand million bits – 10-5 s = 0.00001 s; use closest SI prefix

• 1×10-5 s = 10 × 10-6 s or 10 μs or

• 1×10-5 s = 0.01 × 10-3 s or 0.01 ms

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Typical Ranges

Voltage (V) Current (A) • 10-8 Antenna of radio • 10-12 Nerve cell in brain receiver (10 nV) • 10-7 Integrated circuit • 10-3 EKG – voltage memory cell (0.1 µA) produced by heart • 10×10-3 Threshold of • 1.5 Flashlight battery sensation in humans • 12 Car battery • 100×10-3 Fatal to humans • 110 House wiring (US) • 1-2 Typical Household • 220 House wiring (Europe) appliance • 107 Lightning bolt (10 MV) • 103 Large industrial appliance • 104 Lightning bolt Electrical & Computer Engineering Basic Circuits and Simulation (4 of 22)

2 Electrical Quantities

• (positive or negative) – (Coulombs, C) - q – Electron: 1.602 x 10 • Current (Ampere or Amp, A) – i or I – Rate of charge flow, – 1 1

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Electrical Quantities (continued)

• Voltage (Volts, V) – w=energy required to move a given charge between two points (Joule, J) – – 1 1

1 Joule is the done by a constant 1 N force applied through a 1 m distance. so… 1 J = 1 Nm 1 V = 1 Nm/C

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3 Circuit elements (Sources)

Voltage Source (V) Current Source (I)

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Circuit Elements (Passive Elements)

Resistor (R) (L) (C) Ohms,  Henrys, H Farads, F

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4 Simple Circuit

Notice that current is shown in the direction of positive charge flow, even though the actual flow is the movement of electrons.

VS = VR because both elements are connected to the same points electrically Active Sign (from the top wire to the Passive Sign Convention Convention bottom wire).

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Passive Components

• In a load or passive component, such as a light bulb, , or – (flow of positive charges) moves through the device under the influence of the voltage in the direction of lower , from the positive terminal to the negative – So work is done by the charges on the component; flows out of the charges; and flows from the circuit into the component

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5 Active Components

• In a source or active component, such as a battery or , current is forced to move through the device in the direction of greater electric potential energy, from the negative to the positive voltage terminal – This increases their potential energy, so electric power flows out of the component into the circuit – Work must be done on the moving charges by some source of energy in the component, to make them move in this direction against the opposing force of the E

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Passive Sign Convention

• Defining the current variable as entering the positive terminal means that if the voltage and current variables have positive values, current flows from the positive to the negative terminal, doing work on the component, as occurs in a passive component – So power flowing into the component from the line is defined as positive; the power variable represents power dissipation in the component. – Therefore Active components (power sources) will have and negative power flow – Passive components (loads) will have positive resistance and positive power flow

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6 Active Sign Convention

• Defining the current variable as entering the negative terminal means that if the voltage and current variables have positive values, current flows from the negative to the positive terminal, so work is being done on the current, and power flows out of the component. So power flowing out of the component is defined as positive; the power variable represents power produced – Active components will have positive resistance and positive power flow – Passive components will have negative resistance and negative power flow – This convention is rarely used, except for special cases in power engineering

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Resistance

• The most basic circuit equation is Ohm’s Law (passive convention): V = IR • The voltage across a resistor is equal to the current flowing through it times the resistance value – The unit for resistance is the Ohm (named after a German physicist, George Simon Ohm) with a symbol of . – A reminder: you need to be careful when using Ohm’s Law in a circuit with multiple or multiple sources • This law refers to a single resistor and refers to the voltage across that particular resistor and the current flowing through that particular resistor. Electrical & Computer Engineering Basic Circuits and Simulation (14 of 22)

7 Resistance Equivalence

• If the polarity of a voltage is reversed, the magnitude also has to be negated. The branches are equivalent. In the same way, if a current direction is reversed, the magnitude has to be negated. See below. Each representation is equivalent for both voltage and current.

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Special Cases

• When R = 0 , referred to as a short circuit, V = IR = 0. You can think of this situation as a perfect conductor that is capable of carrying current with no voltage drop across it.

• When R = ∞, referred to as an open circuit, I = V/R = 0. You can think of this situation as a perfect insulator that is capable of supporting a voltage without permitting current flow.

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8 Power

• Another important equation is the equation, P = IV. – Power is measured in Watts (named after the Scottish engineer, James Watt) – The unit of Watts can also be broken down further.

• I (Coulomb/s) and V (Joule/Coulomb) multiplied together result in Coulombs cancelling out and therefore, the unit of Watt is equivalent to Joule/s (rate of energy expenditure)

P = IV = I*(IR) = I2R P = (V/R)*V = V2/R

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Example

• To find I in the circuit, use Ohm’s Law: V = IR.

– I = V/R – I = 6V/3 = 2 Amps. • If you change the resistor value to 3 k, – I = 6/(3 × 103) = 2 × 10-3 or 2 mA • Increasing the value of resistance decreases the current flow

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9 Example (continued)

• All forms of the equation yield the same magnitude for power – We can distinguish if an element is absorbing or supplying power by using the passive sign convention – In this circuit, “positive” current is entering the “positive” voltage terminal of Now look at power, the resistor. We use the “sign” of the power to show that a “positive” power P = I2R = 22(3) = 12 W indicates that the element (resistor) is absorbing power P= V2/R = 62/3 = 12 W – Note in this circuit, “positive” current is entering the “negative” voltage terminal P = IV = 2(6) = 12 W of the power supply. A “negative” power (2 * -6) = -12 W indicates this element is supplying 12 W of power

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Ohm’s Law Simulation

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10 Ohm’s Law Simulation (continued)

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Basic Circuit Simulation

• Start OrCAD Capture CIS Lite • Select new project – Select project name and location – Project type should be “Analog or Mixed A/D” – Select “Create a blank project” • Create circuit by placing components – Place->PSpice Component… • After circuit is complete, create a PSpice simulation profile – Pspice->New Simulation Profile – The analysis type should be “Time Domain (Transient)” • Run simulation using “PSpice Run” • Tool will allow you to display parameters such as currents through each device, voltage across each device, power supplied/dissipated by each device

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