Review of Basic Electronics

Material Introductory to

A Course in Computer Design and Architecture

Edward L. Bosworth, Ph.D.

TSYS School of Computer Science

Columbus State University

Columbus, GA

bosworth_edward@colstate.edu

A Basic Circuit

Here is a simple electronic circuit for our inspection. It has three basic parts:
a battery, a switch, and a light bulb. The bulb can be off or on.

When the switch is closed, current can flow through the circuit and the light
is illuminated. When the switch is open, no current flows and the light is off.

More properly, in terminology that we shall soon use:

1. When the switch is closed, its resistance is very low (almost zero) and
the battery induces a voltage drop across the light bulb.

2. When the switch is open, its resistance is extremely high. For all
practical purposes the entire voltage drop is across the switch.
There is no voltage drop across the light bulb, so it is off.

Circuit Elements

It is easier to describe circuits by drawing pictures of them.

For this purpose, we need a standard set of symbols to represent the elements
of the circuit. For direct–current circuits, the following symbols are common.

There is one redundant element in the above.

A light bulb is just a resistor that emits visible light (and usually heat)
as a result of the voltage drop across it.

Batteries and Other Voltage Sources

Technically, a battery is a device for converting chemical energy to
electrical energy. It can be viewed as a voltage source.

A generator is another type of direct–current voltage source. It is one
that converts mechanical energy into electrical energy.

All we need for these lectures is the idea of a voltage source, without close
investigation of the mechanism by which the electrical energy is generated.

For this reason, we shall use the battery as our typical voltage source.

A battery can be thought of as an electron pump.

It provides an electrical pressure, called a voltage, to the electrons that
flow though the circuit and gets them moving.

Water pumps, such as used by a municipal utility, are good analogs of
batteries. They put water under pressure and make it move through pipes.

Switches and Relays

A switch is an electro–mechanical device for controlling the flow of
electrons in a circuit.

More precisely, it is a two–state resistance device.

Low resistance In this state of almost no resistance,
it easily conducts electrical current.

High resistance In this state of extremely high resistance,
it effectively blocks the flow of electrical current.

A relay is just a switch that can be operated electrically.

When the magnet is energized, the switch closes. Otherwise, it is open.

The Idea of an Electrical Ground

Two–wire circuits are easily drawn for simple devices, but the clutter of
return wires can become bothersome for circuits even of modest complexity.

For this reason, a ground was introduced as a circuit element.

In some circuits, such as radios and antennas, this is an actual ground in
that it connects to a conducting spike placed in the dirt beneath our feet.

Consider a standard flashlight with a metallic casing.

In this circuit, the metallic body of the flashlight returns current to the battery.

Another Example of an Electrical Ground

Those of us who like to look under the hoods of cars will note that the
battery has two wires coming from it.

The red wire connects to the positive terminal of the battery and carries
current to the other electrical devices in the engine, such as the starter
motor, the horn, and (indirectly) the spark plugs.

The black wire connects to the negative terminal of the battery and
the body of the car. It does not connect directly to any electrical device.

The iron body of the car serves as a ground. It allows the current loop
to be complete by providing a common return path at zero voltage.

The student might remember that iron is not a particularly good conductor
of electricity. However, the body of the car is quite large.

Think of the car body as a fat wire of moderate conductivity as opposed
to a thin copper wire of excellent conductivity. Both do the job.

Two Equivalent Circuits

These two circuits do exactly the same thing: either the three lights
are turned on or they are not.

The bottom circuit appears to have a simpler diagram.

Voltage as a Pressure

Again, we can use water analogies to describe these. As we said, a voltage is
an electrical pressure. It is important to note that most pressure measurements
are relative and not absolute.

Consider the figure at left. The water at the bottom of the pipe has a pressure.

This pressure is due to the difference in
the height of the top of the pipe and its
bottom. The absolute altitudes (say
above mean sea level, or the center
of the planet) are not important.

Another example: you decide to jump
off a cliff, the top of which is at 1000
feet above sea level.

Important question: what is the
elevation of the bottom of the cliff?

One use of a ground is to provide a reference zero voltage.

Current and Resistance

We continue our water analogies. When a pressure is applied to a pipe or
hose, water flows through it. The current is measured in terms of quantity of
water per unit time; say, two gallons per second.

Electrical currents are quite similar; indeed the early 19^th century formulation
of electrical theory was based on thinking about water flows.

A current is a quantity of electrical charge (measured in coulombs) over a time.
The standard unit of current measurement is the ampere, which is defined as
one coulomb per second.

Some water hoses can carry more water than others. Put another way, for a
given pressure difference across the hose (from one end to another), some
water hoses will sustain a larger current; a fire hose vs. a garden hose.

The resistance of a circuit element is defined by Ohm’s law. It is simply the
voltage drop across the circuit element divided by the current though it.

The Voltage Drop

Consider the following circuit, in which the voltage supplied by the
battery is denoted by V. This is assumed to be a positive voltage.

The voltage at the top of R₁ is V₁ = V.

The voltage at the bottom of R₂ is 0. All we know is that V₁ ≥ V₂ ≥ 0.

The voltage drop across R₁ is (V₁ – V₂). That across R₂ is V₂.

The total voltage drop across the series of resistors is the sum
of the voltage drops across the individual resistors.

Ohm’s Law and the Power Law

Consider a circuit element of resistance R with a voltage drop of V across it.

In algebraic terms, Ohm’s law is easily stated: V = I·R, where
V is the voltage across the circuit element,
I is the current through the circuit element, and
R is the resistance of the circuit element.

The power dissipated by the circuit unit is stated by the power law, which
states that the power is given by P = V·I, where
P is the power emitted by the circuit element, measured in watts,
V is the voltage across the circuit element, and
I is the current through the circuit element.

Consider a light bulb with resistance 240 ohms and a voltage drop of 120 volts.

The current through the bulb is given by I = 120/240 = 0.5 amps.
The power emitted by the bulb is 120·0.5 = 60 watts.

Variants of the power law: P = E·I P = E² / R P = I²·R

Resistors in a Series

Consider again the following circuit, in which the voltage supplied by the battery is denoted by V. This is assumed to be a positive voltage.

The current through R₁ can be derived from (V – V₂) = I·R₁.

The current through R₂ can be derived from V₂ = I·R₂.
It is a fundamental circuit law that this is the same current.

We add the two to get V = (V – V₂) + V₂ = I·R₁ + I·R₂ = I·( R₁ + R₂ ).

From this, we determine that the resistance of the sequence is the sum
of the resistances of the individual circuit elements.

Voltage Drops across Individual Resistors

Here again is our circuit, with slightly different labeling.

Ohm’s law gives the current through the circuit as I = V / (R₁ + R₂).

Again applying Ohm’s law we can obtain the voltage drops across each of the two resistors. Let V₁ be the voltage drop across R₁ and V₂ be that across R₂.

Then V₁ = I·R₁ = V·R₁ / (R₁ + R₂), and

V₂ = I·R₂ = V·R₂ / (R₁ + R₂).

The voltage at point 1 is given by V. That at point 2 by V₂ = V·R₂ / (R₁ + R₂).

Two Special Cases of Voltage Drop

Consider the two circuits below. We shall use each of these to represent
one of the two states of a switch.

In the circuit at left, the voltage drop across R₂ is V₂ = V·0 / (R₁ + 0) = 0.
The voltage at point 2 is given by zero. At point 1, the voltage is V.

In the circuit at right, the voltage drop across R₂ is given by the same equation:
V₂ = V·R₂ / (R₁ + R₂) = V / (1 + R₁/R₂). If R₂ is very much larger than R₁, then
it is almost the case that V₂ = V and the voltage drop across R1 is zero.

In our vase V₂ = V / 1.001 = 0.999001·V.

A Resistor and a Switch in Series

The example above is useful in the analysis of a resistor in series with a switch.

The Circuit Switch Closed Switch Open

What is the voltage at point 2?

If the switch is closed, point 2 is connected directly to ground.
The voltage at point 2 is 0.

If the switch is open, the voltage at point 2 is essentially the full battery voltage.

A Useful Circuit

The following is a circuit that we shall find useful when considering
the connection of a number of devices to a common bus.

If all of the switches are open, then the voltage at the monitor is
the full battery voltage.

If one or more of the switches is open, then the voltage at the monitor is zero.

The real reason for the use of this circuit is that closing two or more switches
cannot cause any electrical problems.

The Power Dissipated by a Switch

As we shall see in the course, the switch is the basic building block of a computer. One key issue in the design of computers is the design of a switch
dissipating very little power.

Who cares if a switch dissipates one microwatt (10^–6 watt) of power? A large
chip will contain 10⁹ switches, thus dissipate 1000 watts and melt.

We again reuse an earlier circuit.

The voltage drop across the switch is given by V₂ = I·R₂.

The power dissipated by the switch is given by P₂ = I·V₂ = I²·R₂.

The Power Dissipated by a Switch (Part 2)

When the switch is closed, we have R₂ = 0; the switch dissipates no power.

When the switch is open, R₂ is extremely large. We must do a bit of algebra.

As R₂ becomes very large (as it does for an open switch) the power becomes 0.

Why Binary Digital Computers?

There are some theoretical reasons to prefer a three–state computer.

There is one very sound reason to prefer a binary (two–state) digital computer. This is the two–state switch.

As noted above an ideal two–state (closed or open) switch emits no power
when it is in a stable state.

Again, it is absolutely necessary to minimize the power dissipated by the
switches in a digital computer.

In the TTL (Transistor–Transistor Logic) implementation that forms the
basis of our discussions, there are two standard voltages.

High Ideally five volts positive.

Low Ideally zero volts.

Broken Wires and the High–Impedance State

In a standard TTL circuit, we can easily see two standard voltage levels:
high and low. It may be a surprise that there is a third voltage level.

This level is undefined (high impedance). This level appears to be the same
as the zero voltage level in that it can deliver no power. It is not the same.

Consider the following circuits. What is the voltage at point 1 in each?

In the circuit at right, the voltage is definitely the full battery voltage.

In the circuit at left, the voltage cannot be the full battery voltage,
because the light will not illuminate when the switch is closed.

Broken Wires and the High–Impedance State (Part 2)

Consider this pair of circuits. What is the voltage at point 1 on each?

In the circuit on the right, the voltage is definitely zero.

In the circuit on the left, the voltage at point 1 is definitely not zero. The light
will not illuminate when the switch is closed.

Here is another example that shows the difference. What happens in each circuit when the switch is closed?

Real Circuit Elements vs. Ideal Circuit Elements

Consider again this circuit, which is highly dangerous.

If we stay with what we have said above, we would imagine attempting to place a voltage drop across a zero resistance; thus an infinite current.

In reality, this does not occur. For starters, the battery has an internal resistance.

The fact is that a real battery has a small internal resistance, which is very much smaller than the external resistance in the intended circuit. If short–circuited, the battery will heat up due to its internal resistance.

The Capacitor

We now consider another circuit element, the capacitor. This was once called
a condenser, but that terminology is obsolete.

The figure at the left is a symbol for a capacitor. It is a device for storing electric charge and delivering current in a short time.

In general, each of a battery and a generator can be viewed as an electron pump. The capacitor is an electron storage device.

Again, the best analogy comes from water systems, which have:

Water pumps to pressurize the pipes.

Water tanks to hold water and equalize the pressure.

A capacitor is very much like a water tank. It can store electric charge and,
when attached properly to a circuit, dampen the voltage spikes.

Another good analog to the capacitor is the water tank on a flush toilet.

Real Capacitors

The symbol in the previous slide shows an ideal capacitor.

Any real capacitor must be viewed as a combination of

an ideal capacitor, and

one or two ideal resistors.

Here is a circuit representation of a real capacitor.
R₁ is very low
R₂ is very high.

Due to the presence of the external resistor R₂, the capacitor will leak charge
by gradually causing a small current to flow through that resistor.

Lumped Parameter Circuits

Consider the following circuit, copied from an earlier slide.

In the standard circuit analysis, as we learned in a basic physics course, we would compute the equivalent resistance of the circuit and then use that to determine the current provided by the battery.

We might then ask about the current through each light bulb.

What we have done is to view this circuit as a lumped–parameter circuit, in which the time taken to propagate the electronic signals is insignificant.

Distributed Parameter Circuits

In a distributed–parameter circuit, we must account for the propagation of the
voltages across the circuit. This may be necessary for one of two reasons:

1. The time scales of interest are small, or

2. The distances are large.

Consider a garden hose attached to a faucet. What happens when at the
nozzle when the faucet is turned on?

1. Nothing happens at first, as the water takes time to
travel the length of the hose.

2. At first the water flow is sporadic, as air is
blown out of the hose.

3. At last, the water flow becomes stable at the flow rate that would be
predicted from the water pressure and resistance of the hose.

The first two steps must be analyzed using distributed–parameter techniques.

The last step can be analyzed using lumped–parameter techniques.

Some Distributed Parameter Electronic Circuits

Consider a power line that is about 1000 miles long.

Suppose that the power line connects a power plant to a
power distribution center in a remote city.

What happens when the line is first energized? Just as in the case of the water
hose, we can watch the voltage pulse propagate from one end to the other.

NOTE: The speed of light in a vacuum is about 3·10⁸ meters per second.

The speed of signal propagation (voltage pulse) in a copper wire
is about 2·10⁸ meters per second, or one meter per five nanoseconds.

Consider a system bus operating at 200 MHz, one pulse per five nanoseconds.

If the system bus is one meter long, then the time for the clock pulse to
propagate the length of the bus is the same as the clock period.

In that case, we need to apply analysis based on distributes parameter systems.

The System Clock

While we shall be interested in general signals on a bus,
we can use the bus clock pulse as an example.

The clock produces a pulse that periodically changes between
logic 1 (five volts) and logic 0. Here is a typical depiction.

In general, we must use distributed–parameter analysis if the time to
propagate the signal across the bus exceeds 1/8 of the cycle time.

We shall not apply this analysis, but must be aware that it is required.

Digital Logic Gates

A binary digital computer functions by use of three basic digital circuits, as
well as related circuits. The basic circuits are called OR, AND, and NOT.

At this point, we shall discuss only the NOT gate.

If the gate input is logic 1 (5 volts), its output is logic 0 (0 volts).

If the gate input is logic 0 (0 volts), its output is logic 1 (5 volts).

The basic circuit element used is the MOS (metal oxide semiconductor) transistor. This transistor can be driven to one of two states: ON or OFF.

Each type of MOS transistor has a control input that can be used to set its state.
There are two types, differing in the response to the control input.

P–channel MOS transistors act as an open switch for a positive voltage and
as a closed switch (conducting) for a low voltage.

N–channel MOS transistors act as a closed switch (conducting) for a positive
voltage and as an open switch for a low voltage.

CMOS Gates

A Complementary Metal–Oxide–Semiconductor gate is based on a pairing
of the two transistor types. Here is a CMOS implementation of a NOT gate.

If the input voltage is zero, then

the n–channel transistor at bottom acts as an open switch, and
the p–channel transistor at top acts as a closed switch.

The output is connected to full voltage.

If the input voltage is zero, then

the n–channel transistor at bottom acts as a closed switch, and
the p–channel transistor at top acts as an open switch.

The output is connected to ground.