Let basic electricity

University of Manchester Department of Computer Science

Basic Electricity
The intention of this lecture is to describe basic electrical
characteristics in a qualitative way.

Lecture objectives:
o provide some basic knowledge of analogue electronics
o to give some “feel” for electronic effects on digital circuits

Much of the following theory should be familiar; what may be new is
some of its application.

Note:
Much of the ‘skill’ is to understand the associated jargon, especially
as terminology is often used for things not directly related to its strict
definition.
For example “D.C.” literally refers to Direct Current, an electrical
current which always flows in the same direction. It is loosely used
to describe any value (electrical or otherwise) which does not vary
with time.

CS1222 – Computer Technology Basic Electricity Slide 1

Electrical Basics
What is …
Charge?
Charge is measured in coulombs and is the amount of “electricity” present (or flowing).
Charge can be positive or negative. Like charges repel each other. Unlike charges attract each
other.
In the vicinity of a charge there is an electric field. The field points in the direction that a posi-
tive charge would move.
Charge moves about and may be stored (e.g. in a capacitor or battery).

Current? (A.C. ? D.C.?)
Current is a flow of charge; the rate of movement of charge through a system. It is analogous to
the flow of water in a hydraulic system (in litres/s). It is measured in amps; an amp is quite big.
A.C. is alternating current, where the current flows first one way then the other (repeatedly).
This does not mean it cannot transmit energy. D.C. is Direct Current where a current flows in
the same direction at all times (normally implies constant value as well as direction).

Voltage?
Voltage is electrical “pressure”. It is analogous to the pressure of a hydraulic system (say like
the height of a reservoir). Voltage is measured in volts; contrary to media opinion, volts do not
flow.

Impedance is the ‘resistance’ to current flow. It is a very important concept in any electrical
circuit. For instance the (internal) impedance of a gate’s output should be low so that it may
drive its output more easily. The input impedance of a gate should be high so that it may be
driven easily (without it absorbing a large current, which would lead to a high power loss).
Impedance is a general term. For many applications ‘resistance’ is equally applicable, how-
ever capacitors and inductors have different properties.

Energy is a measure of work done. Power is the work done per unit time. Thus if a battery
contains so much energy it can power something for a particular time. If the power needs of the
equipment is reduced then the same energy can power it for longer. (These two terms are not
restricted to electrical circuits.)


Ohm’s Law
V=IxR
This is only true for resistive loads. Most loads are more complex
than this. In general:
V=IxZ
where Z is the impedance of the load. This may depend (for
example) on the frequency of an A.C. signal.

Kirchhoff’s Current law
What goes in, comes out.

A simple application:
Potential divider
V0
R2
V = V0 x (R1/(R1+R2))
V

R1

There is a tacit assumption here that no current flows in the output.


Basic Laws
Ohm’s law (which should be familiar) is a very useful rule. Note that it only applies to resis-
tive loads however. The impedance of other passive components may vary with (e.g.) fre-
quency (e.g. capacitors) and many components do not obey this rule at all (diodes, transistors
etc.).
Resistance determines how much charge flows per second whe a voltage is applied. Resist-
ance is lower if the material the device is made from has many charges (normally electrons) in
it and if the charges can move easily through the material. Both of these depend on tempera-
ture.
Kirchoff’s law, which is common sense, states that the sum of currents at a join in wires is
always zero, i.e. any charge (current is a flow of charge) which goes in must come out some-
where.

Potential divider
The potential divider is a simple application of these laws.

R2

X

R1

The current through R1 must be the same as the current through R2. The voltage at point X can
therefore be found from the ratio of the two resistors.
The potential divider is a simple, cheap way of producing an arbitrary voltage. It is not always
the best way; consider what happens if something is connected to point X which sources or
sinks current.

Question. If R1=10Ω, R2=20Ω or if R1=10kΩ, R2=20kΩ the voltage at point X is the same.
What would be the reasons for choosing particular values for the resistors?

Note: Resistor values are often written as (e.g.)47R, which means 47Ω (no Ω character
available), 33K (33kΩ), or 1K5 (1.5kΩ). The last style is easier to interpret on a circuit
diagram where a “.” may easily become lost after photocopying, with possibly traumatic
results!


Capacitors
A capacitor is a charge storage device.

It allows A.C. signals to pass through but blocks D.C. signals. Why?

The impedance of a capacitor is Zc = 1/ωC (ω = 2πf)

o A high frequency (ω = big) signal passes through easily
(low impedance)
o A low frequency (ω = small) signal passes through with
difficulty (high impedance)
o A D.C. (ω = 0) signal is blocked (infinite D.C. impedance)

A capacitor will charge/discharge with a delay proportional to RC
where C is the capacitor’s value and R is the charging (or
discharging) impedance.

Everything has some inherent capacitance.

Capacitance is usually the enemy in digital circuits, slowing down
signal edges and therefore circuit operation:-(


Capacitors
A capacitor is a charge storage device. It comprises two conducting plates separated by an
insulator. The charge (Q) stored is related to the voltage across the capacitor (V) by:
Q=CxV
Where C is the “Capacitance”. To change the voltage on a capacitor, charge must flow into or
out of the capacitor. In a circuit the charge flow rate is limited by any resistance present, so the
time taken for the voltage to change is given by T=RC, the ‘time constant’ of the circuit.

Simple filters
Think of the potential divider …

R 1 ⁄ ( ωC )
C Vout = ----------------------------- Vin
- Vout = ----------------------------- Vin
-
R + 1 ⁄ ( ωC ) R + 1 ⁄ ( ωC )
R
Vin Vout Vin Vout

R C

High pass Low pass

“Handwaving” explanation
The high pass filter only transmits high frequencies from input to output (low frequency cur-
rents are blocked by the capacitor). In the low pass filter the capacitor will ‘short’ any high fre-
quencies to ground, allowing only the lower frequencies to affect the output.
For those more interested calculate the ratio of input to output voltage for the circuits at two or
three trial frequencies - say ω = 1/(10RC), 1/(RC) and 10/(RC).

Capacitance is usually a Bad Thing in digital logic because it slows things down (voltages take
T=RC to change). It is exploited in some circumstances however:
o Decoupling power supplies
o DRAM storage elements
o Dynamic CMOS logic (a form of VLSI circuit)

Types of capacitors
Capacitors come in many sizes, shapes and colours. Different capacitors can (should) be used
for different jobs. Capacitance is measured in farads. A farad is a big unit and typical devices
range from 1pF to 1000µF.


Resistors
Resistors in series are added together – resistance increases.
R1 + R2
R1 R2

In parallel resistance is reduced
R
R1

R2 1 = 1 + 1
R R1 R2
In particular if R1 = R2 then R will be half of R1 (or R2).

Capacitors
Capacitors in parallel are added together – capacitance increases.
C1 + C2

C1

C2
In series capacitance is reduced.
C

C1 C2
1 = 1 + 1
C C1 C2

Many

types of large value capacitors are polarised – i.e. they must be placed so that one terminal is
always more positive that the other. They will also have a voltage limit which should not be
exceeded. Failure to observe these restrictions will cause a failure of the circuit in the near
future.


Inductors

An inductor is a device that tries to keep a constant current flowing
through itself.

As electronic components inductors are bulky and much rarer than
resistors or capacitors. However the property of inductance is real
and some appreciation of it is needed.

Many electrical components are highly inductive:
• motors
• transformers
• relay drivers

The impedance of an inductor is given by:
ZL = ω.L
i.e. zero at D.C. and increasing with frequency

Everything (e.g. wires) has some inherent inductance.


Resistance in VLSI
Most VLSI circuits do not contain components that are explicit resistors. However all materi-
als (other than superconductors) have some resistance to the flow of electricity.

All the wires and, particularly, the ‘channels’ of the transistors on a VLSI chip have some
resistance and this influences the design of the device. In general a higher resistance causes a
gate to switch more slowly.

Resistances add when connected in series. This means that:
o two (or more) series transistors have a higher resistance than one, alone.
o more series transistors cause the circuit to go more slowly.

It is also resistors (or, rather, components with resistance) which dissipate power. The power
dissipation in a (pure) resistor is given by:
V2
P = = I2 R
R
However it is rare that this is a concern in VLSI circuits; it is more important to measure the
energy transfer each time a gate switches.

Capacitance in VLSI
Most VLSI circuits do not contain components that are explicit capacitors (although they are
occasionally included). However all wires, transistors etc. have some capacitance. Particularly
important contributions come from the MOSFET gates (described later).

Capacitances add when placed in parallel. This means that the capacitance of a network
increases if it is connected to more things (higher fan-out).
o more connections cause the circuit to slow down.

The energy stored on a capacitor is given by:
1
E = C V2
2
More importantly the energy transferred by cycling a capacitor from 0 ⇒ V ⇒ 0 is:
E = C V2
o more connections ⇒ more capacitance ⇒ more energy per cycle
⇒ more power dissipation


Electric Fields

o Like charges repel
o Unlike charges attract

An electric field exists between any two objects at different voltages.

Electrons (negative) will move (if they can) in an electric field.

– – – – + + + + – – – – + + + +

electrons

Electron movement Electric field

The redistribution of electrons in an electric field is the key to the
operation of the Field Effect Transistor (FET).

A change in electric field arises from a redistribution of charge
(i.e. a current flow).


Inductors
o A capacitor is a device which stores energy in its charge.
o An inductor is a device which stores energy in a magnetic field (due to its current).
Energy cannot change instantly (implies infinite power dissipation)
o A capacitor ‘acts’ to keep a constant charge (voltage) across its terminals.
o An inductor ‘acts’ to keep a constant current flowing through itself.

Inductance in electronics is the property analogous to inertia in mechanical systems (keeps
things moving).

Inductance in VLSI
Inductance does not form an explicit part of VLSI design. It is generally seen as undesirable
and the effects of inductance are usually negligible.

The only circuits of direct interest which exploit or suffer from inductance are power supplies.
Inductance is exploited in transformers to change the supply voltage (usually
from 230V to something ~5V).
The properties of digital circuits are such that they are required to either remain
static or switch rapidly from one digital state to another. This means that electric
currents should turn on and off quickly. Inductance opposes this.
This is an especial problem for the power supply wires: firstly these have to be led
into the chip over a (comparatively) long distance, and secondly they carry the
accumulated current for many signal switching transitions.
This change in current in the inductive wires gives rise to voltage changes (spikes).
These can cause interference or ‘cross talk” between devices, and can also be used
to dicover the operation of devices - e.g. cracking codes of smart cards by measur-
ing current flows and voltage spikes on power supplies.

Effect of inductance and capacitance on a digital signal
When an inductance and a capacitance get together an oscillator results; thus any disturbance
in the circuit conditions causes ringing until the inherent resistance damps this down. This can
be seen on all signal and power supply wires in digital circuits; it is undesirable, but inevitable.
1 1 Inductance reluctant to let edge start
2 2 Edge slowed by capacitance
Theory Reality
4 3 Inductance drives overshoot
3 4 Damped oscillation


CS1222 – Computer Technology Basic Electricity

Electromagnetic Radiation
The electromagnetic spectrum:
Mobile v = f.λ = 3 x 108 m/s f = 1 GHz, λ = 3 cm
’phones
Frequency f (Hz)
106 108 1010 1012 1014 1016 1018 1020

Visible
Radio Microwave Infra red Ultra violet X-ray Gamma ray

10 10-1 10-3 10-5 10-7 10-9 10-11 10-13
Wavelength λ (m)

CPU frequencies VLSI Transistors

Electromagnetic radiation is used for a huge variety of tasks and the radio spectrum is very
crowded. The use of the radio spectrum is carefully controlled and rationed.

An electromagnetic wave consists of an alternating electric and an alternating magnetic field;
one transfers its energy to the other and vice versa. They can be generated by accelerating
charge; another way of stating this is that electromagnetic waves can be generated by alternat-
ing a current.
Digital circuits switch currents continuously. As these flow along wires (aerials) they emit
radiation. This unwanted radiation creates ElectroMagnetic Interference (EMI). As proces-
sor speeds approach many of the frequencies used for mobile communications (and harmonics
will stretch further up the spectrum) there can be a serious problem maintaining ElectroMag-
netic Compatibility (EMC) both with other computer equipment (a transmitting aerial also
receives outside interference) and other radio equipment.

Points to remember:
o radio waves will not penetrate a conductor (e.g. metal box)
o radio waves will go through holes of about their wavelength (or larger)
m A computer monitor displaying 1280 x 1024 pixels at 75 frames per second has
a bit rate of about 100 MHz. It’s E.M. emissions have λ ~ 30 cm and will pass
easily through a window (can be detected in the street....)
o radio transmission (and reception) works best with an aerial of about a wavelength
m power supply wiring is particularly good at this as are (e.g.) keyboard cables

Let basic electricity

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