University of Manchester Department of Computer Science Basic ElectricityThe intention of this lecture is to describe basic electricalcharacteristics in a qualitative way.Lecture objectives: o provide some basic knowledge of analogue electronics o to give some “feel” for electronic effects on digital circuitsMuch of the following theory should be familiar; what may be new issome of its application.Note:Much of the ‘skill’ is to understand the associated jargon, especiallyas terminology is often used for things not directly related to its strictdefinition.For example “D.C.” literally refers to Direct Current, an electricalcurrent which always flows in the same direction. It is loosely usedto describe any value (electrical or otherwise) which does not varywith time.CS1222 – Computer Technology Basic Electricity Slide 1
Electrical BasicsWhat 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 eachother.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 tothe 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 inthe 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 likethe height of a reservoir). Voltage is measured in volts; contrary to media opinion, volts do notflow.Impedance is the ‘resistance’ to current flow. It is a very important concept in any electricalcircuit. For instance the (internal) impedance of a gate’s output should be low so that it maydrive its output more easily. The input impedance of a gate should be high so that it may bedriven 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 batterycontains so much energy it can power something for a particular time. If the power needs of theequipment is reduced then the same energy can power it for longer. (These two terms are notrestricted to electrical circuits.)
University of Manchester Department of Computer Science Ohm’s Law V=IxRThis is only true for resistive loads. Most loads are more complexthan this. In general: V=IxZwhere Z is the impedance of the load. This may depend (forexample) on the frequency of an A.C. signal. Kirchhoff’s Current lawWhat goes in, comes out.A simple application:Potential divider V0 R2 V = V0 x (R1/(R1+R2)) V R1There is a tacit assumption here that no current flows in the output.CS1222 – Computer Technology Basic Electricity Slide 2
Basic LawsOhm’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, transistorsetc.).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) init 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 isalways zero, i.e. any charge (current is a flow of charge) which goes in must come out some-where.Potential dividerThe potential divider is a simple application of these laws. R2 X R1The current through R1 must be the same as the current through R2. The voltage at point X cantherefore 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 alwaysthe best way; consider what happens if something is connected to point X which sources orsinks 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!
University of Manchester Department of Computer Science CapacitorsA 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 RCwhere C is the capacitor’s value and R is the charging (ordischarging) impedance.Everything has some inherent capacitance.Capacitance is usually the enemy in digital circuits, slowing downsignal edges and therefore circuit operation:-(CS1222 – Computer Technology Basic Electricity Slide 3
CapacitorsA capacitor is a charge storage device. It comprises two conducting plates separated by aninsulator. The charge (Q) stored is related to the voltage across the capacitor (V) by: Q=CxVWhere C is the “Capacitance”. To change the voltage on a capacitor, charge must flow into orout of the capacitor. In a circuit the charge flow rate is limited by any resistance present, so thetime taken for the voltage to change is given by T=RC, the ‘time constant’ of the circuit.Simple filtersThink 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” explanationThe 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 orthree 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 takeT=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 capacitorsCapacitors come in many sizes, shapes and colours. Different capacitors can (should) be usedfor different jobs. Capacitance is measured in farads. A farad is a big unit and typical devicesrange from 1pF to 1000µF.
University of Manchester Department of Computer Science ResistorsResistors in series are added together – resistance increases. R1 + R2 R1 R2In parallel resistance is reduced R R1 R2 1 = 1 + 1 R R1 R2In particular if R1 = R2 then R will be half of R1 (or R2). CapacitorsCapacitors in parallel are added together – capacitance increases. C1 + C2 C1 C2In series capacitance is reduced. C C1 C2 1 = 1 + 1 C C1 C2CS1222 – Computer Technology Basic Electricity Slide 4Many
types of large value capacitors are polarised – i.e. they must be placed so that one terminal isalways more positive that the other. They will also have a voltage limit which should not beexceeded. Failure to observe these restrictions will cause a failure of the circuit in the nearfuture.
University of Manchester Department of Computer Science InductorsAn inductor is a device that tries to keep a constant current flowingthrough itself.As electronic components inductors are bulky and much rarer thanresistors or capacitors. However the property of inductance is realand some appreciation of it is needed.Many electrical components are highly inductive: • motors • transformers • relay driversThe impedance of an inductor is given by: ZL = ω.Li.e. zero at D.C. and increasing with frequencyEverything (e.g. wires) has some inherent inductance.CS1222 – Computer Technology Basic Electricity Slide 5
Resistance in VLSIMost 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 someresistance and this influences the design of the device. In general a higher resistance causes agate 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 powerdissipation in a (pure) resistor is given by: V2 P = = I2 R RHowever it is rare that this is a concern in VLSI circuits; it is more important to measure theenergy transfer each time a gate switches. Capacitance in VLSIMost VLSI circuits do not contain components that are explicit capacitors (although they areoccasionally included). However all wires, transistors etc. have some capacitance. Particularlyimportant contributions come from the MOSFET gates (described later).Capacitances add when placed in parallel. This means that the capacitance of a networkincreases 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 2More 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
University of Manchester Department of Computer Science Electric Fields o Like charges repel o Unlike charges attractAn 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 fieldThe redistribution of electrons in an electric field is the key to theoperation of the Field Effect Transistor (FET).A change in electric field arises from a redistribution of charge(i.e. a current flow).CS1222 – Computer Technology Basic Electricity Slide 6
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 (keepsthings moving). Inductance in VLSIInductance does not form an explicit part of VLSI design. It is generally seen as undesirableand 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 signalWhen an inductance and a capacitance get together an oscillator results; thus any disturbancein the circuit conditions causes ringing until the inherent resistance damps this down. This canbe 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
University of Manchester Department of Computer ScienceCS1222 – Computer Technology Basic Electricity
Electromagnetic RadiationThe 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 TransistorsElectromagnetic radiation is used for a huge variety of tasks and the radio spectrum is verycrowded. 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 acceleratingcharge; 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 emitradiation. This unwanted radiation creates ElectroMagnetic Interference (EMI). As proces-sor speeds approach many of the frequencies used for mobile communications (and harmonicswill stretch further up the spectrum) there can be a serious problem maintaining ElectroMag-netic Compatibility (EMC) both with other computer equipment (a transmitting aerial alsoreceives 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