chapter6 electronic-components

Elec3017:Electrical Engineering Design

Chapter 6: Electronic Components

A/Prof D. S. Taubman

August 16, 2006

1 Purpose of this ChapterConsidering the dizzying array of electronic components which exist, we cannothope to cover them all in this chapter (or even an entire course). Instead, thefocus of this chapter is to get you into the habit of asking the right questionsabout components. It also helps to know something about the materials usedin components and the associated construction methods, since these should giveyou some idea of the weaknesses to watch out for. This is particularly true forsimple components like resistors and capacitors. For more complex components,it is essential that you get into the habit of reading manufacturer data sheets.You learn this by doing it, while keeping important questions in your mind,relating to parameters such as leakage current, offset voltage, output impedance,operating temperature, propagation delay, supply voltage and many others.Some of the most important types of questions to ask are as follows:

What are reasonable parameter values? You should generally be aware ofwhat is readily available and what is difficult to achieve. For example,commonly available capacitors typically have capacitances in the range 1picofarad through to several millifarads — a 1F capacitor is huge!

What are reasonable ratings? Ratings define the limits over which you canreliably operate the component — beyond these, the component may bedestroyed. Maximum ratings apply to such parameters as voltage, powerand current. If the power dissipation is too large, the component willget too hot. If the applied voltage is too large, dielectric breakdown mayresult — this usually means irreversible damage. If the current passingthrough a semiconductor junction is too large, the internal junction maybe permanently destroyed.

What nominal values are available? This is a matter of knowing whatparts you can actually get. For digital IC’s, this includes questions such

1

c°Taubman, 2006 ELEC3017: Electronic Components

as “What are the available nominal speed ranges?” For resistors and ca-pacitors, the question is “What nominal resistance values can be easilypurchased?”

How accurate are the nominal parameter values? This question is con-cerned with precision. The actual measured parameter values for anyspecific component will generally differ from its advertised nominal pa-rameters. The question is how much variation can be expected — ±1%,±5%, ±20%?. Precision may also be affected by operating temperatureand time. How significant is this?

What happens at extreme frequencies? Here we are interested in the im-pact of parasitic components (typically, parasitic capacitance, inductanceand resistance) which limit the range of frequencies over which the elec-tronic component behaves in a predictable manner. Parasitics often cannotbe precisely controlled during manufacture, so that their presence is bestunderstood as limiting the range of operating frequencies over which thebehaviour can be predicted reliably.

What happens with very small signals? When signal levels are verysmall, noise effects can be critical. Transistors and resistors manufac-tured using different technologies can exhibit very different noise behav-iour. Other small signal issues include unpredictable voltage offsets (e.g.,the input voltage offset of an opamp) and hysteresis — a type of long termmemory effect, exhibited by certain types of materials.

In the remainder of this chapter, we consider various types of electroniccomponents in the light of these questions. Of course, the material here can-not be completely comprehensive, particularly in regard to analog and digitalintegrated circuits. The goal, however, is to get you reading data sheets for thespecific components you are interested in.

2 Questioning ResistorsNominally, resistors follow Ohm’s law, which states that

V = I ·R

where V is the voltage applied across the resistor and I is the current passingthrough the resistor. Ohm’s law is essentially just a statement that the relation-ship between voltage and current in many materials is linear — at least to a verygood approximation. Depending on the context, you may find it convenient tothink of resistors as converting current into voltage or voltage into current. Ineither case, heat is produced with power

P = V · I = V 2/R = I2R


An obvious question, then, is how much heat can be produced (i.e., how muchpower can be dissipated) before the device is destroyed, or becomes dangerouslyhot.There are three basic types of resistors, as follows:

Wire wound resistors: Wire is wound around a non-conductive core (alsocalled a former) so that a large length of wire can be accommodated ina relatively small package. To minimize inductance, the wire is normallywound in both directions — e.g., clockwise along the former and then anti-clockwise back again. Since wire wound resistors are made from solid metalwire they tend to have good power handling properties. On the otherhand, they tend to be bulky and exhibit significant levels of capacitance(between the turns) and inductance.

Film resistors: The most common and inexpensive type of resistors are thosemade from carbon film deposited on a non-conductive core. Metal film re-sistors are also widely available; they offer superior precision for a slightlyhigher price.

Carbon composite resistors: These consist of a solid pellet of resistive ma-terial (typically carbon) bonded to the external metallic leads. They havesuperior power handling capacity to film resistors, where the film can berapidly vaporized by short term power surges — this is particularly truefor metallic film resistors.

While individual resistors are the most common, it is worth noting thatresistors can be purchased in pre-packaged networks. These occupy less space onthe PCB (Printed Circuit Board) and reduce handling, insertion and solderingcosts.

2.1 What are reasonable parameter values?

For resistance of less than 1Ω, you will generally be looking at wire woundvarieties, where values down to 0.1Ω can be sourced. Such low resistors arenormally used only in very high current applications, such as power amplifiers.For resistances of more than 1MΩ, you will generally be interested in car-

bon film resistors. Metal film resistors with very large resistances require thefilm to be extremely thin, due to the higher conductivity of metal (typicallyaluminium).Beyond about 10MΩ resistors become problematic. One reason for this is

that surface conductivity around the package itself becomes significant, andthis is also influenced by ambient conditions such as humidity. More generally,for large values of resistance, the range of useful operating frequencies is con-siderably reduced, since the reactance of parasitic capacitance rapidly becomecomparable to the DC conductance of the resistor.


2.2 What are reasonable power and voltage ratings?

Resistors which can dissipate more than 1W of power are generally of the wirewound variety. That said, you could potentially use a combination of multiplefilm resistors to dissipate a small number of watts. Carbon film resistors arecommonly available with 0.5W and 1W power ratings, while metal film resistorsare typically rated at 14W or 12W — smaller metal film resistors with a 1

8W ratingcan also be obtained.The above information relates to average power handling. In practice, the

power dissipated by a resistor in a circuit will almost certainly be time varying.By and large, the average power dissipation is what counts, with averages takenover, say 0.1 seconds. If you need to be able to handle larger power surges forperiods of a second or more, you may need to de-rate the resistor (i.e., select aresistor with a larger power rating). This is particularly true for film resistors,where the film can be easily vaporized during short term power surges, even ifthe temperature of the entire package remains within safe limits. Wire woundand resistive pellet resistors have much more thermal inertial than film resistors,allowing them to better withstand short term power surges.Voltage ratings are often overlooked for resistors. Primarily, the voltage

rating depends upon the separation between the leads. Longer resistors canwithstand larger voltages, just because the electric field strength is proportionalto the ratio between voltage and distance. Many small resistors (e.g., 0.25Wand 0.5W film resistors) are only rated for around 250V to 350V, which couldbe a limitation in some circuits.

2.3 What are the preferred nominal values and manufac-turing tolerances?

Commonly available resistance values are governed by standard logarithmic se-ries of the form

R = rn−1, n ∈ ZHere, r = 101/k is the common ratio (logarithmic step size) between availableresistance values, where k is a small positive integer which indicates the numberof distinct values available in each decade. The actual resistance values R,given by this formula, are generally rounded to 2 significant digits. Thus, theE3 series, has k = 3 values per decade, with the following pattern:

· · · , 1Ω, 2.2Ω, 4.7Ω, 10Ω, 22Ω, 47Ω, 100Ω, · · ·The most common series for resistors are the E12 and E24 series, with valuesas follows:

· · · 1 1.2 1.5 1.8 2.2 2.7 3.3 3.94.7 5.6 6.8 8.2 10 12 15 18 · · ·

and· · · 1 1.1 1.2 1.3 1.5 1.6 1.8 2.02.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.75.1 5.6 6.2 6.8 7.5 8.2 9.1 10 · · ·


R Ls

Cp

R Ls

Cp

Figure 1: Simple model of a resistor R with parasitics Ls and Cp .

Wire wound resistors typically have tolerances of ±5% (sometimes evenworse), meaning that the actual value of any particular resistor that you pur-chase from a manufacturer is only guaranteed to be within ±5% of the quotednominal value. The effect of temperature changes and time may produce largerdeviations from the nominal values. Carbon film resistors also typically havea tolerance of ±5%. For greater precision, metal film resistors are preferred,with typical tolerances of ±1%. Laser trimming of individual metal film resis-tors can bring the precision to within ±0.01%, if required for special purposeapplications.

2.4 What is the effect of temperature and time?

Over time, carbon-based resistors suffer from a susceptibility to water absorp-tion. This can increase the resistance by as much as 5 to 10%. Water absorptionis minimized by conformal coatings, but these cannot completely stop the ingressof water vapour.The resistance of all materials is sensitive to temperature. In some applica-

tions, this can be useful, forming the basis of a temperature sensing mechanism.In most cases, though, it is a nuisance. The effect is non-linear, but a linearapproximation can be useful over a temperature range of some 10’s of degreescentigrade. The linear relation is expressed through a temperature coefficient,specified in ppm/C (parts-per-million / degree). A temperature coefficient of 5means that the resistance increases by 0.0005% when the temperature increasesby 1C. As a general rule, carbon-based resistors have negative temperaturecoefficients, while metal resistors have positive temperature coefficients.

2.5 What happens at extreme frequencies?

Figure 1 shows the common high frequency model for a resistor, with para-sitic inductance and capacitance. The inductance in wire wound resistors canbe significantly larger than in film resistors, for obvious reasons. The maincontribution to inductance in film resistors comes from the leads themselves,suggesting that you should cut your leads as short as possible. The capacitancein wire wound resistors is mostly formed between the turns. In film resistors,capacitance is formed by the presence of electrical contacts separated by a di-electric material (the core); it is generally smaller than 1pF.


It is worth remembering that parasitic inductance and capacitance do notcome as lumped elements, as suggested by the figure. Instead, the resistor isbetter modeled as a cascade of numerous resistive elements, each with their ownseparate series inductance and parallel capacitance. In the limit as the numberof resistive elements goes to infinity, we obtain a true model for the device, withdistributed inductance and capacitance (essentially a transmission line model),but this is too complex to work with in most practical applications.At high frequencies, the parasitic capacitance tends to reduce impedance,

while parasitic inductance tends to increase impedance. In film capacitors,the overall effect is usually a decrease in impedance with increasing frequency,as capacitance dominates. In wire wound devices, the presence of significantinductance usually leads to impedance increasing with frequency.

2.6 What happens with very small signals?

At very small signal levels, noise becomes a problem. In wireless communicationapplications, noise in the receiving electronics is the dominating effect whichlimits communication distance. Resistors are key elements in any electroniccircuit, used to establish bias currents, sense current, establish voltage ratios,and so forth. Together, resistors and capacitors are also the key building blocksfor most analog filter circuits, except at very high frequencies where the addedexpense of inductors can be justified.Carbon-based resistors have the worst noise performance. There are two

reasons for this: 1) voltage transients are created as electrons “jump” acrossimperfections in the carbon lattice; and 2) the interface between metal leads andthe carbon film or pellet creates a potential barrier to electron flow. The noiseprocess in carbon-based resistors largely follows a Poisson distribution (alsocalled “shot noise”) and can be particularly noticeable at very low frequenciesand low currents.Metal-film and wire wound resistors generally have the best noise behaviour,

being susceptible only to thermal noise due to Brownian motion of the electronsin the conductor.

3 Questioning CapacitorsCapacitors are the most economical and most reliable electronic componentswhich can store energy. Energy in a capacitor is stored in the electric field.By contrast, inductors store energy in a magnetic field, while batteries useelectrochemical processes to store energy. The relationship between current andvoltage in a capacitor is given by

I = CdV

dt

where C is the capacitance, measured in Farads (amp-seconds/volt). At a fun-damental level, the voltage which appears across a capacitor is a linear function


of the amount of charge separation Q, across its terminals. Specifically,

V =Q

C

and the current flowing in the capacitor is equal to the time-rate of change ofcharge, i.e.,

I =dQ

dt.

The energy in the capacitor can be obtained by integrating I (t)V (t) withrespect to time, yielding

E (t1)−E (t0) =

Z t1

t0

CV (t)dV

dtdt =

1

2C¡V 2 (t1)− V 2 (t0)

¢.

A more intuitive approach is to recognize that the amount of energy required tocarry a small charge dQ across a potential difference V is equal to V · dQ, fromwhich we conclude that the energy stored in a capacitor with applied voltage Vmust be

E =

ZV · dQ =

ZQ

C· dQ = 1

2

Q2

C=1

2CV 2

Based on these fundamental relations, we can conclude that:

1. Capacitors store and release energy — ideal capacitors do not lose (dissi-pate) any energy in the process.

2. The voltage across a capacitor cannot change discontinuously — that is,capacitors “smooth” voltage.

3. Capacitors integrate current over time — this is because they accumulatecharge and charge on a capacitor is proportional to voltage.

Capacitors are fundamental building blocks for filters, power supply regulationand circuits which integrate or average signals. There are three main types ofinterest:

Ceramic chip capacitors: These are formed from small chips of ceramic ma-terial with a high dielectric constant. They are relatively inexpensive andoffer the smallest levels of parasitic inductance, providing good behaviourup to very high frequencies, into the GHz range.

Film capacitors: These are typically constructed from a thin film of poly-ester or polystyrene, with aluminium electrodes plated on each side. Thefilm capacitor is then wrapped up into a small package. This processallows for very large plate surface areas within a small package, leadingto relatively large capacitances within a given volume, despite the factthat the dielectric material typically has a much lower dielectric constant(e.g., ˜2.6 for polystyrene) than the dielectric used for ceramic capacitors.


Unfortunately, coiling the film up into a small package tends to producesignificant parasitic inductance, so that film capacitors are less useful athigher frequencies. Film capacitors tend to be somewhat more expensivethan ceramic capacitors. The most well-known example is the so-called“green-cap,”, which has become something of a universal name for in-expensive polyester film capacitors, even though many of them are nowcoloured red rather than green. Polystyrene and other materials tend tobe more expensive, but offer superior manufacturing tolerances.

Electrolytic capacitors: The dielectric material in this case consists of anelectrolytically formed oxide of the anode material, which also serves asthe positive electrode of the capacitor1. The most commonly employedmetals are aluminium and tantalum. Since the oxide is formed by elec-trolysis, it can also be destroyed if a sufficient reverse voltage is applied.For this reason, electrolytic capacitors are polarized. One terminal willbe marked as the +ve terminal and the other as the −ve terminal, andyou must be careful not to allow significant reverse voltages to appearacross the capacitor. Destruction of the oxide layer will cause the insu-lation between the plates to disappear. Electrolytic capacitors can havevery large capacitances for a given volume, mainly because the oxide layercan be made very thin. At the same time, a thin dielectric can easilybe punctured by the appearance of significant voltages across the capaci-tor plates. Larger aluminium can-style electrolytics are commonly used inpower supply regulation applications to smooth the supply voltage. Thesecontain a coiled capacitive foil and typically exhibit large levels of parasiticinductance. Smaller tantalum electrolytics can have respectable levels ofcapacitance without the need for coiling, by virtue of the high dielectricconstant of tantalum oxide. These also play a key role in power supply reg-ulation, suppressing higher frequency voltage transients on power supplylines.

3.1 What are reasonable parameter values?

Ceramic capacitors are generally used in the range 1pF to 10nF, although largerceramic capacitors of 0.1µF and above can also be readily obtained.Polyester and polystyrene film capacitors are generally found in the range

1nF to 1µF. Larger values, ranging up to about 10µF, can also be obtained,although they tend to be very bulky.Tantalum electrolytics are typically manufactured with capacitances in the

range 0.1µF to 100µF, while aluminium foil electrolytics are readily obtainablewith capacitances in the tens of millifarads. It is possible to find aluminiumelectrolytics with capacitances as large as 1 Farad.

1Oxides of many conductors are insulators, and hence can serve as dielectrics.


3.2 What are reasonable voltage ratings?

Small ceramics typically have voltage ratings on the order of about 50V, mainlydue to their small physical size. High voltage ceramics can be obtained, however,with voltage ratings in excess of 1000V.In film capacitors, the breakdown voltage depends on the thickness of the

film. For film capacitors, the breakdown voltage depends on two things: 1) thethickness and dielectric strength of the film itself; and 2) the physical size of thecomponent. In small polyester film capacitors (green-caps), the voltage ratingis typically around 100V due to their small physical size. In larger green-caps,the breakdown strength of the film itself dominates the voltage rating, whichis typically around 600V. More expensive polystyrene film capacitors can havesomewhat larger voltage ratings of about 1000V.By contrast with the foregoing types, electrolytic capacitors often have quite

low voltage ratings. The reason for this is the thickness of the oxide layer whichis used as a dielectric. Very thin oxides allow for large capacitances, sincecapacitance is inversely proportional to the separation between the conductingelectrodes. At the same time, thin oxides can be punctured by comparativelylow voltages. Physically small electrolytics with large capacitance values maybe rated for only 16V or even less2. You must pay very close attention to thiswhen selecting components!

3.3 What are the preferred nominal values and manufac-turing tolerances?

It is generally more difficult to control capacitance than resistance during manu-facture. The reason for this is that most capacitors involve the use of thin layersof dielectric material. The dielectric constants of some materials are difficultto control, while the thickness of very thin dielectric films is also difficult tocontrol. Compounding this problem is the fact that the capacitance varies withthe reciprocal of the dielectric thickness3.Due to these difficulties, capacitors tend to have larger tolerances than re-

sistors. For small ceramic capacitors, ±10% is typical. Larger ceramics (i.e.,those in the 10’s or 100’s of nanofarads) may have tolerances of ±20% or evenmuch worse (e.g., −20%/ + 80%). Such capacitors are useful only in crudesmoothing applications, such as power supply regulation. The thin oxide filmsin electrolytic capacitors also renders them particularly hard to control duringmanufacture, with tolerances of ±20% or worse. Polyester film capacitors (i.e.,green-caps) also have relatively poor tolerances, on the order of ±10%.Amongst this field of poor performers, you may be wondering how you can

design a circuit which calls for accurate capacitances. One way to do thisis to use some of the more expensive film capacitors, such as those based on

2Very large capacitors, with capacitances on the order of 1F, may have voltage ratings aslow as a few volts!

3 Some thought should convince you that the average value of reciprocal thickness is muchmore susceptible to local variations than the average thickness itself.


polystyrene rather than polyester. Polystyrene capacitors can have tolerancesof less than ±1%. The other possibility is to stick with low valued capacitors(picofarads), based on stable materials with small dielectric constants (e.g.,glass).As a consequence of the poor repeatability of most capacitor manufacturing

processes, there is little value in offering a large set of nominal values. Preferrednominal capacitor values tend to be obtained by sub-sampling the E12 series.One of the most common patterns, for example, is

· · · 1 2.2 3.3 4.7 10 22 · · ·

Even though this pattern provides 4 values per decade, its elements do notcorrespond to the standard E4 series.

3.4 What is the effect of temperature and time?

Electrolytic capacitors tend to be most sensitive to changes in temperature.The temperature stability of aluminium oxide, as a dielectric, is particularlypoor, with virtually all capacitance being lost at temperatures below −55C.Tantalum oxide is better in this regard. By contrast, film capacitors can haveexcellent temperature stability and ceramic capacitors can also be manufacturedwith a well-defined temperature coefficient.Electrolytic capacitors also have poor stability over time. In some cases,

reliable operation may be guaranteed only for a few thousand hours of use.

3.5 What happens at extreme frequencies?

A simple parasitic model for capacitors is shown in Figure 2. In this model, se-ries resistance Rs and inductance Ls arise primarily from the leads and plates.This can be rendered extremely small in solid core capacitors, such as ceram-ics and small tantalums. Both parameters become much larger in film andfoil electrolytics, where capacitive foils with large area are coiled up into smallpackages. Rs and Ls (in particular) are responsible for limiting the usabilityof capacitors at high frequencies. This is quite simply because the parasiticimpedance (Rs + jωLs) becomes large in comparison to 1

jωC when ω = 2πFbecomes large. As a result, ceramic capacitors have far better performance athigh frequencies than film capacitors or electrolytics.The parallel resistance term Rp in Figure 2 models dielectric leakage. In

an ideal capacitor, no real current actually flows between the capacitor plates.Instead, charge is pumped from one plate to the other via the rest of the circuit4 .The fact that the dielectric material is not a perfect insulator, and small currentscan also flow around the surface of the package, is modelled by Rp. The valueof Rp determines the lowest frequencies at which at capacitor can be reliably

4Whatever your intuition might tell you, charge does not actually flow between the capaci-tor plates in an ideal capacitor — it flows around the rest of the circuit to move from one plateto the other.


Ls CRs

Rp

Ls CRs

Rp

Figure 2: Simple model of a capacitor C with parasitics Rs , Ls and Rp .

employed. This is particularly important for applications in which currents mustbe integrated over extended periods of time. Some of the best capacitors in thisregard are the film capacitors, with typical insulation resistances on the orderof 1010Ω. Ceramic capacitors do not hold their charge so well, with insulationresistances on the order of 108Ω to 109Ω. By far the worst performers, however,are electrolytics. Their extremely thin oxide dielectric layers yield insulationresistances which are typically < 1 MΩ.

3.6 What happens at small signal levels?

Capacitors can exhibit a hysteresis effect, as follows. After applying a significantvoltage to the capacitor and quickly discharging it through a short circuit, asmall voltage may appear across the capacitor’s terminals after the short circuitis removed. This effect adds an unpredictable offset to the voltage predicted fromtheory, which can have a big impact on small signals. Consider, for example,an application which integrates current across a capacitor, starting from a shortcircuit at time t = 0. In this case, you find that

V (t) = Vhysteresis +1

C

Z t

0

I (t) dt,

where Vhysteresis depends in a complex way upon the prior history of the capac-itor.Electrolytic capacitors are particularly offenders in regard to hysteresis, al-

though other materials with high dielectric constants can also exhibit the phe-nomenon. Hysteresis, together with low insulation resistance and poor para-meter tolerances, renders electrolytics a very poor choice for analog integrationapplications. By far the capacitor of choice for such applications is a film capac-itor5 — ideally polystyrene or polycarbonate films, which can be manufacturedto high precision.

5Recall that the dielectric in film capacitors typically has quite a small dielectric constantand very high insulation resistance.


4 What about Inductors and Transforms?Inductors store energy in a magnetic field. Whereas capacitors limit the rate ofchange of voltage, inductors limit the rate of change of current, according to

V = LdI

dt

The inductance L, is roughly proportional to N2, where N is the number ofwiring turns used to construct the inductor. In order for the current in an in-ductor to change rapidly, a large voltage must appear across it. This propertymakes inductors useful in smoothing out the otherwise discontinuous load cur-rents presented by electronic power supplies. As energy storage devices, bothcapacitors and inductors are useful in the construction of filters. In fact, theonly way to build non-trivial passive filters (filters which require no amplifyingelements) is to use both capacitors and inductors.Unfortunately, inductors are more difficult and expensive to manufacture

than capacitors. Moreover, inductors tend to occupy more space and producemore unwanted electromagnetic interference than capacitors. Very small induc-tors can be constructed with an air core, but this leads to appreciable levelsof electromagnetic radiation. Larger inductances can be constructed in smallpackages only with the aid of cores (or formers) of high magnetic permeability,such as iron or ferrite. The use of such cores also reduces electromagnetic radia-tion, particularly in a toroidal configuration. Unfortunately, though, the use ofmaterials with high permeability also introduces some unfortunate side-effects,such as eddy-current loss and magnetic hysteresis.Eddy currents are currents which circulate in a conducting core (particularly

iron cores) due to the induced EMF produced by the magnetic field6. Theseare the dominant source of high frequency power loss in inductors and trans-formers. These power losses are equivalent to an effective frequency-dependentresistance; they adversely impacts the degree of tuning which can be achievedin filters amongst other things. Magnetic hysteresis is a phenomenon observedparticularly in iron cores, but also to a lesser extent with ferrite. The effectarises when a strong current leaves the core magnetised in one direction evenafter the current goes to 0. This effect produces a non-linear relationship be-tween magnetic flux and current, which leads to power losses and non-linearities.Hysteresis and resistance in the windings themselves are the dominant sourcesof power loss at low frequencies.For all of the reasons given above, where it is feasible to use active amplifying

elements (e.g., opamps), filter designs are generally based solely upon capacitorsas energy storage (memory) elements. Only at very high frequencies, or in verylow noise applications, does it become important to consider inductors as wellas capacitors in the design of an analog filter.

6Eddy currents also circulate within the cross-section of the actual conductors with whichthe transformer is wound — an effect which grows with the cross-sectional area of the conduc-tors.


L1 L2 2V1V

1I 2IM

L1 L2 2V1V

1I 2IM

Figure 3: Simplistic model of a two-winding transformer.

Transformers are formed by two or more magnetically coupled inductors, asshown in Figure 3. The behaviour of a 2 winding transformer may be modeledin terms of three quantities: the self-inductances, L1 and L2, of each winding;and the mutual inductance M , between the windings. In an ideal transformer,the mutual inductance is the geometric mean of the two self inductances. Moregenerally, we define the coupling coefficient of a real transformer by

κ =M√L1L2

,

where κ = ±1 for an ideal transformer and |κ| < 1 for all real transformers.Ignoring parasitic capacitance and resistance, as well as eddy current losses,magnetic hysteresis and other sources of non-linearity, the behaviour of a trans-former may be described byµ

V1V2

¶=

µL1 MM L2

¶µdI1dtdI2dt

¶From this relationship, we may deduce the following.

Open-circuit voltage: If I2 = 0, the secondary voltage V2 is given by

V open-circuit2 =

M

L1V1 = κ

rL2L1

V1

Similarly, if I1 = 0, the primary voltage V1 is given by

V open-circuit1 =

M

L2V2 = κ

rL1L2

V2

In the case of an ideal transformer, κ = ±1 andpL2/L1 is the turns ratioof the transformer, which then also gives the ratio between secondary andprimary voltages. This open-circuit view-point is most relevant to appli-cations in which the transformer is interpreted as a voltage transformer.


Short-circuit current: If V2 = 0, the short-circuit secondary current is givenby

I2 = −ML2

I1 = −κr

L1L2

I1

Similarly, if V1 = 0, the short-circuit primary current is given by

I1 = −ML1

I2 = −κr

L2L1

I2

This short-circuit view-point is most relevant to applications in which thetransformer is interpreted as a current transformer.

Based on the discussion so far, you should be able to form many usefulquestions to ask of real transformers. The first, and most obvious is the valueof the coupling coefficient, κ. This can be very close to 1 in toroidal coretransformers. Other questions of interest relate to the power handling capabilityof the transformer’s windings; the winding resistance (a major component ofpower loss); the range of frequencies over which eddy-current losses can beconsidered small; and the extent of hysteresis losses, particularly for iron coretransformers.

5 Questioning Electromechanical ComponentsElectromechanical components include switches, relays, potentiometers, plugsand sockets. In each case, conductors are brought into contact with one anotherby mechanical means. The most important questions for such devices are asfollows:

How many times can it operate before failure? Switches and relays caneventually fail due to metal fatigue, as the contacts are repeatedly openedand closed. Manufacturers may quote the number of operations which canbe expected before such failure occurs. Potentiometers have much greaterfailure rates, due to continual wearing of the resistive material as the wipercontact moves back and forth over it. Carbon-based potentiometers arethe cheapest, but fail much more quickly than their wire-wound counter-parts. Most of you will have experienced potentiometers (e.g., volumeknobs) which have become damaged by excessive use.

What is the typical contact resistance? When metal conductors comeinto contact, the conductivity at the contact itself tends to be much lowerthan that of the solid conductor. One reason for this is that only a smallportion of the conductor surfaces are actually in contact, at a microscopiclevel. Another reason for the appearance of significant contact resistanceis the presence of dirt, grease and oxide films on the conductor surfaces.Contact resistance reduces with applied contact pressure. On the otherhand, increased pressure puts additional mechanical strain on the moving


conductors, which accelerates wear. To minimize contact resistance, plugs,sockets and relay contacts are sometimes plated with gold, being the bestknown conductor. Of course, this adds to the cost of manufacture.

How much current can it handle? Current handling in switches, relays,plugs and sockets is mainly limited by contact resistance. The flow ofcurrent generates heat at the junction between the conducting contacts.While this heat might not be felt externally, it accelerates the rate at whichthe contact surfaces oxidize (burn). This causes further deterioration inthe contact resistance, leading to greater levels of heating, and eventuallydevice failure. Many electromechanical components provide gold-platedcontacts. Not only does this reduce the contact resistance, but it alsoresists oxidation. Current in potentiometers is usually limited by the po-tentiometer’s own resistance, but contact resistance can also be importanthere, particularly when the wiper is moved to one extreme or the other.

How much voltage can it withstand when the contacts are open?This question is mainly relevant to relays and switches. Basically, thefurther apart the contacts can be brought, the higher the voltage that canbe withstood. There is, however, a more subtle problem with switchesand relays. If a large voltage appears across the contacts when they firststart to open, their separation may be small enough for the air gap toionize, i.e., for arcing to occur. Once established, the electric arc canbe maintained even as the contacts are brought further apart. Thiscauses rapid oxidation (or even evaporation) of the contact surfaces andpresents a variety of additional electrical problems. In order to avoid thisphenomenon, three things can be done: 1) the maximum open-circuitvoltage appearing across the contacts can be limited to below the pointat which significant arcing is possible; 2) the voltage can be preventedfrom rising very rapidly while the contacts are in the process of opening7;and 3) the formation of an electric arc may be prevented by blasting gasbetween the contacts while they open. This last, most drastic, method isused for large circuit breakers in the power industry, where an explosiveblast of nitrogen gas is employed to evacuate ionized molecules.

How rapidly can it operate? This question applies only to relays.

What is the contact bounce time? ***

6 Questioning Diodes and TransistorsThe basic building blocks of active circuits are diodes, bipolar junction tran-sistors (BJT’s) and field effect transistors (FET’s and MOSFET’s). Diodes,being the simplest, have relatively few parameters of interest. BJT’s, being

7This is done by placing a capacitor across the contacts, and also ensuring that the contactsopen quickly.


constructed from two diode junctions, inherit many of their parameters fromdiodes, although current gain and collector-emitter saturation are additionalparameters of interest. FET’s and MOSFET’s have quite a different principleof operation, however. Nevertheless, the same basic questions apply to semi-conductor devices as passive devices such as resistors, capacitors and inductors.Again, you need to ask yourself:

What are reasonable parameter values? e.g., reasonable current gain,reasonable channel resistance, etc.

What are the important ratings? e.g., max junction current, max powerdissipation, max reverse breakdown voltage, etc.

How accurate are the nominal values? e.g., variation in HFE (BJT cur-rent gain), variation in forward voltage drop, impact of temperature, etc.

What happens at extreme frequencies? e.g., how fast can my diode turnon; how fast can it turn on; at what frequency does the effective gain froma BJT drop below 1, etc.

What happens with very small signals? Primarily, this is a matter ofnoise performance.

Rather than trying to cover everything here, we consider only a selection ofthe most important parameters in the following sub-sections.

6.1 Diodes

Diodes are characterized principally by their forward voltage drop, reverse leak-age current, reverse breakdown voltage, maximum forward current, and switch-ing speed.The forward voltage drop VF is approximately 0.6V for small signal silicon

diodes carrying a few milliamps. The voltage drop in silicon power diodes tendsto be a little larger, approaching 1V, but this is at much higher current levels.Remember that the current through a diode junction satisfies

IF = I0

³eVFkT − 1

´where I0 is a characteristic current, determined by the device’s construction,k = 8.617385 × 10−5 eVK−1 is Boltzmann’s constant and T is the absolutetemperature, measured in degrees Kelvin. At voltages below 0.5V, essentiallyno current flows. Thereafter, each increment of 0.1V in the value of VF causesthe current IB to be multiplied by a factor of about 50 at room temperature(300 K). The above equation also tells us very precisely how the forward voltagedrop varies with temperature. At higher temperatures, VF decreases.Light emitting diodes (LED’s) formed from silicon emit light in the infra-red

region of the spectrum, with a typical forward voltage of around 1V. In order toemit visible light, materials with a larger band-gap are required. Accordingly,


Vout

RC

GND

+

-

UnregulatedPowerSupply

IC

IE

IB

Rload

RB

5v6Zener

Vout

RC

GND

+

-

UnregulatedPowerSupply

IC

IE

IB

Rload

RB

5v6Zener

Figure 4: Zener diode used to implement a simple voltage regulator.

red LED’s have a forward voltage drop of around 2V, green LED’s have largerVF and blue LED’s have voltage drops of around 3.5V. These differences areimportant if you are designing resistive networks to control the current in anLED. White LED’s, incidentally, are actually blue with a built-in fluorescentcoating to convert some of the high energy photons into lower energy, longerwavelength photons.When reverse biased, diodes act as good insulators, but they are not perfect.

Some reverse leakage current will flow, particularly in power diodes. You willfind the reverse leakage characteristics quoted in comprehensive data sheets.When the reverse voltage across a diode exceeds some threshold VRmax,

the reverse leakage current rises rapidly, leading to breakdown; this is usuallydestructive. One important exception to this occurs in Zener diodes. In theforward direction, Zeners conduct current, exhibiting a voltage drop on the or-der of 0.6V like other silicon diodes. Unlike regular diodes, however, Zeners aredesigned to allow current flow in the reverse direction in a non-destructive way.Zener diodes are designed to provide a stable, well-defined reverse breakdownvoltage. In the simple voltage regulator example of Figure 4, this reverse break-down voltage is 5.6V — a common Zener diode voltage. So long as current flowsin the diode, the voltage across the diode will be roughly constant. This is trueso long as you don’t exceed the Zener diode’s maximum power rating. LargerZener diodes can dissipate 1W of power, while smaller devices might not be ableto dissipate more than 1

8W.All diodes have a maximum forward current ImaxF , beyond which internal

heating in the diode junction may destroy the device. For small signal diodes,IF max might be on the order of 100mA. For power diodes, it may range anywherefrom 1A and up.Another parameter of interest to us is the switching speed. Once a diode


is forward biased, it takes some small amount of time before a forward currentflows. Similarly, once the voltage falls below VF, it takes some time before thediode “switches off,” ceasing to conduct current. These “switch on” and “switchoff” times can be quite different, with the transition to off taking longer thanthat to the on state. The time taken for a diode to transition from the on stateto the off state is known as the “reverse recovery time,” trr ; it is a parameterthat you will find specifically quoted for special types of fast diodes. During thistime, the diode actually conducts a significant current in the reverse direction;this is the current required to clear charge away from the junction.With respect to noise, Zener diodes are the worst offenders. When operated

in the usual reverse biased configuration, as in Figure 4, quite large noise cur-rents can appear. This is a shot-noise process, for which the RMS noise currentis proportional to the square root of the DC current level. The relative contri-bution of noise to the current flowing in resistor RB in Figure 4 is thus inverselyproportional to the square root of the DC current. This means that the noisevoltage at the base of the transistor in Figure 4 can be decreased by increasingthe current flowing through the Zener. In practice, some capacitive smoothingis also generally required.

6.2 Bipolar Junction Transistors (BJT’s)

BJT’s are formed from two diode junctions, with the base in the middle. Ac-cordingly, BJT’s inherit many of their important properties from diodes. Thebase-collector junction is almost never forward biased, so we are normally con-cerned only with its reverse breakdown voltage — this is identified as V max

CB .The base-emitter junction has a maximum forward current ImaxB , and a reversebreakdown voltage, which are both of interest in practical circuits. Other ratingsof interest are the maximum collector current ImaxC , the collector-emitter break-down voltage V max

CE , and the maximum power Pmax which can be dissipated bythe transistor. The major source of power dissipation in a transistor is due tothe collector current flowing across the collector-emitter potential, yielding

P = IC · VCESmall signal transistors typically have ImaxC values of one or two hundred

milliamps, with Pmax usually less than 1W. Power transistors can handle muchlarger currents and dissipate a lot of power. Be particularly careful, however,when interpreting the value of Pmax quoted in data sheets. This value normallycorresponds to the maximum power which can be dissipated when the transis-tor is bolted to a large, highly efficient heatsink. It effectively represents themaximum rate at which heat can be carried away from the transistor junctionthrough the case of the transistor, when the case is held at a constant low tem-perature. In practice, you may destroy the transistor at much lower power levelswhen operating with a small heatsink, or no heatsink at all.One of the most important properties of a BJT is its current gain, β (also


known as the HFE), defined by

β =ICIB

Small signal transistors typically have β (HFE) values in the range 50 to 1000,whereas the gain in power transistors can be considerably smaller. The currentgain is not actually completely linear, so that β is weakly dependent on thecollector current. The value of β is also very difficult to control during manu-facture. It is not uncommon to measure two different transistors of the sametype, from the same manufacturer, with β values differing by more than a fac-tor of 2. For this reason, a more important parameter for design is usually theminimum value, βmin.As with all components, transistors suffer from parasitics which limit their

maximum useful operating frequency. In the case of BJT’s, the worst offendersare the base-emitter and base-collector junction capacitances. These divertcurrent from the base-emitter junction at high frequencies, reducing the effectivecurrent gain of the device. The frequency response of a BJT is commonly quotedin terms of the frequency at which the effective current gain goes to 1. Thisfrequency is known as fT.Another important BJT property is the saturation voltage, reported as V sat

CE .This is the smallest voltage drop which can appear across the collector and emit-ter terminals when the transistor is driven hard on (i.e., with a significant basecurrent). Current amplification ceases once this limit is reached. In saturation,most transistors’ collectors can be brought below the voltage of the base, withtypical V sat

CE values in the range 0.2V to 0.5V.As with diodes, transistor switching times are important to some appli-

cations. There is a fundamental difference between frequency response andswitching speed. Frequency response is measured in the linear region, where thetransistor is not saturated. Switching, however, is concerned with the amountof time required for the transistor to enter and subsequently leave the saturatedcondition. The longer of the two times is the “switch off” time, which mea-sures the time taken for the collector voltage to rise substantially beyond V sat

CEonce it has been in saturation. High speed digital circuits incorporate specialsub-circuits to “yank” transistors out of saturation.

6.3 Field Effect Transistors

In field effect transistors, charge flows from the source to the drain throughmaterial which is either all N-type or all P-type. In an N-channel FET, thetype of charge which flows is negative (electrons), so the drain must be at ahigher voltage than the source. For P-channel FET’s, the type of charge whichflows is positive (holes), so the drain must be at a lower potential than thesource. The channel behaves like a resistance, whose value is determined by thegate-source voltage. There are two fundamental types of FET’s as follows:

Junction FET’s: In JFET’s, the gate-source junction is a reverse-biased P-Njunction. The greater the degree of reverse bias, the more the channel is


cut off, reducing the flow of current. It is important that the P-N junctiondoes not become forward biased, or else it will conduct. For N-channelJFET’s, this means that the gate-source voltage VGS should be no greaterthan 0; remember that VDS > 0 for the N-channel case, so the requirementthat VGS ≤ 0 means that the gate has the lowest potential of all threeterminals. This can be a bit awkward for some circuit configurations. ForP-channel JFET’s things are the other way around, with the gate havingthe highest potential of all three terminals. When VGS = 0 the channel isfully open, with minimum resistance.

Insulated Gate FET’s: IGFET’s are normally made by forming a silicondioxide layer as the insulator between a metal gate and the channel. Thisleads to the name Metal-Oxide-Semiconductor FET (MOSFET). Eventhough gate currents in JFET’s tend to be very small, due to the pres-ence of a reverse biased P-N junction, they are much smaller again inMOSFET’s due to the insulation layer. Also MOSFET’s tend to be moreconvenient to drive, since VGS may take both positive and negative val-ues. In the case of an N-channel MOSFET, positive VGS values causethe channel current to increase; depending on the device, negative gate-source voltages might further reduce channel resistance, increasing currentin the channel. Normally, however, N-channel MOSFET’s are operated byVGS ≥ 0, so that the gate voltage lies between that of the source and thedrain. P-channel MOSFET’s are normally operated with VGS ≤ 0, so thatthe gate voltage again lies between that of the source and the drain.

FET’s are not so commonly found as individual transistors, except in highpower applications. Mostly, you find them in packaged integrated circuits, wherethe operating parameters of interest are those of the overall IC. Nevertheless,a few things are worth pointing out here. Firstly, the channel “ON” resistanceis important. The smaller this is, the more current can be passed throughthe channel to quickly charge or discharge capacitive loads. Gate breakdownvoltages are also important to know if you don’t want to destroy the device.MOSFET devices are particularly sensitive to puncturing of the oxide layer whensignificant voltages are applied. The extremely high gate-channel resistance(usually greater than 1012Ω) makes this particularly problematic around sourcesof static electricity. For this reason, anti-static precautions should be taken whenhandling MOSFET devices. The other important device rating is its maximumpower dissipation.

7 Questioning OpampsMost opamps act as very high gain voltage to voltage amplifiers, with gainsK of 106 or more. The exact value of K is usually not well defined and mayvary significantly from batch to batch within the same manufacturing process.However, we use this high gain operational amplifier to construct amplifyingcircuits whose gain is well defined, regardless of the actual value of K, so long


V+

VCC

VEE

V-

VOopampV+

VCC

VEE

V-

VOopamp

Figure 5: Typical opamp connections.

as K is very large. The opamp has two input voltages V+ and V−; ideally, theoutput voltage VO is proportional only to the difference between V+ and V−.That is,

VO = K · (V+ − V−) (1)

Even this ideal equation raises an interesting question: What is the referencevoltage against which VO is to be measured? It does not matter what we pick forour input reference voltage, since only the difference V+− V− is important. Wetend naturally to think of VO as being measured with respect to the referenceground potential. However, most opamps do not provide a separate groundterminal. Instead, they offer only a negative and a positive voltage supplyrail, normally identified as VCC and VEE, as shown in Figure 5. Fortunately,the answer to this question is not important, because the V+ and V− inputscannot be perfectly matched in real opamps. This leads to the appearance ofan unpredictable input voltage offset Voff , with

VO = K · (V+ − V− + Voff)

= K · (V+ − V−) +K · VoffThe large gainK, rendersK·Voff so large that questions of the reference potentialfor VO become insignificant. For example, if K = 106 (a modest value) andVoff ≈ 1mV (an optimistic value), K · Voff already introduces an uncertainty onthe order of 1000V in the output voltage!Before plunging further into a discussion of opamp non-idealities, it is help-

ful to consider an elementary application. Specifically, consider the invertingamplifier circuit shown in Figure 6. To understand the behaviour of this circuit,we assume that no current flows into or out of the opamp’s input terminals.Then all of the current I in resistor RO must flow in RN, meaning that

V− − VinRN

=VO − V−

RO(2)

Noting also that the V+ = 0 (grounded), we have

VO = K (V+ − V− + Voff) = KVoff −KV−


V+VCC

GND

+

-

Two-SidedPowerSupply

+

-VEE

V-opamp

RN

RO

Vin

VOI

V+VCC

GND

+

-

Two-SidedPowerSupply

+

-VEE

V-opamp

RN

RO

Vin

VOI

Figure 6: Simple opamp-based inverting amplifier.

Substituting V− = Voff − VO/K into equation (2), we obtain

−VinRN

=VO − V−

RO− V−

RN

=VORO

+

µVOK− Voff

¶µ1

RO+

1

RN

¶=

VORO

·µ1 +

1

K+

ROKRN

¶− Voff

µ1

RO+

1

RN

¶(3)

For very large K, assuming Voff = 0, this simplifies to

VinRN≈ − VO

RO(4)

or

VO ≈ −VinRORN

(5)

What is actually going on is this. If V− becomes even slightly negative, theopamp’s huge gain serves to produce a large output voltage VO, which pullsV− back up again via RO. Similarly, if V− becomes even slightly positive, VOfalls below ground and pulls V− back down again. This is called “negativefeedback.” Systems which have negative feedback reach a stable equilibrium.In this case, the negative feedback causes V− to remain extremely close to theground potential all the time.Armed with the observation that the presence of negative feedback keeps

V− ≈ V+, we analyze opamp circuits to first order precision by simply assumingthat V− = V+. To summarize, our ideal model of the opamp has just twoproperties:

Property 1: Input currents I+ and I− may be safely taken to be 0; and

Property 2: Input voltages V− and V+ may be safely taken to be identical.


These two properties are sufficient to derive equation (4) much more simply. Inparticular, the current flowing from V− to Vin must be −Vin/RN and this mustbe identical to the current flowing from VO to V- , which must be VO/RO.Although we have considered only the simple case of an inverting amplifier,

the two simplifying properties given above are central to the analysis and designof all opamp circuits, at least in the first instance. As part of the design process,however, we must be prepared to consider how our circuit will be impacted bythe non-idealities of real opamps. These are considered in the following sub-sections.

7.1 Input offset voltage

Ideally, VO = 0 when V+ = V−. In practice, however, this condition is reachedwhen V+ − V− = −Voff . The significance of Voff to the behaviour of our opampcircuit needs to be considered separately in each case. In the case of the invertingamplifier, equation (3) tells us that Voff behaves roughly as an additive offsetto the amplifier’s input voltage Vin — to see this, note that for an amplifierwith significant gain, RO À RN. In most opamps, Voff is on the order ofmillivolts. The value of Voff can vary from device to device and with temperatureand other conditions. The presence of non-zero Voff is important if you wantprecise amplification of very small signals. This problem arises in measurementapplications and also when amplifying the signals produced by certain types ofsensors. For these applications, you may require a precision opamp. Precisionopamps are designed to have offset voltages in the 10’s of microvolts; they alsousually come with additional pins to which you can attach an offset trimmingcircuit.

7.2 Finite open-loop gain, K

Ideally, the open-loop gain K is infinite. Property 2, above, holds only if Kis infinite, Voff = 0 and the circuit configuration involves negative feedback.Considering the equation (3) more carefully, however, we see that it is reasonableto ignore the actual value of K only if it is much greater than RN/RO, whichis the magnitude of the gain of our inverting amplifier. A similar result holdsfor other amplifier configurations. As already mentioned, the open-loop gain Kin practical opamps is typically in excess of 106. However, this is the DC gain.At higher frequencies, the gain progressively rolls off. The way in which thishappens is different for each opamp. In the simplest case, K rolls off as 1/f (i.e.,20 dB/decade); in this case, the frequency-dependence of K can be expressedthrough a Gain-Bandwidth Product (GBWP), from which you can calculate

K (f) = min

½GBWP

f,K0

¾where K0 is the DC open-loop gain. Both K0 and GBWP will be quotedon manufacturers’ data sheets. For more exotic opamps, with complex pole-zero arrangements designed to extend the useful operating frequency as far as


possible, you should be able to find plots of K (f) versus frequency f , in themanufacturers’ data sheets.

7.3 Phase margin

This parameter is easily overlooked by novice designers. In particular, it is easyto forget that the transfer function from the opamp’s input terminals to itsoutput involves delay. This delay means that feedback in your opamp circuitis not instantaneous. Delayed feedback can lead to ringing and, eventually,oscillation in your circuit. Oscillation will occur if the loop gain in a feedbackcircuit is greater than 1 at any frequency for which the feedback path involvesa total phase change of 0. Of particular interest is the buffer configurationshown in Figure ??. In this case, we expect VO = Vin due to the presence ofnegative feedback. The loop gain in this configuration is exactly equal to K,since the opamp’s output is fed back without attenuation to its input. At DC,the feedback path involves a total phase change of π (negative feedback). Thus,for oscillation to occur, there must be some frequency f, such that

K (f) > 1 and φ (f) = −π,

where φ (f) is the phase change associated with internal delay in the opamp.Invariable, φ (f) is a continuous function of frequency, which starts at φ (0) = 0.We are thus interested in the minimum value of φ (f) over all frequencies forwhichK (f) > 1. This is essentially what the phase margin tells us. Specifically,the phase margin is equal to φ (f) + π at the unity gain frequency f — i.e., atthe frequency for which K (f) = 1.If the phase margin is less than 0, the buffer configuration in Figure ?? is

unstable and will oscillate. The larger the phase margin, the easier it is to buildopamp circuits which are stable. Stability becomes particularly uncertain ifyour feedback path involves its own delay, or additional gain. Inserting anotheropamp into the feedback path, for example, often produces instability.

7.4 Input bias current

Property 1, above, states that the current flowing into or out of the opamp’sinput terminals is so small that we can ignore it. This is a very useful propertyfor opamp circuit design. Of course, though, some current always does flow. Inbipolar opamps (those based on BJT’s), the actual input currents are typicallyless than 1µA, but this might well be significant. These so-called input biascurrents have to flow somewhere, and it is quite common for novice designersto create circuits involving diodes or other components which actually providenowhere for the input bias currents to flow. Where the input terminals are con-nected to resistors, the input bias currents create voltage drops in the resistorswhich have essentially the same effect as an input offset voltage. In the exampleof Figure 6, the presence of an input bias current iB, in the inverting opampterminal, is equivalent to an offset in Vin of iB · RN. Evidently, circuits which


use large resistors will be more susceptible to the effects of input bias currentthan those which use small resistors.If input bias currents are problematic to your design, you should consider

using an opamp which has FET or MOSFET input transistors. These havetruly negligible input bias currents, although their high frequency performanceis usually less desirable, due to the presence of significant input capacitance.

7.5 Supply voltage and output saturation voltages

Many opamps do not operate well with small values of the supply voltage,VCC − VEE. In particular, if you want to run your opamp from a 5V supply,or even a 9V supply, you may need to carefully select the component based ondata sheets.By and large bipolar opamps cannot pull VO too close to the rail voltages.

One reason for this is the residual saturation voltages associated with the outputdrive transistors. The drive circuitry in many bipolar opamps actually requiresone or two extra base-emitter forward voltage drops to sit between VO and oneor both rail voltages. The humble LM741 opamp, for example, loses a coupleof volts at each rail. This is particularly problematic if you need to operate atlow supply voltages. Suppose, for example that VCC − VEE = 7V. The outputvoltage might only be able to swing between 2V and 5V, limiting the rangeof linear amplification to only 3V at the output. This requires careful circuitdesign to ensure that all signals of interest sit within this narrow voltage range.In single-ended supply applications, VEE is normally interpreted as 0V and

takes on special significance as a reference level. This is particularly problem-atic if the opamp is unable to drive VO all the way to VEE. Opamps whichare specially designed to allow this are known as single supply opamps. Theseare normally constructed using CMOS (Complementary MOSFET) technology,since FET’s provide a controlled resistive channel with no saturation voltage.

7.6 Input voltage range

We would not normally expect equation (1) to hold unless VEE < V+, V− < VCC.Interestingly, though, some opamps can function correctly even when the inputvoltages lie slightly above VCC or slightly below VEE, depending on the internaldesign. Single supply opamps are designed in such a way as to ensure that theusable range of input voltages includes VEE. All of this information may begleaned from data sheets.

7.7 Common mode rejection ratio

Common mode rejection refers to the ability of the opamp to ignore the absolutevalues of V+ and V−, amplifying only the difference V+ − V−. The commonmode gain of the opamp is the amount by which changes in the absolute valueof V+ = V− are amplified in the output VO. That is, setting V+ = V− = VC,the common mode gain is KC = ∆VO/∆VC. A figure of merit for opamps is the


common mode rejection ratio, defined as K/KC. This value is typically verylarge, so it is quoted in dB. Many opamps have common mode rejection ratios(CMRR) in excess of 100 dB.

7.8 Output slew rate

Output slew rate is the maximum rate at which VO can change, expressed involts/µs. Slew rate is a different physical property to frequency response. Toillustrate this point, suppose we use an opamp to amplify a sine wave, ideallyproducing an output voltage of the form

VO = A cos 2πft

The maximum slew rate which is required to achieve this is given by¯dVOdt

¯max

= |2πfA · sin 2πft|max = 2πfA

Clearly, the maximum slew rate is dependent upon the frequency f , but it is alsodependent upon the magnitude of the output voltage, A. Frequency responsedepends only on f . Slew rate is most important for applications which requirethe output to be driven quickly between the rails — e.g., comparators (see below).Slew rate is limited by the opamp’s ability to source and sink current to and

from capacitive loads. For this reason, slew rate must be quoted in combinationwith an assumed load capacitance. In some cases, this might just be the compo-nent’s own parasitic load capacitance. If you double this capacitance by addingyour own output load, you should expect the maximum slew rate to halve.

7.9 Opamps and comparators

Many of you may find the need for a comparator in your Elec3017 design project.One way to compare two voltage levels is to apply them to the inputs of anopamp, without any feedback whatsoever. The large opamp gain then ensuresthat VO will swing to its maximum value if V+ > V− and its minimum value ifV+ < V−. A comparator is nothing other than a special purpose opamp, whichis designed to be used in this way, without feedback. As with any opamp, youneed to consider such non-idealities as input voltage offset, input bias currentand common mode rejection. Comparators are normally designed to operate atdigital supply voltages (e.g., 5V) and provide digital output voltage levels forease of interfacing with digital logic gates. Apart from these specifics, though,they are just opamps.

8 Questioning Digital IC’sConsidering the vast array of complex digital IC’s, including mixed ana-log/digital IC’s, there are only a small number of generic things which can


be said here about the behaviour of real components. For everything else, youwill need to get into the habit of consulting manufacturers’ data sheets. Thecommon things to look out for are as follows:

Supply voltage range: Many digital IC’s are designed to operate correctlyover quite a narrow range of supply voltages, unlike many purely analogcomponents. The standard operating voltage for digital IC’s is VCC = 5V,with an allowable variation of perhaps ±0.25V. These days, there existsa proliferation of devices designed for low power operation at even lowervoltages, with 3V and 2.5V being common. Providing highly stable powersupplies for these devices can be something of a challenge, considering thelarge instantaneous current demands associated with high speed digitalswitching.

Input voltage range: Digital devices define two thresholds V maxlow < V min

high ,such that all voltages less than V max

low will be correctly treated as low levelinputs and all voltages greater than V min

high will be correctly treated as highlevel inputs. Input voltages between these two thresholds may produceunexpected behaviour. When mixing logic families, or driving digital de-vices from analog circuitry, you need to pay particular attention to thesethresholds. Another parameter of relevance is the range of input voltagesover which the component can be operated safely. For example, TTLlogic devices can be safely operated at input voltages in the range −0.5Vto VCC +0.5V. Members of the TTL family with Schottky input circuitryalso contain clamping diodes, which can hold input levels within thesesafe limits so long as not too much current is involved. Driving a highervoltage opamp’s output directly into one of these devices, however, couldeasily damage it. More generally, when interfacing digital inputs to analogcircuitry, you need to include sufficient voltage clamping and/or currentlimiting to ensure that the digital input circuitry will not be damaged.This is generally done with the aid of diodes and resistors. Damage maynot manifest itself immediately, so that your prototype operates success-fully, but the customer’s product malfunctions after some period of use.

Input and output currents: An important property of digital circuits istheir ability to drive multiple outputs from a single input. This is re-lated to the current sourcing (or sinking) capability of the outputs, whichis required to charge/discharge capacitive loads, as well as supplying thequiescent current needs of other inputs. MOSFET devices have extremelysmall input currents, so quiescent load is not a problem. MOSFET inputsdo, however, have significant capacitance so that driving multiple inputsfrom a single output slows everything down. The term “fan-out” is usedto describe the maximum number of digital inputs which a single outputis designed to drive, while satisfying timing specifications.

It is worth noting that the current which a digital output can source inthe high state is not generally the same as the current which it can sink


in the low state, due to the use of different transistor types to pull theoutput up and down.

It is also important to know whether or not it is acceptable to leave inputsunconnected. For TTL devices, unconnected inputs generally attain a highstate, but this is not very reliable and can be highly susceptible to noise onthe supply line. Nevertheless, if the state of an input pin is unimportant,you can leave it disconnected. For MOSFET devices, inputs should notgenerally be left unconnected, unless the data sheets say otherwise, dueto the risk of damage from static electricity.

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