Chapter6 electronic-components

Elec3017:
Electrical Engineering Design
Chapter 6: Electronic Components
A/Prof D. S. Taubman
August 16, 2006

1 Purpose of this Chapter
Considering the dizzying array of electronic components which exist, we cannot
hope to cover them all in this chapter (or even an entire course). Instead, the
focus of this chapter is to get you into the habit of asking the right questions
about components. It also helps to know something about the materials used
in components and the associated construction methods, since these should give
you some idea of the weaknesses to watch out for. This is particularly true for
simple 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 of
what is readily available and what is difficult to achieve. For example,
commonly available capacitors typically have capacitances in the range 1
picofarad through to several millifarads — a 1F capacitor is huge!
What are reasonable ratings? Ratings define the limits over which you can
reliably operate the component — beyond these, the component may be
destroyed. Maximum ratings apply to such parameters as voltage, power
and current. If the power dissipation is too large, the component will
get too hot. If the applied voltage is too large, dielectric breakdown may
result — this usually means irreversible damage. If the current passing
through a semiconductor junction is too large, the internal junction may
be permanently destroyed.
What nominal values are available? This is a matter of knowing what
parts you can actually get. For digital IC’s, this includes questions such

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°Taubman, 2006 ELEC3017: Electronic Components Page 2

as “What are the available nominal speed ranges?” For resistors and ca-
pacitors, the question is “What nominal resistance values can be easily
purchased?”
How accurate are the nominal parameter values? This question is con-
cerned with precision. The actual measured parameter values for any
specific 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 temperature
and time. How significant is this?
What happens at extreme frequencies? Here we are interested in the im-
pact of parasitic components (typically, parasitic capacitance, inductance
and resistance) which limit the range of frequencies over which the elec-
tronic component behaves in a predictable manner. Parasitics often cannot
be precisely controlled during manufacture, so that their presence is best
understood as limiting the range of operating frequencies over which the
behaviour can be predicted reliably.
What happens with very small signals? When signal levels are very
small, 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 term
memory effect, exhibited by certain types of materials.

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

2 Questioning Resistors
Nominally, 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 passing
through 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 very
good approximation. Depending on the context, you may find it convenient to
think of resistors as converting current into voltage or voltage into current. In
either case, heat is produced with power

P = V · I = V 2 /R = I 2 R

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

Wire wound resistors: Wire is wound around a non-conductive core (also
called a former) so that a large length of wire can be accommodated in
a relatively small package. To minimize inductance, the wire is normally
wound in both directions — e.g., clockwise along the former and then anti-
clockwise back again. Since wire wound resistors are made from solid metal
wire they tend to have good power handling properties. On the other
hand, 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 those
made from carbon film deposited on a non-conductive core. Metal film re-
sistors are also widely available; they offer superior precision for a slightly
higher price.
Carbon composite resistors: These consist of a solid pellet of resistive ma-
terial (typically carbon) bonded to the external metallic leads. They have
superior power handling capacity to film resistors, where the film can be
rapidly vaporized by short term power surges — this is particularly true
for metallic film resistors.

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

2.1 What are reasonable parameter values?
For resistance of less than 1Ω, you will generally be looking at wire wound
varieties, where values down to 0.1Ω can be sourced. Such low resistors are
normally used only in very high current applications, such as power amplifiers.
For resistances of more than 1M Ω, you will generally be interested in car-
bon film resistors. Metal film resistors with very large resistances require the
film to be extremely thin, due to the higher conductivity of metal (typically
aluminium).
Beyond about 10M Ω resistors become problematic. One reason for this is
that surface conductivity around the package itself becomes significant, and
this 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 become
comparable to the DC conductance of the resistor.

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2.2 What are reasonable power and voltage ratings?
Resistors which can dissipate more than 1W of power are generally of the wire
wound variety. That said, you could potentially use a combination of multiple
film resistors to dissipate a small number of watts. Carbon film resistors are
commonly available with 0.5W and 1W power ratings, while metal film resistors
are typically rated at 1 W or 1 W — smaller metal film resistors with a 1 W rating
4 2 8
can 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 taken
over, say 0.1 seconds. If you need to be able to handle larger power surges for
periods of a second or more, you may need to de-rate the resistor (i.e., select a
resistor 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 if
the temperature of the entire package remains within safe limits. Wire wound
and 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 can
withstand larger voltages, just because the electric field strength is proportional
to the ratio between voltage and distance. Many small resistors (e.g., 0.25W
and 0.5W film resistors) are only rated for around 250V to 350V, which could
be 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 ∈ Z
Here, r = 101/k is the common ratio (logarithmic step size) between available
resistance values, where k is a small positive integer which indicates the number
of distinct values available in each decade. The actual resistance values R,
given by this formula, are generally rounded to 2 significant digits. Thus, the
E3 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 values
as follows:
··· 1 1.2 1.5 1.8 2.2 2.7 3.3 3.9
4.7 5.6 6.8 8.2 10 12 15 18 · · ·
and
··· 1 1.1 1.2 1.3 1.5 1.6 1.8 2.0
2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7
5.1 5.6 6.2 6.8 7.5 8.2 9.1 10 · · ·

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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 even
worse), 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 quoted
nominal value. The effect of temperature changes and time may produce larger
deviations from the nominal values. Carbon film resistors also typically have
a 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 purpose
applications.

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 absorption
is minimized by conformal coatings, but these cannot completely stop the ingress
of 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 linear
approximation can be useful over a temperature range of some 10’s of degrees
centigrade. The linear relation is expressed through a temperature coefficient,
specified in ppm/◦ C (parts-per-million / degree). A temperature coefficient of 5
means that the resistance increases by 0.0005% when the temperature increases
by 1◦ C. As a general rule, carbon-based resistors have negative temperature
coefficients, 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 can
be significantly larger than in film resistors, for obvious reasons. The main
contribution to inductance in film resistors comes from the leads themselves,
suggesting that you should cut your leads as short as possible. The capacitance
in 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.

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It is worth remembering that parasitic inductance and capacitance do not
come as lumped elements, as suggested by the figure. Instead, the resistor is
better modeled as a cascade of numerous resistive elements, each with their own
separate series inductance and parallel capacitance. In the limit as the number
of resistive elements goes to infinity, we obtain a true model for the device, with
distributed 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 significant
inductance 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 communication
applications, noise in the receiving electronics is the dominating effect which
limits communication distance. Resistors are key elements in any electronic
circuit, used to establish bias currents, sense current, establish voltage ratios,
and so forth. Together, resistors and capacitors are also the key building blocks
for most analog filter circuits, except at very high frequencies where the added
expense 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” across
imperfections in the carbon lattice; and 2) the interface between metal leads and
the carbon film or pellet creates a potential barrier to electron flow. The noise
process in carbon-based resistors largely follows a Poisson distribution (also
called “shot noise”) and can be particularly noticeable at very low frequencies
and 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 electrons
in the conductor.

3 Questioning Capacitors
Capacitors are the most economical and most reliable electronic components
which can store energy. Energy in a capacitor is stored in the electric field.
By contrast, inductors store energy in a magnetic field, while batteries use
electrochemical processes to store energy. The relationship between current and
voltage in a capacitor is given by
dV
I =C
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

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of the amount of charge separation Q, across its terminals. Specifically,
Q
V =
C
and the current flowing in the capacitor is equal to the time-rate of change of
charge, i.e.,
dQ
I= .
dt
The energy in the capacitor can be obtained by integrating I (t) V (t) with
respect to time, yielding
Z t1
dV 1 ¡ ¢
E (t1 ) − E (t0 ) = CV (t) dt = C V 2 (t1 ) − V 2 (t0 ) .
t0 dt 2

A more intuitive approach is to recognize that the amount of energy required to
carry a small charge dQ across a potential difference V is equal to V · dQ, from
which we conclude that the energy stored in a capacitor with applied voltage V
must be Z Z
Q 1 Q2 1
E = V · dQ = · dQ = = CV 2
C 2 C 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 accumulate
charge and charge on a capacitor is proportional to voltage.

Capacitors are fundamental building blocks for filters, power supply regulation
and circuits which integrate or average signals. There are three main types of
interest:

Ceramic chip capacitors: These are formed from small chips of ceramic ma-
terial with a high dielectric constant. They are relatively inexpensive and
offer the smallest levels of parasitic inductance, providing good behaviour
up 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. The
film capacitor is then wrapped up into a small package. This process
allows for very large plate surface areas within a small package, leading
to relatively large capacitances within a given volume, despite the fact
that the dielectric material typically has a much lower dielectric constant
(e.g., ˜2.6 for polystyrene) than the dielectric used for ceramic capacitors.

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Unfortunately, coiling the film up into a small package tends to produce
significant parasitic inductance, so that film capacitors are less useful at
higher frequencies. Film capacitors tend to be somewhat more expensive
than 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 now
coloured red rather than green. Polystyrene and other materials tend to
be more expensive, but offer superior manufacturing tolerances.
Electrolytic capacitors: The dielectric material in this case consists of an
electrolytically formed oxide of the anode material, which also serves as
the positive electrode of the capacitor1 . The most commonly employed
metals 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 will
be marked as the +ve terminal and the other as the −ve terminal, and
you must be careful not to allow significant reverse voltages to appear
across the capacitor. Destruction of the oxide layer will cause the insu-
lation between the plates to disappear. Electrolytic capacitors can have
very large capacitances for a given volume, mainly because the oxide layer
can be made very thin. At the same time, a thin dielectric can easily
be punctured by the appearance of significant voltages across the capaci-
tor plates. Larger aluminium can-style electrolytics are commonly used in
power supply regulation applications to smooth the supply voltage. These
contain a coiled capacitive foil and typically exhibit large levels of parasitic
inductance. Smaller tantalum electrolytics can have respectable levels of
capacitance without the need for coiling, by virtue of the high dielectric
constant of tantalum oxide. These also play a key role in power supply reg-
ulation, suppressing higher frequency voltage transients on power supply
lines.

3.1 What are reasonable parameter values?
Ceramic capacitors are generally used in the range 1pF to 10nF, although larger
ceramic 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 obtainable
with capacitances in the tens of millifarads. It is possible to find aluminium
electrolytics with capacitances as large as 1 Farad.
1 Oxides of many conductors are insulators, and hence can serve as dielectrics.

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3.2 What are reasonable voltage ratings?
Small ceramics typically have voltage ratings on the order of about 50V, mainly
due 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) the
thickness and dielectric strength of the film itself; and 2) the physical size of the
component. In small polyester film capacitors (green-caps), the voltage rating
is typically around 100V due to their small physical size. In larger green-caps,
the breakdown strength of the film itself dominates the voltage rating, which
is typically around 600V. More expensive polystyrene film capacitors can have
somewhat 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 which
is used as a dielectric. Very thin oxides allow for large capacitances, since
capacitance is inversely proportional to the separation between the conducting
electrodes. At the same time, thin oxides can be punctured by comparatively
low voltages. Physically small electrolytics with large capacitance values may
be rated for only 16V or even less2 . You must pay very close attention to this
when 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 layers
of dielectric material. The dielectric constants of some materials are difficult
to control, while the thickness of very thin dielectric films is also difficult to
control. Compounding this problem is the fact that the capacitance varies with
the 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 even
much worse (e.g., −20%/ + 80%). Such capacitors are useful only in crude
smoothing applications, such as power supply regulation. The thin oxide films
in electrolytic capacitors also renders them particularly hard to control during
manufacture, 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 this
is to use some of the more expensive film capacitors, such as those based on
2 Very large capacitors, with capacitances on the order of 1F, may have voltage ratings as

low as a few volts!
3 Some thought should convince you that the average value of reciprocal thickness is much

more susceptible to local variations than the average thickness itself.

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polystyrene rather than polyester. Polystyrene capacitors can have tolerances
of 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. Preferred
nominal 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 not
correspond 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 particularly
poor, with virtually all capacitance being lost at temperatures below −55◦ C.
Tantalum oxide is better in this regard. By contrast, film capacitors can have
excellent temperature stability and ceramic capacitors can also be manufactured
with 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 and
foil electrolytics, where capacitive foils with large area are coiled up into small
packages. Rs and Ls (in particular) are responsible for limiting the usability
of capacitors at high frequencies. This is quite simply because the parasitic
1
impedance (Rs + jωLs ) becomes large in comparison to jωC when ω = 2πF
becomes large. As a result, ceramic capacitors have far better performance at
high 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 currents
can also flow around the surface of the package, is modelled by Rp . The value
of Rp determines the lowest frequencies at which at capacitor can be reliably
4 Whatever 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 plate
to the other.

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Rs Ls C

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 must
be integrated over extended periods of time. Some of the best capacitors in this
regard are the film capacitors, with typical insulation resistances on the order
of 1010 Ω. Ceramic capacitors do not hold their charge so well, with insulation
resistances on the order of 108 Ω to 109 Ω. By far the worst performers, however,
are electrolytics. Their extremely thin oxide dielectric layers yield insulation
resistances which are typically < 1 MΩ.

3.6 What happens at small signal levels?
Capacitors can exhibit a hysteresis effect, as follows. After applying a significant
voltage to the capacitor and quickly discharging it through a short circuit, a
small voltage may appear across the capacitor’s terminals after the short circuit
is removed. This effect adds an unpredictable offset to the voltage predicted from
theory, which can have a big impact on small signals. Consider, for example,
an application which integrates current across a capacitor, starting from a short
circuit at time t = 0. In this case, you find that
Z
1 t
V (t) = Vhysteresis + I (t) dt,
C 0

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 integration
applications. By far the capacitor of choice for such applications is a film capac-
itor5 — ideally polystyrene or polycarbonate films, which can be manufactured
to high precision.
5 Recall that the dielectric in film capacitors typically has quite a small dielectric constant

and very high insulation resistance.

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4 What about Inductors and Transforms?
Inductors store energy in a magnetic field. Whereas capacitors limit the rate of
change of voltage, inductors limit the rate of change of current, according to
dI
V =L
dt
The inductance L, is roughly proportional to N 2 , where N is the number of
wiring 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 property
makes inductors useful in smoothing out the otherwise discontinuous load cur-
rents presented by electronic power supplies. As energy storage devices, both
capacitors and inductors are useful in the construction of filters. In fact, the
only way to build non-trivial passive filters (filters which require no amplifying
elements) 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 produce
more unwanted electromagnetic interference than capacitors. Very small induc-
tors can be constructed with an air core, but this leads to appreciable levels
of electromagnetic radiation. Larger inductances can be constructed in small
packages 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 of
materials 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 . These
are the dominant source of high frequency power loss in inductors and trans-
formers. These power losses are equivalent to an effective frequency-dependent
resistance; they adversely impacts the degree of tuning which can be achieved
in filters amongst other things. Magnetic hysteresis is a phenomenon observed
particularly in iron cores, but also to a lesser extent with ferrite. The effect
arises when a strong current leaves the core magnetised in one direction even
after 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 sources
of 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 capacitors
as energy storage (memory) elements. Only at very high frequencies, or in very
low noise applications, does it become important to consider inductors as well
as capacitors in the design of an analog filter.
6 Eddy currents also circulate within the cross-section of the actual conductors with which

the transformer is wound — an effect which grows with the cross-sectional area of the conduc-
tors.

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I1 I2
M

V1 L1 L2 V2

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

Transformers are formed by two or more magnetically coupled inductors, as
shown in Figure 3. The behaviour of a 2 winding transformer may be modeled
in 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. More
generally, we deﬁne the coupling coeﬃcient of a real transformer by
M
κ= √ ,
L1 L2

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 by
µ ¶ µ ¶ µ dI1 ¶
V1 L1 M dt
= dI2
V2 M L2 dt

From this relationship, we may deduce the following.

Open-circuit voltage: If I2 = 0, the secondary voltage V2 is given by
r
op en-circuit M L2
V2 = V1 = κ V1
L1 L1
Similarly, if I1 = 0, the primary voltage V1 is given by
r
M L1
V1op en-circuit = V2 = κ V2
L2 L2
p
In the case of an ideal transformer, κ = ±1 and L2 /L1 is the turns ratio
of the transformer, which then also gives the ratio between secondary and
primary voltages. This open-circuit view-point is most relevant to appli-
cations in which the transformer is interpreted as a voltage transformer.

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Short-circuit current: If V2 = 0, the short-circuit secondary current is given
by r
M L1
I2 = − I1 = −κ I1
L2 L2
Similarly, if V1 = 0, the short-circuit primary current is given by
r
M L2
I1 = − I2 = −κ I2
L1 L1
This short-circuit view-point is most relevant to applications in which the
transformer is interpreted as a current transformer.

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

5 Questioning Electromechanical Components
Electromechanical components include switches, relays, potentiometers, plugs
and sockets. In each case, conductors are brought into contact with one another
by mechanical means. The most important questions for such devices are as
follows:

How many times can it operate before failure? Switches and relays can
eventually fail due to metal fatigue, as the contacts are repeatedly opened
and closed. Manufacturers may quote the number of operations which can
be expected before such failure occurs. Potentiometers have much greater
failure rates, due to continual wearing of the resistive material as the wiper
contact moves back and forth over it. Carbon-based potentiometers are
the cheapest, but fail much more quickly than their wire-wound counter-
parts. Most of you will have experienced potentiometers (e.g., volume
knobs) which have become damaged by excessive use.
What is the typical contact resistance? When metal conductors come
into contact, the conductivity at the contact itself tends to be much lower
than that of the solid conductor. One reason for this is that only a small
portion of the conductor surfaces are actually in contact, at a microscopic
level. Another reason for the appearance of significant contact resistance
is the presence of dirt, grease and oxide films on the conductor surfaces.
Contact resistance reduces with applied contact pressure. On the other
hand, increased pressure puts additional mechanical strain on the moving

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conductors, which accelerates wear. To minimize contact resistance, plugs,
sockets and relay contacts are sometimes plated with gold, being the best
known 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 of
current generates heat at the junction between the conducting contacts.
While this heat might not be felt externally, it accelerates the rate at which
the contact surfaces oxidize (burn). This causes further deterioration in
the contact resistance, leading to greater levels of heating, and eventually
device failure. Many electromechanical components provide gold-plated
contacts. Not only does this reduce the contact resistance, but it also
resists oxidation. Current in potentiometers is usually limited by the po-
tentiometer’s own resistance, but contact resistance can also be important
here, 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, the
further apart the contacts can be brought, the higher the voltage that can
be withstood. There is, however, a more subtle problem with switches
and relays. If a large voltage appears across the contacts when they first
start to open, their separation may be small enough for the air gap to
ionize, i.e., for arcing to occur. Once established, the electric arc can
be maintained even as the contacts are brought further apart. This
causes rapid oxidation (or even evaporation) of the contact surfaces and
presents a variety of additional electrical problems. In order to avoid this
phenomenon, three things can be done: 1) the maximum open-circuit
voltage appearing across the contacts can be limited to below the point
at which significant arcing is possible; 2) the voltage can be prevented
from 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 gas
between the contacts while they open. This last, most drastic, method is
used for large circuit breakers in the power industry, where an explosive
blast 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 Transistors
The 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
7 This is done by placing a capacitor across the contacts, and also ensuring that the contacts

open quickly.

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constructed from two diode junctions, inherit many of their parameters from
diodes, although current gain and collector-emitter saturation are additional
parameters of interest. FET’s and MOSFET’s have quite a different principle
of 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 power
dissipation, 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 turn
on; how fast can it turn on; at what frequency does the effective gain from
a BJT drop below 1, etc.
What happens with very small signals? Primarily, this is a matter of
noise performance.

Rather than trying to cover everything here, we consider only a selection of
the 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 tends
to be a little larger, approaching 1V, but this is at much higher current levels.
Remember that the current through a diode junction satisfies
³ VF ´
IF = I0 e kT − 1

where I0 is a characteristic current, determined by the device’s construction,
k = 8.617385 × 10−5 eV K−1 is Boltzmann’s constant and T is the absolute
temperature, measured in degrees Kelvin. At voltages below 0.5V, essentially
no current flows. Thereafter, each increment of 0.1V in the value of VF causes
the 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 voltage
drop 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 to
emit visible light, materials with a larger band-gap are required. Accordingly,

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RB RC

IC + Unregulated
IB
Power
5v6 Supply
Zener -
IE

Vout Rload
GND

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 larger
VF and blue LED’s have voltage drops of around 3.5V. These differences are
important if you are designing resistive networks to control the current in an
LED. White LED’s, incidentally, are actually blue with a built-in fluorescent
coating to convert some of the high energy photons into lower energy, longer
wavelength 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 will
find the reverse leakage characteristics quoted in comprehensive data sheets.
When the reverse voltage across a diode exceeds some threshold VR max ,
the reverse leakage current rises rapidly, leading to breakdown; this is usually
destructive. One important exception to this occurs in Zener diodes. In the
forward direction, Zeners conduct current, exhibiting a voltage drop on the or-
der of 0.6V like other silicon diodes. Unlike regular diodes, however, Zeners are
designed to allow current flow in the reverse direction in a non-destructive way.
Zener diodes are designed to provide a stable, well-defined reverse breakdown
voltage. 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 flows
in the diode, the voltage across the diode will be roughly constant. This is true
so long as you don’t exceed the Zener diode’s maximum power rating. Larger
Zener diodes can dissipate 1W of power, while smaller devices might not be able
to dissipate more than 1 W.
8
max
All diodes have a maximum forward current IF , 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 anywhere
from 1A and up.
Another parameter of interest to us is the switching speed. Once a diode

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is forward biased, it takes some small amount of time before a forward current
flows. Similarly, once the voltage falls below VF , it takes some time before the
diode “switches off,” ceasing to conduct current. These “switch on” and “switch
off” times can be quite different, with the transition to off taking longer than
that to the on state. The time taken for a diode to transition from the on state
to the off state is known as the “reverse recovery time,” trr ; it is a parameter
that you will find specifically quoted for special types of fast diodes. During this
time, 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 current
is 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 inversely
proportional to the square root of the DC current. This means that the noise
voltage at the base of the transistor in Figure 4 can be decreased by increasing
the current flowing through the Zener. In practice, some capacitive smoothing
is 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. The
base-collector junction is almost never forward biased, so we are normally con-
max
cerned only with its reverse breakdown voltage — this is identified as VCB .
max
The base-emitter junction has a maximum forward current IB , and a reverse
breakdown voltage, which are both of interest in practical circuits. Other ratings
max
of interest are the maximum collector current IC , the collector-emitter break-
max
down voltage VCE , and the maximum power Pmax which can be dissipated by
the transistor. The major source of power dissipation in a transistor is due to
the collector current flowing across the collector-emitter potential, yielding

P = IC · VCE
max
Small signal transistors typically have IC values of one or two hundred
milliamps, with Pmax usually less than 1W. Power transistors can handle much
larger currents and dissipate a lot of power. Be particularly careful, however,
when interpreting the value of Pmax quoted in data sheets. This value normally
corresponds to the maximum power which can be dissipated when the transis-
tor is bolted to a large, highly efficient heatsink. It effectively represents the
maximum rate at which heat can be carried away from the transistor junction
through 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 levels
when 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

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known as the HFE), defined by
IC
β=
IB
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 current
gain is not actually completely linear, so that β is weakly dependent on the
collector 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 same
type, 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 the
minimum value, β min .
As with all components, transistors suffer from parasitics which limit their
maximum useful operating frequency. In the case of BJT’s, the worst offenders
are the base-emitter and base-collector junction capacitances. These divert
current from the base-emitter junction at high frequencies, reducing the effective
current gain of the device. The frequency response of a BJT is commonly quoted
in terms of the frequency at which the effective current gain goes to 1. This
frequency is known as fT .
sat
Another important BJT property is the saturation voltage, reported as VCE .
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 base
current). Current amplification ceases once this limit is reached. In saturation,
most transistors’ collectors can be brought below the voltage of the base, with
sat
typical VCE 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 and
switching speed. Frequency response is measured in the linear region, where the
transistor is not saturated. Switching, however, is concerned with the amount
of time required for the transistor to enter and subsequently leave the saturated
condition. The longer of the two times is the “switch off” time, which mea-
sat
sures the time taken for the collector voltage to rise substantially beyond VCE
once it has been in saturation. High speed digital circuits incorporate special
sub-circuits to “yank” transistors out of saturation.

6.3 Field Effect Transistors
In field effect transistors, charge flows from the source to the drain through
material which is either all N-type or all P-type. In an N-channel FET, the
type of charge which flows is negative (electrons), so the drain must be at a
higher voltage than the source. For P-channel FET’s, the type of charge which
flows is positive (holes), so the drain must be at a lower potential than the
source. The channel behaves like a resistance, whose value is determined by the
gate-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-N
junction. The greater the degree of reverse bias, the more the channel is

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cut off, reducing the flow of current. It is important that the P-N junction
does not become forward biased, or else it will conduct. For N-channel
JFET’s, this means that the gate-source voltage VGS should be no greater
than 0; remember that VDS > 0 for the N-channel case, so the requirement
that VGS ≤ 0 means that the gate has the lowest potential of all three
terminals. This can be a bit awkward for some circuit configurations. For
P-channel JFET’s things are the other way around, with the gate having
the highest potential of all three terminals. When VGS = 0 the channel is
fully open, with minimum resistance.
Insulated Gate FET’s: IGFET’s are normally made by forming a silicon
dioxide layer as the insulator between a metal gate and the channel. This
leads to the name Metal-Oxide-Semiconductor FET (MOSFET). Even
though 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 in
MOSFET’s due to the insulation layer. Also MOSFET’s tend to be more
convenient to drive, since VGS may take both positive and negative val-
ues. In the case of an N-channel MOSFET, positive VGS values cause
the channel current to increase; depending on the device, negative gate-
source voltages might further reduce channel resistance, increasing current
in the channel. Normally, however, N-channel MOSFET’s are operated by
VGS ≥ 0, so that the gate voltage lies between that of the source and the
drain. P-channel MOSFET’s are normally operated with VGS ≤ 0, so that
the gate voltage again lies between that of the source and the drain.

FET’s are not so commonly found as individual transistors, except in high
power applications. Mostly, you find them in packaged integrated circuits, where
the operating parameters of interest are those of the overall IC. Nevertheless,
a few things are worth pointing out here. Firstly, the channel “ON” resistance
is important. The smaller this is, the more current can be passed through
the channel to quickly charge or discharge capacitive loads. Gate breakdown
voltages 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 when
significant voltages are applied. The extremely high gate-channel resistance
(usually greater than 1012 Ω) makes this particularly problematic around sources
of static electricity. For this reason, anti-static precautions should be taken when
handling MOSFET devices. The other important device rating is its maximum
power dissipation.

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

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VCC

V+
VO
opamp
V-

VEE

Figure 5: Typical opamp connections.

as K is very large. The opamp has two input voltages V+ and V− ; ideally, the
output 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 reference
voltage against which VO is to be measured? It does not matter what we pick for
our input reference voltage, since only the difference V+ − V− is important. We
tend naturally to think of VO as being measured with respect to the reference
ground potential. However, most opamps do not provide a separate ground
terminal. Instead, they offer only a negative and a positive voltage supply
rail, 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− inputs
cannot be perfectly matched in real opamps. This leads to the appearance of
an unpredictable input voltage offset Voff , with

VO = K · (V+ − V− + Voff )
= K · (V+ − V− ) + K · Voff

The large gain K, renders K·Voff so large that questions of the reference potential
for VO become insignificant. For example, if K = 106 (a modest value) and
Voff ≈ 1mV (an optimistic value), K · Voff already introduces an uncertainty on
the 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 inverting
amplifier 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− − Vin VO − V −
= (2)
RN RO
Noting also that the V+ = 0 (grounded), we have

VO = K (V+ − V− + Voff ) = KVoff − KV−

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VCC
V+
+ Two-Sided
opamp Power
V- Supply
RO VO
-
I
+
Vin RN
- GND
VEE

Figure 6: Simple opamp-based inverting amplifier.

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

Vin VO − V− V−
− = −
RN RO RN
µ ¶µ ¶
VO VO 1 1
= + − Voff +
RO K RO RN
µ ¶ µ ¶
VO 1 RO 1 1
= · 1+ + − Voff + (3)
RO K KRN RO RN

For very large K, assuming Voff = 0, this simplifies to
Vin VO
≈− (4)
RN RO
or
RO
VO ≈ −Vin (5)
RN
What is actually going on is this. If V− becomes even slightly negative, the
opamp’s huge gain serves to produce a large output voltage VO , which pulls
V− back up again via RO . Similarly, if V− becomes even slightly positive, VO
falls below ground and pulls V− back down again. This is called “negative
feedback.” Systems which have negative feedback reach a stable equilibrium.
In this case, the negative feedback causes V− to remain extremely close to the
ground 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 assuming
that V− = V+ . To summarize, our ideal model of the opamp has just two
properties:

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.

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These two properties are sufficient to derive equation (4) much more simply. In
particular, the current flowing from V− to Vin must be −Vin /RN and this must
be 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 design
of 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 by
the 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 reached
when V+ − V− = −Voff . The significance of Voff to the behaviour of our opamp
circuit needs to be considered separately in each case. In the case of the inverting
amplifier, equation (3) tells us that Voff behaves roughly as an additive offset
to the amplifier’s input voltage Vin — to see this, note that for an amplifier
with significant gain, RO À RN . In most opamps, Voff is on the order of
millivolts. The value of Voff can vary from device to device and with temperature
and other conditions. The presence of non-zero Voff is important if you want
precise amplification of very small signals. This problem arises in measurement
applications and also when amplifying the signals produced by certain types of
sensors. For these applications, you may require a precision opamp. Precision
opamps are designed to have offset voltages in the 10’s of microvolts; they also
usually come with additional pins to which you can attach an offset trimming
circuit.

7.2 Finite open-loop gain, K
Ideally, the open-loop gain K is infinite. Property 2, above, holds only if K
is infinite, Voff = 0 and the circuit configuration involves negative feedback.
Considering the equation (3) more carefully, however, we see that it is reasonable
to ignore the actual value of K only if it is much greater than RN /RO , which
is the magnitude of the gain of our inverting amplifier. A similar result holds
for other amplifier configurations. As already mentioned, the open-loop gain K
in 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 this
happens 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 expressed
through a Gain-Bandwidth Product (GBWP), from which you can calculate
½ ¾
GBWP
K (f ) = min , K0
f
where K0 is the DC open-loop gain. Both K0 and GBWP will be quoted
on manufacturers’ data sheets. For more exotic opamps, with complex pole-
zero arrangements designed to extend the useful operating frequency as far as

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

7.3 Phase margin
This parameter is easily overlooked by novice designers. In particular, it is easy
to forget that the transfer function from the opamp’s input terminals to its
output involves delay. This delay means that feedback in your opamp circuit
is not instantaneous. Delayed feedback can lead to ringing and, eventually,
oscillation in your circuit. Oscillation will occur if the loop gain in a feedback
circuit is greater than 1 at any frequency for which the feedback path involves
a total phase change of 0. Of particular interest is the buffer configuration
shown in Figure ??. In this case, we expect VO = Vin due to the presence of
negative 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 for
which K (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., at
the 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 build
opamp circuits which are stable. Stability becomes particularly uncertain if
your feedback path involves its own delay, or additional gain. Inserting another
opamp 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’s
input terminals is so small that we can ignore it. This is a very useful property
for opamp circuit design. Of course, though, some current always does flow. In
bipolar opamps (those based on BJT’s), the actual input currents are typically
less than 1µA, but this might well be significant. These so-called input bias
currents have to flow somewhere, and it is quite common for novice designers
to create circuits involving diodes or other components which actually provide
nowhere 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 resistors
which have essentially the same effect as an input offset voltage. In the example
of Figure 6, the presence of an input bias current iB , in the inverting opamp
terminal, is equivalent to an offset in Vin of iB · RN . Evidently, circuits which

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use large resistors will be more susceptible to the effects of input bias current
than 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 have
truly negligible input bias currents, although their high frequency performance
is 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 on
data 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 output
drive transistors. The drive circuitry in many bipolar opamps actually requires
one or two extra base-emitter forward voltage drops to sit between VO and one
or both rail voltages. The humble LM741 opamp, for example, loses a couple
of volts at each rail. This is particularly problematic if you need to operate at
low supply voltages. Suppose, for example that VCC − VEE = 7V. The output
voltage might only be able to swing between 2V and 5V, limiting the range
of linear amplification to only 3V at the output. This requires careful circuit
design 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 which
are specially designed to allow this are known as single supply opamps. These
are 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 input
voltages lie slightly above VCC or slightly below VEE , depending on the internal
design. Single supply opamps are designed in such a way as to ensure that the
usable range of input voltages includes VEE . All of this information may be
gleaned from data sheets.

7.7 Common mode rejection ratio
Common mode rejection refers to the ability of the opamp to ignore the absolute
values of V+ and V− , amplifying only the difference V+ − V− . The common
mode gain of the opamp is the amount by which changes in the absolute value
of 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

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common mode rejection ratio, defined as K/KC . This value is typically very
large, 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 in
volts/µs. Slew rate is a different physical property to frequency response. To
illustrate this point, suppose we use an opamp to amplify a sine wave, ideally
producing an output voltage of the form

VO = A cos 2πf t

The maximum slew rate which is required to achieve this is given by
¯ ¯
¯ dVO ¯
¯ ¯ = |2πf A · sin 2πf t|max = 2πf A
¯ dt ¯
max

Clearly, the maximum slew rate is dependent upon the frequency f , but it is also
dependent upon the magnitude of the output voltage, A. Frequency response
depends only on f . Slew rate is most important for applications which require
the 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 combination
with 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 adding
your 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 an
opamp, without any feedback whatsoever. The large opamp gain then ensures
that VO will swing to its maximum value if V+ > V− and its minimum value if
V+ < V− . A comparator is nothing other than a special purpose opamp, which
is designed to be used in this way, without feedback. As with any opamp, you
need to consider such non-idealities as input voltage offset, input bias current
and common mode rejection. Comparators are normally designed to operate at
digital supply voltages (e.g., 5V) and provide digital output voltage levels for
ease of interfacing with digital logic gates. Apart from these specifics, though,
they are just opamps.

8 Questioning Digital IC’s
Considering 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

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

Supply voltage range: Many digital IC’s are designed to operate correctly
over quite a narrow range of supply voltages, unlike many purely analog
components. The standard operating voltage for digital IC’s is VCC = 5V,
with an allowable variation of perhaps ±0.25V. These days, there exists
a proliferation of devices designed for low power operation at even lower
voltages, with 3V and 2.5V being common. Providing highly stable power
supplies for these devices can be something of a challenge, considering the
large instantaneous current demands associated with high speed digital
switching.
max min
Input voltage range: Digital devices define two thresholds Vlow < Vhigh ,
max
such that all voltages less than Vlow will be correctly treated as low level
min
inputs and all voltages greater than Vhigh will be correctly treated as high
level inputs. Input voltages between these two thresholds may produce
unexpected behaviour. When mixing logic families, or driving digital de-
vices from analog circuitry, you need to pay particular attention to these
thresholds. Another parameter of relevance is the range of input voltages
over which the component can be operated safely. For example, TTL
logic devices can be safely operated at input voltages in the range −0.5V
to VCC + 0.5V. Members of the TTL family with Schottky input circuitry
also contain clamping diodes, which can hold input levels within these
safe limits so long as not too much current is involved. Driving a higher
voltage opamp’s output directly into one of these devices, however, could
easily damage it. More generally, when interfacing digital inputs to analog
circuitry, you need to include sufficient voltage clamping and/or current
limiting to ensure that the digital input circuitry will not be damaged.
This is generally done with the aid of diodes and resistors. Damage may
not 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 is
their ability to drive multiple outputs from a single input. This is re-
lated to the current sourcing (or sinking) capability of the outputs, which
is required to charge/discharge capacitive loads, as well as supplying the
quiescent current needs of other inputs. MOSFET devices have extremely
small input currents, so quiescent load is not a problem. MOSFET inputs
do, however, have significant capacitance so that driving multiple inputs
from a single output slows everything down. The term “fan-out” is used
to describe the maximum number of digital inputs which a single output
is designed to drive, while satisfying timing specifications.
It is worth noting that the current which a digital output can source in
the high state is not generally the same as the current which it can sink

c

in the low state, due to the use of diﬀerent transistor types to pull the
output up and down.
It is also important to know whether or not it is acceptable to leave inputs
unconnected. For TTL devices, unconnected inputs generally attain a high
state, but this is not very reliable and can be highly susceptible to noise on
the supply line. Nevertheless, if the state of an input pin is unimportant,
you can leave it disconnected. For MOSFET devices, inputs should not
generally be left unconnected, unless the data sheets say otherwise, due
to the risk of damage from static electricity.

Chapter6 electronic-components

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