Analog Circuit Techniques with Digital Interfacing

318 Pages·2001·20.55 MB·English

by  T. H. Wilmshurst

viii
Preface
This text derives initially from the notes for the course on reading. Exceptions have been the material on MOS de-
Analog Electronics given to students taking the MSc vices and s-parameters where I am heavily indebted to the
courses in Electronics and Microelectronics in the De- specialist texts quoted. All chapters, however, have re-
partment of Electronics and Computer Science of the Uni- quired some degree of reference, with the texts quoted in
versity of Southampton. These are students normally with the Reference section.
a first degree in an allied subject such as Mathematics,
Physics or Electrical Engineering. As such, a feature is Acknowledgements
the coverage of a large amount of material in a relatively
Working now at home, I am most grateful for the help and
short space, hopefully good value for money!
patience of past colleagues whom I have repeatedly
With the material much the same as for the Analog
phoned at inconvenient moments for confirmation of vari-
component of the three-year undergraduate course in
ous points, in no particular order, Bill Redman-White
Electronic Engineering, the book has been expanded to
(oversampling ADC) Arthur Bnmnschweiler
suit this readership also, in particular Chapter 1 on Basic
(Microelectronics), David Stewart and Steve Braithwaite
Circuit Techniques.
(Communications), Bob Greef (Physical Chemistry), Ed
With some of the material given to research chemists
Zaluska (Digital Electronics), and my son Richard (Nortel
and to undergraduates taking the Physics-with-Electronics,
at Paignton, (Opto-Electronics).
and Chemistry-with-Electronics courses, the interests of
I also gratefully acknowledge the free three-month loan
the experimental scientist have also been covered.
of the full version of PSpice from MicroSim and the gen-
With all of the above courses including laboratory
erous gift of a complete copy of SpiceAge from Those
work, that given in the final exercises section of most
Engineers. With both used in Chapter 21, the earlier sub-
chapters is thoroughly 'road tested'.
section work was mainly with the freely available evalua-
All of the numeric calculations have been checked, by
tion version of PSpice, with the later 'whole system'
hand with the calculator, and by simple BASIC programs.
simulations with SpiceAge. For the two column format of
the book, it was convenient to Coreldraw hand trace both
Use as reference text
sets of graphs.
With the book intended for use in this mode as much as
for the above teaching support, careful attention has been Notation
given to indexing, and to the content of chapter, section,
Reference to all equations is by the use of square brackets.
and sub-section headings.
For example, for an equation in view
SPICE 'with I d as in 5.2 the first term is usually dominant',
The book is not a SPICE manual, but the audio power while for the equation not in view
amplifier in Chapter 21 provides an excellent example of
the use of this method of circuit simulation. 'with I d = Idsexp(qVd/kT ) - 1 as in 5.21
the first term is usually dominant'
Analog-to-digital conversion (ADC)
As the title implies, coverage includes examples of both --- means 'is approximately equal to' as usual
this and the complementary digital-to-analog converter - means 'is roughly equal to' from say xl/3 to x3.
(DAC). The now popular oversampling ADC and DAC
are included, with experimental exercises for each. ...and finally
Milne's 'bear of little brain' was fascinated to see that
Optoelectronics every time he dropped in a fir cone 'on the other side' it
With this subject of great current interest, the last chapter came out 'on this side'. This is the first approach to our
includes a brief coverage of the topic, with particular em- subject but some can't leave it at that, they want to know
phasis on the fibre-optic digital data link. how it works. This book is for them.
Winnie the Pooh's little book of wisdom, Methuen, 1999.
Source texts
My source of knowledge has mainly been lectures and
hands-on experience in the company of many experts in
the various areas of the subject, rather than from extensive
1
Basic circuit techniques
Summary The Laplace transform, a method for dealing with
waveforms that cannot be resolved into Fourier compo-
nents, is covered in Chapter 11.
This chapter introduces the passive components and basic
analytical tools that are used in the following chapters.
1.1 Resistor
The components are the resistor, capacitor, inductor and
transformer. Active components such as the bipolar tran-
sistor are covered later. For the resistor R in Fig. 1.1(a), the hydraulic (water)
For a text on analog circuit techniques, it is appropriate analog is as in ,)oC a section of pipe offering resistance to
to start with the familiar hydraulic analog of the flow of flow. With Io~V then by Ohm's law
current through a resistor in Fig. 1.1, and the possibly
I=V/R (I.I)
less familiar analogs of the capacitor, inductor and
resonator that follow. After this the basic network
With the 'conductance' G=I/R, these two relations need
theorems such as Th~venin and superposition are intro-
be taken as memorised, to avoid tedious repetition.
duced, extending to the method of nodal analysis, here for
resistor-only networks.
I
v(cid:127) R/ pmup
Reactive components
T
The trouble with the inductor and capacitor is that they
change the shape of an applied signal. For example, with
I=CdV/dt for the capacitor, and for the applied current I (a) (b)
constant then, instead of the resulting voltage V being
constant as for the resistor, for the capacitor V is a stead-
Fig. 1.1 Resistor connected to constant voltage supply.
ily rising ramp.
)a( Circuit diagram.
An important exception is the sine wave, for which dif-
)oC Water analog.
ferentiation or integration changes the phase and the am- Voltage V ~ pump pressure.
plitude but not the sinusoidal shape, making calculation of Current I ~ flow rate.
the circuit waveforms less difficult. The corresponding R ~:c pipe resistance.
techniques are known as AC theory, the sine wave being
an 'alternating current'. The unit of resistance is the ohm (s For the widely used
metal-film resistor, R typically ranges from lt2 to .2f701
As for normal practice, we use the notation in Table 1.1
Fourier analysis
to represent the various orders of ten. Here the range of
All periodic waveforms, dna some others, can eb resolved lf2 to 107f2 for the metal-trim resistor would be stated as
into sinusoidal components, by the method of Fourier from lf2 to 1OMQ.
analysis. The effect of the network on each of the input The convention applies equally to all other variables,
stnenopmoc nac then eb calculated, dna eht resulting tes of for example 3 x 102V is 30inV.
output components recombined to give the actual output The unit of conductance is the siemens (S), with
waveform. IS= 1/lf2, 1/lkf2= lmS, etc.
2 Analog circuit seuqinhcet
Preferred values where f is the frequency in hertz (Hz = cycles/see). This
relation is in constant use and so also needs be taken as
The 'preferred values' for manufactured components are
memorised.
logarithmically graded. For resistance R= 10, 15, 22, 33,
47, 68, and 100f~, then continuing, 150, 220, 330fl, etc.
RMS value
Here the increment is 10 6/I = 1.5. For higher precision
the increment is ,21/101 giving 10, 12, 15, 18, etc. This is a concept first encountered in the supply industry,
Values beyond the lf~ and 10Mf~ limits for the metal- where some areas were once supplied with 'direct
film resistor exist using other methods of manufacture. current' (DC) and others with AC. Here the requirement
was to state the supply voltage in a way that the power
Pico Nano Micro Milli delivered to a resistive load could be calculated from
lpn ln.Q Q.jII lmf~ P=Ve/R as in 1.2 regardless of the type of supply.
10-12~ 10-9~ 2f6-01 10-3~ With caV the peak value of the AC supply voltage caV
then the instantaneous power caP is only equal to R/cZaV at
Kilo Mega Giga
the peak of Vac. The mean power caP is less. Thus the
lk.O 1Mr1 ~fG1
10on 103~ 2f601 109~ value of caV quoted is Vac, that for which 1.2 does
apply, giving
Table 1.1 Symbolic representation of orders of ten, sa for caP =( caV ) 2/R
.ecnatsiser
With the instantaneous
caP = caV 2/R
Variable resistor
These are normally in the form of a resistive strip, with a then c--aV = ,R/c2aV
movable contact in addition to the two end contacts. The
strip is in the form of a nearly complete circle for front-
where c2aV is the 'mean square' value of Vac.
panel knob operation. For the preset 'trimmer', the strip
may be either circular or linear. The linear trimmer is
screw driven, giving more turns to cover the range than Thus raV = (1.6)
the circular device. Both are screwdriver operated.
the 'root-mean square' value of Vac.
Power With V = V sin(cot)
The resistor dissipates power P as heat. With P=IV then as in 1.4 then
p=V2/R (1.2) or P=I2R (1.3)
am V 2 = niSc2aV 2 (cot)= Va2c/2
The unit of power is the watt (W: James Watt). A manu- giving
factured resistor has a power rating, the maximum con-
tinuous power it is able to dissipate without overheating.
0.6W is typical for the commonly used metal-film resis-
With the stated 240V mains voltage the rms value Vac,
tor.
then the peak value caV =340V.
Sine wave
This is defmed as in Fig. 1.17. The vector of unit length Problem For the three-phase distribution system the
in (a) rotates at the angular frequency oc to trace phasors for the three 'lines' are spaced at 120 ~ inter-
sin(0)=sin(ox) on the vertical axis as in (b). The as- vals. Draw the resulting phasor diagram and thus show
sociated cos(ox) is traced on the horizontal axis. A vector that, for the stated 240V rms between line and
which rotates in this way is known as a 'phasor'. The sine 'neutral', the rms line-to-line voltage is 415V.
wave is the natural output of the rotating power alternator
giving
Noise fluctuation
V= V sin(cot) (1.4)
The rms value of 1.6 is a valid indicator of the power
where V is the peak value of V. With oc the frequency in transferred to the load for any time-varying voltage or
radians/sec then current that has a definable mean, in particular for the
(o=2/tf (1.5) random noise fluctuation of Chapter 17.
Basic circuit techniques 3
1.2 Capacitor V = V.sin(cot) (1.10)
Fig. 1.2(a) shows the capacitor C connected to a constant then I = Vtt~C.cos(tot) (1.11)
voltage supply. At its simplest, the capacitor is two metal
Thus for an applied AC voltage there is a proportional AC
plates separated by an insulator. Current cannot flow
current (a pump of alternating pressure will drive an al-
through it, but charge Qc, in the form of conducting elec-
ternating flow, as the membrane is alternately stretched in
trons, can be added to one plate and removed from the
one direction and the other). In short, a capacitor is a
other, giving
component that will pass an AC but not a DC current.
Qc =CV (1.8)
where C is the 'capacitance' of the component. C is pro- Reactance
portional to the plate area and inversely proportional to
From 1.10 and 1.11
the separation. While no current can flow through the ca-
pacitor, a current will flow in the outer circuit while the "~//i = 1/~C (1.12)
charge is being established.
Here 1/(oC is somewhat equivalent to R for the resistor,
Water analog except for the resistor I and V are in phase, while for the
The water analog of the capacitor is the elastic membrane capacitor Iin leads Vin by 90 ~ Thus 1/coC is termed the
stretched across the pipe in Fig. 1.20). No water flows 'reactance' of C, with the symbol for reactance X. With
through the membrane, but there is a flow through the X c the reactance of the present C, we write
adjoining pipework as pressure is applied to stretch the lY~I
= 1/(oC (1.13)
membrane.
If two shutters are inserted across the pipe to isolate the rather than Xc= 1/toC, since l/toC is only the magnitude
stretched membrane, this is equivalent to disconnecting of Xc. A representation of cX which gives both the magni-
the capacitor once it has been charged. The charge is then tude and the 90 ~ phase difference is given in Section 1.7.
held until the wire ends are shorted together (the two Much as G= I/R for the resistor, for the 'susceptance'
shuttered ends of the pipe bent round to meet and the B of a reactive component B= 1/X. This too needs to be
shutters removed). Then an instantaneous and theoretically memorised.
infinite current (a current 'impulse') flows as the capacitor
discharges. Example. For C = 100nF and f= 10kHz then I Xc I = 159D.
Alternatively the capacitor may be connected to a resis-
tor R (attach narrow pipe - remove shutters). The dis- Values
charge then takes the non-zero time T where, as shown in
The unit of capacitance is the farad (F: Michael Faraday).
Section 11.1, T = CR.
For manufactured devices C ranges from approximately
The water analogy extends to the breakdown of the in-
lpF to one farad, with the usual preferred values. For a
sulator (rupture of the membrane) for excessive V.
capacitor formed of two circular plates (Compton, 1990)
I membrane
C = Eo%A/d (1.14)
v --c
where s o is the permittivity of free space, 8 r is the relative
permittivity of the dielectric, A is the area of one face of
one of the plates, d is the plate separation, and d<<D
(a) (b) where D is the plate diameter.
Fig. 1.2 Capacitor C connected to constant voltage supply.
Example. For A= lcm ,2 d=lmm, air as the dielectric,
)a( Circuit diagram.
and with oS =8.85 x 10 -12 then C = 0.885pF.
)b( Water analog.
Voltage V >=< pump pressure.
Charge Q=CV r volume displaced by membrane. Electrolytic capacitor
C r membrane elasticity.
With C*,l/d as above then for C>II.tF the capacitor will
normally be of the 'electrolytic' type, where the very thin
Capacitor current
insulating film is developed electrochemically within the
With the current I at a point in a circuit defined as the rate device. Normally the electr, olytic deposition will allow a
dQ/dt at which charge Q moves past that point, and with mean voltage of only one polarity across the capacitor,
the capacitor charge Qc as in 1.8, then for the present that used to form the film. The other polarity will reverse
capacitor the process and destroy the film. Any capacitor has a
I=CdV/dt (1.9) voltage rating, the value above which the dielectric may
For the alternating break down.
4 Analog circuit techniques
High-k capacitor
Problem By integrating the instantaneous power VxI
These use a type of dielectric for which the dielectric flowing into a capacitor C over one cycle of the applied
constant is extremely high, allowing values of C up to voltage, show that, with the phase of I and V differing
about 100nF with the capacitor still in the form of two by , 900 the mean power transferred over one cycle of
metal plates separated by a single layer of dielectric. The the sinusoidal applied voltage is zero.
conducting 'plates' are two metal films deposited on a disc
of the high-k material. The high-k capacitor is particularly Similarly show that, regardless of the charging wave-
suitable for high-frequency applications where the form, when C is charged to Vc the stored energy
parasitic series inductance Lp needs to be as low as E=CV2/2.
possible.
Polyester type construction 1.3 Inductor
For a capacitor of the above kind of value using a normal
dielectric, the construction will be in the form of two long The inductor is simply a coil of wire, sometimes with a
strips of conducting foil separated by a strip of flexible core of iron or ferrite. If a current I is passed through the
insulating material (e.g. polyester). The assembly is then coil this sets up a magnetic flux O. If I changes then so
rolled up for compactness, making a l.,p good deal larger. does O, to develop the voltage
V=NdO/dt (1.15)
Imperfections
where N is the number of turns on the coil. The unit of
Apart from the larger Lp, the conventional capacitor flux is the weber (Wb), which is such that if the flux
approximates very well to the ideal. When an alternating linking a coil of one turn is changing at the rate of one
voltage is applied to a capacitor to give a current of Wb/sec then the induced voltage will be one volt. With V
proportional amplitude then for the ideal capacitor no ,,dO/dt as in [1.15] and 0o, I then
power is dissipated. Energy is simply accepted over one
half of the cycle and returned over the next. Unfortunately = V LdI/dt . (1.16)
the same is not true for the high-k component for which,
where the constant L is termed the 'inductance' of the
although the series l.,p is minimal, there is also a small
component. The inductor is thus the complement of the
effective series Rp. This becomes progressively more
capacitor. It develops no voltage for constant I, while the
important as the frequency f of the applied voltage
capacitor allows no current for constant V.
increases.
It is also difficult to manufacture the high-k component
to an exact value. The quoted tolerance thus tends to be Water analog
relatively large.
The analog of the inductor is as in Fig. 1.3Co). The fly-
Finally, for the high-k the variation of C with tempera-
wheel with non-leaking paddles requires pressure (V) to
ture (the 'temperature coefficient') is higher than for other
make the speed (I) change, but for constant speed (I) no
types.
pressure (V) is needed.
The high-k capacitor is thus best suited to power
With the inductor connected as in (a), the constant V
decoupling applications, where the applied voltage is es-
gives constant dI/dt. Thus I increases at a steady rate.
sentially DC, the exact value (and variations in it) do not
Correspondingly for the flywheel, constant pressure (V)
matter, and a low series inductance is a prime require-
gives constant acceleration and thus a steadily increasing
ment.
flow rate (I).
Variable capacitors
These exist in several forms. The knob-controlled type
normally consists of two sets of interleaved plates, each in
the form of a filled half circle, and on a common axis.
One set of plates is then rotated into the other, as far as is
needed for the required C.
For a pre-set 'trimmer' the sets of plates are cylindrical,
Fig. 1.3 L Inductor connected ot constant voltage supply.
the one rotating on a screw into the other. Alternatively )a( Circuit diagram.
two sets of rectangular plates are separated by slips of )b( Water analog.
plastic insulator (often mica). The plates are springy and Voltage V- LdV/dt r pump pressure.
are closed on to the dielectric using a screw, again to the Current I r flow rate.
degree needed for the required C. L r moment flywheel of inertia.