Scottish Schools Equipme… Research Centre Graphics/SSERCGRAPH.iso/electroncs/elecdraw/samples/rationale6

Text File | 1993-04-14 | 13KB | 225 lines

This course centres around three simple op-amp circuits: a sine wave
oscillator (Oscil8 and OscilDiag4), a summing amplifier (SumAmp5 and
SumDiag3), and a speed controller.  All are crude designs in the extreme,
designed principally to show that simplistic approaches to electronics do
work: to encourage participants to take that first step.  It is hoped that
they can be helped to understand the deficiencies in these circuits, and to
see that an iterative approach to design is effective.

The first circuit to tackle practically is the oscillator, as unlike the
summing amplifier it stands alone.  Use the diagram of the breadboard layout
to help with construction.  A discussion of its operation, using the circuit
schematic, is best left until after a discussion of the operation of the
summing amplifier.

When participants have succesfully constructed an oscillator, there is an
opportunity for them to become acquainted with the oscilloscope.  They should
look at waveforms at both the subsidiary outputs as well as the main output,
all at various settings of VR1.

This is the point to introduce the circuit schematic, but only to discuss the
filter stages, not the main oscillator.

R5 and C3 form a low pass filter, as do R6 and C4.  Each filter reduces the
size of the output signal, but reduces the higher frequencies in the signal
more than the lower frequencies.  The oscillator itself produces more or less
a triangular waveform, with a considerable amplitude of third harmonic in
addition to the fundamental.  After two low pass filters1 the amplitude of the
third harmonic is much reduced, and the wave looks and sounds like a true sine
wave.

1Each produces a 3 dB per octave rolloff.  3 decibels (0.3 bels) means a
reduction by a factor of 2 in amplitude (the logarithm of 2 is 0.3).  An
octave is a factor of 2 in frequency.  So a 3 dB per octave rolloff means an
amplitude reduction by a factor of 2 for each factor of 2 in frequency.
Similarly, each filter reduces the third harmonic by a factor of 3 relative to
the fundamental; two filters reduce the harmonic by a factor of 9.  The
harmonic only had about one third the amplitude to begin with.

Remember that an important part of the learning experience is the translation
between schematic and breadboard.  Draw attention to the relationship.  Later
in the course participants will be expected to produce their own layout on a
blank breadboard drawing.

The summing amplifier activity can begin with a discussion of the operation of
the circuit using the schematic OHP.  Feedback is the important idea to get
across, and the fact that the amplification is the ratio of the feedback
resistor to the input resistor.  The amplification may of course be different
for different inputs, and there is no restriction to two inputs.

Once the summing amplifier is built, the outputs of oscillators can be added.
Both inputs and the output should be simultaneously displayed on
oscilloscopes.  It should be possible to show waveform A added to waveform B
producing waveform C.  Getting your oscilloscope to display waveforms like C
can be tricky: the trigger level has to be set to catch the largest peaks
while ignoring the smaller ones.

This is the point to reintroduce the oscillator circuit schematic, and look at
how the oscillator works.

Consider the effect of a small offset on the op-amp inputs, with the inverting
input slightly below the non-inverting.  The output will therefore swing all
the way to the positive supply rail (or as close to it as the op-amp can
manage).  C1 will charge up slowly through R2; once the voltage on C1 is
appreciably above zero, it will start to charge C2 through R1.  The inverting
input of the op-amp will be pulled up, changing the output of the op-amp to a
large negative value.  This does not simply settle down to some central,
balanced value like an ordinary amplifier, because of the delay involved in
charging C1 and C2: C2 doesn't react to wide swings of the output until a
little while after they happen.

There are important subsidiary activities in altering resistors and capacitors
in the oscillator and filters to change the oscillator frequency range, and
altering the feedback or input resistors in the amplifier to change the
amplification.  It should then be possible to show D plus E making F.  G, H
and J can be produced as beats between signals of nearly equal frequenies but
differing amplitudes.

We are now ready for a discussion of the equivalence of C, G, H or J to the
product of a low (modulating) signal and a high (carrier) signal.  The
construction of a multiplier circuit is beyond the aspirations of this course.

In G, H, and J, the modulating signal is displaced - that is, it has a d.c.
component.  This is necessary if we want to retrieve the modulating signal
easily, as shown in the right hand diagram in each case.  G is still
overmodulated, and without special arrangements we would be liable to recover
a distorted signal.  H is critically modulated; any increase in the signal
would result in overmodulation.

Conversely, when a carrier is modulated by a sine wave, a signal is produced
which is identical to the sum of two nearby frequencies, one each side of the
carrier frequency.  If the modulating signal is more complicated, containing a
variety of frequencies, there will be a whole band of frequencies produced.

This leads to frequency/amplitude diagrams (frequency domain) rather than
time/voltage (time domain), and the concept of bandwidth.  The bandwidth (the
range from minimum frequency to maximum) of the modulated signal is in fact
the same as the bandwidth of the modulating signal (the highest frequency
present in the signal).

It is now possible to see that the explanation given earlier of how the
oscillator works is a time domain view of things.  A frequency domain view
goes like this:

An op-amp with negative feedback adjusts its output so that its inputs are at
the same voltage; an op-amp with positive feedback produces a saturated
output.

If the feedback (as in our circuit) contains inductive or capacitive elements,
the amount of feedback will vary with frequency - and in particular, there
will be a phase difference which will vary with frequency.  The effective
feedback around the op-amp is dependant on the in-phase component of the
impedance of the feedback network.  If the phase difference is greater than
90█, then the feedback is effectively inverted, and becomes positive feedback
when applied to the inverting input of the op-amp.  Hence at some frequencies
the circuit has negative feedback, but at others it has positive feedback.

Our circuit has negative feedback at low frequencies, but at some frequency
determined by R1, R2, C1, C2 and the setting of VR1, the feedback becomes
positive.  The switch-on transients will contain some (possibly minute)
component at this frequency.  This will be amplified each time around the
circuit, until the circuit saturates at each extreme.

We need two R/C pairs in the feedback network as each produces somewhat less
than 90█ phase lag.

It is highly desirable that participants should understand both ways of
looking at the operation of oscillators, and how the two viewpoints reinforce
each other.

Now that we can produce oscillators with significantly differing frequencies,
we can also attempt to add the second or third harmonic to a wave.  There is
an OHP showing the expected results.  Note that the appearance (but not the
sound) of the summed waveform is dramatically affected by the relative phase
of the harmonic.  Unless the frequency of the harmonic is exactly the
appropriate multiple of the frequency of the fundamental, the phase
relationship will change continuously.  If this change is slow enough, you can
watch the changing waveform on the scope; otherwise it just makes a blur on
the screen.

This brings us to considering how oscillators can lock into step.  We want
this to happen if we want a stable phase relationship.  To achieve this, all
we have to do is arrange that a little of the output from one oscillator (the
master) is allowed to get to an input of the other (the slave).  A very small
amount is all that is required if the master's frequency is very close to the
frequency the slave would oscillate at without forcing.  In fact, if the two
are close enough, stray capacitances, inductances, and leakages via power
supply lines and/or the summing amplifier connections can be sufficient,
without any deliberate forcing circuit at all.

In general, this crosstalk makes it difficult to avoid oscillators locking
into step.  Usually neither is particularly master or slave; the output of
each leaks slightly to the input of the other, and the two form a complicated
compound oscillator circuit.  It should be possible to see this effect: set up
two oscillators running at nearby frequencies, and adjust one slowly nearer to
the other.  At some point, with a slight jump in the frequency of each, they
will suddenly lock into step.  It may well take a larger movement of the
control to get them out of step again, and then they will show a larger jump
in frequency.

We can now look at ways to reduce the crosstalk, which is necessary if we want
to have our oscillators working at nearly the same frequency without locking
into step.  The first thing to do is to prevent stray signals passing via the
power rails.  What is needed is either separate supplies, or at least a simple
filter in the line - a series resistor followed by a parallel capacitor to
ground, in the positive and negative rail to each oscillator.

Next we increase the input resistors in our summing amplifier - and of course,
the feedback resistor in the summing amplifier, in proportion.  This reduces
crosstalk between the outputs of the two oscillators - and of course, the
outputs of each oscillator are connected back to the inputs via the
oscillators' feedback network.

By providing adjustable crosstalk, we can study the summing of harmonics
locked into phase, or slowly changing phase.  These circuits do not give us
control of the relative phase when they are locked in step.  They may prove
difficult to lock on even harmonics (for sawtooth shapes), but should lock on
odd harmonics (for squares and symmetrical triangles) easily.  Participants
probably shouldn't attempt to add more than two signals; but discussion and
possibly demonstration of series such as those shown on the OHP is desirable,
perhaps with some discussion of fourier transforms.

Detailed mathematical description of the operation of the oscillator circuit
is beyond our aspirations - but the basic ideas to undertake it are all here
for anyone who is interested.  It is important to realise that the detailed
mathematical description is not essential to the design process for simple
circuits like these, or even considerably more complicated ones.  Once one has
an qualitative understanding, one can build circuits which do something, and
then modify them until they perform as required.  A feel for the approximate
values of components needed comes with experience.  One can also do rough
order-of-magnitude calculations once one has a feel for the dominant features
of the arithmetic, and what one can neglect.

The final circuit is the speed controller.  Here the feedback comes from a
motor used as a tachogenerator.  It is vital that this has a large number of
commutator segments (at least about 9) so that the ripple on the voltage
generated is relatively small.  The best way to ensure that the feedback is
negative is trial and error!  When the feedback is negative, the speed should
be proportional to the potentiometer setting, and it shouldn't vary
significantly under variations of load.  This is subject to a maximum load, of
course: when the op-amp saturates, or the current drawn reaches the limit of
the supply, the system will no longer be able to control the speed!

By this stage it is hoped that a circuit schematic will be sufficient; but
participants should be encouraged to draw their own layout on a blank
breadboard drawing, before constructing the circuit.  They will eventually not
need to do this, but at this stage it is a useful excercise, and it is
certainly something they will need to do for their pupils on occasions.

Again, the effects of altering the feedback resistor can be investigated.
Over a wide range no effect should be observable, but the effects outside that
range are instructive.

Note the use of a separate supply for the motor: this may not be important in
this application, but is good practice and should be the subject of
discussion.  The issues are isolation of the electronics from the generation
of electrical noise in the motor circuit, and the difference in
characteristics of the required supply - electronics generally need little
current, but a noise-free supply; motors need a relatively large current, but
noise is largely irrelevant.

This is only a speed controller: a position controller requires a
bidirectional output amplifier instead of the simple transistor output.