volume control (R7). R7 has an audio taper instead of a
linear taper. With a linear pot, the ohms per degree of
rotation is constant. As a voltage divider, 20 degrees
rotation gives twice the voltage of 10 degrees rotation.
For most applications, that’s what you want. But the way
our hearing works, loudness increases with the logarithm
of the sound power. An audio taper pot varies the
resistance so that the change in loudness per degree
of rotation is constant.
The wiper of R7 goes to the input of power amplifier
IC2. Unlike IC1, IC2 has a built-in resistor network to
establish signal ground for its inputs. C6 is a bypass cap
for that internal bias network. Note that IC2 is used in
non-inverting mode. Since IC2 is a power amp, it can
draw relatively large current “slugs” from the battery
which could cause small fluctuations in the nine-volt
supply. Such fluctuations could be picked up at the input
of IC1 causing an accidental feedback loop. If IC1 and IC2
were both inverting (or both non-inverting), it would be
positive feedback and the whole circuit could oscillate. If
one amplifier is inverting and one is non-inverting, it’s
negative feedback which is stable. There are other possible
feedback paths through the supply. That’s why we use
C11 across the battery and C10 from power to ground at
IC2. Figure 3 shows the schematic of the LM386 used for
IC2. For stability, the LM386 needs a 10Ω load at high
frequencies, which is supplied by R9. C8 allows IC2 to “see”
R9 only at higher frequencies. With pins 1 and 8 open, IC2
has a fixed gain of 20. To increase AC gain, a resistor (R8) in
series with a capacitor (C7) is placed between pins 1 and 8.
The AC gain is given by the formula:
AV = 30K / REQ
where REQ = 150 + (R8 1.35K)/ (R8 + 1.35K). In this
circuit, R8 is a jumper wire to get the maximum gain of 200.
The DC gain stays at 20. The output of IC2 is coupled via
C9 to the headphones jack J2. The 10Ω resistor in series
with C9 does two things. First, it makes the output of
IC2 look more like a current source for low impedance
headphones. That can improve the sound quality. Second, it
prevents IC2 from seeing a shorted output.
The total gain of the amplifier circuit is approximately
P RARABOLIC EFLECTORS
Parabolic reflectors are
everywhere, from radio telescopes to
dish antennas for satellite TV to the
reflector in a flashlight. Figure PR-1
is a photo of a parabolic reflector.
Parabolic reflectors like the one
in figure PR-1 are based on the
properties of a parabola, one of those
conic sections you may remember
from high school math. Figure PR-2
is the graph of a parabola showing
y as a function of x.
The equation describing a
parabola is y = x2 / 4P where P is a
constant, as shown on the graph.
What’s so special about a parabola?
It’s all about that point P, called the
focal point. Imagine a bunch of ball
bearings rolling across a table in
straight lines parallel to the y-axis
and hitting the inside of the parabola,
which is lying on its side.
All the ball bearings
would bounce off the
parabola and land at
point P as shown in
Figure PR- 3. They are
reflected to the focal
If we rotate the
parabola around the
y-axis, we get a three-dimensional figure: a
parabolic dish. (New technology? No;
the properties of a parabola have
presumably been known since the
time of Euclid.) Parabolic reflectors
are characterized by their focal
length: the shorter the focal length,
the deeper the dish. In terms of the
graph in Figure PR-2, the focal length
is how high up the y-axis the point
P is located.
Instead of ball bearings, energy
in the form of waves can also be
concentrated at a focal point using a
parabolic reflector. The size of the
reflector depends on the wavelength
of the waves your trying to focus.
Wavelength is how far a wave travels
during one cycle of the wave, and
is represented by the Greek letter
lambda (λ). We define wavelength as:
λ= s / f
For best reflection, the diameter of
the dish should be much bigger
than λ. With RF microwaves, the
wavelength is a few centimeters.
With light, the wavelength is in
nanometers. But with sound, the
wavelength at 1000 Hz is about 34
centimeters (one foot). Because
human detectable sounds can have
frequencies from 100 Hz to 20,000 Hz,
the wavelength can be equal to the
diameter of the reflector at some
frequency. Also, since sound is a
longitudinal wave, the wavelength
can interact with the focal length to
cause cancellation at a specific
A large, deep dish reflector
would be best for sound waves. But a
10 foot dish would not be hand-held,
so some trade-off has to be made
between the size of the dish and its
ability to focus sounds.
where s is the speed of propagation
and f is the frequency of the wave.
■ FIGURE PR-2
■ FIGURE PR- 3
■ FIGURE PR-1
December 2008 35