Nuts and Volts - December 2008

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:

A_V= 30K / R_EQ

where R_EQ= 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.

Hiss Filter

The total gain of the amplifier circuit is approximately

^PR^ARABOLICEFLECTORS

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 point.

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 frequency.

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.