from the transducer is fairly small. However, once
the energy strikes the object, it will be reflected in
A flat, hard, “smooth” surface will reflect the
energy back in a “specular” fashion (Figure 1a). Other
surfaces will reflect the energy back in a “diffuse”
manner (Figure 1b), spreading the energy out. A
specular reflection “bounces” all the energy in a mirror-like
way, while the diffuse reflection scatters the energy.
“Smooth,” in this case, is a function of the surface variation relative to the wavelength of the energy (for 40 kHz
ultrasonic energy, the wavelength is approximately 0.33 inches). A surface with variations much greater than one wavelength
would definitely be rough, and a surface with variations much less than one wavelength would definitely be smooth.
So, the reflected energy echoed back to the receiver is not only a function of distance (as we already know), but a
function of the object’s surface and geometry. In addition, the orientation of the object to the sensor also plays a role.
The bottom line for all this discussion about smoothness, object geometry, orientation to the receiver, etc., is that the
received signal will vary considerably. The received signal can easily vary by a factor of 500 over the range of, say, one foot to
Handling a Large
Dynamic Range with a
Okay, so we need to design for a large range of signal
values. How might we handle that? Let’s recognize that
we’re going to incorporate a microcontroller in our design,
and most modern microcontrollers have multiple analog
One way to digitize a large range of values with a fairly
simple design approach is to cascade two or three amplifiers
as in Figure 2. Each of the amplifier outputs can be sampled
and digitized. We can use the output of the first amplifier
for signals that are at short distances, and use the second or
third amplifiers at the longer distances.
Amplifiers are easy to design using op-amps. For an
inverting amplifier, the gain is given by -Rƒ/Ri and for a
non-inverting amplifier, the gain is 1+Rƒ /Ri. If each of three
stages has a gain of 10, we can digitize just about any
valid signal coming from an object as far away as 20 feet
while achieving sufficient accuracy with the analog-to-digital
converter (A/D; typical microcontroller A/Ds have about 10
bits of resolution).
In many cases, we’ll want to AC-couple the individual
gain stages. This keeps small DC offsets at the input to the
cascaded chain of amplifiers from being multiplied by the
gain of each stage. For an inverting amplifier, AC-coupling is
as simple as just adding a capacitor before the input resistor
of the amplifier.
How Does Feedback Work
with an Op-amp?
A feedback amplifier using an op-amp is a powerful
design component for most analog applications and its
operation is straightforward. Let’s start with an op-amp and
write down a few characteristic equations for it (Figure 3).
An ideal op-amp has high impedance inputs that allow
no current to flow into them, so the important equations are
So, the output voltage is equal to the difference
between the input voltages multiplied by the op-amp’s
Figure 1. (a) Specular and (b) diffuse reflections.
Figure 2. Cascaded amplifiers provide
extended dynamic range.
Figure 3. Op-amp with gain of Av.
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SERVO 09/10.2018 9
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