How Does Resonance
In order to understand piezoelectric ultrasonic devices,
we need to understand resonance. Lasers, microwave
ovens, that squeal your car makes burning out causing the
neighbors to stare — these are all examples of resonance.
One example that we’re all familiar with is a child
swinging (Figure 1).
A child merely pushing with their feet from a starting
position causes the swing to move only slightly. To make
the swing move great distances requires the child “to
swing.” What this really means is that the child must learn
to move the lower legs forward or backward in synchrony
with the swing’s movement.
When the swing reaches its backward-moving limit,
the child rapidly rotates the lower legs forward and,
likewise, at the forward-moving limit, the lower legs are
quickly moved back. In this way, additional energy is
imparted to the swing with each iteration, resulting in a
large steady-state “amplitude.”
Before we leave this resonance example, let’s think
about one more aspect of the situation that is typical of all
such resonant systems.
The system (in this case, the child and the swing) has
a natural frequency at which it operates. The swing and
the child, in fact, constitute a pendulum. The natural
frequency of this system depends only on the length of
the swing chains.
In the case of a piezoelectric device, the device’s
natural frequency is determined by its dimensions and the
device material. Consider the situation when a voltage is
generated across the device.
The wall of the device moves, creating a wavefront
that moves through the device, striking the opposite wall
of the device, then heading back to the originating
wall. This roundtrip time of travel constitutes the
period of the natural frequency.
If we vary the voltage across the device at this
natural frequency, we create a resonant behavior
within the device, much like the child on the swing.
After several periods of such voltage change, the
amplitude of the wall movement (and therefore the
transmitted sound) becomes relatively large.
Okay, so a piezoelectric transducer can convert
electrical energy into mechanical energy and
thereby allow us to create ultrasonic pulses. But
how can we sense ultrasonic energy?
It turns out that the same type of piezoelectric
transducer that was used for electrical-to-mechanical transformation can be used to do the
opposite. When piezoelectric devices are subjected to
external force, the device generates a voltage which can
be amplified and detected.
In fact, some applications use a single transducer in a
half-duplex mode to transmit a sequence of pulses and
then “listen” for the return of those pulses (such a circuit
will be discussed later in this series).
Most applications use separate transducers for
transmit and receive. Although the force to which the
piezoelectric transducer receiving the acoustic wave is
small and the associated output voltage is low amplitude,
an amplifier with sufficient gain raises the amplitude to a
Simple radar applications use Time-of-Flight (TOF) to
determine distance to an object. This is a fairly
straightforward calculation. In the case of ultrasonics, the
wavefront travels to the object, then back to the ultrasonic
receiver, at the speed of sound. So the distance is simply
where D is the distance and c is the speed of sound (343
meters per second).
Unfortunately, the calculation is muddied a bit by the
fact that it may not be exactly clear how to make the TOF
Figure 2 shows typical transmit and receive
waveforms for an ultrasonic transducer. We reasonably
choose the start of the transmit signal as the beginning of
the time-of-flight, but where should we choose to say
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Figure 2. Transmit and receive signals.