Biomedical Engineering Reference
In-Depth Information
4
R A ð f Þ R g
EL ð f Þ¼
ð
16
:
31a
Þ
2
1
o C 0 þ o L s
2
ð R A ð f Þþ R g þ R s Þ
þ X A ð f Þ
0
If the capacitance is tuned out by a series inductor,
L S ¼
1
=ðo
C 0 Þ
and
R s ¼
0, then at
resonance,
R A ð f 0 Þ R g
½ R A ð f
4
EL ð f 0 Þ¼
ð
16
:
31b
Þ
2
Þþ R g
0
Notice that if
1.
The determination of acoustic loss is a more complicated function of frequency, but it is
straightforward to determine its value at resonance. In the simple transducer model intro-
duced in Section 16.2.3, a simplifying assumption was made that the acoustic loading on
both sides of the piezoelectric crystal was the same acoustic impedance as that of the crys-
tal; however, this is not the case in general, as illustrated in Figure 16.11.Notethe
arrangement in this figure is rotated 90 from that in Figure 16.8. On the top of this figure,
the piezoelectric is loaded by a backing material and below the lens, by water or tissue.
The bottom of the crystal shown here is usually regarded as the “business end” of the
transducer, where the forward waves propagate along the positive
R A ¼ R g , and
R s R g , then
EL
(
f 0 )
-axisthatisdirected
downward in Figure 16.11. Waves in the backward direction are suppressed or absorbed
by a backing material that aids in broadening the spectrum of the transducer. By the left-
right convention of Figure 16.8, if the acoustic impedance looking out of the crystal to the
left is
z
Z L
, then that to the right along the positive
z
-axis is
Z R
. In the case shown on the left
FIGURE 16.11 Construction of a single-crystal mechanical transducer. Forward propagation is directed
downward.
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