Biomedical Engineering Reference
In-Depth Information
Find
R
A
from Eq. (16.27c):
R
A
¼
49
2
0
:
F
¼
128
:
2 ohms
10
6
Hz
10
12
p
2
3
63
:
3
ohm
1
. Then, since at
Note that the units in the denominator are Hz -
F
¼
amps/volt
¼
resonance
X
A
¼
0, from Eq. (16.25),
10
6
Hz
10
12
Z
T
¼
128
i
=ð
2
p
3
63
:
3
F
Þ¼
128
i
838 ohms
Transducer Frequency Response
Transducer design is concerned with altering the shape of the spectrum to achieve a
desired bandwidth and a short, well-behaved pulse shape, or impulse response. Another
design goal is to improve the electroacoustic efficiency of the transducer. One measure of
this efficiency is transducer loss, the ratio of time average acoustic power reaching the
desired medium, usually tissue,
W
R
, divided by the maximum electrical power available
from an electrical source,
W
g
,
TL
ð
f
Þ¼
W
R
W
g
ð
16
:
29a
Þ
and defined in dB as
TL
ð
f
Þ¼
10 log
10
TL
ð
f
Þ
ð
16
:
29b
Þ
dB
The transducer loss can be broken down into an electrical loss factor,
EL
(
f
), and an
acoustic loss factor,
AL
(
f
):
TL
ð
f
Þ¼
EL
ð
f
Þ
AL
ð
f
Þ
ð
16
:
30
Þ
Theproblemofoptimizingthetransferofelectrical power into the radiation resistance
is that of maximizing
) over a desired bandwidth. Figure 16.10 shows the relevant
parameters involved. The transducer electrical impedance is connected through a tuning
inductor to a voltage source with impedance
EL
(
f
R
g
. An expression for electrical loss for this
situation is
R
s
L
s
R
g
W
RA
R
A
(f)
V
g
iX
A
(f)
−
i/
ω
C
0
FIGURE 16.10
Electrical voltage source with tuning inductor connected to transducer equivalent circuit.
