Transducer Characterization
Learning Objectives
Pulse-echo experimental determination of impedance,
sensitivity of commercial transducers
Experimental determination of effective radii and
focal lengths of commercial transducers
Transducer impedance, sensitivity
Ft (ω )
Z rA;a SvIA
tG (ω ) =
= A; e
Vi (ω ) ( Z in T11 + T12 ) + ( Z inA;eT21 + T22 ) Z ie
VR (ω )
K Z oe SvIB
= B ;e
t R (ω ) =
FB (ω ) ( Z in R11 + R12 ) + ( Z inB ;e R21 + R22 ) Z oe
To fully characterize these generation and
reception transfer functions, we need to be
able to obtain the transducers input electrical
impedance and their sensitivities
Transducer impedance
Measurement of the transducer input impedance, Zin :
Current probe
I
Pulser
V
Short cable
Transducer
water
V
Zin =
I
Transducer impedance
Example impedance measurements of two 5 MHz transducers:
transducer 1
1500
150
130
1000
120
amplitude
110
phase
500
100
90
0
0
5
10
Frequency (MHz)
15
80
20
Phase (Deg)
Amplitude (Ω)
140
Transducer impedance
transducer 2
1500
150
130
1000
120
110
amplitude
500
phase
100
90
0
0
5
10
Frequency (MHz)
15
80
20
Phase (Deg)
Amplitude (Ω)
140
Transducer impedance
Impedance of a capacitor, Z =1/(-iωC)
8
91
6
90.5
magnitude 4
90
2
0
0
89.5
1
2
3
4
5
6
frequency
7
8
9
89
10
phase
Transducer sensitivity
Pulse-echo measurement setup for determining sensitivity
pulser/receiver
ρ1 , c p1
solid
D
Transducer sensitivity
1. measure voltage and current when transducer is
radiating into the fluid but before any reflected waves
have arrived
v1 ( t ) , i1 ( t )
a
ρ1 , c p1
b
solid
D
Transducer sensitivity
2. do FFT of the measured voltage and current and relate to
the voltage and current at the transducer by compensating
for the cabling
I1 (ω )
V1 (ω )
I in (ω )
[ T]
vt = SvIA I in
Vin (ω )
Z inA;e
⎧Vin ⎫
1 ⎡ T22 −T12 ⎤ ⎧V1 ⎫
⎨ ⎬=
⎢ −T
⎥ ⎨I ⎬
T
I
det
T
[
]
11 ⎦ ⎩ 1 ⎭
⎣ 21
⎩ in ⎭
A; e
Note: then the impedance of the transducer is just Z in =
Vin
I in
Transducer sensitivity
3. measure voltage and current generated by the waves
reflected from the surface of the block:
v2 ( t ) , i2 ( t )
a
ρ1 , c p1
b
solid
D
Transducer sensitivity
4. do FFT of the measured voltage and current and relate to
the voltage and current at the transducer electrical port by
compensating for the cabling
Z inA;e IT (ω )
SvIA FB
VT (ω )
I 2 (ω )
[ T]
V2 (ω )
⎧VT ⎫
1 ⎡ T22 −T12 ⎤ ⎧V2 ⎫
⎨
⎬=
⎢ −T
⎥ ⎨I ⎬
T
I
−
det
T
[
]
11 ⎦ ⎩ 2 ⎭
⎣ 21
⎩ T⎭
Transducer sensitivity
5. From these measurements and a knowledge of the
acoustic/elastic transfer function for this setup we can
obtain the sensitivity of the transducer from:
SvIA =
Vin IT + VT I in
t A Z rA;a I in2
[Note: in all these division processes in the frequency
domain, a Wiener filter is used to desensitize the
process to noise]
Transducer sensitivity
Example sensitivity calculated for a
5MHz planar transducer:
0.35
100
0.3
50
0.25
0.2
-50
0.15
Phase (deg)
Amplitude (V/N)
0
-100
0.1
-150
0.05
0
0
5
10
f (MHz)
15
-200
20
Transducer sensitivity
Cabling effects need to be accounted for in determining
the sensitivity:
Amplitude (V/N)
0.3
Compensation
No compensation
0.2
0.1
0
0
5
10
f (MHz)
15
20
0
5
10
f (MHz)
15
20
Phase (deg)
400
200
0
-200
Transducer Effective Parameters
Use of manufacturer specifications for parameters such as
transducer radius and focal length in transducer models
do not always lead to good agreement with experimental
measurements.
a
R0
Thus, we need to determine experimentally "effective" values
for these parameters.
Transducer Effective Parameters
Effective radius for an unfocused (piston) immersion probe
sample
FFT
z
5 MHz
2
plot 5 MHz component
versus z
1.8
|p|
ρcv0
1.6
1.4
1.2
1
find zmin
0.8
0.6
determine
aeff
0.4
0.2
0
zmin
0
0.5
1
1.5
2
z/N
2.5
3
3.5
4
aeff = 2λ zmin
Transducer Effective Parameters
Effective radius and focal length for a spherically focused probe
12
aeff =
10
zmax
2λ zmin ( R0 )eff
( R0 )eff
− zmin
8
|p|
ρcv0
( R0 )eff
6
4
⎧⎪
⎫⎪
π −x
= zmax ⎨
⎬
⎪⎩π − x ( zmax / zmin ) ⎭⎪
2
where x is the root of:
0
0
zmin
0.5
1
1.5
2
2.5
3
3.5
4
π − x ( zmax / zmin )
sin ( x )
x cos ( x ) =
π −x
Transducer Effective Parameters
Effective transducer parameters determined experimentally:
Probes
Manufacturers Specs
focal length radius
(cm)
(cm)
Estimated Parameters Center
focal length
radius Frequency
(cm)
(cm)
(MHz)
A
7.62
0.476
13.47
0.451
10
B
7.62
0.635
20.74
0.556
5
C
7.62
0.476
7.45
0.469
15
These values should be independent of frequency but in
practice they do vary somewhat with the frequency component
used in their determination.