Ultrasonic System Overview
Learning Objectives
Overview of the UT system components that
will be discussed
The ultrasonic system components
oscilloscope display
pulser/
receiver
cabling
transmitting
transducer
receiving transducer
flaw
1
voltage versus
time pulse, v(t)
amplitude, volts
0.6
0.2
-0.2
-0.6
Fourier
Transforms
-1
-2.5 -2 -1.5 -1 -0.5 0
0.5
1
1.5
2
2.5
time, μseconds
(a)
magnitude of the
frequency spectrum
of the pulse, V(f)
(only positive
frequencies shown)
amplitude, volts/MHz
0.4
f = frequency
(in cycles/sec or Hz)
ω = 2πf
=frequency
(in rad/sec)
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
frequency, MHz
(b)
8
9
10
The ultrasonic pulser and its equivalent circuit
pulser
voltage pulse
v(t)
cable
pulser
(V (ω ) , I (ω ) )
I
electrical impedance
voltage source Vi (ω )
Z ie (ω )
V
voltage, current
cabling and its equivalent transfer matrix
V1
I1
I2
I2
I1
V1
[T ]
V2
⎧V1 ⎫ ⎡T11 (ω ) T12 (ω ) ⎤ ⎧V2 ⎫
⎨ ⎬=⎢
⎥⎨ ⎬
T
ω
T
ω
I
(
)
(
)
22
⎩ 1 ⎭ ⎣ 21
⎦ ⎩ I2 ⎭
V2
a sending transducer and its equivalent transfer matrix
force, velocity
voltage, current
v
Vin
F
A
I in
(a)
v
I in
Vin
[TA]
(b)
F
a sending transducer modeled as an impedance and sensitivity
Iin
vt
⎡⎣T A ⎤⎦
Vin
Ft
Z rA;a
acoustic radiation
impedance
(a)
I in
sensitivity
vt = SvIA I in
Z inA;e
Vin
= Ft / Z rA;a
electrical impedance
(b)
putting all the sound generation components together
Vi (ω )
pulser
A
Ft (ω )
output
force
(a)
Z ie (ω )
Vi (ω )
vt = SvIA I in
[ T]
Z
A; e
in
(b)
Vi (ω )
tG ( ω )
(c)
Ft (ω )
Ft = Z rA;a vt
the receiving transducer also can be modeled by an
impedance and sensitivity
V
incident and
scattered waves
B
I
(a)
voltage Vs (ω )
= SvIB (ω ) FB (ω )
impedance
Z inB ;e (ω )
blocked force
generated by the
(b)
waveson the transducer
I
V
model of the receiver as an electrical impedance and gain factor
output voltage
VR
receiver
I 0 (ω )
V0 (ω )
(V0 , I 0 )
impedance
Z 0e (ω )
VR (ω ) = K (ω ) V0 (ω )
gain
putting all the sound reception components together
FB (ω )
receiver
VR (ω )
output
voltage
(a)
Z inB ;e
[R]
SvIB FB
V0
Z
e
0
(b)
FB (ω )
t R (ω )
(c)
VR (ω )
VR = KV0
Modeling all the wave propagation and scattering
components as a transfer function
Vi (ω )
VR (ω )
pulser
receiver
Ft (ω )
tA
FB (ω )
acoustic/elastic
processes
VR (ω )
Vi (ω )
Ft (ω ) SvIB FB
Ft (ω )
t A (ω )
FB (ω )
acoustic/elastic transfer function
Modeling an entire ultrasonic measurement system
receiver
pulser
T
VR (ω )
R
Sf
flaw
VR (ω )
Vi (ω )
Ft (ω ) SvIB FB
Ft (ω ) = tG (ω )Vi (ω )
sound generation
transfer function
VR (ω ) = t R (ω ) FB (ω )
FB (ω ) = t A (ω ) Ft (ω )
sound reception
transfer function
In terms of transfer functions the ultrasonic system looks like:
Vi (ω )
tG ( ω )
t A (ω )
t R (ω )
VR (ω )
Can also combine the sound generation and reception
transfer functions with the voltage source of the pulser
tin a single function called the system function:
system function
s (ω )
t A (ω )
output voltage
VR (ω )
acoustic/elastic transfer function