Ultrasound Transducers

Question 1

What is a matched load?

Answer 1

Z_B = Z_P = Z_T

(impedance matched)

no acoustic reflections at transducer faces due to matched impedance

Z_B = backing
Z_P = piezoelectric element
Z_T = Transmission medium

Question 2

What happens when a single positive voltage step is applied to piezoelectric element in matched load?

Answer 2

Pulses of opposing polarity emitted in both directions from front and back faces of elements

(2 wave emitted in opposite outwards directions in +ve & -ve x direction and 2 waves emitted inwards from faces towards each other in -ve direction)

Question 3

What happens when λ&raquo_space; L (thickness of slab) in matched load?

Answer 3

Acoustic waves emitted by opposite faces cancel and output is close to zero (waves out of phase)

Question 4

What is the equation for the transducer frequency when it is resonant?

Answer 4

fc = c/2L

(this is the maximum output when only mechanical behaviour of transducer is considered)

Question 5

What happens when λ = L in matched load?

Answer 5

Acoustic waves emitted by opposite faces cancel and output is zero

Question 5

What happens when λ = 2L in matched load?

Answer 5

Constructive interference leading to large output (assuming ρ and c_0 are constant)

Question 6

How can transducer bandwidth be calculated?

Answer 6

Using full-width at half maximum (FWHM) of frequency response

Question 7

What is the acoustic pressure, p(f) for response of matched load?

Answer 7

|p(f)| = |2sin (π f L / c) |

Question 8

What are the conditions of the air backed scenario with piezoelectric element?

Answer 8

Z_B &laquo_space;Z_P = Z_T

With air backing so impedance is mismatched (more realistic as in practise impedance is never matched)

Backward travelling wave from front surface will reflect from air-interface and be inverted

Question 9

What can the reflected wave in the air backed cause be modelled as?

Answer 9

An image source

Question 10

What happens when λ&raquo_space; L in air backed case?

Answer 10

Wave emitted from front face are almost in phase and there is some output even though wave from rear face is out-of-phase (low frequency)

Question 11

What happens when λ = 6L in air backed case?

Answer 11

Summation of all three waves cancel and output is zero

Question 12

What happens when λ = 2L in air backed case?

Answer 12

Constructive interference of all three waves (max frequency at fc = c/2L)

Question 13

What is the acoustic frequency response equation for air backed case?

Answer 13

|p(f)| = √ (3 - 4cos(kL) + 2cos(2kL))

Question 14

What happens in a real air backed transducer?

Answer 14

Waves reflect between transducer faces resulting in a highly resonant behaviour (due to impedance mismatched) which leads to a high Q-factor

Question 15

What does a high Q factor look like on an amplitude vs frequency graph?

Answer 15

Tall peak that doesn’t broaden (high Q affects image due to long pulses produced which resonate)

(low Q produces wide short peak)

Question 16

What is the relationship between time and frequency?

Answer 16

Inverse relationship

Question 17

What do resonant transducers need to produce for imaging?

Answer 17

Short pulses for good axial resolution so Q factor needs to be reduced

Question 18

How can the Q factor for a transducer material be reduced?

Answer 18

Add backing layer to rear of element

Add matching layer between element and tissue

Question 19

What are the requirements for the backing layer?

Answer 19

Matched acoustic impedance to minimise reflections

Highly absorptive so ultrasound is not reflected from rear of backing

Question 20

What happens if perfect matching is achieved?

Answer 20

Ringing is eliminated and frequency response is the same as matched load case

Question 21

What is the backing layer made from?

Answer 21

A mixture of rubber and tungsten directly bonded to transducer

Question 22

What does large mismatch result in?

Answer 22

Poor transmission efficiency: most of the acoustic wave emitted by rear face is reflected back from front face.

Question 23

What can be used to over come the existing impedance mismatch when backing layer is used?

Answer 23

A quarter wave matching layer of thickness L_ML and impedance Z_ML

(it cancels reflected wave (become out of phase) as has lower impedance than PZT and pulse is inverted)

Question 24

In a matching layer what are the reflection and transmission coefficients a function of?

Answer 24

frequency

Question 25

When is 100% transmission reached for continuous wave in matching layer?

Answer 25

f = c_ML / 4L_ML

Question 26

What happens in pulse excitation?

Answer 26

Matching layer acts as a frequency filter resulting in low transmission of frequencies far from centre frequency - bandwidth is reduced

Question 27

How can the typical fractional bandwidth (FWB) be increased?

Answer 27

Using a few matching layers with gradually decreasing impedance (used when a broader response is required)

Question 28

What are the components of single-element transducers?

Answer 28

connector/cable

acoustic insulator

casing/housing

backing layer

piezoelectric element
(surrounded by electrodes)

matching layer

Question 29

When piezoelectric element is considered as a receiver, what happens to output for a matched load?

Answer 29

λ&raquo_space; L: max output

λ = L : zero output

Question 30

What is the total voltage output of piezoelectric element as a receiver?

Answer 30

Total output: S(t) is given by the sum of the contributions provided by each slice
i.e. integrate pressure over L

Question 31

What is the useable frequency range defined as?

Answer 31

bandwidth or Q factor

Question 32

When is high Q factor useful?

Answer 32

Continuous wave applications (e.g. therapy)