Ultrasound Transducers Flashcards
What is a matched load?
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
What happens when a single positive voltage step is applied to piezoelectric element in matched load?
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)
What happens when λ»_space; L (thickness of slab) in matched load?
Acoustic waves emitted by opposite faces cancel and output is close to zero (waves out of phase)
What is the equation for the transducer frequency when it is resonant?
fc = c/2L
(this is the maximum output when only mechanical behaviour of transducer is considered)
What happens when λ = L in matched load?
Acoustic waves emitted by opposite faces cancel and output is zero
What happens when λ = 2L in matched load?
Constructive interference leading to large output (assuming ρ and c_0 are constant)
How can transducer bandwidth be calculated?
Using full-width at half maximum (FWHM) of frequency response
What is the acoustic pressure, p(f) for response of matched load?
|p(f)| = |2sin (π f L / c) |
What are the conditions of the air backed scenario with piezoelectric element?
Z_B «_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
What can the reflected wave in the air backed cause be modelled as?
An image source
What happens when λ»_space; L in air backed case?
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)
What happens when λ = 6L in air backed case?
Summation of all three waves cancel and output is zero
What happens when λ = 2L in air backed case?
Constructive interference of all three waves (max frequency at fc = c/2L)
What is the acoustic frequency response equation for air backed case?
|p(f)| = √ (3 - 4cos(kL) + 2cos(2kL))
What happens in a real air backed transducer?
Waves reflect between transducer faces resulting in a highly resonant behaviour (due to impedance mismatched) which leads to a high Q-factor
What does a high Q factor look like on an amplitude vs frequency graph?
Tall peak that doesn’t broaden (high Q affects image due to long pulses produced which resonate)
(low Q produces wide short peak)
What is the relationship between time and frequency?
Inverse relationship
What do resonant transducers need to produce for imaging?
Short pulses for good axial resolution so Q factor needs to be reduced
How can the Q factor for a transducer material be reduced?
Add backing layer to rear of element
Add matching layer between element and tissue
What are the requirements for the backing layer?
Matched acoustic impedance to minimise reflections
Highly absorptive so ultrasound is not reflected from rear of backing
What happens if perfect matching is achieved?
Ringing is eliminated and frequency response is the same as matched load case
What is the backing layer made from?
A mixture of rubber and tungsten directly bonded to transducer
What does large mismatch result in?
Poor transmission efficiency: most of the acoustic wave emitted by rear face is reflected back from front face.
What can be used to over come the existing impedance mismatch when backing layer is used?
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)
In a matching layer what are the reflection and transmission coefficients a function of?
frequency
When is 100% transmission reached for continuous wave in matching layer?
f = c_ML / 4L_ML
What happens in pulse excitation?
Matching layer acts as a frequency filter resulting in low transmission of frequencies far from centre frequency - bandwidth is reduced
How can the typical fractional bandwidth (FWB) be increased?
Using a few matching layers with gradually decreasing impedance (used when a broader response is required)
What are the components of single-element transducers?
connector/cable
acoustic insulator
casing/housing
backing layer
piezoelectric element
(surrounded by electrodes)
matching layer
When piezoelectric element is considered as a receiver, what happens to output for a matched load?
λ»_space; L: max output
λ = L : zero output
What is the total voltage output of piezoelectric element as a receiver?
Total output: S(t) is given by the sum of the contributions provided by each slice
i.e. integrate pressure over L
What is the useable frequency range defined as?
bandwidth or Q factor
When is high Q factor useful?
Continuous wave applications (e.g. therapy)
