Download 16. Modelling and design of SAW devices

16. MODELLING AND DESIGN OF SAW DEVICES
16.1. Objective of the test
Get acquainted with acoustic wave devices and design of surface
acoustic wave (SAW) filters.
16.2. SAW devices
ICs are small and contain many (at present – to 108) elements. At
the same time it is important that ICs contain only transistors, diodes,
resistors and capacitors. Practically inductive elements cannot be
integrated in monolithic ICs.
When small ICs appeared the problem of miniaturisation of
filters, delay lines and other components that included inductive
elements arose. As a result of search of ways to miniaturise mentioned
components, surface acoustic wave devices were created.
Principles of SAW devices design are revealed in this laboratory
test by an example of a SAW filter consisting of input transducer,
SAW waveguide, output transducer and absorbers (Fig 16.1).
The design goal of the filter is to select material for the
waveguide, determine the main filter dimensions, examine its
frequency characteristics correspondence to the given specification
and make work drawings necessary for fabrication.
Input
transducer
Wavequide
A bsorber
Output
transducer
A bsorber

Fig 16.1. SAW filter
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16.3. Preparing for the test:
Using lecture-notes and referenced literature [2, p. 145–170],
examine principles of operation, structures and properties of
acoustic wave devices.
Familiarize with design calculations of the SAW filter presented
in Appendix (section 16.6).
Prepare to answer the questions:
Name the types of acoustic wave devices.
What properties of acoustic waves are used in SAW electronic
components?
What effects are used in electromechanical transducers?
Name types of bulk acoustic wave devices.
Explain the structure and operation of monolithic filter. Characterise its properties.
Name and characterise the types of SAW devices.
How is SAW filter arranged?
Explain the structure and operation of an interdigital transducer.
What materials are used for SAW waveguides? Characterize their
properties.
Describe the structure, operation and properties of a SAW delay
line.
Describe the structures and operation of dispersive SAW delay
lines.
Explain the properties and application of optimum filters.
16.4. In laboratory:
1. Answer the test question.
2. According to specified data design SAW filter.
Using presented PC programme carry out necessary calculations,
plot filter frequency response and examine the results. Repeat the
calculations, if it is necessary.
Sketch drafts of the filter.
3. Prepare the report.
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16.5. Contents of the report
Objectives.
Initial data.
Results of calculations and their analysis.
Graphs and sketches.
Conclusions.
16.6. Appendix. Sequence of SAW filter design calculations
The main electrical parameters (central frequency of the passband f0 and bandwidth F of the filter) are presented as initial data for
design calculations.
The goal of the calculations is to select material for the
waveguide, determine main dimensions of filter elements and examine
its frequency characteristics correspondence to the given specification.
Interdigital transducers (IDTs) are the main elements of a SAW
filter consisting of input transducer, waveguide and output transducer.
An IDT is shown in Fig 16.2.
In the simplest case the filter contains identical IDTs. Then design
calculations sequence can be like this.
1. Number of IDT fingers is calculated using the formula:
(16.1)
N  2f 0 F .
Here  is a coefficient (=0.6–0.8).
2. The efficiency of an IDT is maximal when N is close to the
optimal number Nopt, dependent on substrate material:
2
.
N opt   k m
(16.2)
Here k m2 is piezoelectric coupling coefficient (see Table 16.1).
3. If N  N opt , the deviation from the optimum is characterised
by a coefficient P:


P  N opt N 2 .
(16.3)
4. The step  of IDT fingers must satisfy condition:
  s 2 f0 ,
where s is SAW velocity.
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(16.4)
L
LK
a
W
d

b
Fig 16.2. IDT of SAW filter
The width d of the finger usually is half a step: d   2 .
5. The overlap of IDT fingers must be at least
Wmin  L s ,
(16.5)
where L is the distance between the input and output transducers, s is
SAW wavelength. The distance L is recommended to be 8–10 mm.
6. The IDT length is given by
(16.6)
Lk  N   2 .
7. The substrate length must be
(16.7)
b  L  2Lk  l  ,
where l is the distance between IDT and substrate end.
8. The substrate width is given by
(16.8)
a  W  2  l  .
Selection of filter dimensions and other parameters can be
followed by the calculations of its electrical parameters and characteristics:
9. Reflection coefficient B1 of SAW from the IDT, transition
coefficient B2 and IDT attenuation B3 (in decibels) are given by
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Table 16.1. Parameters of piezoelectric materials
Material
SAW
velocity s
km/s
Quartz
LiNbO3
Bi12GeO20
Bi12SiO20
LiTaO3
Piezoceramics
3.15 – 3.2
3.5 – 4.0
1.62 – 1.7
1.7
3.2 – 3.4
2–4
Coupling
coefficient
k m2
0.0012 – 0.0024
0.005 – 0.058
0.007 – 0.0164
0.018
0.0069 – 0.0093
0.043
Relative
dielectric
permittivity  r
4.52–4.55
25–60
38–45
43–51
100-300


 10 lg P 1  P   ,
 10 lg 2 P 1  P   .
B1  10 lg 1 1  P 2 ,
B2
B3
2
2
(16.9)
2
10. SAW filter attenuation is given by
B  2B3 .
11. Level of distortion signals caused by reflections:
Bd  2B3 .
12. Static capacitance of an IDT is given by
(16.10)
(16.11)
(16.12)
C0  NC1 W 2 ,
where C1 is capacitance of a finger given by
C1  21  r  6.5s 2  1.08s  2.37 .
Here r is relative dielectric permittivity of the substrate material,
s is ratio, s  d  .


13. Radiation resistance Rr of the IDT at f = f0 is given by
(16.13)
R0  Rr  f 0   2km2 2 f 0C1W .
14. To avoid capacitive component of the input resistance of the
IDT an inductive element is used in series with the IDT [2]. Its
inductance can be find using formula:
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L  1 4f 02C0 .
(16.14)
15. The transfer function of the SAW filter is given by
K F  j 
K1  j
K  j
.
K 2  jK3  j 4
K1  j0 
K 4  j0 
(16.15)
Here K1  j is the transfer function of the SAW filter input
circuit
K1  j 
Z
,
R  jL  Z
(16.16)
where
R  PR0 ,
Z  Ra  f   jX a  f   1 jC0 ,
Ra  f   R0 sin X X 2 ,
X a  f   R0 sin 2 X  2 X  2 X 2 ,
X  N  f  f 0  2 f 0 .
K 2  j and K 3  j are transfer functions of the input and output
IDTs:
K 2  j  K3  j 
sin X
.
X
(16.17)
K 4  j is the transfer function of the SAW filter output circuit,
consisting of Z, L and load resistance R:
(16.18)
K 4  j  R R  Z  jL .
16. When the reflected wave is taken into account the transfer
function of the SAW filter is given by
K  j  K F  j  K p exp 2tL  ,
(16.19)
where t L is the delay time given by tL  L  LK   p and Kp is
transfer coefficient corresponding to attenuation Bd.
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