IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-17, NO. 11, NOVEMBER 1969
927
Characteristics of Microwave Acoustic Transducers
for Volume Wave Excitation
THOMAS M. REEDER,
MEMBER, IEEE, AND
DONALD K. WINSLOW,
SENIOR MEMBER, IEEE
Invited Paper
Abstract-Transducers which utilize acoustoelectric conversion in a
piezoelectric film, plate, or surface have found wide application for gen­
erating planar volume-acoustic waves at microwave frequencies. A review
is given of the electrical impedance, conversion loss, and bandwidth
characteristics for piezoelectric film or plate transducers which vibrate in
one-dimensional thickness extensional or shear modes. The transducer
response is related to the electric and acoustic parameters that describe
METAL TOP ELECTRODE
(Zi. VI)
ACOUSTIC
SUBSTRATE
:3
(Z'o. vo)
the transducer configuration, and experimental examples are given to
illustrate the operation of typical transducer configurations. Methods for
achieving low conversion loss and/or broad bandwidth are discussed and
experimental examples given. Tables of bulk material constants are sup­
plied for commonly used plate and film devices, and transducer fabrication
methods are reviewed. Other types of volume wave transducers, such as
those utilizing a single piezoelectric surface, a diffusion layer in a piezo­
electric semiconductor, or mode conversion at a boundary are also briefly
discussed.
1. INTRODUCTION
RECURRING problem in research on microwave
acoustic delay lines, amplifiers, and related devices
is the design of transducers for converting energy
from electric to acoustic form and vice versa. In general, the
desired characteristics for a transducer are low conversion
10ssl concomitant with large bandwidth. Transducer opera­
tion is a function both of the electric and acoustic parameters
that describe its physical configuration and the electric cir­
cuit to which it is connected. The optimum design for a given
application is frequently a compromise based on a selection
of available transducer materials and the required conversion
loss and bandwidth.
In the present paper we review the design and fabrication
of microwave transducers which utilize acoustoelectric
conversion in a piezoelectric film, plate, or surface to gen­
erate planar volume-acoustic waves. The analysis and design
of transducers which excite surface acoustic waves is con­
sidered elsewhere in this issue [I], [2] . As the majority of
volume wave transducers in use today make use of a film or
plate vibrating in either the thickness extensional or shear
A
Manuscript received July 31, 1969. This research was sponsored by
the USAF Systems Command, Rome Air Development Center, Griffiss
AFB, Rome, N. Y., under Contract AF 30602-6B-C-0074.
The authors are with Stanford University, Stanford, Calif. 94305.
In this paper the term conversion loss is defined as the one way
conversion of electric to acoustic power (or vice versa, since the device
is reciprocal). If two transducers are assembled at opposite ends of an
acoustic substrate to form a delay line, the total insertion loss for the
configuration is the sum of the transducer conversion losses plus the
loss due to propagation through the acoustic substrate.
1
:3
PIEZOELECTRIC L AYER
(Z'O. vol
Fig. 1.
METAL COUNTEF! ELECTRODE
(Z'2. V2)
The piezoelectric layer transducer.
mode, we shall focus our attention on the thickness mode
layer-transducer configuration shown in Fig. 1 . [n Section II
a one-dimensional model is developed and use:d to predict
the electric input admittance, conversion loss, and bandwidth
characteristics of the layer transducer. Low conversion-loss
transducer design by impedance matching of the electric and
acoustic circuits is considered in Section III, as are methods
for achieving broad-band operation. Section IV presents a
survey of film and plate transducer data for piezoelectric
materials of current interest. Fabrication methods are out­
lined, and a discussion of typical reported data is given.
Transducers other than the layer type are considered III
Section V and concluding remarks given in Section VI.
II. IMPEDANCE, CONVERSION Loss, AND BANDWIDTH
We consider the layered transducer configuration shown
in Fig. 1 . The piezoelectric layer, hereafter called the piezo
layer, can be made to vibrate in one or more acoustic modes
by application of a harmonic potential to the metal top and
counter electrodes. In order to simplify the analysis we make
the following assumptions. The transducer lateral dimensions
are large compared to the acoustic wavelength and the
crystal symmetry of the piezo layer is properly chosen [3],
[4] so that the transducer layers can be excited in a pure one­
dimensional mode, with acoustic propagation in the thick­
ness direction. Acoustic loss in the layers is assumed small
enough to be neglected. The acoustic substrate has crystal
symmetry appropriate to the desired mode [5] (i.e., longi­
tudinal or shear) and the electrode layers transmit acoustic
power without mode conversion. Electric contact to the top
928
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, NOVEMBER 1969
!;t
'"
TOP
ELECTRODE
,
, Ii
COUNTER
ELECTRODE
PIEZOELECTRIC LAYER
�r---�tl--�I-+�==�����r-�I---2t -�--�
R1.81
R2.82
L----;R
tl�
I:1
_Co
C
____
ELECTRIC PORT
Fig. 2.
I
i
2
I\- MASON
i EQUIVALENT
J
""'""
Equivalent circuit model for the layer transducer.
defined by the top electrode dimensions. Because of the
central importance of the piezo layer to the acoustoelectric
conversion process, we find it convenient to define normal­
ized electrode thicknesses given by [8]
dl = fo/II = VOh/VIto
d
2 fo/f2 = VOt2/V2tO,
(5)
TI ZI'/ZO' = RI/Ro
Tz = Z 2'/ZO' = R2/Ro
TD = ZD'/ZO' = RD/Ro,
(6)
(7)
(8)
=
(4)
where/I and/2 are, respectively, the top and counter electrode
half-wavelength frequencies. We further define a set of
normalized acoustic impedance ratios,
=
where RI and R2, and RD are the electric unit equivalents of
the electrode and substrate acoustic impedances. For the
ideal lossless transducer the parameters k, Co,/o, dl, d2 , r1,
r2, and rD are f>ufficient to describe transducer operation. In
general, for a given choice of layers and acoustic substrate a
different set ofparameters is found for shear and longitudinal
operation. As seen from the tables given in Section IV, the
electromechanical coupling constant usually falls in the
range 0.I<k<0.7 and the typical range of normalized
electrode and substrate acoustic impedances is 0. 1 <r< 5.
electrode is made such that the free surface is undisturbed.
Acoustic energy generated by the piezo layer is radiated into
the acoustic substrate such that the initial beam size is
defined by the dimensions of the top electrode. Transducers
satisfying the above description may be analyzed by the
one-dimensional theory developed by Mason [6] and ex­
tended by Berlincourt [3], Sittig [7]-[9], and others [10] ­ A. Transducer Electrical Input Impedanc e
[13].
As is shown in the Appendix, the electrical input imped­
The results of the one-dimensional analysis are con­
ance
of the lossless layer transducer has the form
veniently summarized by the equivalent circuit shown in
Fig. 2 where the piezo layer is represented by the Mason
Za IjjwCo + Za,
(9)
circuit [6], the electrode layers are modeled by transmission
lines, the top electrode free surface is assumed to be an where Za= Ra+jXa is a radiation impedance resulting from
acoustic short circuit, and the substrate is represented by a acoustic excitation. Electrical power flow into the real part
real impedance load. Following Berlincourt et al. [3] we of this impedance Ra represents the flow of mechanical power
define electric unit equivalents for the thickness directed into the acoustic substrate. The configuration of layers and
substrate form a one-dimensional acoustic resonator which
force (FD and particle velocity (Ui) as follows
may be operated in fundamental and overtone resonance
(1) modes. The resonator cannot be excited at even mUltiples of
Vi Fi/�
Ii Ui'�
(2) the piezo layer half-wavelength frequency (/0) due to phase
cancellation of the piezoelectrically induced stress. Thus,
where �=hCo may be regarded as the turns ratio of an the frequency response of Ra, which mirrors the response of
acoustic to electric circuit transformer, h if> the appropriate the acoustic resonator, has fundamental and overtone re­
piezoelectric constant, and Co is the clamped (constant sponse lobes that extend from frequency 0 to 2/0, 2/0 to 4[0,
strain) capacitance of the piezo layer. The above definitions and so on. The present discussion will be principally con­
allow the piezo layer specific acoustic impedance2 (Zo') to be cerned with operation in the fundamental mode between
expressed in electrical ohms by
frequencies 0 and 2/0, but operation in the overtone modes is
also important for some applications.
AZo'
11"
)
= --Ro = -(3
Where the electrode layers are acoustically thin (d!,
wOCOk2
�2
d2<0.1), the frequency response of Za has the relatively
where /0= wo/211" vo/2to is the half-wavelength frequency simple form given in (44) through (47). The real and imag­
defined by the piezo layer acoustic velocity Vo and thickness inary parts of Za exhibit essentially even and odd symmetry
to, the quantity k is the appropriate electromechanical cou­ about/o, respectively, with
pling constant [3], [4] , and A is the transducer active area
(10)
Ra = Ra (4k2/1I"TD) (1/woCo)
(11)
Xa = 0
2 The specific acoustic impedance of a material is defined by Z' =pv
=
=
=
=
=
where p is the material mass density and v is the acoustic wave velocity.
The prime is used in this paper to set apart acoustic impedances, which
have the units kg!m2·s in the MKS system, from electric impedances,
which are defined in ohms.
at /=/0' The frequency response over the fundamental andl
overtone ranges is identical for
f this case with range center
frequencies given by /n=nodd O'
REEDER
AND
WINSLOW: CHARACTERISTICS OF MICROWAVE ACOUSTIC TRANSDUCERS
For use in impedance matching considerations it is desir­
able to assess the electric Q of the transducer input imped­
ance. However, the usual definition of circuit Q is somewhat
difficult to apply since the radiation impedance is a function
of frequency. Since the transducer response is related to the
piezo layer/0, it is convenient to define at/ =/0 a transducer
radiation Q given by
Qr = l/woCoRa,
(12)
=
Z8e + l/jwCo + Za.
20
..,
Iii 16
_
12
"
..!...
'"
8
9 4
o
(13)
As the typical layer transducer may have parameters in the
range 0.1<k<0.7 and 0.1<rD<5, the radiation Q can cover
a wide range of values depending on the transducer con­
figuration. For many microwave designs the value of Qr is
in the range 5 to 50. The resultant electric impedance be­
havior is quite reactive and can present some difficult design
problems. As an example, consider the case of a longitudinal
mode thin-film transducer with the thin electrode (ZnO/Z­
oriented sapphire) configuration. Parameter values for this
case are frequently l /wo Co=50 ohms, k=0.2, and rD= 1.24.
The corresponding values of Ra and Qr are then 2.1 ohms and
24, respectively.
In the above discussion we have tacitly assumed that the
transducer layers are electrically lossless. For most layer
transducers the piezo layer is a high-quality dielectric so
that conduction losses through the layer may be neglected.
However, the effect of series contact and electrode conduc­
tion impedances are often significant at microwave frequen­
cies and cannot be neglected. We shall represent the series
impedance by Zse=R.e+jXse so that the total input imped­
ance for the transducer becomes
Za
24·r-�--------n--'
Q
which for the thin electrode case reduces to
Q, = l/woCoRa = 7rrD/4k2.
929
(14)
Although current flow through thin electrode layers may
contribute to Z8., the major portion of Zse usually arises
from the available methods of electric contact to the top
electrode layer, which is typically obtained with a miniature
metal spring 01 thin bonded wire. For typical microwave con­
figurations the component X8e is inductive with inductance
values in the range 0.1 to 1 nH [14]. Values of Rse in the
range 0.1 to 2 ohms have been reported [15], [16], and for
devices operating above 1 GHz, R8e is frequently equal or
larger than Ra.
B. Untuned Conversion Loss
If the transducer is connected directly to a source with
real impedance Zo, the transducer is said to be untuned. Un­
tuned conversion of electromagnetic to acoustic power (and
vice versa by reciprocity) is given by the loss ratio
(15)
where PAis the power available from the source under
matched conditions and PL is the power absorbed by the
real part of the transducer radiation impedance [17]. By
straightforward circuit analysis the conversion-loss ratio
Fig. 3.
Acoustic bandshape response for layer trans­
ducers with acoustically thin electrodes.
becomes
T(f)
(Zo + R8e + Ra)2 + (X.e + Xa - 1/wCo)2
=
4ZoRa
(16)
where, in general, the frequency dependence of Ra and Xa
are given by (44) and (45). Equation (16) may be expressed
as the product of two conversion-loss bandshape functions
T(f)
=
(17)
[Me(f)][Ma(f)]
where Me(!) and MaC!), respectively, are related to the
response of the electrical circuit and to the response of the
acoustic resonator formed by the layers and substrate. We
shall define the electric bandshape function by
M (f) =
.
(Zo + Rse + Ra)2 + (X8e + Xa - l/wCo)2
'
4ZoRa(wo/w)2
(18)
and the acoustic bandshape function by
Mif) =
Ra(wo/w)2
(19)
Ra
Although the response of the electric and acoustic portions
of the transducer are not independent for values of k greater
than zero, the above definitions allow the acoustic resonator
response to be compared with an electric response function
that is primarily controlled by the input electric circuit. We
shall see that the bandwidth of electric and acoustic re­
sponses can be quite different, and from (17) note that the
conversion-loss bandwidth will be limited by the bandshape
function with narrowest response.
For acoustically thin electrode layers the acoustic band­
shape function reduces to the simple form
Ma(f)
(sin (Jo)2 + (rD cos (Jo)2
=
(rn/2)2(1 -
cos
(20)
(Jo)2
by combining (39) through (43) with d1 = d2 O. Thus, for
thin electrodes, Ma(J) is unity at/I.ro = 1 and is symmetrical
about/o. The series of curves calculated from (20) and given
in Fig. 3 shows that the acoustic bandshape is a pronounced
function of rD. Substrates with normalized acoustic imped­
ance higher than rD = v!2 give a double minimum response.
=
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, NOVEMBER 1969
930
24
24 ,-,,-----r-.
I
20
iii
:e 16
-- d2
=
0.0
- - - d2
=
0.2
--- d 2
=
1.0
n
I
h
20
iii
:e 16
r;::1
!::
0
::E
�
'"
'" 8
9
Q 4
9
12
8
� 4
•
•
,
,
.
'.
\\
\ \
I
1\
I
'
•
\
I
,
\
I
\
\\
I
I
\
\
'-'
\,
I
1\
I \,
/
\•
\
0
o
-4������_f��--���-L--��
o
0.2 0.4 0.6 0.8 1.0
1.2 1.4
1.6 1. 8 2.0
NORMALIZEO FREQUENCY
(flfol
Fig. 4. Acoustic bandshape response as a function of counter elec­
trode thickness. Curves computed for the longitudinal mode
(ZnO/Au/Z-oriented sapphire) configuration with d,=O, r2=1.71,
and rD=1.24.
Where the resonance of the piezo layer is heavily loaded by
the acoustic substrate, the fractional bandwidth exhibited by
Ma(f) is relatively large. For configurations with rD in the
range 0.5 to 2, the 3-dB bandwidth ranges from 0.23 to 1.1.
When the electrode layers are not acoustically thin, the
acoustic bandshape will not in general be symmetrical about
/0 and may be considerably distorted compared to the simple
response given in (20). For example, consider a longitudinal
mode thin-top electrode transducer with the (ZnO/ Au/Z­
oriented sapphire) configuration. Assuming single-crystal
bulk media, rD=1.24 and r2=1.71. Calculated bandshape
curves are shown in Fig. 4 for values of normalized counter
electrode thickness of d2=0, 0.2, and 1. Note that significant
perturbation of the bandshape occurs even for the relatively
thin counter electrode with d2=0.2, which corresponds to
an electrode thickness of 0.1 wavelength at ///0=1. The
frequency of minimum loss now occurs at///o=0.74. For
thick counter electrode layers a ripple of approximately 2
dB is introduced into the passband for the present configura­
tion, and if d2 is an integer the acoustic bandshape will be
symmetrical about/o. Thus, if fabrication requirements de­
mand a relatively thick counter electrode and if the passband
ripple so incurred can be tolerated, the layer thickness may
still be chosen for symmetrical response and large acoustic
bandwidth.
For the case of a finite thickness top electrode and acousti­
cally thin counter electrode, the perturbation of acoustic
bandshape is even more pronounced, since the effect of the
top electrode is to introduce one or more poles of loss in the
acoustic response [18] . Acoustic bandshape curves for the
previously discussed ZnO transducer are shown in Fig. 5 for
a gold top electrode of normalized thickness d1=0, 0.1, and 1.
Even the relatively thin electrode with d1=0.1 has caused a
significant passband perturbation by introducing a loss pole
at///0=1.54. The frequency of minimum loss is moved down
to ///0=0.80 but the 3-dB fractional bandwidth is almost
unchanged. As d1 becomes larger than 0.5, additional poles
of loss are added to the acoustic bandshape, splitting up the
passband into several segments. The top electrode perturba­
tion is a serious limitation at the higher microwave frequen-
4
- 0
0.2
0.4
0.6
0.8
1.0
1.2
NORMALIZ ED FREQUENCY
1.4
(f Ifol
1.6
1.8
2.0
Fig. 5. Acoustic bandshape response as a function of top electrode
thickness. Curves computed for the longitudinal mode (Au/ZnO/
Z-oriented sapphire) configuration with r, = 1.71, d2 = 0 , and
rD= 1.24.
cies since fabrication requirements usually dictate a mini­
mum electrode thickness for reliability. For the above ZnO
transducer with a gold top electrode of only 0.05 Mm the
normalized thickness is about 0.3 at X-band. If/o=10 GHz,
a pole of loss is introduced at 11.5 GHz and the frequency
of minimum loss occurs at 6.0 GHz.
The electric bandshape function for untuned transducers
with moderate coupling constants (k2«1) and contact
impedance much less than the source impedance simplifies
from (18) to the approximate form
ro./
7rrD
M.(f)= 16k2
[1 + (wCOZO)2] .
woCoZo
(21)
For a given frequency the minimum loss occurs for wCoZo
=1, and at frequencies where wCoZo»l the electric band­
shape response increases as w2• This type of electric circuit
response is expected where the transducer electric Q is high
since the input impedance is then dominated by the reac­
tance l/wCo.
In Fig. 6 the measured untuned conversion loss of a longi­
tudinal mode thin-film transducer is compared with the
response calculated from the above analysis [19 ] . The trans­
ducer has the (CdS/ Au/Z-oriented sapphire) configuration
with an acoustically thin counter electrode. A top electrode
layer was not used; the transducer was mounted in a coaxial
adaptor such that the outer conductor contacted the counter
electrode and the center conductor pressed gently against the
CdS film-free surface. The resultant electrode capacitance
was measured, and the transducer acoustic constants were
calculated from bulk material data. The effective coupling
constant was used as an adjustable parameter to allow a best
fit of the theoretical curve and experimental data, but the
value found, k=0.022, is much lower than the value k=0.15
measured for bulk crystal CdS layers [3 ]. However, a lower
value of k is expected here since the electric field filling factor
is likely to be reduced when the top electrode layer is not
used. The conversion-loss response seen in Fig. 6 has the
shape expected from a multiplication of the electric band­
shape function given in (21) with a symmetrical acoustic
bandshape function of the form shown in Fig. 3.
REEDER AND WINSLOW: CHARACTERISTICS OF MICROWAVE ACOUSTIC TRANSDUCERS
931
10 r------------.
60 r------.
50
8
iii 40
�
::l
9
". . .
z
o
in
Trans. ER
ffi 20
8 10
••••
tCdS = 0.83J.'m
tAu = 0.07J.'m
f=0 .
fo
�
..
. .
.J
f· fo
0.8
-- T HEORY
6
• ••• EXPERIMENT
Z
o
in
-- THEORY
CdS-Au-SAPP
>
z
.
If)
II:
UJ
>
Z
o
u
EXPERIMENT
f= 1.5 fo
4
2
4.4
FREQUENCY (GHz)
Fig. 6. Untuned conversion loss for a longitudinal mode thin-film
transducer with the (CdS/Au/Z-oriented sapphire) configuration.
Theory curve computed for k=0.022, Co=2.6 pF, /0=2.59 GHz,
d1=0, d2=0.12, r2=2.85, and rD=2.06. (After Reeder [19].)
C. Tuned Conversion Loss
In order to achieve low conversion-loss operation, the
reactive transducer impedance must be conjugately matched
to the source impedance Zoo The effect of transducer reac­
tance may be canceled by the addition of an appropriate
series or shunt tuning inductor at the transducer electric
terminals. However, shunt inductive tuning is preferred for
frequencies above 1 GHz for several reasons. If series tuning
is used, the inductor is designed to be resonant with the
transducer reactance, Xse+Xa-l/ wCo• The remaining real
part of the impedance, Rse+ Ra, is typically on the order of
several ohms, so that a mismatch loss of approximately 10
dB is stilI incurred where Zo is 50 ohms. One could design
the transducer capacitance to be small enough that Ra
= (4k2/'lrrD)(l/wOCo) is approximately equal to Zo, but for
transducers operating at 1 GHz and above this design would
result in relatively small transducer lateral dimensions. For a
longitudinal mode thin-film ZnO transducer driven from a
50-ohm source the value of Co needed to provide Ra=Zo is
approximately 0.1 pF with the corresponding top electrode
dimensions on the order of 0.1 mm. Such small dimensions
would make electrical connection to the microwave circuit
difficult and the small capacitance would likely be dominated
by spurious circuit effects. Further, a collimated acoustic
beam is usually desired in the acoustic substrate, which
implies a top electrode with lateral dimensions large com­
pared to the acoustic wavelength so that acoustic beam
diffraction is minimized [20], [21].
Where shunt inductive tuning is used the inductor is
designed to electrically resonate the shunt susceptance of the
transducer. The transducer shunt conductance increases as
Co increases, and a convenient value of Co can usually be
found such that a conjugate match is obtained. If we express
the transducer admittance by Ya=Gd+Ga+jBT, the shunt
tuned conversion-loss ratio [ 17] is given by
5
•
L_
O �__�____-L____�____
0.42
0. 3 0
FREQUENCY
0. 4 6
___.J_____J
0.50
0.5 4
(GHz)
Fig. 7. Tuned at each frequency conversion loss for a longitu­
dinal mode thin-film transducer with the (Au/ZnO/Au/fused
quartz) configuration. Theory curve computed for Rs.=0.5 ohm,
L••=X,./w=0.5 nR, k=0.20, Co=37 pF, /0=0.52 GHz, d1=d2=
0.065, r1=r2=1.71, and rD=0.364.
Ra, respectively; the total transducer susceptance is BT; BL
is the susceptance of the shunt tuner; and Yo is the source
admittance. For transducers with moderate coupling con­
stant and small contact impedance (IZ8e+Z" 1 « l /w Co) the
admittance components are given approximately by
Gd '" Rse(wC0) 2
(23)
�"'&��2
BT"'" wCo + (Xse + Xa)(wCO)2.
��
(25)
When the transducer is shunt resonant at frequency JR the
conversion-loss ratio becomes
(26)
Minimum tuned loss occurs for Gd+Ga = Yo, in which case
(26) becomes
T(fR) = 1 + Gd/Ga ,..., 1 + R,e/Ra•
(27)
Thus, if series contact resistance is appreciable comparable
to Ra, the minimum conversion loss will be greater than zero
even when conjugate match conditions prevail. However, it
is possible to design active matching networks that essen­
tially add negative resistance to cancel out the effect of Rse,
as is shown by Ho and Bahr [22]. It should also be pointed
out that if the transducer is lossless (Rse=O) and if a con­
jugate impedance match is achieved at the transducer elec­
tric terminals, the acoustic impedance seen by signals im­
pinging on the transducer from the acoustic substrate is also
conjugately matched so that no acoustic reflections occur.
Simultaneous electric and acoustic impedance match is not
possible, however, when R8e is greater than zero.
An example of tuned conversion-loss data is shown in
(Yo + Gd + Ga)2 + (BT + BL)2
(22) Fig. 7 for a longitudinal mode thin-film transducer with the
T(f)
4 YOGa
(Au/ ZnO/ Au/ fused quartz) configuration. Shunt inductive
where Ga and Ga are conductances proportional to R.e and tuning was used to obtain electric resonance at each fre=
932
IEEE TRANSACTIONS ON MICROWAVE THEORY
quency of measurement. Contact impedance and transducer
capacitance were estimated by experimental measurement at
frequencies away from maximum acoustic excitation. The
theoretical curve shown in the figure was found using bulk
material acoustic constants with k adjustable for the best
theory-experiment comparison. A value of k=0.20 was
found in this case as is typical of vacuum deposited ZnO
layers which vibrate in the longitudinal mode. This trans­
ducer was designed to have a relatively large susceptance
(woCo/Yo=6) in order to achieve the minimum tuned loss
condition Gd+Ga= Yo at a frequency near /0=0.52 GHz.
For the transducer capacitance and contact impedance
actually achieved during fabrication the optimum condition
obtained at/=0.42 GHz.
The tuned-loss expression (22) can also be written as the
product of electric and acoustic bandshape functions as was
done above for the untuned case. The bandshape functions
are in this case
M.(f) =
(Yo + Gd + Ga)2 + (BL + BT)2
4 YoGa
(28)
with Ga=(4k2/7rrD)(wO CO) and
Mif) = Ga/Ga.
(29)
For transducers with electric Q greater than 5, the acoustic
bandshape is approximately
Ma(f) "-' Ga/Ra(WCo)2 = Ra(WO/W)2/Ra
(30)
AND
TECHNIQUES, NOVEMBER 1969
I
L______________ ....'-- MATCHING
NETWORK
Fig. 8. Two-element network for moderate
bandwidth electric-circuit matching.
reflection loss over the desired bandwidth, and the higher the
load Q, the higher the reflection loss required. An excellent
review of these broad-band restrictions is given by Matthaei
et al. [25J .
In this section we first consider simple methods of electric
and acoustic circuit matching which allow efficient trans­
ducer operation over moderate bandwidths up to 15 to 20
percent. Methods of broad-band operation (bandwidth
greater than 20 percent) are then discussed from two points
of view. For low-coupling high electric Q devices, the reflec­
tion filter method of Matthaei [26] is described. The second
approach, discussed by Sittig et al. [9] uses a thin-plate piezo
layer of relatively high coupling constant (k�O.5) to achieve
low-transducer electric Q with broad-band untuned opera­
tion.
A. Electric Circuit Matching
which is the same as defined for untuned conversion loss.
In Section II a method of shunt-tuned electric impedance
When fixed tuned at /=/R we may view the transducer as matching was discussed which used the transducer capaci­
two coupled resonators, one electric and the other acoustic. tance as a parameter in order to match the total shunt con­
Where the loaded Q of the electric resonator is large, the ductance to the source admittance. For many transducer
bandwidth of MeCf) will be small. If the acoustic response applications this method is unacceptable since a specific
expressed by Ma(f) is relatively broad-band with/=/R well acoustic beam size, and hence a specific capacitance, is
inside the acoustic passband, the transducer frequency re­ desired. Here we consider the two element network shown in
sponse is essentially determined by the electric circuit Fig. 8 which provides impedance matching with a fixed value
response.
of transducer capacitance. The network consists of series
and
shunt inductors which can be designed to give a con­
III. DESIGNS FOR Low CONVERSION
jugate
impedance match at one frequency. The inductance
Loss AND BROAD BANDWIDTH
Ls. provides a useful immittance transformation as may be
One of the continuing problems in the fabrication of seen by evaluating the admittance at terminals 3' and 3'.
practical microwave transducers is the design of impedance Assuming X. .=wLs• is not close to series resonance with the
matching networks which allow efficient operation over a transducer reactance XT=Xa-l/ wCo, the admittance com­
broad bandwidth. We have seen in Section II that the ponents are given approximately by
acoustic response of typical layer transducers may be quite
B "-' Bsh - 1 /(X + XT)
(31)
broadband; 3-dB acoustic bandwidths of one octave are
easily achieved. However, the relatively small electro­
Rs./XT2
Gd�----�----�-(32)
mechanical coupling factors available for most piezo layer
- - I X. /XT I )2
.
(1
materials result in high-Q electric circuit response.
Broad-band impedance matching of reactive loads was
Ra/XT2
Ga "-'
(33)
considered many years ago by Bode [23] and Fano [24], and
(1
I X8./XT I )2
useful guidelines and network requirements were set forth.
In particular, when an ideal matching network is inserted If the transducer resistance R..+ Ra is less than the source
between the reactive load and a resistive source, there is a impedance, a value of Ls. can be found such that the condi­
definite relationship between the integral of the network in­ tion Gd+Ga= Y o obtains at a given frequency. A conjugate
put reflection coefficient and the load Q. Broad-band opera­ match and minimum conversion loss are then obtained by
tion is obtained only by designing the network for uniform adjusting L." for shunt resonance, and the conversion loss is
••
_
933
REEDER AND WINSLOW: CHARACTERISTICS OF MICROWAVE ACOUSTIC TRANSDUCERS
iii
3
9
en
en
o
in
z
�
a::
8
16
16,r---.-.------rr----,
12
12
8
iii 8
'"
4
O�--�----L---�--�
1.6
1.8
2.0
2.2
2.4
(a )
9
7
•••••
o
�O
\
\
\
\
\
\
\
\ I
'"
9
2
-4
-8
EXPERIMENT
-- d2
=
0.0
---- d2
=
0.5
...L..-l
-12 �-:'-::---:L----:�-1_-,L_�---l'-_...L_.
-- THEORY
o
�
M
M
M
W
�
NORMALIZED FREQUENCY
a::
:=
�
(fifo)
�
�
W
Fig. 10. Acoustic bandshape curves, with and without an Al counter
electrode, for a longitudinal mode (ZnO/Z-oriented sapphire) trans­
ducer. Curves computed for d1=0, r2=0.478, and rp =1.24.
en
>
FREQUENCY (GHz)
(b)
Fig. 9. Tuned at each frequency (a) conversion loss and (b) in­
put VSWR for a longitudinal mode thin-film transducer of the
(Au/ZnO/Au/Z-oriented sapphire) configuration. Theory curves
computed for R,,=0.5 ohm, L.. =0.6 nH, k=0.17, Co=5.9 pF,
/0=2.1, d1 =d2 =1, r1 =r2=1.71, and rD=1.24.
again given by (27). A complete analysis shows that the
conversion-loss bandwidth when X is present is reduced by
approximately the factor (1-1 X / XTI)2 compared to the
shunt tuned case with X = O. At the same time the conver­
sion-loss ratio is reduced by about the same factor indicating
that the ratio of conversion loss and bandwidth remains
almost constant. Thus, the two-element matching network
simply trades lower conversion loss for reduced bandwidth,
as is expected from ideal matching network theory [23], [24].
In some cases the small value of L obtained when making
contact to the transducer can be used with the appropriate
choice of Co to provide a conjugate match. This method was
used to design the longitudinal mode ZnO transducer whose
conversion loss and VSWR characteristics are shown in
Fig. 9. The theoretical curves were calculated using the cir­
cuit in Fig. 8. Bulk material acoustic constants were used,
and the values of LB. and Co were estimated from tuned
impedance measurements. The effective coupling constant
and contact resistance were used as adjustable parameters to
allow a best fit of theory and experimental. The tuned at
each frequency 3-dB bandwidth seen in Fig. 9 is 33 percent.
However, the bandwidth when fixed tuned at a given fre­
quency ranged from 10 to 20 percent.
••
••
••
••
B. Acoustic Circuit Matching
A conjugate impedance match under the condition of
shunt electrical resonance may also be obtained by a suitable
Zo
Fig. 11.
Zb
ACOUSTIC
SU BSTRATE
Transducer with multilayer acoustic matching configuration.
sions. Thus, the counter electrode parameters should be
selected to increase Ga at the frequency of shunt electrical
resonance fR' This is equivalent to decreasing the value of
MaCfR) as may be seen from (29).
One case of particular interest is where the electrical
resonance coincides with the piezo layer half-wavelength
frequency (fR=fo). If we design the counter electrode to be a
quarter-wavelength thick at fo (normalized thickness
d2= 0.5), the radiation conductance atfo is then
Ga(fo) = (4rDk2/7r) (woCo) h) -2.
(34)
A counter electrode with a sufficiently low value of normal­
ized acoustic impedance could be used to proviide Ga(fo) Yo.
Fig. 10 compares the acoustic bandshape curves for a longi­
tudinal mode transducer of the (ZnO/ Al/Z-oriented
sapphire) configuration, with counter electrodes of zero and
quarter wavelength thickness. The aluminum electrode, with
normalized impedance r2=0.478, produces an 8.3-dB reduc­
tion in the value of Ma(fo), which from (29) means a 6.8
fold increase in Gifo). One finds from an analysis of multi­
layer acoustic resonators [27] that the bandwidth of acoustic
response tends to fall off faster than the increase in Ga(fo).
This statement is born out by the curves in Fig. 10 which
=
show that the addition of the matching layer has reduced the
choice of counter electrode thickness and acoustic imped­ 3-dB acoustic bandwidth from 92 to 10 percent.
Counter electrodes consisting of muItilayers arranged in
ance. For the discussion that follows we assume an acousti­
cally thin top electrode, zero series contact impedance, and pairs [28] as shown in Fig. 11 can be used to provide much
a moderate value of piezo layer coupling constant. As dis­ larger values of Ga(fo) than available with a siingle layer, but
cussed earlier, the ratio Ga/ Yo-:::R
: a/Zo is typically much less with still greater sacrifice in bandwidth. Assuming that these
than one for convenient choices of transducer lateral dimen- matching layers are all one-quarter wavelength thick at fo
IEEE TRANSACTIONS ON MICROWAVE THEORY
934
16
12
Iii
�
.-.
-
0
::;
'-'
'"
3
�
B
4
0
-4
-B
AND TECHNIQUES, NOVEMBER
1969
50 r----,
.". --- ....,
"
\
\
\
\
\
\
\
\
\
40
,/
I
I
I
I
I
,
I
\
I
I
I
\
, I
, I
, I
, I
,I
II
"
- - - - - COMPUTED
I
-- d.=db =
----- d. = db =
0.5
0::
ILl
>
z
o
t.>
-12 L---'-----'--'--L---1--'
o
0.2 0.4 0.6 O.B
1.0
1.2
1.4 1.6
I.B
2.0
NORMALIZED FREQUENCY (fIfO)
(normalized thicknesses cia = db 0.5), the radiation con­
ductance is
=
GaCfo) = (4k2/7f'TD)(woCo) (Tb/Ta)2N.
"
I
10
O
\
��
500
���
____
1000
FREQUENCY
/ \'
,
I
,
I
I
\
I
I
I
r
,
���
__
I,
1\
' ,
\
I
,
I
I
"
III
(�I
'I I\
\\I1'
4.5
Fig. 12. Acoustic bandshape curves, with and without Al/Au match­
ing layers, for a longitudinal mode (ZnO/Z-oriented sapphire)
transducer.
\
I
I
." 30
U)
U)
o
oJ
z 20
o
iii
0.0
I
I
/'
m
I
I
I
I
1\
:\
\
-- MEASURED
"".... --....
, I�\
I
I
I
'I
\I
�
IUI I' " ".,
�
1II1
� "J
. ,
,
�
��
____
nl'
I, II
lit III
II' .1
I
I
I
,
��
____
MHz
Fig. 13. Tuned at each frequency conversion loss for a longitudinal
mode (CdS/Au/SiO/Z-oriented sapphire) transducer. The acoustic
constants are /0=1.74 GHz, da=1.1, ra=2.85, db=1.0, 10=0.778,
and rD=2.06. (Mter Winslow and Shaw [29].)
(35)
layers since the transformation ratio provided by two layers
is usually sufficient to achieve Ga-:::::" Yo and the fabrication
problems increase rapidly as more layers are used. Success­
ful acoustic matching experiments of the type discussed
above have thus far yielded, for a given conversion loss, fixed
tuned bandwidths much less than that obtained for simple
electric circuit matching.
It should also be pointed out that where two or more
layers are used such that the acoustic bandwidth narrows to
a few percent or less, the acoustic bandshape loss will be
significantly increased by the presence of
] [ ] small
[ relatively
acoustic transmission losses in the layers 4 2 , 44 . Similar
loss effects are observed for narrow-band electromagnetic
filters
[25].
(36)
Thus, a low-impedance layer "a" followed by a higher­
impedance layer "b" is needed to enhance GaUo). The
acoustic bandshape for a longitudinal mode, (ZnOIAllAu
IZ-oriented sapphire) transducer is compared in Fig. 12
with the equivalent curve for thin electrodes. The matching
films result in a decrease of MaUo) of 11 dB or an increase in
GaC/o) of 13. However, the 3-dB bandwidth of the MaCn
curve is reduced to 5 percent.
Another case of interest occurs for electrical resonance at
the piezo layer quarter wavelength frequency (fR=/o/2).
For a single counter electrode layer designed to be a quarter
wavelength at/o/2, the radiation conductance is
GaCfo/2) = (k2j-Tr'rD)(wOCO)(r2)2
so that an electrode normalized impedance greater than one
is needed to increase GaC/o/2). If a multiquarter-wavelength
layer configuration is used, the conductance becomes
C. Broad-Band Methods
Although the synthesis of microwave networks for broad­
band operation of reactive loads is a difficult task, several
have been discussed in the
[design
] [ methods
]
[
(37) straightforward
GaCfo/2) = (k2rD/7r)(WOCO)(Talrb)2N
literature 26], 30 , 3 1 . The design of a practical network
indicating that the layer impedance ratio ralrb should be is very dependent upon the actual values of load impedance
greater than one to achieve matching. An experimental and Q. For broad-band operation of microwave transducers
[ ]
example of the multilayer type of matching is shown in the coupled resonator approach of Matthaei et al. 26 has
Fig. 13 for a longitudinal mode (CdSIAu/ SiO/ Z-oriented been used to design efficient networks which are conveniently
sapphire) transducer [29]. This transducer used a miniature
fabricated in transmission-line format [32]. Fig. 14 shows
spring contact without a top electrode layer, and a coaxial the form of a three-resonator network of this type. The net­
multistub tuner was used to electrically match the device to work consists of two transmission-line resonators and the
the source at each frequency. Contact effects were important shunt resonant transducer which are coupled together by
so that a perfect match with zero-dB conversion loss was not transmission-line impedance inverters. Calculation of the
possible, but the response was clearly optimized at /,'''fo/2 network line impedances is carried out by transforming the
= 0.87 GHz.
bandpass circuit in Fig. 14 into low-pass filter form for which
In comparison with the simple electric circuit matching standard design methods are available. Although the choice
method, acoustic circuit matching is less useful since a of line impedances is not unique for a given network re­
limited number of counter electrode materials are available sponse, impedance values in the practical range of 10 to 100
whose acoustic properties may be selected concomitant ohms can usually be obtained for microwave transducers of
with the electric contact and layer fabrication requirements. the type considered here. The network can be designed to
In practice, one rarely uses more than two acoustic matching yield a Chebyshev response with a ripple less than 3 dB over
REEDER AND WINSLOW: CHARACTERISTICS OF MICROWAVE ACOUSTIC TRANSDUCERS
). R/4
Zo
).R/4
ZI
1
24 r----------�
iii 20
�
gj
9
z
� �
).R
4
Fig. 14.
).R
4"
Three-resonator network for broad-band transducer operation.
935
ffi
>
�
�
(.)
CONVERSION LOSS
16
�t
12
E
8
4
12
'
�--���-L--�--L-�
O.����-1.4
VSWR
fR
1.2
1.3
1.5
1.6
1.7
1.8
FREQUENCY (GHz)
1.9
2.0
10
8 a:
�
6 '"
>
4
2
2.1
I
bandwidths up to 30 percent. The three-resonator network Fig. 15. Conversion loss and VSWR for a broad-band L-band
transducer utilizing a three-resonator network. The longitudinal
is capable of near ideal response for moderate bandwidth de­
mode thin-film transducer has the (Au/ZnO/Au/Z-oriented sap­
signs, but for bandwidths over 30 percent the nonideal fre­
phire) configuration with electric Q =22 and Gd+Ga =4.1 m!J at
/R =1.65 GHz. The transmission-line impedances are Zl=Z23 70!J,
quency dependence of the impedance inverters and trans­
Z2=23!J, and Z3=16!J. (After Reeder and Olson [32].)
ducer shunt conductance causes increased passband ripple.
[ ]
Experimental data for a successful L-band transducer 32
utilizing the three-resonator circuit is shown in Fig. 1 5. The
50
transducer is a longitudinal mode thin-film device with the
iii
(Au/ZnO/Au/Z-oriented sapphire) configuration. A thirty­
� 40
percent bandwidth design was chosen here, and the average
'"
'"
0 30
passband VSWR predicted by this choice is 5.5, indicating
...J
Z
that the network should reflect about 3 dB of the incident
0
i= 20
a:
power in order to provide constant coupling over the band­
'"
'"
10
width. The average conversion loss seen in Fig. 15 is 8 dB
�
3fO
which is consistent with the above prediction in that the
0
100
400
500
600
transducer used exhibited 5 dB conversion loss when shunt
FREQUENCY (MHz)
tuned and impedance matched at 1 .7 GHz.
In principle, the coupled-resonator approach could be Fig. 16. Insertion loss for a broad-band VHF delay line utilizing
bonded single-crystal transducers and untuned terminations
used at all frequencies where thin-film transducers can be
(woCoZo�l). Each transducer consists of a 35° rotated Y-cut
fabricated and electrically resonated (i.e., 0.1 to over 10
LiNb03 plate bonded through acoustically thin Au/In layers to the
fused delay line substrate. (After Meitzler and Sittig l36].)
GHz). However, at frequencies below 1 GHz the network
size becomes unwieldy unless high-dielectric constant strip­
lines are used. At frequencies higher than S-band the com­
posite transducer and network becomes increasingly more shown in Fig. 16 by subtracting the acoustic propagation
difficult to fabricate and test since the size tolerance becomes loss in the 6.35-mm-long quartz delay line and dividing the
small and the effect of spurious circuit effects tends to in­ remainder by two. At the minimum loss frequency (160
MHz) a delay line loss of[ approxima
tely 1.5 dB is estimated
crease.
]
Recent advances in transducer materials and fabrication from published loss data 37 yielding a minimum conversion
techniques have made possible the operation of bonded loss of 1 dB. The 6-dB insertion-loss bandwidth shown cor­
single-crystal piezo
[ ]layers
[ ] with fundamental mode operation responds to a 3-dB conversion-loss bandwidth of 43 percent.
above 0. 1 GHz 33 - 35 . Such devices can typically exhibit The frequency position of minimum conversion loss may be
coupling constants in the range 0.3 <k<0.7, and for some understood from (16) and frequency response of Ra and Xa
configurations may have electric circuit Qs as low as one. given in (44) through (47). Although Ra peaks near /=/0
As described by Sittig et al. [9], relatively efficient broad­ and has even symmetry about /0, the reactance Xa has odd
band conversion-loss response is obtained with untuned symmetry about/o with an inductive peak slightly below and
operation and transducer capacitance chosen such that capacitance peak slightly above /0' Minimum loss occurs
woCoZo'""1. Fig. [16 ]shows measured insertion-loss data for a near the inductive peak since the transducer electrode capac­
VHF delay line 36 using longitudinal mode LiNb03 trans­ itance is appreciably canceled by the addition of Xa.
=
ducers with coupling constants of approximately k=O.S.
As a result of their high-coupling constants, bulk crystal
The piezo layers were fabricated from 35° rotated Y-cut piezo layers are at present capable of lower conversion loss
plates which were bonded to the fused quartz delay line over broader bandwidths than are vacuum deposited layers.
substrate through acoustically thin Au/In bonding layers. However, the extreme problems of fabricating a bulk crystal
After final polishing the piezo layer thickness was reduced to with thickness less than a few micrometers has at the present
20 JIm corresponding to an /0 of 185 MHz. The transducer limited the use of these devices in their fundamental mode to
conversion loss can be obtained from the insertion loss frequencies below 1 GHz.
IEEE TRANSACTIONS ON MICROWAVE THEORY
936
TABLE I
BULK MATERIAL CoNSTANTS FOR CoMMON PIEZOELECI'RIC LAYERS
AND TECHNIQUES, NOVEMBER
1969
[38], [40], [42]
Cut
Mode
k
ES/EO
vo(1()3 m/s)
Zo'(10· kg/s·m2)
X
Longitudinal
ku=0.093
4.5
5.00
13.3
Y
Shear
k12=0.14
4.5
3.80
10.1
Z
Longitudinal
k,=0.15
9.5
4.46
21.5
X
Shear
k15=0.19
9.0
1.76
8.5
Z
Longitudinal
k,=0.28
8.8
6.33
36.0
X
Shear
k15=0.32
8.3
2 .72
15.5
AIN
Z
Longitudinal
k,=O.17
8.5
LiNb03
Z
X
Yllf'
Longitudinal
Shear
Longitudinal
k,=0.17
k=0.68
k=0.5
29.0
44.0
7.33
4.80
7.40
34.0
22.6
35.0
Z
Longitudinal
k.=0.30
8.5
6.10
25.6
X
Shear
k15=0.17
7.0
3.31
13.9
Material
SiO.
CdS
ZnO
LiGaO.
10.4
34.0
TABLE II
BULK MATERIAL CONSTANTS FOR SELECI'ED ACOUSTIC SUBSTRATES AND ELECI'RODE LAYERS
Material
Propagation
Direction
Mode
Z
Longitudinal
Z
Shear
6.04
25.2
Z
Longitudinal
6.32
16.7
Be
Shear
5.00
13.4
Longitudinal
5.97
13.1
Shear
3.76
8.3
[100]
Longitudinal
3.21
61.3
[100]
Shear
1.47
28.4
[100]
Longitudinal
3.44
36.1
[100]
Shear
2.09
21.9
[100]
Longitudinal
6.35
17.2
[100]
Shear
3.25
8.8
Longitudinal
2.5
18.0
Shear
l.3
9.4
v(1()3 m/s)
11.1
Zo'(10· kg/s·m·)
44.3
67
Ab03
SiO. (crystal)
SiO. (fused)
Au
Ag
Al
In
IV. TRANSDUCERS USING THIN PIEZOELECTRIC
FILMS AND PLATES
In the previous sections it has been shown that the fre­
quency response and conversion loss for piezo-1ayer trans­
ducers is principally determined by the quantities k, Co, and
the acoustic parameters of the configuration illustrated in
Fig. 1 . In this section we list the material parameters for
commonly used transducer layers and substrates, and sum-
Reference
38
62
39
39
39
62
marize the fabrication and experimental results for a variety
of layer transducer configurations that have been reported
in the literature. For commonly used piezo layers, Table I
gives the orientation and material parameters needed to
characterize the layer vibration in longitudinal and shear
modes. Table II gives similar data for materials typically
used as electrode layers and acoustic substrates. The data
shown in these tables
from measurements on
]
[ ]is[ obtained
bulk crystal media 38 - 40 . It would have been desirable
REEDER AND WINSLOW : CHARACTERISTICS OF MICROWAVE ACOUSTIC TRANSDUCERS
937
TABLE III
CoNVERSION Loss AND ELECTROMECHANICAL COUPLING CONSTANT FOR PIEZOELECTRIC THIN FILMS
Material
Orientation
Mode
k
Z
Loagitudinal
0 . 12-0 . 1 5
0 . 1-1 GHz,
0 . 1-2 GHz,
2-8 dB
6-12 dB
4, 16
Z ! 39°
Shear
0 . 14-0 . 17
0 . 1-1 GHz,
5-10 dB
4
Z
Longitudinal
0 . 1 5-0 . 25
0 . 1-1 GHz,
1-2 GHz,
1-4
3-6
4, 65
Z ! 90°
Shear
0 . 1 2-0 . 18
0 . 1-3 GHz
Z
Longitudinal
0.15
1-2 GHz,
Longitudinal
0 . 08
0 . 5GHz,
CdS
ZnO
AlN
LiNbOa
to also include a table of acoustic data for vacuum deposited
thin films since these films, in general, exhibit physical
constants that are noticeably different from bulk crystal
media [41 ] . However, precision measurements of film acous­
tic parameters has only recently begun [41]. [42]. and were
not sufficient for inclusion here.
A. Thin-Film Transducers
Transducers utilizing thin-film layers fabricated by vacuum
depositing the layers directly onto the acoustic substrate.
For fundamental mode operation at frequencies ranging
from 0.1 to 10 GHz the piezo-layer thickness ranges from
about 20 to 0.2 ,um. In general, these depositions must be
performed under carefully controlled conditions in order to
achieve oriented crystalline films of the proper stoichiometry.
Piezo layers produced by most deposition methods are
oriented polycrystalline films, and single-crystal films de­
posited under special conditions have been reported [43].
As seen in Section II, the most important parameter of a
piezo layer is its electromechanical coupling constant k since
the transducer electric Q and conversion loss are strong func­
tions of k. Experimental measurements of coupling constant
and conversion loss are given in Table III for a number of
thin-film transducers of current interest. Here, an attempt is
made to summarize the better experimental results obtained
at several laboratories. Several methods have been used to
estimate the values of k listed in Table III, and all involve the
use of theory-experiment curve fitting with the coupling
constant chosen to provide the best fit. Probably the easiest
method to use is the untuned conversion-loss measurement
described in Section II and illustrated in Fig. 6. If the trans­
ducer is designed to have acou stically thin electrodes with
electrode capacitance satisfying woCoZo= 1 and the measure­
ment is performed at/=/0, the untuned conversion-loss ratio
reduces to the simple form T(jo),,'-'7frD/8k2 for moderate
coupling con stant devices. Thus, a knowledge of substrate
Typical Tuned Conversion Loss
dB
dB
Reference
66
10--1 2 dB
9dB
42, 50
51
was used to find k in the theory-experiment comparisons
shown in Figs. 7 and 9. However, the work involved to carry
out accurate determination of k is much greater for tuned
measurements than for untuned studies since more param­
eters must be assessed.
A third method for k determination is obtained by theory­
experiment comparisons of the transducer electric input
impedance [16], [36] , [44]. Here again, the parameters of
the electric circuit must be measured carefully, since contact
impedances may be larger than the transducer radiation
impedance for moderate coupling constant devices.
In all three methods considerable care must be exercised
to achieve high accuracy in the determination of k. At best,
the tolerance achieved is probably five percent [16], and is
typically 10 to 20 percent. The experimentally estimated
values of k given in Table II may be compared with the
corresponding values shown in Table I for bulk material.
CdS, ZnO, and AIN are all hexagonal crystals (class 6 mm)
and the appropriate values of k (i.e., kt and k16) are given
for longitudinal and shear modes of CdS and ZnO. Data
for AlN has been reported only for longitudinal mode vibra­
tion along the Z axis [38]. The values of kt given for AIN in
Tables II and III are those found by Wauk [42]. Quartz
(Si02) and lithium niobate (LiNb03) are trigonal of class
32 and 3 m, respectively. Lithium gallate (LiGa03) is ortho­
rhombic of class 2 mm. An excellent review of properties of
piezoelectric crystals as electroacoustic transducers is given
by Jaffe and BerIincourt [38].
The values of conversion loss shown in Table III are
typical values obtained in a variety of electromagnetic cir­
cuits when the transducer is made electrically shunt resonant
and is impedance matched to the source. For a given trans­
ducer the minimum conversion loss is then limited by the
ratio Rse/Ra as seen in (27). Unfortunately, this ratio
depends rather critically on the actual electric circuit and
contact method employed. The minimum conversion loss
piezo-layer acoustic impedance ratio and experimental , expected for a given configuration is therefore hard to premeasurement of conversion loss and frequency are all that is dict without a thorough diagnostic study of the electric in­
put circuit.
needed to estimate k in this case.
Cadmium sulphide (CdS) layers have been deposited by
The value of k can also be estimated from tuned conver­
sion-loss measurements provided the parameters of the thermal evaporation of CdS with an additional dopant
electric tuning circuit are carefully determined. This method (usually sulfur) to obtain high resistivity [45], [46]. For
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, NOVEMBER 1969
938
TABLE IV
CONVERSION Loss OF PLATE TRANSDUCERS
Material
Cut
Mode
X
Longitudinal
Si02
Y
ZnO
Z
Longitudinal
X
Shear
LiNbO.
Y! 35°
Typical Tuned Conversion Loss
0 . 1-1
0 . 1-1
Shear
Longitudinal
Bond
GHz,
10-20 dB
Indium
GHz,
dB
Indium
1-2 GHz,
15-25
8-10 dB
Indium or
Phenyl Benzoate
0 . 1-2
GHz,
2-10
dB
0 . 1-0 . 8
GHz,
1-5
Indium or
Phenyl Benzoate
dB
Indium/Gold
direct beam evaporation the layers are polycrystalline, and
the film Z axis tends to deposit at the same angle relative to
the acoustic substrate as the directed evaporant beam. This
latter feature is important as CdS films with Z axis normal
to the substrate will vibrate in a pure longitudinal mode,
whereas films deposited with the Z axis aligned approxi­
mately 39° away from the substrate
[ ] normal will produce pre­
dominantly shear vibrations 4 . Single crystal CdS films
with
U Z-axis orientation have been deposited on sapphire
S bstrates by evaporating Cd and S in separate crucibles, but
with a baffle plate inserted between the evaporant
[ ] sources
and substrate to insure an indirect deposition 43 . High­
quality CdS films have also been fabricated on sapphire,
fused quartz, and metal film surfaces
[ by] direct beam evapora­
tion of cadmium and sulphur 29 . High-qu
[ ] ality poly­
crystalline CdS films have demonstrated 16 effective cou­
pling constants for longitudinal mode operation that, within
experimental error, are equal to the bulk crystal value
(k = 0. 1 5).
The material zinc oxide (ZnO), which has higher values of
shear and longitudinal coupling constants than CdS, has
been the subject of many recent studies. High-quality films
for both longitudinal and shear use have been prepared by
physical sputtering of polycrystalline
[ ] [ ] ZnO targets in an
argon/oxygen atmosphere 47 , 48 . The thermal evapora­
tion of zinc in a carefully controlled atmosphere of oxygen
has
[ ] also yielded good ZnO films for longitudinal operation
49 .
Aluminum nitride (AlN) films have been obtained by the
thermal evaporation of alumilJum with a carefully controlled
pressure of ammonia
and high substrate temperature (about
]
1 l00°C) [50 . The results of measurements on these films
indicate that they have low electrical and acoustical losses
and coupling constants comparable to CdS.
Lithium niobate (LiNb03) longitudinal wave transducers
have been deposited using the triode sputtering
process
[ ]
similar to that used for sputtered ZnO films 5 1 .
B. Plate Transducers
Before the advent of thin-film piezoelectric transducers,
microwave transducers were frequently fabricated from thin
plates of bulk crystals such as quartz. Fabrication restric­
tions limited the minimum thickness to approximately 0.5
mm with fundamental mode operation in the 50 to 100 MHz
Reference
28, 52
53
53
58, 34
36, 9
range. However, overtone operation at frequencies up to and
above 2 GHz
[ ] be obtained with conversion loss of 20
[ ]could
dB or less 52 , 53 . As ZnO and LiNb03 crystals became
available, overtone conversion loss under 10 dB could be
obtained at frequencies up to L-band. Compared to thin­
film devices, plate transducers have higher voltage break­
down and therefore are used for high acoustic power appli­
cations (acoustic power in the range 10 to 100 watts) where
thin-film devices are prone to burn out. Recently, methods of
bonding the piezo plate to an acoustic substrate have been
developed which allow the plate to be mechanically polished
down to a thickness of perhaps 5 Mm after bonding. Funda­
mental mode
] high as 0.8 GHz has been obtained
[ ] [ as
[ ]operation
.
,
36
in this way 9 33 For low-loss operation very thin and uniform bonds are
required between the piezo plate and the acoustic substrate.
Perhaps the easiest bonding material to use for both longi­
tudinal and shear waves is a transparent material, phenyl­
benzoate, which when melted at 70°C allows the observation
of the optical interference pattern
[ ] between the bottom of the
crystal and metal electrode 53 . This allows for the thickness
of the bonding material to be controlled to about a half wave­
length of light in the bonding material. Other materials such
as salol (phenyl salicylate) melting at 43°C are similarly
used. Metal bonds such as indium, tin, and germanium-gold
allow have been used according to the restrictions imposed
by their operating temperatures. At cryogenic temperatures,
materials
such as silicones and epoxy resins
[ ]
[ ]have been used
54 . Optical bonds have also been used 55 , but primarily
to propagate acoustic waves from one propagating medium
to another rather than in transducer applications. The reflec­
tion of 3 and 9 GHz longitudinal waves from an optical­
contact bond between two X-cut quartz rods was measured
to be on the
of 1 percent of the incident acoustic power
[ order
]
at ISK 56 .
Typical conversion loss for commonly used plate trans­
ducers is given in Table IV for operation in a shunt resonant,
impedance matched electrical circuit .
V. OTHER METHODS OF GENERATING
VOLUME ACOUSTIC WAVES
Acoustic waves at microwave frequencies were first ob­
served
[ ] by using single surface excitation in crystal quartz
57 . One end of the piezoelectric delay line is inserted into
REEDER AND WINSLOW: CHARACTERISTICS OF MICROWAVE ACOUSTIC TRANSDUCERS
the high electric field of a reentrant cavity resonator. For a
two-port delay line the other end is inserted into a similar
cavity. The conversion loss is typically 35 to 40 dB for
quartz, and the crystal orientation for longitudinal or shear
waves is that given in Table 1. For lithium niobate,
a
[ with
]
the
38
higher electromechanical coupling
coefficient
,
[ ]
conversion loss is about 25-30 dB 53 . The conversion loss
for single surface excitation is highly dependent on cavity
geometry and is increased as compared to thin films and
plates because of the decreased electric field filling factor.
Another type of [single
] surface excitation consists of a
dielectric resonator 58 made of a high dielectric constant
piezoelectric crystal such
[ ]as LiNb03• This has been called an
"integral delay line" 59 since the crystal is both the elec­
trical resonator and the delay medium. Two opposite faces
of the crystal are polished flat and parallel, with the crystal
cut determining the type of wave generated. The crystal is
excited electrically in the appropriate fundamental dielec­
tric mode and the electric fields parallel to the polished crys­
tal faces excite the acoustic wave by single surface excitation.
A novel method used to
microwave shear waves is
[ obtain
]
that of mode conversion 60 . For example, if a longitudinal
wave with the particle displacement in the direction of propa­
gation is reflected from a free surface of an isotropic medium
at the proper angle, the only reflected wave is a shear wave
with the displacement in the same direction and the direction
of propagation changed by 90° from the incident longitudinal
wave. This has been accomplished experimentally in yttrium
aluminum garnet [(YAG)
with no measurable loss for the
]
mode conversion 60 .
Circularly and elliptically polarized microwave acoustic
waves have been obtained in YAG by exciting a linearly
polarized wave which in turn excites both displacement
components in[ the
] crystal corresponding to the slow and fast
shear waves 61 . Single-crystal plates of YAG with the
correct orientation and
[ ]thickness have been used as acoustic
quarter-wave plates 61 .
A summary and discussion with references of both deple­
tion layer and diffusion layer transducer along with other
types of transducers
for frequencies above 50 MHz has been
[ ]
reported 62 . Present depletion layer and diffusion layer
transducers are applicable primarily for use with piezoelec­
tric semiconductor devices and for frequencies from 50-500
MHz. Tuned conversion losses of less than 5 dB from 30 to
600 MHz
been reported for ZnO diffusion layer trans­
]
[ have
ducers 63 .
The high field domains in gallium arsenide, GaAs, operat­
ing as a Gunn oscillator, have been used to generate co­
herent acoustic waves
[ ] in a delay medium which was bonded
to the oscillator 64 . The high fields at the surface of the
GaAs generate acoustic waves due to the piezoelectric
properties of the GaAs.
939
majority of microwave transducers in use today at frequen­
cies above 0. 1 GHz make use of moderate coupling constant,
vacuum deposited films of CdS and ZnO ; but for frequencies
between 0.1 and 1 GHz, where the bonding of thin single­
crystal plates is practical, the use of high-coupling constant
materials such as LiNb03 and LiGa02 is becoming in­
creasingly popular. Although the one-dimensional analysis
discussed here is equally valid for piezo-layer transducers in
both classes, the concepts of acoustic and electric bandshape
discussed in Section II are more useful for desci'ibing moder­
ate coupling constant devices for which the effects of acous­
tic and electric response may be conveniently separated. In
the latter case, broad-band transducer design may be car­
ried out by designing the acoustic and electric responses to be
separately broad-band ; the overall response is the product of
the two.
Electric circuit design for low conversion loss is also differ­
ent for the two transducer classes. Moderate coupling con­
stant devices, which have high electric circuit Q, require
multielement matching networks of fairly elaborate design
to achieve low conversion loss over a broad bandwidth. High
coupling constant transducers, because of the:ir inherently
low electric circuit Q, can exhibit low loss and broad band­
width with simple untuned electric termination.
ApPENDIX
ELECTRICAL INPUT IMPEDANCE FOR
THE LAYER TRANSDUCER
We assume that the layer transducer in Fig. 1 vibrates in a
pure one-dimensional mode as described in Section II and
that the lossless equivalent circuit given in Fig. 2 applies.
The electroacoustic properties of the piezo
[ ] layer can then be
described by the three-port equation 3
[l f
Vl
V2J
V3
=
-
RO cot 80 Ro csc 80
.J Ro csc eo Ro cot eo
�.
l/wCo
l/wCo
l/WCO
l/wCo
l/wCo
II
][ ]
12
(38)
13
where Ro is the electric unit equivalent of the piezo-layer
acoustic impedance (see Section II), Co is the clamped
capacitance, 80 = 7f'J/Jo is the acoustic transit angle, and sub­
scripts 1, 2, 3 refer to the two acoustic boundary surfaces
and the electric terminals, respectively. The voltage and
current at ports 1 and 2, defined by (1) and (2), are the
electric unit equivalents of the corresponding force and
particle velocity at the piezo-layer acoustic surfaces. Assum­
ing that electric contact is made to the top electrode layer
such that the free surface is undisturbed, the: normalized
impedance seen by the left-hand surface of the piezo layer is
ZI =
.
-
VI/II
�-
Ro
.
= Jr l tan 81
(39)
where e1 = 7f'J/Jl = 7f'dd/Jo is the layer transit angle and
VI. CONCLUDING REMARKS
Yl = ZI'/Zo' is the normalized acoustic impedance defined in
Microwave acoustic transducers which utilize a piezo­ Section II. Similarly, the normalized impedance seen at the
electric layer for acoustoelectric conversion may be con­ right-hand surface is
veniently divided into two classes : those which have moder­
V2/12
rD cos 82 + jr2 sin 82
ate or small electromagnetic coupling constant (k <0.3),
r2
(40)
Z2
and those which have large coupling constant (k> 0.3). The
Ro
r2 cos 82 + jrD sin 82
=
-
-�
=
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, NOVEMBER 1969
940
with 0 2 = 7r///2 = 7rdd//o, r2=Zl/Zo', and rD =ZD'/ZO" The
transducer input impedance is obtained from (38)-(40) with
the result
Za
where
=
Va
fa
-
=
1
P (f)
+
jwCo
Ro(wCo) 2
--
---
2j( 1 - cos (0) + (Zl + Z 2) sin 00
(1 + ZlZ2) sin 00 - j(Zl + Z 2) cos 00
P (f)
(41)
(42)
From (41) we note that the transducer input impedance is
composed of the piezo-1ayer capacitive reactance l/jwCo in
series with an acoustoelectrically induced radiation imped­
ance,
which may be cast in the form
Ra = Ra(Wo/W)2Hr(f)
Xa
=
Ra(wo/w) 2H,(f)
(44)
(45)
with Ra= (4k2/7rrD)(1/wCo). For the case of acoustically thin
electrodes the normalized impedances seen by the piezo
layer are approximately Zl= O and Z2 = rD. The response
functions Hr(f) and Hi(f) are then
�W
HiW
=
=
(rD/2) 2 (1 - cos (0) 2
(sin (0) 2 + (rD cos (0) 2
(1/2) sin 00 [1 + (rD 2/2 - 1) cos 00]
(sin (0) 2 + (rD cos (0) 2
�
(47)
Thus, for thin electrodes the functions Hr(f) and H,(f)
have, respectively, even and odd symmetry about/n = nOdd/O
with HrC/n) = 1 and H,(fn) = O. The function Hr(f) is seen
to be the reciprocal of the acoustic bandshape function
defined in (20).
ACKNOWLEDGMENT
The authors are indebted to researchers in many labora­
tories, who in the past twenty years, have developed the
one-dimensional theory that forms the basis of this paper. In
particular, we acknowledge the helpful advice and experi­
mental data contributed by A. J. Bahr, N. F. Foster, F. A.
Olson, and E. K. Sittig.
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