U.S. patent application number 09/884218 was filed with the patent office on 2001-12-20 for bulk acoustic wave device.
This patent application is currently assigned to KONINKLIJKE PHILIPS ELECTRONICS N.V.. Invention is credited to Milsom, Robert F..
Application Number | 20010052739 09/884218 |
Document ID | / |
Family ID | 9893950 |
Filed Date | 2001-12-20 |
United States Patent
Application |
20010052739 |
Kind Code |
A1 |
Milsom, Robert F. |
December 20, 2001 |
Bulk acoustic wave device
Abstract
A bulk acoustic wave device has a number of resonator elements
(14) which are laterally spaced such that a signal (26) applied
between to one resonator element (14.sub.1) at a resonant frequency
of the device is coupled to the other resonator elements (14.sub.2,
14.sub.3, 14.sub.4) by acoustic coupling between piezoelectric
layers of the resonator elements (14). There are two outer
resonator elements (14.sub.1, 14.sub.5) and at least one inner
resonator element (14.sub.2, 14.sub.3, 14.sub.4). The terminals of
the inner resonator elements are electrically connected together.
This connection provides an AC short which eliminates the effect of
the parasitic capacitances of the inner resonator elements, and
provides electromagnetic shielding between the input and output of
the device, by reducing the parasitic capacitance between the input
and output upper electrodes.
Inventors: |
Milsom, Robert F.; (Redhill,
GB) |
Correspondence
Address: |
Corporate Patent Counsel
U.S. Philips Corporation
580 White Plains Road
Tarrytown
NY
10591
US
|
Assignee: |
KONINKLIJKE PHILIPS ELECTRONICS
N.V.
|
Family ID: |
9893950 |
Appl. No.: |
09/884218 |
Filed: |
June 19, 2001 |
Current U.S.
Class: |
310/366 ;
310/322 |
Current CPC
Class: |
H03H 9/564 20130101;
H03H 9/02125 20130101 |
Class at
Publication: |
310/366 ;
310/322 |
International
Class: |
H01L 041/04 |
Foreign Application Data
Date |
Code |
Application Number |
Jun 20, 2000 |
GB |
0014963.3 |
Claims
1. A bulk acoustic wave device, comprising: one or more acoustic
reflector layers formed on a substrate; a lower electrode formed on
said acoustic reflector layer or layers; a piezoelectric layer
formed on said lower electrode; and, at least three upper
electrodes formed over said piezoelectric layer each upper
electrode at least partially overlying the lower electrode and
defining with an underlying piezoelectric layer portion and the
lower electrode a resonator element, in which said upper electrodes
are laterally spaced such that a signal applied between one of said
upper electrodes and said lower electrode at a resonant frequency
of the device is coupled to the other resonator elements by
acoustic coupling between the piezoelectric layer portions and in
which the upper electrodes are arranged so that there are two outer
and at least one inner upper electrodes and in which the or each
inner upper electrode is electrically connected to the lower
electrode.
2. A device according to claim 1, in which each resonator is
centred on the same resonant frequency.
3. A device according to claim 1 or 2, in which the or each inner
upper electrode and the lower electrode are connected to a common
potential.
4. A device according to claim 3, in which the common potential is
earth potential.
5. A device according to any preceding claim, in which a separation
between the laterally spaced upper electrodes is between 0.5 and
2.0 .mu.m.
6. A device according to any preceding claim, in which the
piezoelectric layer is selected to have a thickness equal to one
half wavelength of an acoustic wave at the resonant frequency of
the device.
7. A device according to any preceding claim, in which the
piezoelectric layer is made of a material selected from the group
consisting of ZnO, AIN, PZT and PLZT.
8. A device according to any preceding claim, having an area
between 100 and 10,000 .mu.m.sup.2.
9. A device according to any preceding claim, in which the one or
more acoustic reflector layers is or are made of porous silicon
oxide.
10. A radio frequency band pass filter comprising a device as
claimed in any preceding claim.
11. A radio frequency receiver and/or transmitter comprising a band
pass filter as claimed in claim 10.
12. A method of designing a bulk acoustic wave device having two
outer resonators and at least one inner resonator each of the
resonators being laterally spaced with respect to the adjacent
resonator or resonators and each resonator having an upper
electrode, a lower electrode and an interposed piezoelectric layer,
the method comprising the steps of: determining an optimum upper
electrode width for energy-trapping a single mode of oscillation
within the locality of the electrode; determining normalized
low-pass prototype values for a selected filter type and from these
determining the loaded quality factors of the outer resonators;
determining required areas for the outer upper electrodes of the
filter in dependence on loaded quality factors of the outer
resonators; in dependence on these areas, and the optimum electrode
width for energy-trapping a single mode, calculating the lengths of
each of the outer electrodes; from the normalized low-pass
prototype values determining the inter-resonator coupling
coefficients, and then determining the widths of the gaps between
the resonators, in dependence on a previously-determined
relationship between coupling coefficient and inter-resonator
spacing.
13. A method according to claim 12, further comprising the step of:
using a full 2D field model for the filter to adjust the resonator
and gap widths such that the response of the filter is optimised.
Description
[0001] The present invention relates to a bulk acoustic wave (BAW)
device and its manufacture, and particularly a filter comprising
solidly mounted BAW resonators. The invention also relates to
communications equipment (for example a radio frequency receiver
and/or transmitter) comprising such filters.
[0002] Mobile communications products, such as cellular phone
handsets, are required to be small and light. It is predicted that
in the future even smaller communication devices will be available
integrated into, for example, wristwatches and clothing. All such
products require radio-frequency (RF) filters approximately
covering the range 0.5 GHz to 10 GHz to protect the received signal
from interference, either from the transmitter in the same handset
and/or from unwanted externally generated signals. These filters
must have low pass-band insertion loss (typically<2 dB) in order
to achieve adequate signalto-noise ratio. To achieve this, the
resonators, which are the basic building blocks of filters, must
have high quality factor Q. This is defined as the energy stored
per cycle in a resonator at the resonant frequency divided by the
energy lost per cycle by the resonator at the same frequency.
Typically, values for Q in excess of 500 are desirable and
achievable.
[0003] Resonators normally employ some form of standing wave in a
cavity. Both discrete and distributed reflections may be used.
Conventional bulk acoustic wave and surface acoustic wave (SAW)
resonators are examples of resonators relying on these two options.
To keep size to a minimum, discrete reflections are preferred
because the length of the cavity is then typically only 1/2 a
wavelength of the mode employed at the resonant frequency. Thus BAW
resonators are potentially much smaller than SAW resonators for
which a cavity length of the order of 100 wavelengths may be
required, and are preferred for this reason.
[0004] Resonators are available that rely on acoustic waves or
electromagnetic waves. Acoustic wave resonators are preferred to
those employing electromagnetic waves for two principal reasons.
Firstly, the velocity of acoustic waves propagating in a material
is typically 4 to 5 orders of magnitude lower than the velocity of
electromagnetic waves, so that a substantial size reduction is
possible for any given frequency. Secondly, achievable mechanical
quality factors are typically larger than achievable electrical
quality factors for the same materials.
[0005] Two general types of BAW resonators have been studied for RF
applications. In the first of these a thin membrane forms the
resonating cavity.
[0006] This approach is unattractive because the membranes are
fragile and subject to buckling caused by stress. In the second,
so-called SMRs (solidly-mounted resonators) are used as shown in
FIG. 1. In devices such as these, one or more acoustically
mismatched layers 2 are mounted on a substrate 4 and act to reflect
the acoustic wave. Upper 6 and lower 8 electrodes are formed on the
substrate 4 separated by a piezoelectric layer 10. Since the
reflector layer(s) are deposited on a solid substrate, the
structure of a SMR is robust.
[0007] In the BAW resonator shown in FIG. 1, the required
conversion between electrical and mechanical energy is achieved by
the layer 10 of piezoelectric material arranged between two metal
layers in which electrodes 6.sub.1, 6.sub.2 and 8 are formed.
Although the SMR employs a more distributed reflection than the
thin membrane resonator, resonator size is not significantly
increased because thickness is predominantly determined by the
substrate in both cases. Each upper electrode 6.sub.1 and 6.sub.2
defines an individual resonator with the underlying piezoelectric
layer and lower electrode. These two resonators are effectively
electrically connected in series, with the common lower electrode 8
at the junction between them. A resonator is a one-port device. In
the construction shown in FIG. 1, its two terminals are formed by
electrodes 6.sub.1 and 6.sub.2.
[0008] RF filters reported to date have been constructed by
electrically connecting SMRs in either a ladder or lattice
configuration. Ladder configurations of the filters have
demonstrated good performance with passband insertion loss at less
than 2 dB and very low levels of spurious response. However, there
are a number of disadvantages with such arrangements. For example,
at frequencies removed from the acoustic resonances, each resonator
appears as a capacitor, so the overall filter stop-band response is
essentially that of a capacitor network. This leads to a
requirement for additional resonators just to reduce the stop-band.
Consequently, both the area occupied and the insertion loss in the
pass-band are increased without improving selectivity. A large
number of resonators is required for even a moderate stop-band
level (e.g. a minimum of 9 resonators for approximately 45 dB
stop-band). With the drive towards the miniaturization of filters
in RF applications this is a serious problem.
[0009] In addition, series and shunt resonators in the ladder
configuration are required to be centred on different frequencies
due to the arrangement of the individual resonators. This means,
for example, that an additional mass-loading layer, of very precise
thickness, must be deposited on the shunt resonators to reduce
their anti-resonance (minimum-admittance) frequency to the same as
the resonance (minimum-impedance) frequency of the series
resonators.
[0010] FIG. 2 shows a schematic representation of an electrical
equivalent circuit model for a conventional BAW resonator such as
that shown in FIG. 1. C.sub.0 is the static capacitance of the
resonator, C.sub.m and L.sub.m are respectively the motional
capacitance and inductance, and R.sub.m is the motional resistance
which characterises the mechanical losses of the resonator. The
resonant frequency is given by f.sub.0=1/[2.pi.{square
root}(C.sub.mL.sub.m)], and the unloaded quality factor is given by
Q.sub.u =(2.pi.f.sub.0L.sub.m)/R.sub.m.
[0011] The manufacturing process for a thin film bulk acoustic wave
resonator will be known by those skilled in the art. For example,
International Patent Application number W098/16957 discloses a thin
film bulk acoustic wave resonator and a method of manufacturing the
same, the contents of which are incorporated herein by
reference.
[0012] As explained above, in a filter it is usual to arrange more
than one resonator in a lattice or ladder configuration connected
electrically to each other to obtain optimum filter
characteristics. Connecting a number of filters like the one shown
in FIG. 1 causes an inherent lack of design flexibility due to the
presence of the static capacitance C.sub.0 in each resonator. As a
consequence, approximations to standard ideal filter types such as
Butterworth or Chebyshev are not readily implemented. The
electrical connection of the resonators in a ladder configuration
also produces the need for the series and shunt resonators to be
centred on different frequencies.
[0013] According to the present invention, there is provided a bulk
acoustic wave device comprising:
[0014] one or more acoustic reflector layers formed on a
substrate;
[0015] a lower electrode formed on said acoustic reflector layer or
layers;
[0016] a piezoelectric layer formed on said lower electrode;
and,
[0017] at least three upper electrodes formed over said
piezoelectric layer each upper electrode at least partially
overlying the lower electrode and defining with an underlying
piezoelectric layer portion and the lower electrode a resonator
element, in which said upper electrodes are laterally spaced such
that a signal applied between one of said upper electrodes and said
lower electrode at a resonant frequency of the device is coupled to
the other resonator elements by acoustic coupling between the
piezoelectric layer portions and in which the upper electrodes are
arranged so that there are two outer and at least one inner upper
electrodes and in which the or each inner upper electrode is
electrically connected to the lower electrode.
[0018] The invention provides a device employing SMRs, which are
acoustically rather than electrically coupled. This acoustic
coupling enables the device to be smaller and leads to more
flexible filter design. The electrical connection between
electrodes is such as to provide a fixed potential between the
inner upper electrode(s) and the lower electrode. This potential is
preferably zero, and they are preferably earthed. This earthing
provides electromagnetic shielding between the input and output of
the device, by reducing the parasitic capacitance between the input
and output upper electrodes.
[0019] The connection between the inner upper electrode and the
lower electrode is typically by means of one or more vias.
[0020] Preferably, each resonator is centred on the same resonant
frequency. This enables a simpler layer structure and is possible
because all the resonators form shunt arms, the equivalent of
series arms being implicitly provided by the acoustic coupling
between adjacent resonators. Thus, it is possible to increase the
number of resonators in the device to achieve a higher-order
filter, rather than just to decrease the stop-band level as in
existing designs. It is thus possible to implement a filter design
without resorting to the conventional ladder configuration in which
shunt resonators have an anti-resonance frequency set at the same
frequency as the resonance frequency of series resonators. The
invention improves the simplicity of manufacture and therefore
reduces the costs of manufacturing the device.
[0021] Preferably, the separation between the laterally spaced
upper electrodes is between 0.5 and 2.0 .mu.m and more preferably
between 0.7 and 1.3 .mu.m. Having a separation of the order of 1
.mu.m ensures that the acoustic coupling between adjacent upper
electrodes and the associated resonators is achieved.
[0022] Preferably, the piezoelectric layer is selected to have a
thickness substantially equal to 1/2 a wavelength of the dominant
acoustic mode at the resonant frequency.
[0023] According to a second aspect of the present invention, there
is provided a method of designing a bulk acoustic wave device
having two outer resonators and at least one inner resonator each
of the resonators being laterally spaced with respect to the
adjacent resonator or resonators and each resonator having an upper
electrode, a lower electrode and an interposed piezoelectric layer,
the method comprising the steps of:
[0024] determining an optimum upper electrode width for
energy-trapping a single mode of oscillation within the locality of
the electrode;
[0025] determining normalized low-pass prototype values for a
selected filter type and from these determining the loaded quality
factors of the outer resonators;
[0026] determining required areas for the outer upper electrodes of
the filter in dependence on loaded quality factors of the outer
resonators;
[0027] in dependence on these areas, and the optimum electrode
width for energy-trapping a single mode, calculating the lengths of
each of the outer electrodes;
[0028] from the normalized low-pass prototype values determining
the inter-resonator coupling coefficients, and then determining the
widths of the gaps between the resonators, in dependence on a
previously-determined relationship between coupling coefficient and
inter-resonator spacing.
[0029] Examples of the present invention will now be described in
detail with reference to the accompanying drawings, in which:
[0030] FIGS. 1a and 1b show a section and a plan view respectively
of a conventional solidly mounted BAW resonator formed as two
series connected resonators;
[0031] FIG. 2 shows an electrical equivalent circuit for a
conventional BAW resonator;
[0032] FIGS. 3 and 4 show respectively a plan view and section of
an example of a filter according to the present invention;
[0033] FIG. 5 shows an electrical equivalent circuit for the filter
of FIGS. 3 and 4;
[0034] FIG. 6 shows the response characteristic of a fifth order
filter according to the present invention predicted by the
equivalent circuit in FIG. 5 for three different values of
parasitic capacitance between input and output of the device;
and,
[0035] FIG. 7 shows the variation of pass band response of the
filter of FIG. 6 for three different values of Q.
[0036] FIGS. 3 and 4 show a possible configuration for a
fifth-order filter according to the present invention in plan and
section respectively. The thin-film layer structure is essentially
that shown in FIG. 1a and is described below with reference to FIG.
4. The configuration shown is suitable for common-mode
connection.
[0037] Referring to FIGS. 3 and 4, the filter 12 has a set of upper
electrodes 14.sub.1, to 14.sub.5 formed from an upper layer of
metal 18. Upper electrodes 14.sub.1 and 14.sub.5 function as the
input and output electrodes of the device and are electrically
isolated from electrodes 14.sub.2 to 14.sub.4. A number of earthing
contacts 20 are provided connecting electrodes 14.sub.2 to 14.sub.4
to ground. The contacts 20 indicate possible locations for either
flip-chip or wire-bond connections. A lower layer of metal 32 is
provided and in this example this is earthed by a connection to
electrodes 14.sub.2 to 14.sub.4 by two vias 22. A piezoelectric
layer 30 is provided separating the upper and lower layers of metal
and serves to convert an electrical signal applied to the device
between upper electrodes 14.sub.1 and 14.sub.2 to an acoustic
vibration. The layout in FIG. 3 has the same number of resonators
as the order of the filter, in this case five. As in FIG. 1, one or
more acoustically mis-matched layers 24 are mounted on a substrate
25 and act to reflect the acoustic wave generated by the
piezoelectric layer 30.
[0038] In use, an electrical signal is received by input 26 which
is connected to electrode 14.sub.1 thereby generating acoustic
waves in the piezoelectric layer 30. As will be explained below,
the acoustic waves are reflected by the acoustically mis-matched
layers 24 and a wave at the resonant frequency of the device is
acoustically coupled to electrode 14.sub.2. This process is
repeated between consecutive pairs of the electrodes until the
signal is output from electrode 14.sub.5 via output 28.
[0039] The acoustic modes supported by layered structures differ
significantly from those present in single crystals. The resonators
and filter shown in FIGS. 3 and 4 employ specific modes of
oscillation, namely thickness modes whose resonant frequency is
largely determined by the thickness of a resonator (i.e. the
combined thickness of the piezoelectric and electrode layers)
rather than its other dimensions. The filter employs
acoustically-coupled resonators relying on the concept of
"energy-trapping". This is the confinement of an acoustic vibration
to an electroded region of a resonator and it occurs because of the
different wave-guiding properties and cut-off frequencies of the
electroded and unelectroded regions of the resonator. The relevant
guided wave is required to be a cut-off mode of the unelectroded
region, so the stored energy decays rapidly with distance from the
electrode edge. The width of the electrode determines how many
modes are energy-trapped, while the spatial rate of decay of the
evanescent energy and the width of the gap between adjacent
resonators determines the degree of coupling between them. A
separation between the edges of adjacent resonators in the region
of 0.5 to 2.0 .mu.m, preferably 0.7 to 1.3 .mu.m, provides a
satisfactory amount of acoustic coupling.
[0040] A SMR generally relies upon the lowest thickness extensional
mode known as TE1, for which the particle motion is normal to the
surface (at least in a 1D approximation). Excitation of this
particular mode is a consequence of the orientation of the
deposited thin films of piezoelectric material. Recommended
materials for use as the piezoelectric layer are any materials
which naturally form c-axis normal layers such as ZnO, AIN, PZT and
PLZT.
[0041] In the 1D SMR model, the resonant mode appears as a pure
thickness extensional (TE) mode at all frequencies, so coupling to
other modes is not taken into account. For the proposed structure
it is necessary to consider field variations and components of
particle motion in directions parallel to, as well as normal to,
the layer surfaces. The field equations must be solved to obtain
the wavenumbers as functions of frequency (i.e. the dispersion
relationships) for each mode and each region. These solutions show
which layer configurations and thicknesses can support the required
oscillations, and which are likely to support energy-trapped modes.
The relationships between electrodes and gap widths and
inter-resonator coupling also follows from the dispersion
relationships.
[0042] The acoustic coupling in the device of the invention
typically results from both thickness extensional (TE) and
thickness shear (TS) modes. However, other modes may be excited at
a level that gives rise to unacceptable spurious responses unless
the proposed structure is optimally designed.
[0043] FIG. 5 shows an electrical equivalent circuit for the
resonator of FIG. 3. The circuit includes a number of circuits like
that shown in FIG. 2, coupled in parallel. The acoustic coupling
between resonators means that the inner resonators (i.e. all apart
from the input and output resonator) do not transmit the signal by
means of their electrical terminals. This enables those terminals
to be connected electrically, for example both connected to earth,
which eliminates the effect of the static capacitances of those
resonators.
[0044] As shown in FIG. 5, the acoustic coupling may be
characterised by mutual inductances M between the adjacent
resonators in the equivalent electrical circuit model. Mutual
inductors M.sub.j,j+1 are included between motional inductances
L.sub.m,j and L.sub.m,j+1 of each pair of adjacent resonators. The
static capacitance is excluded from each of the internal resonators
since, in this particular design, both of the electrodes of these
resonators are grounded, thus shorting out C.sub.0 and hence
increasing filter design flexibility. C.sub.p is the parasitic
capacitance between the input and output upper electrodes which may
be determined using electrostatic analysis. Approximate values for
C.sub.0 (for each end resonator) and C.sub.m, L.sub.m and R.sub.m
(for all resonators) may be obtained from a 1D acoustic field model
of the resonator.
[0045] Determination of the M.sub.j,j+1 requires (at least) a 2D
acoustic field model, the extra dimension included being the
direction parallel to the short sides (in the direction X) of the
resonators in FIGS. 3 and 4. Approximate values for these
components are given by matching the resonant frequencies predicted
by the circuit model and the 2D field model for two closely-spaced
resonators. Each gap width and mutual inductance value also
corresponds to a coupling coefficient required in the filter design
procedure described below. Higher values of mutual inductance and
coupling coefficient correspond to closer inter-resonator
spacing.
[0046] The design of a BAW device according to the invention will
now be described in greater detail. It is assumed that a layer
structure, suitable for stand-alone resonators at the desired
centre frequency f.sub.0 of the filter, has been determined, and
that the 1D model has been used to determine normalized
single-resonator equivalent-circuit component values (i.e. values
for unit area). A possible filter design procedure for the layout
in FIGS. 3 and 4 is then as follows:
[0047] Use the 2D model to determine the optimum resonator width
for energy-trapping a single mode. Then, from the filter
specification a filter type is chosen such as Butterworth or any
other desired type with appropriate 3 dB bandwidth, filter order
and pass-band ripple.
[0048] The corresponding so-called "normalized low-pass prototype"
values are then computed or obtained from published look-up tables.
From these values the loaded quality factors Q.sub.L of the input
and output resonators i.e. the resonators at the input and output
of the filter, and the de-normalized single-resonator
equivalent-circuit component values are computed. The denormalised
static capacitances are used to determine required areas for these
two resonators.
[0049] From these areas, and the previously-computed optimum width
for energy-trapping a single mode, the lengths of each of the input
and output resonators is calculated. Initially the widths and
lengths of the internal resonators can be set to the same values.
From the normalized low-pass prototype values it is then necessary
to compute and de-normalize the inter-resonator coupling
coefficients which are used to quantify the efficiency of the
coupling between adjacent resonators, and then use the
previously-determined relationship between coupling coefficient and
inter-resonator spacing to determine the first estimate of the
widths of the gaps between resonators, and also the mutual
inductances for the equivalent circuit model.
[0050] Finally the full 2D acoustic field model can be used to
optimise the resonator and gap widths such than the response is as
close as possible to that specified, and to ensure that responses
due to coupling to unwanted modes are adequately suppressed.
[0051] A number of advantages are obtained by adopting the filter
structure described with reference to FIGS. 3 and 4. Firstly, for
any configuration of filter the ultimate stop-band level is
degraded by electromagnetic (mainly capacitive) coupling between
input and output. By using vias and other connections to short all
electrodes except the input and output to ground, as in FIG. 3,
maximum shielding is obtained. Secondly, as described above, the
unwanted parasitic static capacitances of the internal resonators,
that limit filter design flexibility, are effectively removed
without modifying the useful motional components. Finally, it
should be noted that the fabrication of filters according to the
present invention, employing acoustically-coupled resonators, is
simpler than for the electrically-coupled type since all resonators
can be centred on the same frequency and therefore use the same
layer structure.
[0052] The response, predicted using the equivalent circuit in FIG.
5, of a fifth-order Chebyshev filter (employing PZT-4 in the
piezoelectric layer) is shown in FIGS. 6 and 7. The potential
degradation of the stop-band due to parasitic capacitance between
input and output, which is minimised in the layout in FIG. 3, is
shown in FIG. 6. A resonator Q of 1000 was assumed. The graph shows
the response of the filter assuming different values of parasitic
coupling capacitor C.sub.p between input and output electrodes:
C.sub.p=0 (bottom curve), C.sub.p=0.01 C.sub.0 (middle curve),
C.sub.p=0.05 C.sub.0 (top curve)
[0053] FIG. 7 shows the effect on the pass-band of the device for
different values of quality factor Q. This suggests that 2 dB
insertion loss is possible with a Q of 500, a value which is within
the capabilities of the technology. The area of the filter would be
about 50 .mu.m square, excluding pads for connections. This is much
smaller than filters with comparable performance using any known
technology and design approach. A filter of such dimensions could
be integrated with other components on silicon (for example), or
flip-chip mounted on the substrate of a small MCM (multi-chip
module). The size is sufficiently small to consider designing, for
example, a bank of RF filters to provide the front-end selectivity
in a multi-mode multi-band UMTS/GSM handset.
[0054] FIG. 3 shows one specific possible configuration for
resonators in the device of the present invention, although
alternatives are also possible. For example, it would be possible
to have a first and second row of resonators arranged in parallel
between differential mode terminations, with each pair of
corresponding resonators in the two rows connected in series.
Various other modifications will be apparent to those skilled in
the art.
* * * * *