design of rf mems phase s hifter using capacitive shunt ...design of rf mems phase s hifter using...
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Design of RF MEMS Phase Shifter using
Capacitive Shunt Switch 1B. Nataraj,
2K.R. Prabha,
3S. Surya Sri,
4G. Suguna and
5K.A. Swathi
Associate Professor, 1Department of Electronics and Communication Engineering,
Sri Ramakrishna Engineering College,
Coimbatore, Tamil Nadu, India.
Assistant Professor 2Department of Electronics and Communication Engineering,
Sri Ramakrishna Engineering College,
Coimbatore, Tamil Nadu, India. 3Department of Electronics and Communication Engineering,
Sri Ramakrishna Engineering College,
Coimbatore, Tamil Nadu, India. 4Department of Electronics and Communication Engineering,
Sri Ramakrishna Engineering College,
Coimbatore, Tamil Nadu, India. 5Department of Electronics and Communication Engineering,
Sri Ramakrishna Engineering College,
Coimbatore, Tamil Nadu, India.
Abstract This paper presents the design and analysis of RF MEMS phase shifter
using capacitive shunt switches for broadband applications in microwave
and millimeter wave devices. The equivalent circuit of the phase shifter
have been examined with the capacitance of MEMS switches in both up
and down states in bilateral inter-digital coplanar waveguide. A control
voltage is applied between the center conductor and the switch’s upper
surface which actuates it and pulls down the surface, which creates a slow-
wave transmission line. The loading capacitance is summed up with the
International Journal of Pure and Applied MathematicsVolume 119 No. 10 2018, 1053-1066ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
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line capacitance, thus varying the transmission line’s characteristic
impedance. The phase velocity of the signal is varied by this change in
impedance which produces a phase shift. In order to overcome the defects
of conventional waveguide, tapered coplanar waveguide is used and this
results in an increase in phase shift per unit length with a small decrease in
insertion loss. By further design implementation of the taper sections, the
losses can be reduced to a large extent.
Key Words:MMIC, MEMS, CPW, DMTL, quasi-TEM, phase shifter,
switches.
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1. Introduction
In modern communication technology, antennas play a crucial role. It’s size is
the most demanding factor and therefore, it is to be integrated with common
very-large-scale integration (VLSI) technology. Phase shifter is an important
device in communication system. It should be designed in such a way that it
reduces electromagnetic interference and size should be small to consume less
power. In order to overcome the defects of conventional electronics beam
steering (Garver, 1972), Phase shifters are widely used in phased array
antennas. Phase Shifters can either be analog or digital. Continuous phase shift
is provided by analog phase shifter whereas digital phase shifter gives discrete
phase shift. Analog phase shifter has a very low insertion loss compared to
digital phase shifter. For low-cost microwave applications, many monolithic
microwave integrated circuit (MMIC) phase shifters are developed.
In recent years, RF Micro electromechanical Systems (MEMS) devices have
undergone enormous development and it provides many solutions for novel
components and system implementation. MEM is truly an enabling technology
allowing the development of smart products by augmenting the computational
ability of microelectronics with the perception and control capabilities of micro
sensors and micro actuators. The three characteristic features of MEMS
fabrication technologies are miniaturization, multiplicity, and microelectronics.
This technology has gained potential in defence and commercial
communication systems over a wide range of frequency. The development of
radio frequency Micro Electro Mechanical Systems (RF MEMS) technology
lead to miniaturization, low power consumption applications, low insertion loss
and wide bandwidth operation features at high frequency. It has most promising
role in applications like reconfigurable components such as switches, filters,
varactor diodes and phase shifters with low losses, low power consumption,
lesser inter-modulation products and high linearity are achievable using this
technology. To overcome huge size and losses that conventional phase shifters
exhibit, RFMEMS phase shifters are used in phased-array radar applications.
Phased array antennas are actually an electronically scanned array, from which
the beam of radio waves are projected in different directions without moving the
antennas. Feed network (Transmitter), phase shifters and antennas compute a
typical phased-array antenna. Hybrid topology of these components increases
the network’s size and it results in parasitic capacitive effects, package costs
and increased losses. These complications can be prevented by putting these
individual components on a single substrate, producing monolithic phased
arrays, possible through MEMS technology. Design analysis of conventional
coplanar waveguide (CPW) and tapered CPW for the use in phase shifter design
using RF MEMS technology is discussed in this paper. In this study, phase
shifter is designed to operate at 10 GHz and employs analog distributed
transmission line phase shifters. The phase shifters presented in this study are
used to obtain maximum phase shift with minimum wavelength using various
International Journal of Pure and Applied Mathematics Special Issue
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types of CPW circuits.
2. Coplanar Waveguide
Nowadays, High power electronic applications can be operated at frequencies of
100 GHz and beyond the frequency ranges. At such frequencies, for device are
connected and signal is distributed through transmission lines. Comparing
various transmission lines, coplanar waveguides are preferred due to its
structure in which all the conductors supporting wave propagation are located
on the same plane. CPWs play a vital role for signal characterization and
MMICs. The high impedance CPW transmission line and its equivalent circuit
are shown in Figure. 1 a and b.
The first analytic formulas were proposed by Wen (1969) for the calculation of
quasi-static wave parameters of CPW’s using conformal mapping, based on the
thickness of the substrate and the ground wires of the CPW’s are infinitely
extensive. A mathematical study by Veyres and Fouad Hanna (1969) expanded
the implementation of conformal mapping to CPW’s with definable dimensions
and thickness of the substrate. The analyzed results are accurate only if the
thickness of substrates are greater than the line dimensions. Ghione et al. (1984)
have discovered more widely applicable formulas that the phase velocities of
complementary lines are equal, using the duality principle.
Figure 1a): Layout of the CPW b): Equivalent Circuit of the CPW
There exist two types of coplanar lines: the first, called coplanar waveguide
(CPW) which has a center conductor strip and two ground conductor planes
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placed on the same side of a dielectric substrate (Quartz) whose widths can be
varied, as shown in Fig.1. The surface of the substrate is often in contact with
the center conductor, that is coated with metal, or metalized. Here the ground is
at the same side of the surface as the center conductor, therefore the inductance
coupled with accessing ground is remarkably reduced. The width and area of
the center conductor determines the characteristic impedance of the
transmission line.
The conformal mapping is applied to obtain the characteristics of transmission
lines using the assumption that the propagation mode in the CPW transmission
lines is quasi-static, i.e., it is a pure TEM mode. The effective dielectric
constant, velocity of the phase, and characteristic impedance of a CPW
transmission line are given as (Gupta, 1979):
eff =
=
Zo =
where CCPW is the line capacitance of the CPW transmission line, C0 is the line
capacitance of the transmission line when no dielectrics exist, and c is the speed
of light in free space. To obtain the quasi-static wave parameters of a
transmission line, the capacitances CCPW and C0 -is to be found.
The Veyres and Fouad Hanna (1969) approximation (superposition of partial
capacitances) is used, in which the line capacitance of the CPW is the sum of
two line capacitances, i.e,
=
= 4 o
where K is the elliptical integral of the 1st kind, and K’(k) = K(k’). The
variables k and k’ are given as
k =
=
C1= capacitance in which the electrical field exists only in a dielectric layer
with h1(thickness) and effective dielectric constant of -1.
= 2 o )
Where
=
=
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The absolute elliptical integrals of the 1st kind using the approximations given
by Hilberg (1969) is given as
≈ ln(2 ) for 1 ≤ ≤ ∞ and
≤ k ≤ 1
for 0 ≤ ≤ 1 and 0≤ k ≤
3. Phase Shifter Design
The circuit suggested here is based on a CPW distributed MEMS transmission
lines were phase velocity is varied by using a single control voltage and the
height is varied by the MEMS loading capacitors, and the capacitive load
distributed to the transmission line and its propagation characteristics, as shown
in Figure. 2a. This results in the analog control of the phase velocity and,
therefore a true time delay phase shifter. The design requires a small value of
loading capacitance per unit length, which results in very high actuation
voltage. The topology of the CPW transmission line presented here, which
varies the impedance, helps to increase the phase shift per unit length, resulting
in a reduced physical line length, reduced pull down voltage and high
capacitance ratio. The impedance and propagation velocity of the slow-wave
trans-mission line are determined by the size of the MEMS bridges and their
periodic spacing. The equivalent circuit of the loaded distributed MEMS
transmission line is shown in Figure 2b. The shunt capacitance associated with
the MEMS bridges is in parallel with the distributed capacitance of the
transmission line, shown in Figure 2b.
From the analysis of CPW using conformal mapping, the per unit length
capacitance is obtained. i.e. Ct=Ccpw. The unloaded lines per unit length
capacitance and inductance are given by (Barker, 1998)
= and =
where eeff is the effective dielectric constant of the unloaded CPW transmission
line, Z0 is the characteristics impedance of the unloaded CPW line, and c is the
free space velocity. The MEMS bridge only loads the transmission line with a
parallel capacitance Cb, the loaded line impedance Z1 and phase velocity Vl of
the loaded line, become
= and =
where s is the periodic spacing of the MEMS bridges and Cb/s is the distributed
MEMS capacitance on the loaded CPW line.
The MEMS bridge becomes unstable at 2g0/3, where g0 is the zero-bias bridge
height. The voltage at which this instability occurs is the “pull-down” voltage
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and is given by
= V
The relative phase between the two states or the net phase shift is found from
the change in the phase constant given by
= ( - )
The design consists of a 19365µm long CPW trans-mission line whose center
conductor width (W) is 100µm and the gap is 100µm is fabricated on a 100µm
silicon substrate with a dielectric constant of 3.8 and loss tangent=0.001 and
with 15 shunt MEMS bridge capacitors placed periodically over the
transmission line, shown in Figure 3. The height of the bridge above the center
conductor is computed for up state(3µm) and down states(1µm) respectively.
The effective dielectric constant ( eff) of the unloaded CPW line has an average
value of 6.25 and is linearly invariant with frequency. The width and span of the
MEMS bridges are 100µm and 100µm, respectively. The same parameters are
used for designing bilateral inter-digital CPW with wings and without wings.
Figure 2: a) Layout of the ConventionalCPW with MEMS Switch
b) Equivalent Circuit of the ConventionalCPW with MEMS Switch
Figure 3: Layout of Conventional CPW loaded with 11 MEMS bridges
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Results
(a)
(b)
(c)
(d)
Figure 4(a): Layout of bilateral inter-digital CPW Design-I (without wings) having 15
MEMS bridges. (b) (dB)in 1µm(DOWN) and 3µm(UP) states. (c) (dB)in
1µm(DOWN) and 3µm(UP) states.(d) (phase)in 1µm(DOWN) and 3µm(UP) states.
6 7 8 9 10 11 12 13 145 15
-60
-40
-20
-80
0
freq, GHz
dB(S
(1,1
))dB
(bic
pw1_
mom
_1_a
..S(1
,1))
6 7 8 9 10 11 12 13 145 15
-1.5
-1.0
-0.5
-2.0
0.0
freq, GHz
dB(S
(1,2
))dB
(bic
pw1_
mom
_1_a
..S(1
,2))
6 7 8 9 10 11 12 13 145 15
-100
0
100
-200
200
freq, GHz
phas
e(S
(1,2
))ph
ase(
bicp
w1_
mom
_1_a
..S(1
,2))
International Journal of Pure and Applied Mathematics Special Issue
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(a)
(b)
(c)
(d)
Figure 5 (a): Layout of bilateral inter-digital CPW Design-II (with wings) having 15
MEMS bridges. (b) (dB) in 1µm(DOWN) and 3µm(UP) states. (c) (dB) in
1µm(DOWN) and 3µm(UP) states.(d) (phase)in 1µm(DOWN) and 3µm(UP) states.
International Journal of Pure and Applied Mathematics Special Issue
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(a)
(b)
(c)
(d)
Figure 6: (a) Layout of tapered bilateral inter-digital CPW Design-II(without wings) having
15 MEMS bridges. (b) (dB) in 1µm(DOWN) and 3µm(UP) states. (c) (dB) in
1µm(DOWN) and 3µm(UP) states. (d) (phase) in 1µm(DOWN) and 3µm(UP) states.
6 7 8 9 10 11 12 13 145 15
-50
-40
-30
-20
-10
-60
0
freq, GHz
dB(S
(1,1
))dB
(_12
34b_
mom
_3_a
..S(1
,1))
6 7 8 9 10 11 12 13 145 15
-2.0
-1.5
-1.0
-0.5
-2.5
0.0
freq, GHz
dB
(S(1
,2))
dB
(_1
23
4b
_m
om
_3
_a
..S
(1,2
))
6 7 8 9 10 11 12 13 145 15
-100
0
100
-200
200
freq, GHz
phas
e(S
(1,2
))ph
ase(
_123
4b_m
om_3
_a..S
(1,2
))
International Journal of Pure and Applied Mathematics Special Issue
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(a)
(b)
(c)
(d)
Figure 7: (a) Layout of tapered bilateral inter-digital CPW Design-II (with wings) having
15 MEMS bridges. (b) (dB) in 1µm(DOWN) and 3µm(UP) states. (c) (dB) in
1µm(DOWN) and 3µm(UP) states.(d) (phase)in 1µm(DOWN) and 3µm(UP) states.
International Journal of Pure and Applied Mathematics Special Issue
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4. Conclusion
Design-II of tapered bilateral inter-digital coplanar waveguide produce more
phase shift among the three designs with and without wings. Phase shift
changes with respect to number of bridges and the gap between center
conductor and the bridge (bridge gap). So tapping the center conductor gives
rise to the generation of six capacitances in between the center conductor and
bridges, namely , , on the upper surface and , in the lower surface
and thus resulting in relatively low insertion loss. Therefore a maximum phase
shift is obtained with minimum wavelength. The future work is to increase the
isolation, reduce the insertion loss and mainly to increase the phase shift per
unit length.
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International Journal of Pure and Applied Mathematics Special Issue
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