Design and Simulation of Microstrip Ring Resonator is
constructed from one quarter-wave coupled line Coupler
Sameep P Dave#,Harikrishna J Jayanthi*, Rachna D Jani#
#
EC Department, CHARUSAT-Changa University
M.Tech Student, Department of EC,CSPIT,CHARUSAT University, Changa, Dist-Anand(Gujatat -India),388421
[email protected]
[email protected]
*
IPR/ITER-INDIA
A-29, GIDC, Gandhinagar, Gujarat, India
[email protected]
Abstract—This Paper presents a microstrip ring resonator at
50MHz frequency.The resonator constructed from one quarterwave coupled-line Coupler,connected in a square configuration.10dB quarter-wave directional coupler has flat responce for
35MHz to 65MHz for high isolation,high power handling
capacity,minimun amplitude imbalance for adjusting amplifier
gain during VSWR condition.So Microstrip Ring Resonator has
high power handling capacity and high Q-measurments. Epoxy
FR-4 material with 3.2mm height has been used for
substrate.Application point of view,further use of microstrip ring
resonator for amplifier,filter, mixers,oscillators and couplers.
considered. Length of the Microstrip line ring resonator is
defined as,
l = nλg = 2πr
(1.2)
Keywords— Microstrip line, Ring Resonator, Directional
Coupler, S-Parameters, Coupling Factor,FR-04 Substrate, CST
MW Studio.
I. INTRODUCTION
The ring resonator is a simple circuit. The structure would
only support waves that have an integral multiple of the
guided wavelength equal to the mean circumference.
2πr = nλg
for n = 1, 2, 3 ...
(1.1)
Where r is the mean radius of the ring that equals the average
of the outer and inner radii, λg is the guided wavelength, and n
is the mode number. The ring resonator is merely a
transmission line formed in a closed loop. The basic circuit
consists of the feed lines, coupling gaps, and the resonator.
Figure 1.1 shows one possible circuit arrangement. Power is
coupled into and out of the resonator through feed lines and
coupling gaps. If the distance between the feed lines and the
resonator is large, then the coupling gaps do not affect the
resonant frequencies of the ring. This type of coupling is
referred to in the literature as “loose coupling.” Loose
coupling is a manifestation of the negligibly small capacitance
of the coupling gap. If the feed lines are moved closer to the
resonator, however, the coupling becomes tight and the gap
capacitances become appreciable. This causes the resonant
frequencies of the circuit to deviate from the intrinsic resonant
frequencies of the ring. Hence, to accurately model the ring
resonator, the capacitances of the coupling gaps should be
Fig-1 Microstrip Ring Resonator
II. A. EQUIVALENT CIRCUIT
The coupling gap and transmission line of the ring resonator
have been modelled by their lumped-parameter equivalent
circuit. The total equivalent circuit can now be pieced together
to form a two-port network like that shown in Figure 2. The
circuit can be reduced to a one-port circuit by terminating one
of the two ports with arbitrary impedance. The terminating
impedance should correspond to the impedance of the feed
lines. The feed lines will normally have impedance equal to
the impedance of the test equipment that they connect to. The
standard for microwave measurements is 50Ω.
Fig-2.1 Equivalent Circuit For Ring Resonator
B. The input impedance
Because of the symmetry of the circuit, the input impedance
can be found by simplifying parallel and series combinations.
𝑅𝑖𝑛
𝐶(𝐶1 + 𝐶2 )[(𝐶1 + 𝐶2 ) − 𝜔𝐷(𝐶12 + 2𝐶1 𝐶2 )]
=
[(𝐶1 + 𝐶2 ) − 𝜔𝐷(𝐶12 + 2𝐶1 𝐶2 )]2 + [𝜔𝐶(𝐶12 + 2𝐶1 𝐶2 )]2
[𝐷(𝐶1 + 𝐶2 ) − 𝜔−1 ][𝜔𝐶(𝐶12 + 2𝐶1 𝐶2 )]
+
[(𝐶1 + 𝐶2 ) − 𝜔𝐷(𝐶12 + 2𝐶1 𝐶2 )]2 + [𝜔𝐶(𝐶12 + 2𝐶1 𝐶2 )]2
......... (Eq.2.1)
𝑋𝑖𝑛
[𝐷(𝐶1 + 𝐶2 ) − 𝜔−1 ][(𝐶1 + 𝐶2 ) − 𝜔𝐷(𝐶12 + 2𝐶1 𝐶2 )]
=
[(𝐶1 + 𝐶2 ) − 𝜔𝐷(𝐶12 + 2𝐶1 𝐶2 )]2 + [𝜔𝐶(𝐶12 + 2𝐶1 𝐶2 )]2
[𝐷(𝐶1 + 𝐶2 ) − 𝜔𝐶 2 (𝐶1 + 𝐶2 )(𝐶12 + 2𝐶1 𝐶2 )]
+
[(𝐶1 + 𝐶2 ) − 𝜔𝐷(𝐶12 + 2𝐶1 𝐶2 )]2 + [𝜔𝐶(𝐶12 + 2𝐶1 𝐶2 )]2
......... (Eq.2.1)
Width of the Square Ring Resonator w shown in
fig.2.3 is found using same formula of microstrip
line width formula that is express as,
Fig.2.3 Square Ring Resonator
w
Coupling
Gap
Where,
C=
AZb2
(2A)2 + (Za − 2B − Zb )2
D = 1/2 [(Za − Zb ) −
Zb2 (Za − 2B − Zb )
]
(2A)2 + (Za − 2B − Zb )2
A = RC22 /(C1 + C2 )2 + [ωR(C12 + 2C1 C2 )]2
B = (C1 + C2 ) +
ω2 R2 (C12 + 2C1 C2 )(C1 + C2 )
ω(C1 + C2 )2 + ω[ωR(C12 + 2C1 C2 )]2
Where R is the terminated load. The input impedance is
Zin = Rin + jXin
........... (Eq.2.3)
The resonant frequency for the circuit is defined as the
frequency that makes the impedance seen by the source purely
resistive. In other words, the circuit resonates when Xin = 0.
C. Two Structure of Ring Resonator
At, Characteristic Impedance of Ring Resonator is in this
design 50Ω, and frequency 50MHz.
So,
w
expH ′
1
=(
−
)−1
h
8
4expH ′
................ (Eq.2.4)
Zo√2(εr + 1)
π
H′ =
+ 1/2(εr − 1/εr + 1)(ln ( )
119.9
2
+ 1/εr ln(4/π))
................ (Eq.2.5)
1
π
(εr − 1/ εr + 1)(ln ( )
′
2H
2
+ 1/εr ln(4/𝜋))]−2
................ (Eq.2.6)
Using, Equation number 2.4, 2.5,2.6, we can calculate the
width of microstrip ring resonator. Also, find out the length of
the square ring resonator. So, using FR-04(loss free) material
as a substrate in this design with 𝜀𝑟 = 4.3 and substrate
thickness is 3.2mm.
So,
w = 6.224 mm (Width of Microstrip line) (Approx value)
s = 3.000 mm (Coupling gap) (Approx value)
𝜀𝑒𝑓𝑓 = (εr + 1)/2[1 −
E. Design of Microstrip directional Coupler
Fig.2.2 Layouts of (a) annular, (b) square Ring Resonator
D. Design of Square Ring Resonator
Here -10db directional coupler used for design of microstrip
line ring resonator. Requirement of directional coupler for
high power system is high isolation, high power handling
capacity, coupling -10db for 35-65 MHz flat responses, and
minimum amplitude imbalance for adjusting amplifier gain
during VSWR condition.
Uncoupled w
Coupling
gap s
Coupling Width 𝑤𝑐
Uncoupled Width w can found using Eq.2.4 and Eq.2.5.But
Coupling width and gap could not found using Eq.2.4 and
Eq.2.5.So,
Coupling Factor,
𝑍𝑂𝑒 −𝑍𝑂𝑜
𝐶 ′ = 20 log [
𝑍𝑂𝑒 −𝑍𝑂𝑜
] 𝑑𝐵
..........Eq.2.7
Impedance Relationship,
𝑍𝑂2 ≅ 𝑍𝑂𝑒 𝑍𝑂𝑜
...........Eq.2.8
Design Procedure,
• (a) Determine shape ratios for equivalent single
microstrip lines.
• (b) Obtain the shape ratio wlh and the spacing ratio
slh for the desired coupled microstrip structure using
the single-line shape ratios.
• For design stage we use the following relationships:
• Zose = Zoe/2 (for single microstrip shape ratio (w/h)
se)
• Zoso = Zoo/2 (for single microstrip shape ratio
(w/h)so
General Curve for use in the synthesis technique, (Fig.2.4)
Using Eq.(2.4,2.5,2.6,2.7,2.8) and Fig.(2.4,2.5) and also use
design procedure ,we can found coupling width, coupling gap
and uncoupled width,𝑍01𝑒 , 𝑍01𝑜 of the -10dB directional
coupler. Characteristic Impedance Zo = 50Ω, Height of FR-04
substrate h = 3.2 mm.
So,
Coupling Width = 4.23 mm
Coupling Gap = 1.05 mm
Uncoupled Width= 7.065 mm
Guided Wavelength of even and odd mode of coupled
microstrip line,
300
𝜆𝑔𝑒 ≈
𝑍𝑂𝑒 /𝑍01𝑒
...............Eq.(2.9)
𝐹
300
𝜆𝑔𝑜 ≈
𝑍𝑂𝑜 /𝑍01𝑜
............Eq.(2.10)
𝐹
Here F frequency is in GHz.
So, Guided wavelength of coupled line coupler 𝜆𝑔𝑚 is mean
of these two wavelengths and the length of the coupled region
𝜆𝑔𝑚 /4 .
So,
𝑙 = (2𝑛 − 1) 𝜆𝑔𝑚 /4
n=1,2,3..... ...Eq.(2.11)
Finally, Ring Resonator is constructed from one quarter-wave
coupled line coupler.
So, 𝜆𝑔𝑚 = 3318 𝑚𝑚
Port1(I/P)
Numerical results for the even- and odd-mode characteristic
impedances of parallel-coupled microstrip lines: air spaced
(Fig.2.5)
𝜆𝑔𝑚 /4
Port2(O/P)
III. DESIGN AND SIMULATION RESULT
FR-04 is used as a dielectric material called substrate.PEC
(Perfect Electric Conductor) is used as a stripline. Design of
Square Ring resonator, Directional Coupler and Ring
Resonator constructed from quarter-wave coupled line coupler
are using CST Microwave Studio. Using Previous Equations,
Figures and Calculation Results, design of Ring Resonator in
CST MW Studio.
A. Square Ring resonator Design in CST
𝑤 =6.4mm, h=3.2mm, s=3.2mm, λg=3318mm
Simulation result of this Design is,
C. Directional Coupler(-10dB)
𝑤 = 6.75 𝑚𝑚, 𝑤𝑐= 4.5 𝑚𝑚,s=1.05 𝑚𝑚,h=3.2 𝑚𝑚
B. Square Ring Resonator with Compress Dimension of PCB
Simulation result of this Design is,
Simulation result of this Design is,
D. Square Ring Resonator constructed from one quarterwave coupled line coupler with Compress Dimension of
PCB
TABLE I
DESIGN CONCLUSION
SR
NO.
1
2
Simulation result of this Design is,
3
Predefine Value Zo=50Ω,h=3.2mm,f=50MHz,t=0.01mm
Design of
RL dB
S 2,1
VSWR
𝑸(𝑼𝑳)
dB
= 𝒇𝟎 /𝚫𝒇
Square Ring
-17.215
1
35.71
Resonator
0.917
(Full
5
Design)
Ring
-21.7
1
38.46
Resonator(
0.282
With
3
Compress
PCB
Dimension)
Ring
-5.45
2.13
62.5
Resonator(C
15.00
onstructed
2
From
Quarterwave
coupled Line
Coupler )





SR
NO.
1
Q(Un)= Quality Factor Unloaded
VSWR=Voltage Sanding Wave Ratio
RL=Return Loss
S 2,1 =S Parameter For O/P of Port 2
t= thickness of PEC
Predefine Value Zo=50Ω,h=3.2mm,f=50MHz,t=0.01mm
Design of
RL dB
IL dB VSWR
Directivity
Directional -15.86
-24.82 1.3835
-14 dB
coupler
 RL= Return Loss
 IL = Insertion Loss
Power Handling Capacity of microstrip line base Directional
Coupler and Ring resonator and Ring Resonator constructed
from quarter-wave coupled line couple is (mm) watt to few
ten watt (minimum to maximum).
IV. CONCLUSIONS
By design calculation, simulation using CST MW Studio
and design analysis in simulation of square ring resonator,
directional coupler and ring resonator constructed from
quarter-wave coupled line coupler have reliable higher power
handling capacity but comparatively lower than another
transmission line(like…waveguide, stripline, coaxial).Lower
isolation loss and return loss and higher directivity at
particular 50MHz frequency are in Ring Resonator.
Comparatively higher unloaded Quality factor and higher
VSWR in ring resonator (Constructed from Quarter-wave
coupled line coupler) rather than square rind resonator.
Directional coupler is -10dB flat response for 35MHz to
65MHz throughout this band., Tuneable ring resonator using
varactor Diode or PIN Diode is future scope of Ring
Resonator and application point of view further use of
microstrip ring resonator for amplifier, filter, mixers,
oscillators and couplers.
ACKNOWLEDGMENT
This work was supported and guided by MR.Harikrishna J
Jayanthi and Prof. Rachna D JAni. I would like to thank my
guide and Professor to give me the great support and guidance
for this experimental work. Requirement of software and
other tools for this work that I was used from my training
institute or organization, so also thankfully to them for this
work.
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