Novel multiplexer structures based on all-resonator topologies are presented here. The proposed multiplexers consist of only resonators without extra manifolds or circulators or power dividers. They can achieve various requirements of different filtering responses and arbitrary number of channels with miniaturized size. The proposed multiplexers are synthesized using optimization technique where coupling coefficients between coupled resonators are found. Different structures with various properties and responses are presented including symmetrical and asymmetrical channels. Reduction of the complexity of optimization processes is also presented

Skaik, Talal F.

Tubail, Deeb A

English

Institutional Repository of the Islamic University of Gaza

Novel Multiplexer Topologies based on Coupled 
Resonator Structures 
Talal F. Skaik and Deeb A. Tubail 
Electrical Engineering Department 
Islamic University of Gaza 
Gaza, Palestine 
talalskaik@gmail.com 
Abstract-Novel multiplexer structures based on all-resonator 
topologies are presented here. The proposed multiplexers consist 
of only resonators without extra manifolds or circulators or 
power dividers. They can achieve various requirements of 
different filtering responses and arbitrary number of channels 
with miniaturized size. The proposed multiplexers are 
synthesized using optimization technique where coupling 
coefficients between coupled resonators are found. Different 
structures with various properties and responses are presented 
including symmetrical and asymmetrical channels. Reduction of 
the complexity of optimization processes is also presented. 
Keywords- coupled resonator;filter; multiplexer; optimization 
I. INTRODUCTION 
Multiplexers are used to separate signals from common 
port to other ports and they are conventionally constituted 
from channel filters combined together using manifolds or 
circulators or power dividers. Other multiplexer structures 
formed of only resonators have also been proposed in 
literature. Those resonator-based multiplexers can be 
miniaturized in comparison to conventional multiplexers since 
they do not contain external combining circuits. Star-junction 
multiplexers have been proposed in literature where the 
channel filters are combined using a resonating junction [1] as 
shown in Fig. 1 (a). However, such structures are difficult to 
practically implement for large number of channels as the area 
around the resonating junction is limited to few connections. 
In [2], other star-junction multiplexer structures have been 
proposed as depicted Fig. 1 (b) where each two channels have 
only one connection to the resonating junction. However this 
proposed topology is still limited to six channels. Other 
resonator-based multiplexer structures formed exclusively by 
coupled resonators have also been proposed as depicted in Fig. 
1 (c) [3] and Fig. 1 (d) [4,5]. In [6,7], triplexers based on 
coupled resonator structures are designed and implemented. 
The previous resonator-based multiplexer structures are 
convenient for small number of channels and they are not 
generalized for large number of channels. 
In [8], we proposed a generalized novel all-resonator 
multiplexer structure with symmetrical pairs of channels as 
shown in Fig. 2 and it can be noticed that this structure has 
even number of channels. Furthermore, we presented two 
examples of multiplexers with symmetrical pairs of channels, 
['2 
Resonant 
P4 
(a) 
_��-.-�oPl 
['4 o�o--+--+--+--o P2 
0..--+--+----+-0 P3 
(e) 
P3 
r­
r--
P4 
--1 
--1 
P5 
(b) 
(d) 
Fig. I. Coupled Resonator multiplexer topologies in literature (a) Star­
junction Multiplexer [I], (b) Novel star-junction multiplexer with more 
channels and fewer connections to resonant junction [2], (c) Coupled 
resonator multiplexer with distributed coupling [3], (d) Multiplexer based on 
all-resonator structures [4]. (black dots represent resonators and lines 
represent coupling, Pi stands for Port i) 
the first is a four-channel multiplexer while the second is a 
six-channel multiplexer. Here, we present many structures of 
resonator-based multiplexers with different number of 
resonators and with different specifications and characteristics 
including multiplexer with asymmetrical channels and also a 
multiplexer with channels that differ in bandwidth. The 
examples presented here also exhibit topologies with even and 
topologies with odd number of channels. Moreover, 
simplification of the optimization process for large coupled­
resonator multiplexers by sub-dividing the structure into 
smaller blocks is presented. The proposed multiplexers can be 
implemented by any type of resonators such as microstrip 
resonators and air-filled waveguide cavities for 
communications satellites. However, a limitation could arise 
with microstrip multiplexers since undesired couplings may 
exist between resonators that affect the response. 
II. SYNTHESIS OF COUPLED RESONATOR MUTIPLEXERS 
The presented coupled resonator multiplexers here are 
synthesized using optimization technique where the coupling 
coefficients between resonators mij and resonators frequency 
offsets mu are found. The optimization is performed by 
978-1-4673-7602-0/15/$31.00 ©2015 IEEE 
Fig. 2. Coupled resonator multiplexer structure for symmetrical channels [8] 
�ini�ization of a cost function that is related to matrix [A] 
gIven In (1). The cost function and the base methodology of 
the synthesis are presented and explained in [8]. The matrix 
[A] consists of the sum of three matrices, the external coupling 
coefficient matrix, the identity matrix and the coupling 
coe.fficient �atrix, where P is the complex low pass frequency 
vanable, qei IS the normalized external quality factor, mi is the 
�ormali�ed coupling coefficient between resonators i an�lj, mu 
In the dIagonal is the normalized self-coupling coefficient of 
resonator i representing frequency shift since resonators in 
each arm have different self-resonant frequencies from those 
in other arms, and j is the imaginary unit. The multiplexers 
here are normalized in lowpass prototype and they can be 
transformed to practical bandpass frequency domain using 
known transformation formula [9]. 
0 0 
qc l 
0 0 
[A]= 
0 0 
+P 
0 0 
qe(n-l) 0 0 
0 0 
qcn 
mll ml(n-l) mIn 
-j 
m(n_l)I m(n_Ij(n_l) m(n_l)n 
mnl mn(n-l) mnn 
The general formulae of the S-Parameters are given as 
Sxx = I - �[A r 
qex 
xx 
(1) 
(2) 
. ,:here Su is the return loss at port x, and Sxy is the 
insertIOn loss between ports x and y. The normalized external 
quality factors are numerically calculated as 
2 
qe±l 
X 2 -XI 
1 N 1 
- = L -
q el ;=1 q e; 
(3) 
where qexlx2 is the normalized external quality factor of a 
filter with edges x I and x], qe' I is that of filter with edges 
of ± 1, which is numerically calculated from known g-values 
[9] and N is total number of channels . 
III. NUMERICAL EXAMPLES 
A. Example]: Multiplexer with Quasi-Elliptic Channels 
Example 1 illustrates a coupled resonator symmetrical 
multiplexer with Quasi-Elliptic filtering response and equal 
bandwidth four channels. Fig. 3 (a) presents the topology 
where there are four cross couplings (dotted lines) to generate 
the transmission zeros. Fig. 3 (b) presents the response of the 
multiplexer while Fig. 3 (c) shows the isolation between 
multiplexer channels. The calculated normalized external 
quality factors are qe2 = qe3 = qe� = qe5 = 5.5509 and qel = 
l.3877. The optimized normalized coupling coefficients and 
frequency offsets are m12 =1.3489, m23= m2� = 0.4391, m33 =­
m4� = 0.5429, m35= m46 = 0.1031, m39= m4JO = -0.0371, m55 = 
- m66 = 0.5602, m5-r m68 = 0.1219, m77 = - m88 = 0.5627, m79 = 
mSIO = 0.1329, m99 = - m lOla = 0.5588, m211 = 0.8746, m JJ 12 = 
0.9734, m1213= ml2l� = 0.5078, m13l3 = - mUl4 = 1.5098, m13l5 = 
mW6 = 0.1097, m/3/9 = mmo = -0.0271, mJ515 - ml616 
=1.7157, ml5l-r m16l8 = 0.1177, m1717 = - m1818 = 1.7213, 
ml7J9= mlS20 = 0.1371, ml919 = - m2020 =l.7189. 
Port 3 Port 5 
(a) 0 
=- -20 :;::, 
iC 
� " 
E -60 " .. " , 
� -80 '" " -100 -2.5 -2 -1.5 -1 -0.5 0.5 
Normalized Frequency 
(b) 
-40 
=-� -60 
= -80 .� " ] -100 
-120 
-140 
-2.5 -2 -1.5 -1 -0.5 0.5 1.5 2.5 
Normalized Frequency 
(e) 
Fig. 3. Example 1 (a) The structure (b) Reflection and insertion losses (c) The 
IsolatIOn between adjacent channels. 
B. Example2: Multiplexer with Five Chebyshev Channels 
Example 2 is a five channel multiplexer (odd number of 
channels) with ten resonators. Fig. 4 (a) shows multiplexer 
topology and Fig. 4 (b) illustrates multiplexer response. The 
normalized external quality factors are numerically calculated 
as qe2 = qe3 = qe� = qe5 = qe6 = 13.2960 and qel = 2.6592 . The 
optimized normalized coupling coefficients and frequency 
offsets are ml2 = 1.2806, m23 = m2� = 0.2339, m25= 1.0270, m33 
=- m4� = 0.8925, m56 = 0.9376, m67 = m68 =0.2380, m77 =- m88 
=1.7530, m69 = 0.7147, m910 = 0.1111. 
C. Example 3: Multiplexer with Unsymmetrical Channels 
Fig. 5 (a) presents unsymmetrical structure of multiplexer 
where the number of resonators per channel is not the same. 
Fig. 5 (b) shows the response of the multiplexer and it can be 
noticed that the channels differ in number of reflection zeros 
and also in bandwidth. Moreover, it can be noticed that two 
channels have Chebyshev responses and the others have 
Quasi-Elliptic responses. This multiplexer is considered more 
general and complex than previous ones because of 
unsymmetrical structure and different specifications and 
characteristics for the channels. 
The normalized external quality factors are numerically 
calculated as qel = 1.0629, qe2 = 3.8856, qe3 = 4.2580, qe4 = 
6.8128 and qe5 = 3.3133. The optimized normalized coupling 
coefficients and frequency offsets are: m12 = 1.4304, m23 = 
0.4585, m33 = 0.4847, m34 = 0.1422, m4� = 0.4893, m25 = 
0.5452, m55 = -0.5056, m56 = 0.1570, m66 = -0.5081, m67 = 
0.1837, m77 = -0.5079, m28 = 0.7554, m89 = l.l210, m910 = 
0.6703, mlOIO = 1.1484, mlOIl = 0.2281, mllll = 1.6091, mll12 = 
0.1926, m12l2 = 1.6475, m12l3 = 0.1661, m1313 = 1.6360, m13J.1 = 
0.2322, muu = 1.6353, mlOl3 = 0.0354, m915 = 0.6360, ml5l5 = 
-1.2528, m1516 = 0.1877, m1616 = -1.6637, ml617 =  0.1836, mllll 
= -1.6953, ml7l8 = 0.1943, ml8l8 = -1.6814, m15l8= 0.0656. 
$ -10 
:::, -20 
� 
� -30 
e -40 " .. " -50 =--
J, -60 
551 
Port 2 Port4 Port 6 
Port 3 Port 5 
(a) 
531 561 521 
Normalized Frequency 
(b) 
Fig. 4. Example 2 (a) The structure (b) Reflection and insertion losses 
$ -20 
:::, 
� 
� '" 
e " .. " 
=-- -80 
J, 
-100 
-2.5 
/\ .. __ ... _ .. I"\. 
,../ \ / 
,,,." \.' 
, 
-2 -1.5 -1 
Port 4 
Port 3 
(a) 
, 
-0.5 0.5 1.5 
Normalized Frequency 
(b) 
Fig. 5. Example 3 (a) The structure (b) Reflection and insertion losses 
IV. SIMPLIFICATION OF OPTIMIZATION PROCESS 
2.5 
Designing a multiplexer with a large number of resonators 
especially with unsymmetrical channels produces a large 
number of parameters that enter into the optimization process. 
Here we present a method to reduce the complexity of the 
optimization process. 
The optimization process in the previous examples has 
been performed in one step where all the coupling coefficients 
are entered into optimization process. In this case the 
optimization algorithm can converge rapidly for small 
structures but may fail to find a solution for relatively large 
topologies as the number of parameters increases. To simplify 
the optimization process large multiplexer structures can be 
sub-divided into smaller blocks (diplexers) and optimization is 
done for each individual diplexer. Then, the results are taken 
as the initial values in the optimization process for the whole 
multiplexer. Thus reducing the complexity for large structures 
and starting with good initial values. 
A symmetrical four-channel multiplexer is investigated 
here where two of the channels are quasi-elliptic with same 
bandwidth and different from the other two that have smaller 
bandwidth and Chebyshev response. The structure is 
subdivided into two-diplexers and each diplexer is optimized 
individually as shown in Fig. 6 (a). 
The first diplexer is optimized to get some coupling 
coefficients (in vertical arm) to be used as initial values in the 
optimization of the whole structure as follows: m33 =0.4963, 
m35 = 0.1293, m55 = 0.5180. Similarly, the second diplexer is 
optimized to get some coupling coefficients in the vertical arm 
as follows: m99 = l.6751, m9IJ = 0.1438, m9l5 = -0.0736, mllll 
= 1.6986, mll13 = 0.2039, m1313 = 1.7015, mJ3J5 =  0.2032, m15l5 
= 1.7007. 
The optimized normalized coupling coefficients and 
frequency offsets of the whole multiplexer after using results 
of individual diplexers as initial values are m12 = 1.4543, m23 = 
0.4798, m27 = 0.7550, m33 = 0.4951, m35 = 0.1409, m55 = 
0.4942, m78 = 1.1151, m89 = 0.7059, m99 = 1.1479, m9Jl = 
0.2044, mllll = l.6564, mlll3 = 0.2029, m/3/3 = l.7056, m/3/5 = 
0.2048, m15l5 = 1.6787, m915 = -0.0905. The normalized 
external quality factors are qe2 = qe3 = 6.8128, qe4 = qe5 = 
3.8856 and qel = 1.2372. It can be noticed from the results that 
the initial values resulted from optimization of diplexers are 
quite close to final values obtained after optimization process 
is performed for the whole structure. The final response of the 
whole multiplexer is depicted in Fig. 6 (b). 
Port 2 Port 4 
Port 3 Port 5 D i plexer 2 
(a) 
·10 551 541 
$ ·20 
� 
� 
� '" 
8 .. .. .. 
� 
J, 
·80 
-2.5 -2 -1.5 -1 -0.5 0.5 1.5 2 2.5 
Normalized Frequency 
(b) 
Fig. 6. Multiplexer subdivided into two diplexers (a) The structure (b) 
Reflection and insertion losses. 
V. CONCLUSION 
In this paper novel multiplexer topologies based on 
coupled resonator structures are presented. The proposed 
topologies consist of only resonators and hence they can be 
miniaturized in comparison to conventional multiplexers. The 
examples presented here include symmetrical and 
asymmetrical structures with different filtering responses as 
well as different channels bandwidths. The synthesis of the 
presented multiplexer is done using an optimization technique 
whereby coupling coefficients and frequency offsets are 
found. A remarkable advantage of this novel structure is the 
ability of dividing the multiplexer into smaller blocks 
(diplexers) and optimizing each diplexer individually. This 
decreases the complexity of optimization process and saves 
the time consumed in optimization. 
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Novel multiplexer topologies based on coupled resonator structures

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Novel multiplexer topologies based on coupled resonator structures

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