Compact filters based on

stub-loaded parallel-coupled resonators

M. Garcia, E. Pistono, H. Maouche, and P. Ferrari
Institute of Microelectronics, Electromagnetism, and Photonics (IMEP-LAHC), Grenoble INP-UJF-University of Savoy-CNRS
UMR 5130, BP 257, 38016 Grenoble Cedex 1, France

miguel.garcia-Garcia@minatec.inpg.fr
emmanuel.pistono@ujf-grenoble.fr
hana_maouche@yahoo.fr
ferrari@minatec.inpg.fr

Abstract— Results of compact bandpass filters based on stub- simulation results for the determination of the resonant
loaded parallel-coupled resonators are presented in this paper. frequency. In section III, results of a two-pole bandpass filter
The working frequency corresponds to the low UHF band. These are presented, for a proof-of-concept. A first bandpass filter
resonators behave like short-circuited quarter wavelength working around 800 MHz with a 3.3 % 3-dB fractional
resonators, but lead to smaller lengths, allowing obtaining very
bandwidth (for broadcast applications) is simulated and
compact filters in a planar technology, without adding lumped
components. Such filters seem to be efficient candidates to measured. In section IV, a three-pole bandpass filter with a
achieve selective and compact size filters, with high flexibility 5.8 % 3-dB fractional bandwidth is demonstrated. To reduce
and simple design rules. Measurement results carried out on a the area of the filter, folded-stubs are considered by using
single resonator validate the background theory. Next, two-pole microstrip bends. The paper is concluded in section V.
and three-pole filters are designed. Measurements and
simulations are in good agreement. Fractional bandwidths from II. BACKGROUND THEORY
3.3 % to 6.7 % are obtained, with 3.65 dB and 2.8 dB insertion
loss, respectively. A. Topology of the stub-loaded resonator
Fig. 1 presents the topology of the proposed stub-loaded
I. INTRODUCTION resonator.
Since a compact electronic system is cheaper, lighter, and
usually more reliable, the miniaturization of RF and
millimetre circuits involves nowadays active researches. In
order to obtain compact RF and microwave filters based on Ζsc θscc
planar technologies, several miniaturization approaches exist.
First, semi-lumped filters based on a hybrid technology
putting together transmission lines and lumped capacitors can Ζoc Ζoc
be realized [1,2]. Second, the distributed approach considering
meandered transmission lines can be used, but at the expense
θoc θoc
of an important work to model parasitic couplings, for limited
miniaturization ratios. Another issue is related to the use of Fig. 1 Schematic view of the stub-loaded resonator.
high permittivity substrates, but only low characteristic
impedance (lower than 50 Ω) can be achieved, and large gaps
This resonator consists of an open-ended elementary
have to be realized for couplings, thus limiting the practical
realizable filters. It is also possible to carry out filters based on resonator of electrical length 2θoc (“oc” for open circuit), and
lumped elements, i.e. inductors and capacitors, but an characteristic impedance Zoc, loaded by a short-circuited stub
important work of modelling must be performed, due to case of electrical length θsc (“sc” for short circuit) and
parasitics. Also high insertion loss is expected due to the poor characteristic impedance Zsc.
quality factor of inductors. Therefore, this technology is The resonance condition can be easily derived by
especially used for low frequencies and VHF bands. considering the open-ended condition for the elementary
In this paper, a distributed but compact filter topology is resonator, and the short-ended condition for the stub. It is
proposed, based on parallel-coupled stub-loaded resonators. In given by the relation:
section II, a background theory of such resonators is presented, Z
2 ⋅ Tan (θ sc ) ⋅ Tan (θ oc ) = oc . (1)
with a careful comparison between measurement and Z sc
 In a first approximation, considering small electrical dielectric loss tangent tgδ = 0, 0023 ; dielectric thickness
lengths, the resonance frequency fr can be estimated by: h = 813 µm; copper thickness t = 8 µm).
c Z oc Z sc For this resonator, the characteristic impedances Zsc and
fr = 0 ⋅ ⋅ (2)
Zoc are equal to 80 Ω and 35 Ω, respectively, leading to a ratio
2 ⋅π (
2 ⋅ ε reff _ sc ⋅ lsc ⋅ ε reff _ oc ⋅ loc )( ) η equal to 0.44. The microstrip widths are Wsc = 0.8 mm and
where εreff_sc and εreff_sc are the relative effective permittivities Woc = 3.2 mm, respectively. The effective relative
of the short-circuited stub and the open-ended elementary permittivities are εreff_sc = 2.50 and εreff_oc = 2.78, respectively.
resonator, respectively. From this straightforward relation, it is The physical lengths lsc and loc have been fixed to the same
obvious that the resonance frequency is inversely dependent to value lsc = loc = 15.2 mm, to obtain a resonance frequency
the short-circuited stub length lsc and to the open-ended fr equal to 804 MHz.
elementary resonator length loc. The particularity of such Fig. 3 shows the photograph of the unloaded resonator. In
resonators is that the smaller the Z oc Z sc ratio is, the smaller order to measure the resonance frequency, the resonator was
the resonant frequency is. So, highly miniaturized resonators “slightly” coupled to near and far end feeding transmission
can be designed by choosing a small Z oc Z sc ratio. lines, with a 2 mm gap width. Let us notice that the physical
length of the open-ended resonator (2loc) equals 30.4 mm, that
The comparison between the electrical length of the stub-
is 0.14 λ , which is more than three times smaller than a
loaded resonator described in Fig. 1 and that of classical half-
wavelength open-ended and quarter-wavelength resonators is typical half-wavelength resonator, and still shorter than a
carried out in Fig. 2. quarter wavelength resonator. Fig. 4 shows the comparison
between the measured and simulated transmission for this
resonator. Measurement results show a resonant frequency
200
equal to 795 MHz, i.e. 9 MHz (or 1 %) lower than the circuit
180
Half-wavelength open-ended resonator simulation prediction. This value is confirmed by an
160
electromagnetic simulation carried out with Agilent ADS
140 Zoc/Zsc=1
Momentum, which shows a resonance frequency equal to
Electrical length (°)

quarter-wavelength resonator
120
793 MHz. The difference between circuit and EM simulation
100
Zoc/Zsc=0.5 is probably due to the parasitic coupling at the end of the
v
80 feeding lines. The via hole modelling can also introduce some
60
Minimum = 49° differences, because the realization of the via did not exactly
40 Zoc/Zsc=0.2 follows the one simulated in ADS.
20

0
0 5 10 15 20 25 30 35 40 45
Stub electrical length (°)

Fig. 2 Electrical length of the sub-loaded resonator. Dot lines: total electrical
length θsc + 2θoc. Line: 2θoc.

The total electrical length θsc + 2θoc and the electrical

Fig. 3 Photograph of the slightly coupled short-circuited open-ended
length of the open-ended resonator alone 2θoc have been resonator.
plotted, versus the stub electrical length θsc, for three different
characteristic impedance ratios η = Zoc/Zsc. It can be seen that
a great reduction can be achieved by considering small ratios. -20
η = 0.2 leads to a minimum 49° total electrical length, that is -25
EM simulation
the half of a classical quarter-wavelength resonator used for Circuit simulation
-30 Measurement
example in inter-digital filters. Such a small ratio is achievable
in practical realizations, for example with Zsc = 120 Ω, and -35
|S | (dB)

Zoc = 24 Ω. This value of Zoc looks small. However, it has to -40

21

be considered that Zoc will be the result of coupled -45

transmission lines for the filter, thus lowering this -50
characteristic impedance.
-55
B. Measurement of the resonance frequency -60
0.7 0.75 0.8 0.85 0.9
In order to verify the resonance condition given by relation Frequency (GHz)
(1), a resonator was designed with Agilent ADS™ on a
RO4003 Rogers substrate (relative permittivity ε r = 3.38 ; Fig. 4 Measured and simulated transmission parameter for a slightly coupled
short-circuited open-ended resonator.
 III. PROOF-OF-CONCEPT : UNFOLDED TWO-POLE BANDPASS center frequency when a minimal rejection of -25 dB is
FILTER considered. These resonant frequencies are due to the open-
A first two-pole bandpass filter is presented with upright ended elementary resonators which are equal to half-
short-circuited stubs to validate the background theory at the wavelength resonators.
centre frequency fc = 800 MHz with a loaded quality factor
0 0
Q = 30. The filter is carried out on the RO4003 Rogers
substrate specified above. A photograph of the realized filter
-10 -5
microstrip filter is given in Fig. 5.

|S | (dB)
|S | (dB)

11
-20 -10

21
lsc -30 -15
Circuit simulation
Measurement
loc1 -40
0.7 0.75 0.8 0.85 0.9
-20
loc2 Frequency (GHz)

(a)
Fig. 5 Photograph of the two-pole bandpass filter with upright short-circuited
stubs. 0 0

The position of the stub on the resonator and its length can
be used as degrees of freedom to adjust the bandwidth and the -15 -5
centre frequency. The gap width between the parallel coupled

|S | (dB)
|S | (dB)

11
sections is fixed to 300 µm. Then, to obtain the desired -30 -10
couplings between the resonators and then to reach the desired
21

bandwidth, the electrical lengths θoc of these parallel coupled -45 -15
Circuit simulation
sections are optimized. Finally the centre frequency can be Circuit simulation

adjusted by modifying the stub electrical length θsc. Measurement

Measurement
-60 -20
The characteristic impedances Zsc = 48 Ω (microstrip width 0.5 1 1.5 2
Wsc = 2.02 mm) and Zoc = 40 Ω (Woc = 2.7 mm) lead to a ratio Frequency (GHz)
η equal to 0.83. The physical lengths are lsc = 12.2 mm, (b)
loc1 = 35.63 mm and loc2 = 14.4 mm. The physical dimensions Fig. 6 Comparison between the measured and simulated (circuit) S
of this filter are 92.1 mm × 24.4 mm , that is parameters of the bandpass filter: (a) narrow-band measurements and (b)
large-band measurements.
0.25 ⋅ λ0 × 0.07 ⋅ λ0 , where λ0 is the wavelength in vacuum.
Fig. 6 shows the comparison between measurement and
simulation results carried out with a circuit simulator (Agilent Even if there is a slight difference between measurement
ADS™). and simulation results carried out with a circuit simulator,
Fig. 6 (a) shows that a center frequency shift of 2.4 % these results validate the concept of filters realized with stub-
appears between electrical simulations and measurement loaded parallel resonators. In the next section, an optimized
results. This frequency shift is mainly due to a fairly bad filter, realized with folded stubs and on a higher permittivity
modelling of the via holes with the ADS CAD tool. The substrate, is designed and measured.
measured bandwidth equals 26 MHz, compared to 23 MHz for
the simulations, leading to loaded quality factors Q = 30 (3-dB IV. FOLDED THREE-POLE BANDPASS FILTERS
fractional bandwidth 3.3 %) and Q = 34.8 (3-dB fractional In this section a three-pole bandpass filter is demonstrated.
bandwidth 2.9 %), respectively. The minimum insertion loss The working frequency and the bandwidth are fixed to
is 3.65 dB for the measurement, and 3.05 dB for the 800 MHz and 50 MHz (6.25 %), respectively. To improve the
simulation, respectively. The measured return loss is compactness, the short-circuited stubs are folded and the
poor, -7.5 dB, compared to -15.5 dB predicted by the Rogers RO3010 high permittivity substrate is considered
simulation. This discrepancy is due to the existing couplings (relative permittivity ε r = 10, 2 ; dielectric loss tangent
between open-ended sections and short-circuited stubs. Indeed, tgδ = 0, 0023 ; dielectric thickness h = 635 µm; copper
these couplings cannot be easily taken into account in the
electrical ADS tool. Thus, electromagnetic simulations have thickness t = 17.5 µm). In order to obtain a more accurate
to be performed to optimize the desired filter and take all the design, EM simulations were performed with ADS
couplings into account. This is done for the next realizations Momentum. A photograph of the realized folded filter is given
shown in this paper in Fig. 7.
Zsc and Zoc are equal to 34 Ω and 47 Ω, respectively,
Large-band measurements of S11 and S21 are given in
leading to a ratio η = 1.38. The microstrip widths are
Fig. 6 (b). The stop bandwidth extends to about two times the Wsc = 1.2 mm and Woc = 0.65 mm, respectively. The physical
dimensions of this filter are 65.9 mm × 21.2 mm that is 500 MHz, which is only 300 MHz apart from the centre
0.18 ⋅ λ0 × 0.06 ⋅ λ0 , where λ0 is the wavelength in vacuum.. frequency. It also reaches more than 50 dB between the first
spurious and the centre frequency.
This is much smaller compared to the dimensions of the filter
realized in section III, even if this filter is a three-pole instead
of a two-pole. Moreover, the length of a classical three-pole 0 0
parallel coupled filter would be equal to about 0.85 ⋅ λ0 , i.e.
quite five times longer than the actual filter. -10 -5

|S | (dB)
|S | (dB)

11
-20 -10

21
-30 EM simulation -15
EM simulation
Measurement
Measurement
-40 -20
0.7 0.75 0.8 0.85 0.9
Fig. 7 Photograph of the three-pole bandpass filter with folded stubs.
Frequency (GHz)
(a)
EM simulation and measurement results are given in Fig. 8.
0 0
The agreement is quite good. However, the center frequency fc
is shifted from 800 MHz for the EM simulation to 774 MHz -5

for the measurement, i.e. 3 %. The measured bandwidth -20 -10

equals 51 MHz, compared to 53 MHz for the simulations,

|S | (dB)
-15

|S | (dB)

11
leading to a loaded quality factor close to 15. The minimum -40 -20
21
insertion loss is 2.8 dB for the measurement, and 2.85 dB for -25
the simulation, respectively. The measured return loss is better -60 EM simulation -30
than 13.4 dB. EM simulation
-35
0 Measurement
Measurement
0
-80 -40
0.5 1 1.5 2 2.5 3 3.5
Frequency (GHz)
-10 -5
(b)
|S | (dB)
|S | (dB)

11

-20 -10 Fig. 9 Measured and EM post-simulated S parameters of the three-pole stub-
21

folded bandpass filter: (a) narrow-band and (b) large-band.

-30 EM simulation -15
EM simulation V. CONCLUSION
Measurement
Measurement A novel topology of resonators has been demonstrated.
-40 -20
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 The total electrical length of the new resonators can be as
Frequency (GHz) small as the half of a classical quarter-wave length resonator
Fig. 8 Measured and EM simulated S parameters of the three-pole stub- used for example in inter-digital filters, depending on the
folded bandpass filter. desired bandwidth.
Compact and selective two-pole and three-pole bandpass
The origin of the discrepancy between EM simulations and filters have been designed with this new topology of
measurements is mainly due to the via holes modelling. resonators. 3-dB fractional bandwidths included between
Indeed, by adding a series inductance of 0.55 nH and a series 3.3 % and 5.8 % have been measured, with insertion loss of
3.65 dB and 2.8 dB, respectively. The three-pole filter was
resistance of 0.1 Ω with each via hole, an excellent agreement
designed with a EM CAD tool, leading to an excellent
between measurements and EM simulations is obtained, as
agreement between measurement and simulation results. The
shown in Fig. 9, where narrow-band (Fig. 9(a)) and large-band
first spurious frequency appears at about twice the centre
(Fig. 9(b)) results of S11 and S21 are given, when these frequency and a high out-of-band rejection is obtained (more
elements are added in the simulation. Large-band than 50 dB from both sides of the pass-band behaviour).
measurements show that spurious are better rejected compared
to the two-pole filter. This is due to the use of different REFERENCES
resonators for the three-pole filter, leading to different [1] E. Pistono, et al., “Compact Fixed and Tune-All Bandpass Filters
resonances for the first harmonics. This can be compared to Based on Coupled Slow-Wave Resonators”, IEEE Trans. on Mic.
Theory and Tech., Vol. 54, no. 6, pp. 2790-2799, June 2006.
filters realized with Stepped-Impedance Resonators, and [2] H. Issa, et al, "Miniaturized DBR Filter: Formulation and
perhaps opens the door to the design of filters having very Performances Improvement", Proc. IEEE Int. Mic. Theory and Tech.
large rejection bands. The attenuation in the rejected band is Symp., MTT-S 2008, Atlanta, USA, June 10-15, 2008.
very high in the low frequency side; it is greater than 70 dB at