Bandpass filters with multiple transmission
zeros using open/shorted stubs
ISSN 1751-8725
Received on 17th June 2014
Accepted on 19th November 2014
doi: 10.1049/iet-map.2014.0402
www.ietdl.org
Wenjie Feng
✉
, Xin Gao, Wenquan Che
Department of Communication Engineering, Nanjing University of Science and Technology, 210094 Nanjing, People’s Republic of China
✉ E-mail: fengwenjie1985@163.com
Abstract: Two novel bandpass filters with multiple transmission zeros using open/shorted stubs are presented
in this study. By utilising shorted coupled lines and the open/shorted stubs, five and eight out-of-band transmission
zeros can be realised for the two bandpass filters from 0 to 2f
0
( f
0
is the centre frequency of the passband). Five
and eight transmission zeros can be adjusted freely by only changing the electrical length of the open/shorted stubs.
Two planar bandpass filters (3-dB fractional bandwidths 7.44%, 3.88–4.18 GHz and 7.5%, 3.85–4.15 GHz) are
designed and fabricated. The theoretical and measured results all show good in-band filterin g performa nces an d
high selectivity.
1 Introduction
As one of the most commonly used filters, microstrip filters are easy
to be integrated into passive or active microwave components
because of their planar structure, easy fabrication and low cost
[1, 2]. With the increase of the number of the out-of-band
transmission zeros, the bandpass filters rejection levels and
harmonic suppression can be further improved because of the
suppression of the unwanted periodic harmonics.
To realise the number of out-of-band transmission zeros, cross
coupling between non-adjacent resonators is introduced to obtain
an elliptic function [3]. However, four and more resonators are
always needed with disadvantages of large circuit size and
serious insertion loss for this method [4]. In addition, two
transmission zeros can be realised by the implemented zero feed
structure into the design of the second-order microstrip filters,
and less insertion loss can be achieved because of the fewer
resonators [5], mixed electric and magnetic coupling can be also
used to increase the out-of-band transmission zeros [6].
Discriminating coupling, which blocks unwanted signals at
certain frequencies and allows the transmission of signals at other
frequencies, can be used to suppress the harmonics with
additional transmission zeros [7, 8]. Moreover, dual-behaviour
resonators (DBRs) with two stopband structures which bring two
transmission zeros on either side of the passband can be used to
design high performance narrow-band bandpass filters [9–11].
Transversal signal-interaction concepts have also drawn a lot of
attention [12–15]. By introducing intentionally a passband
constructive interference and out-of-band signal energy
cancellations to produce power transmission zeros,
high-selectivity filtering responses and harmonic suppression can
be achieved in this kind of filter structures.
In this paper, two novel bandpass filters with multiple
transmission zeros using only four open/shorted stubs are
proposed. Five and eight transmission zeros without complex
coupling structures can be introduced to suppress spurious
resonances of the both sides of the bandpass responses. The
out-of-band transmission zeros can be adjusted easily by only
changing the electrical length of the four open/shorted stubs. Two
prototypes of the bandpass filters operating at 4.0 GHz are
constructed on the dielectric substrate with ε
r
= 2.65, h = 0.5 mm
and tanδ = 0.003. The proposed designs are very simple and
have good in-band and out-of-band performances.
2 Synthesis design of the proposed bandpass
filters
2.1 Bandpass filter with five transmission zeros
Fig. 1 shows the proposed bandpass filter with five transmission
zeros using four shorted stubs. Two side-coupled lines [electrical
length θ
1
, characteristic impedance Z
1
and even/odd-mode
characteristic impedances Z
oe
, Z
oo
, Z
1
= sqrt(Z
oe
, Z
oo
)] are attached
to two shorted stubs (electrical length θ
2
and characteristic
impedance Z
2
) in Fig. 1, and θ
1
> θ
2
. The input admittance Y
in1
of
Fig. 1 can be written as
Y
in1
=−j cot
u
1
/Z
1
− j cot
u
2
/Z
2
(1)
As discussed in [16, 17], the external quality factor Q
e1
of Fig. 1 can
be calculated as
Q
e1
= R
L
1
v
0
2
dY
in1
d
v
v
0
(2)
where R
L
1
is the load impedance for the open/shorted stubs, ω
0
is the
operation frequency and after further calculation, Q
e1
can be
illustrated as
Q
e1
= 0.5R
L
1
(
u
1
csc
2
u
1
/Z
1
+
u
2
csc
2
u
2
/Z
2
) (3)
When Y
in1
= 0, the resonance condition of shorted stubs of Fig. 1 can
be obtained, and the external quality factor Q
e1
can be chosen to
meet the required value of filter specification, and then the two
unknown variables θ
1
, and θ
2
can be solved when the ratio of Z
1
/
Z
2
is fixed. The shorted stubs using the conditions (1) = 0 and (3)
to solve the three unknown variables (θ
1
and θ
2
) is similar to the
method used in [10], which can avoid the use of additional
impedance transformers.
The transmission zeros and the external quality factor Q
e1
against
θ
1
and the simulated frequency responses of the filter with five
transmission zeros are shown in Figs. 2a–d (Using Ansoft
Designer v3.0). Besides the transmission zero ( f
z2
) of the shorted
stubs (θ
2
), the transmission zero (0.5f
z1
, f
z1
, 1.5f
z1
,2f
z1
) created by
IET Microwaves, Antennas & Propagation
Research Article
IET Microw. Antennas Propag., 2015, Vol. 9, Iss. 8, pp. 769–774
769
&
The Institution of Engineering and Technology 2015