10-05-2014, 12:22 PM
NON-UNIFORM TRANSMISSION LINE TRANSFORMERS AND THEIR APPLICATION IN THE DESIGN OF COMPACT MULTI-BAND BAGLEY POWER DIVIDERS WITH HARMONICS SUPPRESSION
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Abstract
In this paper, the application of compact non-uniform
transmission line transformers (NTLTs) in suppressing and controlling
the odd harmonics of the fundamental frequency is presented. A design
example showing the complete suppression of the odd harmonics of
the fundamental frequency is given. In addition, several compact
NTLTs are designed showing the possibility of controlling the existence
of a fundamental frequency’s odd harmonics. Moreover, multi-band
operation using NTLTs is investigated. Specifically, a design example
of a miniaturized triple-frequency NTLT is introduced. Based on
these compact NTLTs, a 3-way triple-frequency modified Bagley power
divider (BPD) with a size reduction of 50%, and a 5-way modified BPD
with harmonics suppression and size reduction of 34%, are designed.
For verification purposes, both dividers are simulated using the two
full-wave simulators IE3D and HFSS. Moreover, the modified 5-way
BPD with harmonics suppression is fabricated and measured. Both
the simulation and measurement results validate the design approach.
INTRODUCTION
Recent advances in wireless communication applications demand high
performance compact RF circuits with the ability of suppressing
the fundamental frequency’s harmonics and achieving multi-frequency
operation. So, different techniques were proposed in the literature to
suppress the unwanted presence of the odd multiples of the design
frequency and achieving multi-frequency operation for microwave
components, such as power dividers and microwave couplers. In [1],
a miniaturized Wilkinson power divider (WPD) with harmonics
suppression was presented. Nevertheless, parallel combinations of
capacitors and inductors were considered in the design. In [2], reduced
size WPD and branch line coupler with harmonics suppression were
proposed using T-shaped structure, where additional microstrip stubs
had to be added to the conventional design. In [3], a WPD with
size reduction of 68% and higher harmonics suppression was achieved.
In [4], a modified WPD with nth harmonic suppression was proposed,
where a parallel combination of an inductor and a resistor was used for
isolation, and extra stubs were added to the conventional transmission
line transformer (TLT) sections. In [5], a multi-frequency WPD
was presented. Nevertheless, as the number of operating frequencies
increases, more uniform transmission line transformer (UTLT) sections
were needed which results, eventually, into a larger circuit area,
especially at low frequencies.
DESIGN OF COMPACT NTLTS
In this section, the theory of designing compact NTLTs is briefly
presented. A general simple design procedure of NTLTs was introduced
in [14, 15], and their application in the design of compact Wilkinson
power dividers and branch line couplers can be found in [16–18].
Figure 1 shows a typical uniform transmission line transformer (UTLT)
that matches a load impedance ZL to a source impedance Zs , with a
length of d0 = λ/4 and a characteristic impedance Z0 . An equivalent
non-uniform transmission line transformer (NTLT) of length d, with a
varying characteristic impedance Z(z) and propagation constant β(z),
is also shown in Figure 1. The NTLT is designed so that the magnitude
of the reflection coefficient |Γ| is enforced to be zero (or very small)
at a single design frequency or several design frequencies of interest.
Moreover, size reduction is achieved by choosing the length d to be
smaller than d0 .
NTLTs for Harmonics Suppression
First, a NTLT that matches a load impedance of 33.33 Ω to a source
impedance of 100 Ω is designed to operate at a fundamental frequency
of 1 GHz. For an FR-4 substrate with a relative permittivity (εr ) of 4.6,
and a substrate height of 1.6 mm, the length of the UTLT is 41 mm.
Considering Equation (4) with |Γin (fj )| = |Γin (1 GHz)| and choosing
the length of the NTLT as d = 27 mm, a size reduction of 34% is
achieved. Figure 2 shows S11 (in dB) for both the UTLT and NTLT in
the frequency range from 0 to 10 GHz. It can be clearly seen that using
the NTLT results in the complete suppression of the odd harmonics of
the fundamental frequency. The Fourier coefficients for the designed
NTLT are shown in Table 1. It should be mentioned here that the
error value in Equation (4) equals 1.5 × 10−7 .
CONCLUSIONS
The concept of non-uniform transmission line transformers (NTLTs)
was used in the achievement of size reduction, harmonics suppression,
harmonics control, and multi-frequency operation. Based on this
concept, compact Bagley power dividers (BPDs) were designed.
Specifically, a triple-frequency 3-way BPD was designed and simulated,
and a 5-way BPD with harmonics suppression was designed, simulated,
and fabricated. The simulations and experimental results prove the
validity of the design approach. Size reduction of about 50% and
34% were achieved for the 3-way and 5-way BPDs, respectively.
Discrepancies between simulation and measurements are mainly due
to the fabrication process and measurements errors.