High Selectivity Coupled Line Impedance Transformer with Second Harmonic Suppression
 Author: Kim Phirun, Park Junsik, Jeong Junhyung, Jeong Seungho, Chaudhary Girdhari, Jeong Yongchae
 Publish: Journal of electromagnetic engineering and science Volume 16, Issue1, p13~18, 31 Jan 2016

ABSTRACT
This paper presents a design of an impedance transformer (IT) with high frequency selectivity characteristics. The frequency selectivity can be controlled by even and oddmode impedance of a shunt coupled transmission line (TL). For experimental validation, a 50 to 20 Ω IT was implemented at a center frequency (
f _{0}) of 2.6 GHz for the longterm evolution signal. The measured results were in good agreement with the simulations, showing a return loss higher than 19 dB over a passband bandwidth of 0.63 GHz (2.28–2.91 GHz) and good sharp frequency selectivity characteristic near to the passband. The series coupled TL provides a transmission zero at 5.75 GHz, whereas the shunt coupled TL provides three transmission zeros located at 2 GHz, 3.1 GHz, and 7.14 GHz.

KEYWORD
Coupled Line , Impedance Transformer , Selectivity , Transmission Zeros

I. INTRODUCTION
An impedance transformer (IT) is one of the fundamental components in RF and microwave circuits. It transforms a specific impedance to another impedance and has been implemented in various applications, such as power dividers [1], baluns [2,3], and antennas [4]. In [5], an opencircuited coupled line impedance transforming symmetric Chebyshev and asymmetric Butterworth DC blocks were presented. It can provide a perfect matching performance at a center frequency (
f _{0}) with a relatively narrow bandwidth. Similarly, a multiconductor coupled transmission line (TL) was proposed in [6], in which the coupled port was connected back to the input port in order to enhance the bandwidth. However, the outofband suppression is poor. The IT using a lumped equivalent circuit of lefthanded TL section with an impedance transforming ratio (r ) of 2 was mentioned in [7]. All presented works were focused on the passband matching characteristics only and did not consider an outofband suppression characteristic. If a frequency selective IT can be realized, the total size, insertion loss, and outofband suppression of the RF circuit or system can be improved. To enhance the outofband suppression with the bandpass response, coupled TLs IT with shunt TL were proposed in [8,9]. Moreover, an ultrahigh impedance transforming ratio IT was designed using two cascaded coupled TLs [10]. There are three different matching regions which are categorized by different performances. However, the presented works did not provide a high frequency selectivity characteristic. In [11], the high frequencyselectivity impedance transformer was presented using coupled TL and shunt step impedance transmission lines. The transmission zero can be controlled by varying characteristic impedances of shunt TLs. However, the variation of transmission zero is limited due to the realization of high and low characteristic impedance TLs of shunt stub TL.In this paper, a design method for an IT with high selectivity characteristics is presented based on parallel coupled TLs. The characteristic impedance of a shunt coupled TL can be provided with wideband and high selectivity characteristics. To verify the proposed IT network, a 50 to 20Ω IT was designed, simulated, and fabricated at the
f _{0} of 2.6 GHz.II. DESIGN EQUATION
Fig. 1 shows the proposed IT structure. It consists of a series coupled TL with odd and evenmode impedances (
Z _{0}_{o} andZ _{0}_{e} ) and a shunt coupled TL with odd and evenmode impedance (Z _{0}_{os} andZ _{0}_{es} ) connected at the source impedance. The electrical length (θ ) of both coupled TLs is given as the quarterwavelength ( /4) atλ f _{0}. The load impedance (Z_{L} ) can be transformed to the source impedance (Z _{S} ) by controllingZ _{0}_{o} andZ _{0}_{e} of the series coupled TL. Moreover, the shunt coupled TL is used to create passband transmission poles as well as two transmission zeros near to the passband, which are located at the lower and upper sides of the passband, respectively.The reflection and transmission coefficients of the proposed IT network can be derived from [12], as shown in Eqs. (1) and (2)
where
At
f _{0}, the reflection coefficients can be reduced as (3).As seen from this equation, the reflection coefficient only depends on
Z _{0}_{e} andZ _{0}_{o} of the series coupled line, and is independent ofZ _{0}_{es} andZ _{0}_{os} .Using (3), the calculated reflection coefficient (
S _{11}) atf _{0} according toZ _{0}_{e} is shown in Fig. 2 by assumingZ _{0}_{o} = 50 Ω,Z_{L} = 50 Ω,Z_{S} = 20 Ω and 14.3 Ω (r = 2.5 and 3.5). From Fig. 2, the reflection coefficient can be categorized into three different matching regions [8] depending onZ _{0}_{e} , which can be described by (4).The value of
Z _{0}_{e} with specified values ofS _{11},Z_{S} , andr atf _{0} can be found by using (3) and (4a) for an undermatched region, as shown in (5).Similarly, the value of
Z _{0}_{e} for an overmatched region can be found from (3) and (4b), as shown in (6).For the perfect matched region,
S _{11} becomes zero. Therefore, the value ofZ _{0}_{e} can be determined as (7).As seen from (5), (6), and (7), characteristic impedances (
Z _{0}_{e} ,Z _{0}_{o} ) of a series coupled TL can be controlled bythe return loss andr . In addition, characteristic impedances of the shunt coupled TL are determine to provide transmission poles in the passband and transmission zeros in the outofband.From (5), (6), and (7), the coupling coefficient (
C_{eff} ) of series coupled line for different matched regions are obtained as (8).The calculated coupling coefficients of series coupled line are plotted in Fig. 3 according to different
r , matched regions, and return losses. The calculation is done by assumingZ_{L} = 50 Ω,Z _{0}_{o} = 50 Ω, andS _{11} = 20 dB and 30 dB. The calculated values are also shown in Table 1 for different return losses and matched regions. As seen from Fig. 3,C_{eff} decrease asr increases. Therefore, the series coupled TL can be easily realized for highr without any fabrication difficulty. Also, a high return loss characteristic can be achieved using a looseC_{eff} .To verify the analytical design equations, the
S parameter characteristics are shown in Fig. 4 for the maximumS _{11} of 20 dB in the case of the undermatched, perfect matched, and overmatched regions. As seen from Fig. 4, two poles in passband are obtained only in the case of the undermatched region, whereas a single pole is obtained in the perfect matched and overmatched regions. Therefore, the undermatched region is preferable for the widest return bandwidth characteristics.By choosing
Z _{0}_{es} = 98 Ω andZ _{0}_{os} = 50 Ω, the transmission zeros are located at the same frequency for all matched regions.Fig. 5 shows
S parameter characteristics in the undermatched region with different evenmode impedances of shunt coupled TL for investigating selectivity and transmission poles. AsZ _{0}_{es} decreases, the transmission poles are moved to near the passband which provides a good frequency selectivity characteristic. However, the bandwidth of the passband is slightly narrowed with smallerZ _{0}_{es} . Therefore, the tradeoff between the bandwidth and frequency selectivity characteristic is required to choose a properZ _{0}_{es} .III. SIMULATION AND MEASUREMENT RESULTS
For validation of the proposed IT network, the 50 to 20Ω (
r = 2.5) IT with the maximumS _{11} of 20 dB at 2.6 GHz was designed, simulated, and measured. According to the simulation performance shown in Fig. 4, the undermatched region was chosen. The circuit was fabricated on an RT5880 substrate withε_{r} = 2.2 andh = 31 mil. The electromagnetics (EM) simulation was performed using HFSS v15 from Ansoft.The circuit size of the proposed IT is 27 mm × 30 mm. Fig. 6 shows the EM simulation layout and photograph of the designed IT network. The calculated and optimized physical dimensions are shown in Table 2.
Fig. 7 shows the EM simulation and measurement results of the fabricated circuit. The measured results are in good agreement with the simulations. From the measured results, the return loss was determined to be 19.6 dB at
f _{0}. Similarly, 19 dB return loss bandwidth is 0.63 GHz (2.28–2.91 GHz). The maximum insertion loss in the same passband is smaller than 0.4 dB. As seen from the measurement result, one transmission zero is obtained on the lower side near the passband and three transmission zeros are on the upper side, providing good selectivity characteristics. Aλ /4 shunt coupled TL generates three transmission zeros at 2 GHz, 3.1 GHz, and 7.14 GHz, respectively. Moreover, theλ /4 series coupled TL generates a transmission zero at 5.75 GHz. The proposed IT provides sharp frequency selective matching and outofband suppression characteristics. The selectivity characteristic of the proposed IT is beneficial when it is applied to frequency selective circuit designs, such as high power, high efficiency, and high linear amplifier designs. The performance comparisons with previous published works are summarized in Table 3. Although reference [11] provides a wider fractional bandwidth (FBW), the selectivity is worse than the proposed circuit.IV. CONCLUSION
This paper presents the design of an impedance transformer with frequency selectivity characteristics. The frequency selective characteristic can be controlled by changing the shunt evenmode impedances of the shunt coupled transmission line. Both the simulation and measurement results were provided to validate the proposed impedance transformer. The proposed impedance transformer is simple to design and fabricate in the microstrip line.

[Fig. 1.] Structure of proposed impedance transformer.

[]

[]

[]

[]

[]

[]

[]

[]

[]

[]

[]

[]

[]

[]

[]

[Fig. 2.] Reflection coefficient characteristics at center frequency according to Z0e with different r.

[]

[]

[]

[]

[Table 1.] Calculated values of proposed circuit with different return losses and matched regions

[Fig. 3.] Calculated coupling coefficient values according to r for S11 of (a) 20 dB and (b) 30 dB.

[Fig. 4.] Simulated S11 and S21 of all matched regions.

[Fig. 5.] Simulated S11 and S21 of undermatched regions with different Z0es.

[Fig. 6.] (a) Layout and (b) photograph of the designed IT network.

[Table 2.] Calculated and optimized physical dimensions (mm) of proposed circuit

[Fig. 7.] Simulation and measurement results of proposed impedance transformer.

[Table 3.] Performance comparison with previous works