This article has been accepted and published on J-STAGE in advance of copyediting. Content is final as presented. IEICE Electronics Express, Vol.* No.*,*-* Ultra-wideband bias-tee design using distributed network synthesis
Nam-Tae Kima) Department of Electronic Engineering, Inje University, Gimhae 621-749, Korea a) [email protected]
Abstract: This paper presents a design methodology for ultra-wideband bias tees, using a distributed network synthesis considering both RF and DC performance. For the design of bias tees, transfer functions of distributed circuits are offered using equal ripple approximation, and DC current-handling capacity is incorporated into the network synthesis by calculating capacity in terms of the characteristic impedance of a transmission line. A bias-tee circuit with the desired characteristics can be synthesized by properly adjusting the minimum insertion loss (MIL) and ripple of the transfer function with reference to the required performance. As an example, a distributed network synthesis is applied to design a bias tee for ultra-wideband applications. Keywords: Bias tee; network synthesis; ultra-wideband Classification: Microwave and millimeter wave devices, circuits, and systems
References
[1] G. Aiello and G. Rogerson, “Ultra-wideband wireless systems,” IEEE Microwave Mag., vol. 4, pp.36-47, pp. 36-47, Jun. 2003. [2] B. Minnis, “Decade Bandwidth bias T’s for MIC applications up to 50GHz,” IEEE Trans. Microwave Theory Tech., vol. 35, pp. 597-600, Jun. 1987. [3] P. Bell, N. Hoivik, V. Bright, and Z. Popovic, “Micro-bias-tees using micromachined flip-chip inductors,” IEEE MTT-S Int. Microwave Symp. Dig., Philadelphia, U.S.A., pp. 491-494, Jun. 2003. [4] E. Cullens, K. Vanhille, Z. Popovic, “Miniature bias-tee networks integrated in micro-coaxial lines,” Proc. 40th European Microwave Conf., Paris, France, pp. 413-416, Sept. 2010. [5] M. Mokari-Bolhassan and W. Ku, “Transfer function approximation for a new class of band-pass distributed network structures,” IEEE Trans. Microwave Theory Tech., vol. 25, pp. 837-847, Oct. 1977. [6] R. Levy, “Synthesis of mixed lumped and distributed impedance-transforming filters,” IEEE Trans. Microwave Theory Tech., vol. 20, pp. 223-233, Mar. 1972. [7] J. Helszajn, Synthesis of lumped element, distributed and planar filters, McGraw-Hill, New York, pp. 286-288, 1990.
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IEICE Electronics Express, Vol.* No.*,*-*
[8] Rogers Corporation Design 3.3.2, “Temperature rise estimation in Rogers high frequency circuit boards carrying direct or RF current,” Publication no. 92-332, 2012. [9] J. Hong, Microstrip filters for RF/microwave applications: 2nd Ed., John Wiley & Sons, pp. 75-83, 2011. [10] M. Uhm, K. Kim, and D. Filipovic, “Ultra-wideband bandpass filters using quarter-wave short-circuited shunt stubs and quarter-wave series transformers,” IEEE Microwave Wireless Compon. Lett., vol. 18, pp. 668-670, Oct. 2008. [11] Agilent Technologies, Palo Alto, CA, U.S.A., 2005.
1 Introduction Ultra-wideband components need to be designed for applications including instrumentation, electronic warfare (EW), and software-defined radio (SDR). Additionally, as the Federal Communications Commission (FCC) allocates the frequency spectrum in the range 3.1–10.6 GHz for ultra-wideband systems, ultra-wideband wireless components are increasingly needed [1]. In these applications, bias tees are essential components that provide DC power and control signals to ultra-wideband components. Several studies have focused on designing ultra-wideband bias tees that achieve a desired performance. Bias tees have been designed as a combined structure of band-pass, low-pass, and high-pass networks, and synthesized to provide a decade of bandwidth using commercially available software [2]. Because it uses a microstrip structure, this methodology is compatible with low-cost production methods. In Ref. [3], a bias tee was reported using a micro-machined suspended inductor to reduce its circuit area and parasitic capacitance associated with a substrate. The current handling capability of the bias tee is small, however, due to the reduced size of the inductor. Miniature bias tees have been designed using distributed micro-coaxial lines to accommodate a wide range of system impedances [4]. These bias tees can handle more DC current than those fabricated using MEMS technology. Despite these developments, bias tee design methodologies that consider both RF performance and DC current-handling capacity have not been described. In this paper, we propose a design methodology for ultra-wideband bias tees, using distributed network synthesis considering both RF and DC performance. For the synthesis of wideband bias tees, transfer functions of distributed circuits are provided using equal ripple approximation, and the DC current-handling capacity of a transmission line is calculated using the characteristic impedance for use in distributed network synthesis. A bias tee that meets the required RF and DC performance can be synthesized by setting the appropriate MIL and ripple parameters of a distributed circuit. As an example, we applied a distributed network synthesis to the design of an ultra-wideband bias tee, and used the findings to assess the effectiveness of the methodology.
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2 Distributed network synthesis Distributed network synthesis is an effective design methodology for ultra-wideband bias tees because it allows versatility in the synthesis procedure. Because bias-tee circuits should include at least one shunt shorted stub for DC bias injection, in this section we consider a distributed network synthesis for band-pass and high-pass circuits. A transfer function of a distributed network, which consists of commensurate transmission lines, is given in Ref. [5]:
2 m 2 n 2 K(S ) (1 S ) | S21(S) | 2 (1) Pnrm (S ) , where there are n transmission line elements (TLEs), r low-pass elements (LPEs), 2 and m high-pass elements (HPEs). Here, Pn+r+m(S ) is a strictly Hurwitz polynomial of the order n+r+m in S2, and must provide the desired type of approximation. K is a gain parameter and the Rechards’ variable, S, is equal to Σ+jΩ. When the transfer function of a distributed network exhibits equal ripple and band-pass characteristics, equation (1) can be re-written as: K | S |2 (2) 21 2 , 1 [1 cos(n r m )] 2 b 1 2 where is a ripple parameter of the function and the network order n+r+m must be even. In equation (2), the expressions for b and 1 are derived from quasi-low-pass mapping, as follows [6]:
2 2 2 2 2 2 2 (1 2 2) (1 2 21 2 ) cosb (3) ( 2 2 )(1 2 ) , 2 1
2 2 2 2 1 2 cos1 2 2 (4) 2 1 , where tantanl, tan, and tan. The angles and are the electrical lengths of transmission lines at the lower and upper band-edge frequencies, respectively. To obtain an equation for 2, we assume cos2 = / for high-pass elements from (4). Solving for the constants and by constraining that cos2 = –1 at and cos2 = +1 at , we have:
2 2 2 2 2 (1 2 ) 21 2 cos 2 (5) 2 ( 2 2 ) . 2 1 Additionally, when a distributed circuit exhibits equal ripple and high-pass characteristics, equation (1) is reduced to [7]:
2 K | S21 | 2 2 (6) 1 cos (nh m h ) ,
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2 1 c cosh (7) 2 , 1 cos c (8) h , where c = tanc. The angle c is the electrical length of the transmission lines at the cut-off frequency of a high-pass network. Reflection coefficients for equations (2) and (6) are determined by the unitary condition for a lossless network, and a corresponding impedance function is given by: 1 S (S) z(S) 11 (9) 1 S11(S) , where S11(S) is an input reflection coefficient and z(S) is a normalized input impedance of distributed circuits. By choosing appropriate MIL and ripple parameters of a transfer function at a specific electrical length, we can synthesize ultra-wideband bias tees that meet the desired performance criteria.
3 DC current handling capacity The DC performance of a bias tee using a microstrip structure is determined by the microstrip line that has the highest level of impedance along its DC path. The maximum DC current that a microstrip line can handle for the line width of W is given by [8]: AtT I W (10) h , where I is the current required to raise the trace temperature by T above ground plane temperature. In equation (10), h and t are the dielectric and strip thicknesses, respectively, A is the thermal conductivity of the dielectric substrate, and is the resistivity of the conductor.
20
18
16
14
12
10
8
6
4
DC (A) currenthandling capacity 2
0 20 30 40 50 60 70 80 90 100 110 120 130 140 Characteristic impedance ()
Fig. 1. DC current-handling capacity of a microstrip line with T=100oC -7 (substrate: r= 2.5, h = 0.254 mm, t = 0.018 mm, = 0.17 10 m, and A = 0.19 W/mK).
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To incorporate the DC performance of a bias tee into a distributed network synthesis, current capacity is related to the characteristic impedance of a microstrip line. DC current-handling capacity of a microstrip line can be calculated in terms of the characteristic impedance by using equation (10) and closed-form expressions for a microstrip line [9]. Figure 1 presents DC performance versus the characteristic impedance of a microstrip line.
4 Ultra-wideband bias-tee In this section we describe a design example to illustrate bias-tee applications in a distributed network synthesis. For ultra-wideband applications, a bias tee should have an insertion loss of less than 1.0 dB and a reflection loss greater than 16.0 dB over the range 3.1–10.6 GHz. It should also have a DC current-handling capacity of 1.9 A.
4.1 Network synthesis for a desired bias tee Although bias-tee networks can include several shunt shorted stubs for DC current injection [10], bias tees that contain one shunt shorted stub are preferred because shorted stubs are not easy to implement over wide frequency ranges. This section describes distributed band-pass and high-pass circuits synthesized with five zero-reflection points to find a structure suitable for ultra-wideband bias tees. The frequency margin in the synthesis is chosen as 0.5 GHz from the band-edge frequencies.
63.41, 60o 30.70, 60o 20.73, 60o 30.70, 60o 63.41, 60o @ 11.1GHz @ 11.1GHz @ 11.1GHz @ 11.1GHz @ 11.1GHz
56.38, 60o 44.03, 60o 44.03, 60o 56.38, 60o @ 11.1GHz @ 11.1GHz @ 11.1GHz @ 11.1GHz 50 50 94.13, 60o @ 11.1GHz
(a)
0
-5 S21 S -10 11
-15
(dB)
21 -20
and S and
11 -25
S
-30
-35
-40 1 2 3 4 5 6 7 8 9 10 11 12 13 Frequency (GHz) (b)
o Fig. 2. (a) Synthesized band-pass network (n = 4, r = 5, m = 1, and 2 = 60 ). (b) Insertion and reflection losses.
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First, to design a bias tee, it is necessary to calculate the characteristic impedance of the transmission lines that can handle the required DC current. For a microstrip structure, the line impedance that can handle a DC current of 1.9 A is calculated as 94.2 , as shown in Fig. 1. Therefore, the bias tee should be synthesized to include transmission lines with an impedance of less than 94.2 along the DC current path. To synthesize a band-pass network that contains one high-pass element (HPE), o we choose n = 4, r = 5, m = 1, and = 60 in equation (2) over the frequency range 2.6–11.1 GHz, and then adjust the MIL to 0 dB and the ripple to 0.11 dB to create a circuit with transmission-line impedances of less than 94.2 . Using this 2 2 procedure, |S21(S)| can be obtained from equation (2) and |S11(S)| can be determined from the unitary condition of a lossless network. If we select zeros for 2 |S11(S)| in the left-half of the S-plane, S11(S) can be calculated from the poles and zeros in the left-half plane (LHP). The impedance function can be obtained from equation (9). If we extract the distributed elements in a symmetric topology, a band-pass network is obtained with a shunt shorted stub with an impedance of 94.1 , as shown in Fig. 2(a). In this circuit, the insertion loss is less than 0.11 dB and the reflection loss is greater than 16.07 dB, as shown Fig. 2(b).
45.12, 34.16o 36.66, 34.16o 36.66, 34.16o 45.12, 34.16o @ 2.6GHz @ 2.6GHz @ 2.6GHz @ 2.6GHz
94.14, 34.16o 50 50 @ 2.6GHz
(a)
0
-5
S21 -10 S11
-15
(dB)
21 -20
and S and
11 -25
S
-30
-35
-40 1 2 3 4 5 6 7 8 9 10 11 12 13 Frequency (GHz) (b)
o Fig. 3. (a) Synthesized high-pass network (n = 4, m = 1, and c = 34.16 ). (b) Insertion and reflection losses.
Additionally, a high-pass network is designed to include one HPE, using the same procedure as the band-pass circuit. The synthesis begins by choosing n = 4, o m = 1, and c = 34.16 at a frequency of 2.6 GHz. By setting the MIL to 0 dB and -3 2 2 the ripple to 4.1310 dB, |S21(S)| can be obtained from equation (6) and |S11(S)| 2 can be calculated from the unitary condition. When we select zeros for |S11(S)| in
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2 the LHP, S11(S) can be determined from the poles and zeros of |S11(S)| in the LHP, and the impedance function can be calculated from equation (9). Symmetric element extraction from the function yields the distributed network shown in Fig. 3(a), which also includes a shunt shorted stub with a characteristic impedance of 94.1. The circuit has an insertion loss of less than 0.005 dB and a reflection loss greater than 30.22 dB, as shown Fig 3(b). The high-pass network exhibits band-pass characteristics with a center frequency of 6.85 GHz at = 90o, due to the periodic characteristics of commensurate transmission lines. Compared with the network shown in Fig. 2, the high-pass circuit exhibits better RF performance than that of the band-pass network for the same DC performance. Therefore, the high-pass circuit shown in Fig. 3 provides an appropriate structure for the desired bias-tee network.
4.2 Design and experiments Figure 4 shows an ultra-wideband bias tee constructed using the high-pass network shown in Fig. 3. It includes a capacitor for DC blocking and a capacitor for an RF short of the shunt shorted stub and DC bias injection. The bias-tee network was realized on a TLX-9 copper-clad substrate (Taconic); see Fig. 1 for its characteristics. The capacitors used in the bias tee were 545L-series ultra-wideband capacitors from ATC. The 50- microstrip lines were added to accommodate board connectors for the measurements.
50, 23.0o 45.12, 34.16o 36.66, 34.16o 36.66, 34.16o 45.12, 34.16o 50, 23.0o @ 2.6GHz @ 2.6GHz @ 2.6GHz @ 2.6GHz @ 2.6GHz @ 2.6GHz
100nF RF 94.14, 34.16o RF + DC @ 2.6GHz 50 50 DC 100nF
Fig. 4. Circuit diagram of the ultra-wideband bias tee designed using a distributed network synthesis.
To take into account the effect of microstrip discontinuities, dielectric loss, and conductor loss, circuit simulations were carried out using a commercial microwave CAD software package (Agilent Technologies Advanced Design System 2005A [11]). In the simulations, the capacitors for DC blocking and an RF short were replaced with ideal capacitors because their device models were not available. Figure 5 presents the simulated performance of the bias tee; the insertion loss is less than 0.28 dB and the reflection loss greater than 28.54 dB in the range 3.1–10.6 GHz. The predicted DC current handling capacity is 1.9 A. Figure 5 also presents the measured results of the fabricated bias tee. The maximum insertion loss is 0.8 dB and the minimum reflection loss is 26.1 dB across the operating frequency range. The distortions in the insertion and reflection losses are caused mainly by capacitor losses and interactions between the discontinuities of the coaxial-to-stripline transitions at the two ends of the bias tee.
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Additionally, the measured DC current handling capacity is 2.3 A. The difference between the predicted and measured DC performance is largely due to etching tolerances and tin-plating during the fabrication process. The measured performance of the ultra-wideband bias tee satisfies the required design goals.
0 0
-2 -5 -10 Simulated -4 Simulated Measured Measured -15 -6 -20
(dB) -8 (dB) -25
21
11
S -10 S -30 -35 -12 -40 -14 -45
-16 -50 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 Frequency (GHz) Frequency (GHz) (a) (b)
Fig. 5. Simulated and measured performance of the designed bias tee: (a) insertion loss; (b) reflection loss.
5 Conclusion A design methodology for ultra-wideband bias tees was developed, using a distributed network synthesis considering RF and DC performance. Transfer functions of distributed circuits using the equal ripple approximation were used to synthesize an ultra-wideband bias tee, and the DC current-handling capacity of a transmission line was integrated into the network synthesis by calculating the capacity based on the characteristic impedance. As an example, an ultra-wideband bias tee was designed, and experiments were carried out to assess the effectiveness of the methodology. The experimental results demonstrated that the bias tee designed using a distributed network synthesis met all design criteria.
Acknowledgments This work was supported by the 2012 Inje University research grant.
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