Miniaturized Wilkinson power dividers utilizing capacitive loading

The authors report the miniaturization of a planar Wilkinson power divider by capacitive loading of the quarter wave transmission lines employed in conventional Wilkinson power dividers. Reduction of the transmission line segments from /spl lambda//4 to between /spl lambda//5 and /spl lambda//12 are reported here. The input and output lines at the three ports and the lines comprising the divider itself are coplanar waveguide (CPW) and asymmetric coplanar stripline (ACPS), respectively. The 10 GHz power dividers are fabricated on high resistivity silicon (HRS) and alumina wafers. These miniaturized dividers are 74% smaller than conventional Wilkinson power dividers, and have a return loss better than +30 dB and an insertion loss less than 0.55 dB. Design equations and a discussion about the effect of parasitic reactance on the isolation are presented for the first time.


I. INTRODUCTION
Wilkinson power dividers [1] are indispensable components of microwave amplifier and antenna distribution circuits, however conventional power dividers are quite large, especially below X-Band where the quarterwave transmission lines can be several millimeters long. Consequently, when they are incorporated into Monolithic Microwave Integrated Circuits (MMICs), the circuit's size depends heavily on the size of the power dividers. Therefore, techniques to reduce the size of power dividers are required for low cost and small size circuits. One of the first methods to reduce circuit size used capacitive loading to miniaturize hybrid couplers [2]. Small, lumped element Wilkinson power dividers have recently been reported [3], but these designs are very dependent on the quality factor and self-resonant frequency of the inductors. Other approaches to reduce the size of Wilkinson power dividers include the use of stepped impedances [4], large inductance through the application of transverse slits [5], and capacitive loading [6,7].
In this paper the quarter-wave transmission lines of a Wilkinson power divider are reduced using capacitive loading and the transmission line characteristic impedance is correspondingly increased. To fully illustrate this approach, the characteristics of Wilkinson power dividers with transmission line lengths from L/5 to L/12 are presented and compared to the conventional, L/4 Wilkinson The schematic of the capacitively loaded Wilkinson power divider is shown in Figure 1. To analyze the circuit and determine the values of the transmission line impedance (Zx), the capacitors (Cl and C2), and the resistance (R) for a given transmission line length (/), an even-odd mode analysis was performed [81. For zero reflection from all three ports and infinite isolation between ports 2 and 3, it is found that C2 must equal 2C1 and R=2Zo. Furthermore, Zx and C_ for any desired transmission line where Zo is the characteristic impedance of the system, P0 is the propagation constant at the design frequency, and COo is the angular frequency at the design frequency. Values of Ct and Zx as a function of the transmission line length l are listed in Table 1. Also shown in Table 1 is the percent,_ reduction in transmission line length and circuit area" compared to the conventional, 2/4 Wilkinson power divider.

III. CIRCUIT FABIL1CATIONAND MEASUREMENTS
The circuits were fabricated on high resistivity silicon (I-IRS) (p > 2500 f_ cm) and alumina substrates with dielectric constants of 11.7 and 9.9 and substrate thicknesses of 400 and 500 Ixm, respectively. Standard IC processing that includes four deposition steps consisting of Cr/Au/Cr (200/  Typically, the measured reflection coefficient was less than -30 dB. The measured bandwidth, defined as the frequency band where IS_d < -15 dB, is shown in Figure 4 as a function of the transmission line length. Also shown is the theoretical bandwidth assuming perfect lumped elements (no parasitics and infinite Q) and lossless transmission lines. As expected, the theoretical bandwidth is less than the measured bandwidth, but the difference is small indicating well behaved circuit components. Also shown on Figure 4 is the bandwidth of the lumped element Wilkinson divider 13]; it is seen that the miniaturized dividers presented here and the lumped element designs have similar bandwidth.
It is also seen that for line lengths less than _d8, the bandwidth does not decrease farther.
Lastly, the bandwidth is not dependent on the substrate.  The measured isolation, -20log(S23), is better than 15 dB at the design frequency. However, the frequency of highest isolation increases as the circuit size is reduced; maximum isolation occurs approximately 1.5 GI-Iz higher than fo for a 7712 divider. This phenomenon has been reported and attributed to an impedance mismatch when port 1 is terminated in a 50 f2 load for the isolation measurement [4,5,6]. However, modeling with Advanced Design Systems [I0] circuit simulation software shows that this assumption also causes a shift in $22 and $33 that is not seen in the reported or our results. Furthermore, the shift is not due to lossy transmission lines. Rather, it was determined that the cause of the frequency shift is due to a frequency independent, parasitic reactance that is associated with the TFR.