two ports
Z o = the characteristic impedance of the overall system Z match = the impedance of the quarter wave transformers in the legs of the power divider A scattering matrix (S matrix) contains the scattering parameters used to describe the electrical performance of an RF linear network such as a Wilkinson power divider. Figure 3 shows the S matrix for the simple form of power divider shown in Figure 2. Key characteristics of the S matrix include the following: ■ S ij = S ji (showing the Wilkinson power divider can also be used as a combiner) ■ The terminals are matched (S 11 , S 22 , S 33 = 0) ■ The output terminals are isolated (S 23 , S 32 = 0) ■ The power is equally split (S 21 = S 31 ) Losses are minimized when the signals at Ports 2 and 3 are in phase and have equal magnitude. An ideal Wilkinson power divider delivers S 21 = S 31 = 20 log 10 (1/√2) = (-)3 decibels (dB) (i.e., half the input power at each output port).
Figure 4: The PDW06401’s power divider frequency response. RL represents terminal matching (S 11 , S 22 , etc.), Iso is the isolation between output ports (S 23 , S 32 ) and IL is the output power (S 21 , S 31 ). Image source: Knowles DLI
The return loss, isolation, amplitude balance, and phase balance characteristics of a power divider are critical to the performance of the antenna array in the following ways: ■ The return loss of the product should be low because greater losses directly compromise maximum transmitted or received beam energy ■ Product isolation should be high because this impacts the isolation between signal paths in the antenna array and enhances its gain ■ The device’s amplitude balance should approach 0 dB as it affects the amplitude performance and Effective Isotropic Radiated Power (EIRP) of the antenna ■ The device’s phase balance should approach 0° difference as this promotes maximum power transfer and ensures intended phase length for all branches across the network. A large phase imbalance will deteriorate
dividers are a good solution for low SWaP-C antenna array applications. Commercial options for the Ku band include Knowles Dielectric Labs’ PDW06401 16 GHz two-way Wilkinson power divider. Knowles dielectric and thin-film manufacturing know-how have allowed it to fabricate a low-loss, yet compact SMD for service with Ku band satcom antenna arrays. The PDW06401 measures 3 x 3 x 0.4 mm and uses low-loss materials that minimize performance variation over a wide temperature range. The package’s characteristic impedance (Z 0 ) matches the 50-ohm (Ω) requirement needed to minimize the voltage standing wave ratio (VWSR), and hence return losses in high-frequency RF systems. The device features zero nominal phase shift, an amplitude balance of ±0.25 dB and a phase balance of ± 5°. Excess insertion losses are 0.5 dB. Figure 4 illustrates the PDW06401 power divider’s frequency response.
Microstrip line Wilkinson power
Figure 3: Scattering matrix (S matrix) for the Wilkinson power divider shown in Figure 2. Image source: Steven Keeping
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