But if the veins aren’t functioning properly, fluid can pool. Mahlay says that the arteries are like “supply vessels” and the veins “collectors.” Usually, the veins collect fluid from the periphery and return it to the heart, which circulates it back through the body. “Compression garments help to prevent the blood pooling in the veins, they prevent fluid pooling in the legs, and they help return the blood in the veins back to the heart,” says Natalia Fendrikova Mahlay, MD, an internal medicine doctor at Cleveland Clinic in Ohio.ĭr. Enter compression socks and stockings - specially designed garments that apply gentle pressure to stimulate circulation and relieve discomfort. When port 4 is the input, the outputs are phased at 315 degree increments (port 5 is now at 135 degrees).From long flights to pregnancy and diabetes, many circumstances and conditions can cause pain and swelling in the legs, ankles, and feet. When port 3 is the input, the phase increment is 270 degrees (port 5 is at 45 degrees). When port 2 is the input, the phase increment is now 135 degrees, with port 5 now at 90 degrees. It may be difficult to see, but when port 1 is the input, the four outputs are linearly phased in 45 degree increments (port 5 is at zero phase angle). Below phase responses between four inputs and four outputs are plotted on Smith charts over very small frequency range. We chose the center frequency of of our ideal network to be 10 GHz. Note that two crossovers are required, so the Butler matrix requires some type of 3D interconnect. Two 45 degree fixed phase shifters are needed, here these are series lines sized to provide 45 degrees in length. Quadrature couplers are needed in four places, we chose to use the branchline coupler it is comprised of four lines forming a box, with the vertical elements at impedance equal to Z0, and the horizontal elements at Z0/. The schematic below is for a simple, ideal Butler matrix that will drive four elements. The phase increment between the outputs depends on which input you useīy the way, this is a passive reciprocal network, so it works the same when it transmits energy as when it receives energy, but in our analysis we'll assume that it is employed as a transmitter, with the inputs on the left and the antenna elements on the right.None of the inputs provides a broadside beam.Phases of N outputs are linear with respect to position, so beam is tilted off main axis.N inputs and N outputs, with N usually 4, 8 or 16.The primary characteristics of the Butler matrix are: It is remarkable that the chose not to first describe what they called the "Sanders beam-forming matrix" in an IEEE journal. ![]() Butler was an employee of Sanders Associates in Nashua, New Hampshire, which is now part of BAE. ![]() The Butler matrix was first described by Jesse Butler and Ralph Lowe in a paper titled Beam-Forming Matrix Simplifies Design of Electronically Scanned Antennas, Electronic Design, volume 9, pp. It performs a similar function to a Rotman lens, or a phased array antenna system. Depending on which of N inputs is accessed, the antenna beam is steered in a specific direction in one plane Butler matrices can be combined in two "layers" to facilitate 3D scanning. The Butler matrix is a type of beam-forming network. Click here to go to our main beam-forming network pageĬlick here to go to our main page on antennas
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