2/10/2005 The Wilkinson Power Divider.doc 1/3 Jim Stiles The Univ. of Kansas Dept. of EECS The Wilkinson Power Divider The Wilkinson power divider is a 3-port device with a scattering matrix of: −−⎡⎤⎢⎥⎢⎥−⎢⎥=⎢⎥⎢⎥−⎢⎥⎣⎦022002002jjjjS Note this device is matched, but it is lossy. What makes this device interesting is the behavior of port 1 (i.e., column 1). Say that a signal (1P+) is incident on port 1 only. Provided that all ports are all terminated in matched loads, we find of course that no power is reflected at port 1 : 211110PSP− +== Instead, all the incident power is evenly divided between the outputs of port 2 and port 3: 2211221 33111 22PPPSP PSP++− + − +== ==2/10/2005 The Wilkinson Power Divider.doc 2/3 Jim Stiles The Univ. of Kansas Dept. of EECS In other words, if 10 mW of signal power flows into port 1, then 5 mW will flow out of ports 2 and 3. Q: Hey! This device appears to be lossless! I thought you said it is lossy? A: Yes, from the standpoint of port 1, it does appear to be lossless. That is why the Wilkinson power divider is so useful. However, the device is clearly lossy, as if we put 10 mW in either port 2 or port 3, then 5 mW will leave port 1, but no power will leave the other port—we’ve lost 5mW! 1 2 3 Power Divider 10 mW 5 mW 5 mW 1 2 3 Power Divider 10 mW 5 mW 0 mW2/10/2005 The Wilkinson Power Divider.doc 3/3 Jim Stiles The Univ. of Kansas Dept. of EECS The Wilkinson power divider is therefore a useful device for dividing signal power into two equal parts. No power is lost, either due to reflection at the input port or absorption by the device! We often refer to this device as a 3 dB power divider, as: 10 10110 log 10 log 3 dB2outinPP⎡⎤⎡⎤==−⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦ The Wilkinson Power Divider Pin Pout= Pin/2 Pout= Pin/2
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