General Properties for Determining Power Loss and Efficiency of Passive Multi-Port Microwave Networks

ABSTRACT

Starting from the scattering matrix formulation, three useful properties are derived that characterize the dissipative loss and the corresponding efficiency of a multi-port, passive microwave network. Elementary examples are considered that involve both reciprocal and non-reciprocal networks to demonstrate the utility of the expressions provided. When applied to the equal-split, matched, three-port resistive divider, they recover the known fact that the device is 50% efficient. The relations yield the new result that the efficiency of a three-port Wilkinson power divider is two-third on the average. Using the results presented, it is further shown that the Wilkinson power divider belongs to a class of most efficient, matched, reciprocal three-port networks that are constrained to provide maximum isolation at the output ports.

KEYWORDS:

• Efficiency
• Scattering matrix
• Passive microwave network
• Dissipation
• Hypersphere
• Eigenanalysis

Notes

1. Of course, a device will have several efficiencies – one relating to dissipation, one relating to mismatch, etc. In this paper, we are only concerned with the former.

2. It is straightforward to include non-uniform port excitations into this formulation by including a weight factor w_i inside the summation in Eq. (4(4) ).

3. Note that for a three-port circulator insertion loss, return loss and isolation cannot be chosen independently [12].

Additional information

Notes on contributors

Ramakrishna Janaswamy

Ramakrishna Janaswamy received his PhD degree in electrical engineering in 1986 from the University of Massachusetts, Amherst, the Master's degree in microwave and radar engineering from IIT Kharagpur, India in 1983 and the Bachelor's degree in electronics and communications engineering from REC Warangal, India in 1981. From August 1986 to May 1987, he was an assistant professor of electrical engineering at Wilkes University, Wilkes Barre, PA. From August 1987 to August 2001 he was on the faculty of the Department of Electrical and Computer Engineering, Naval Postgraduate School, Monterey, CA. In September 2001 he joined the Department of Electrical & Computer Engineering, University of Massachusetts, Amherst, where he is a currently a professor. He was a visiting researcher at the Center for PersonKommunikation, Aalborg, Denmark from September 1997 to June 1998. He is a fellow of IEEE and was the recipient of the R. W. P. King Prize Paper Award of the IEEE Transactions on Antennas and Propagation in 1995. He received the IEEE 3^rd Millennium Medal in 2000 for his “outstanding contributions” to the Santa Clara Valley Section. He served as an associate editor of Radio Science from January 1999 to January 2004 and an associate editor of IEEE Transactions on Vehicular Technology from 2003 to 2006. He has been serving as an associate editor of IEEE Transactions on Antennas and Propagation since August 2010 and is currently a member of the IEEE Wave Propagation Standards Committee. He is the author of the book Radiowave Propagation and Smart Antennas for Wireless Communications, Kluwer Academic Publishers, November 2000.

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