ECE 5317-6351 Microwave Engineering. Fall 2011. Prof. David R. Jackson Dept. of ECE. Notes 19. Power Dividers and Couplers Part 1. Three-port networks. Power Dividers and Directional Couplers. General 3-port:. Power Dividers and Directional Couplers (cont.).
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Prof. David R. Jackson
Dept. of ECE
Power Dividers and Couplers
Not physically possible
(There are three distinct values.)
Lossless [S] is unitary
These cannot all be satisfied.
(If only one is nonzero, we cannot satisfy all three.)
At least 2 of S13, S12, S23must be zero.
(If only one is zero (or none is zero), we cannot satisfy all three.)
These equations will be satisfied if:
(There are six distinct values.)
Note that Sij Sji.
Clockwise (LH) circulator
Note: We have assumed here that the phases of all the S parameters are zero.
Circulators can be made using biased ferrite materials.
Counter clockwise (RH) circulator
T-Junction: lossless divider
If we match at port 1, we cannot match at the other ports!
Assuming port 1 matched:
We can design the splitter to control the powers into the two output lines.
For each port we have:
Also, we have
If port 1 is matched:
The output ports are not isolated.
Example: Microstrip T-junction power divider
Same for Zin1 and Zin2
All ports are matched.
By reciprocity and symmetry
Hence we have
All ports are matched, but 1/2 Pinis dissipated by resistors, and the output ports are not isolated.
(This is needed for analyzing the Wilkenson.)
Example: We want to solve for V.
using even/odd mode analysis
Equal-split (3 dB) power divider
Note: No power is lost in going from port 1 to ports 2 and 3.
Obviously not unitary
Example: Microstrip Wilkenson power divider
The other components can be found by using symmetry and reciprocity.
How do you split a transmission line? (This is needed for the even case.)
Voltage is the same for each half of line (V)
Current is halved for each half of line (I/2)
For each half
We add the results from the even and odd cases together:
Note: Since all ports have the same Z0, we ignore the normalizing factor Z0in the S parameter definition.
Port 1 excitation
When port 1 is excited, the response, by symmetry, is even. (Hence, the total fields are the same as the even fields.)
For the other components:
All three ports are matched, and the output ports are isolated.
Figure 7.15 of PozarPhotograph of a four-way corporate power divider network using three microstrip Wilkinson power dividers. Note the isolation chip resistors.Courtesy of M.D. Abouzahra, MIT Lincoln Laboratory.