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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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ECE 5317-6351

Microwave Engineering

Fall 2011

Prof. David R. Jackson

Dept. of ECE

Notes 19

Power Dividers and Couplers

Part 1

for all ports matched reciprocal and lossless

Power Dividers and Directional Couplers (cont.)

For all ports matched, reciprocal, and lossless:

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.)

now consider a 3 port network that is non reciprocal all ports matched and lossless

Power Dividers and Directional Couplers (cont.)

Now consider a 3-port network that is non-reciprocal, all ports matched, and lossless:


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

power dividers
Power Dividers

T-Junction: lossless divider

If we match at port 1, we cannot match at the other ports!

power dividers cont
Power Dividers (cont.)

Assuming port 1 matched:

We can design the splitter to control the powers into the two output lines.

power dividers cont1
Power Dividers (cont.)

For each port we have:

power dividers cont3
Power Dividers (cont.)

If port 1 is matched:

The output ports are not isolated.

power dividers cont5
Power Dividers (cont.)


  • The input port is matched, but not the output ports.
  • The output ports are not isolated.
power dividers cont6
Power Dividers (cont.)

Example: Microstrip T-junction power divider

resistive power divider
Resistive Power Divider

Same for Zin1 and Zin2

 All ports are matched.

resistive power divider cont
Resistive Power Divider (cont.)

By reciprocity and symmetry

resistive power divider cont1
Resistive Power Divider (cont.)

Hence we have

All ports are matched, but 1/2 Pinis dissipated by resistors, and the output ports are not isolated.

even odd mode analysis
Even-Odd Mode Analysis

(This is needed for analyzing the Wilkenson.)


Example: We want to solve for V.

using even/odd mode analysis

“even” problem

“odd” problem

odd problem

Even-Odd Mode Analysis (cont.)

“Odd” problem

short circuit (SC) plane of symmetry


Even-Odd Mode Analysis (cont.)

“odd” problem

“even” problem

By superposition:


Wilkenson Power Divider

Equal-split (3 dB) power divider

  • All ports matched (S11 = S22 = S33 = 0)
  • Output ports are isolated (S23 = S32 = 0)

Note: No power is lost in going from port 1 to ports 2 and 3.

Obviously not unitary


Wilkenson Power Divider (cont.)

Example: Microstrip Wilkenson power divider


Wilkenson Power Divider (cont.)

  • Even and odd analysis is required to analyze structure when port 2 is excited.

 To determine

  • Only even analysis is needed to analyze structure when port 1 is excited.

 To determine

The other components can be found by using symmetry and reciprocity.

top view

Wilkenson Power Divider (cont.)

Top view

A microstrip realization is shown.

Split structure along plane of symmetry (POS)

Even  voltage even about POS  place OC along POS

Odd  voltage odd about POS  place SC along POS


Wilkenson Power Divider (cont.)

How do you split a transmission line? (This is needed for the even case.)

top view

Voltage is the same for each half of line (V)

Current is halved for each half of line (I/2)

(magnetic wall)

Z0microstrip line

For each half

even problem1

Wilkenson Power Divider (cont.)

“Even” Problem

Note: The 2Z0 resistor has been split into two Z0 resistors in series.

Ports 2 and 3 are excited in phase.

odd problem1

Wilkenson Power Divider (cont.)

“Odd” problem

Note: The 2Z0 resistor has been split into two Z0 resistors in series.

Ports 2 and 3 are excited 180o out of phase.


Wilkenson Power Divider (cont.)

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.

In summary,


Wilkenson Power Divider (cont.)

Port 1 excitation

Port 1

When port 1 is excited, the response, by symmetry, is even. (Hence, the total fields are the same as the even fields.)

Even Problem

even problem4

Wilkenson Power Divider (cont.)

Even Problem

Port 1 excitation

Along g/4 wave transformer:



Wilkenson Power Divider (cont.)

For the other components:

By symmetry:

By reciprocity:


Wilkenson Power Divider (cont.)

All three ports are matched, and the output ports are isolated.


Wilkenson Power Divider (cont.)

  • When a wave is incident from port 1, half of the total incident power gets transmitted to each output port(no loss of power).
  • When a wave is incident from port 2 or port 3, half of the power gets transmitted to port 1 and half gets absorbed by the resistor, but nothing gets through to the other output port.

Wilkenson Power Divider (cont.)

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.