Magic Tee (Hybrid Tee Junction) Formula and Calculator

Scenario: A microwave source delivers 20 mW of power to the H-plane arm (Port 3) of a Magic Tee. All other ports are terminated with matched loads. Calculate the power at Ports 1, 2 and 4.

EXAMPLE:

INPUTS:

• Input power to port-3 = 13 dBm (~ 20 mW)

OUTPUTS:

• Output power at port-1 = 9.989 dBm (~ 10 mW)
• Output power at port-2 =9.989 dBm (~10 mW)
• Output power at port-4 = 0 (Due to isolation between port 3 and port 4)

Magic Tee Formula

As mentioned in the following figure, properties of ideal and perfectly matched Magic Tee are defined by its 4 x 4 scattering matrix (S-matrix). The standard port are as follows.

• Ports 1 and 2 : Collinear arms (Side arms)
• Port 3 : H-Plane Arm (i.e. Sum Port)
• Port 4 : E-Plane Arm (i.e. Difference port)

Following equations are used in this magic tee calculator.

Key Properties:

1. All ports are perfectly matched.
2. Ports 1 and 2 are isolated and ports 3 and 4 are isolated.
3. Signal entering port-3 divided equally and in-phase between ports 1 and 2
4. Signal entering port-4 divides equally but 180 degree out-of-phase between ports 1 and 2.

Advantages of Magic Tee

• High isolation between ports
• Power combining/dividing capability
• Phase comparison capability
• Low insertion loss

Summary: The 20 mW input is split equally (10 mW each) between the collinear arms, with no power leaking into the E-plane arm.

References for further study

Text Books:

1. Liao, Samuel Y., Microwave Devices and Circuits, 3rd Edition
2. D. M. Pozar - Microwave Engineering, 4th Edition
3. Concepts and Applications of Microwave Engineering by Sanjay Kumar and Saurabh Shukla

Academic / Standards References:

1. IEEE Microwave Theory and Techniques Society (MTT-S) publications
2. MIT Microwave Engineering Lecture Notes (Hybrid Junctions)
3. NPTEL Microwave Engineering Course (IIT Kharagpur)