Waveguide Tees in Microwave

Wave guide Tees in Microwave:

In microwave circuits, a wave guide with three independent ports is known as a ‘Tee’ junction. The characteristics of Tee junction are,

1. A short circuit can be positioned in one of the arms of 3 port junction in the manner that no power is moved through the other two arms.

2. If the junction is symmetric about one of its arms a short circuit can be placed on that arm. So that, no reflection occurs between other two arms.

3. It is impossible to have matched impedance on all the three arms.

E-Plane Tee in Microwave:

An E plane tee is a waveguide tee junction in which the axis of the side arm is parallel to the electric field. Two arms of the Tee junction are collinear arms. Signal entering at one port is divided among other two ports in such a way that the signals are out of phase with each other. The output of the E-plane will be the difference between input signals. The side arm of E-plane Tee is also known as difference arm.

Since the E-Plane Tee is a 3 port network, the general ‘S’ matrix is represented as

The wave fed into port-3 appears at port 1 and port 2 with equal magnitude and opposite phase.

ie, S₁₃ = -S₂₃ --------------------- (2)

If port 3 is matched, S₃₃ = 0 --------------------- (3)

By the property of symmetry,

S₁₂ = S₂₁

S₁₃ = S₃₁

S₂₃ = S₃₂ ---------------------- (4)

Applying equation (2), (3) & (4) in equation (1)

By unitary property ‘[S][S]* = I’

R₁C₁

=> S₁₁S₁₁* + S₁₂S₁₂* + S₁₃S₁₃* = 1

=> |S₁₁|² + |S₁₂|² + |S₁₃|² = 1 ------------ (6)

R₂C₂

=> |S₁₂|² + |S₂₂|² + |S₁₃|² = 1 ------------ (7)

R₃C₃

=> |S₁₃|² + |S₁₃|² + 0 = 1

=> 2|S₁₃|² = 1

=> S₁₃ = 1/√2 ------------ (8)

R₃C₁

=> S₁₃ S₁₁* - S₁₃S₁₂*= 0

=> S₁₃ (S₁₁* - S₁₂*) = 0

S₁₁* - S₁₂*= 0

S₁₁* = S₁₂*

ie,  S₁₁ = S₁₂ ------------------ (9)

Equating equations (6) and (7)

We get, |S₁₁|² = |S₂₂|²

S₁₁ = S₂₂ --------------------- (10)

Substitute equation (8) & (9) in equation (6)

2|S₁₁|² + ½ = 1

S₁₁ = ½

Therefore, the scattering matrix of E plane Tee is,

H Plane Tee in Microwave:

In H Plane Tee, the side arm or H arm is parallel to the magnetic field. The signal fed to one of the ports will be divided between the other two ports and the signals will be in phase. The output of the H Plane Tee is the sum of input signals.

The general matrix is,

Since, the signals are in phase, S₁₃ = S₂₃ ------------------- (2)

If Port 3 is matched, S₃₃ = 0 -------------- (3)

By Symmetry,

S₁₂ = S₂₁

S₁₃ = S₃₁

S₂₃ = S₃₂ ---------------------- (4)

Applying equation (2), (3) and (4) in (1).

By unitary property, [S][S]* = I

R₁C₁

=> |S₁₁|² + |S₁₂|² + |S₁₃|² = 1 ------------ (6)

R₂C₂

=> |S₁₂|² + |S₂₂|² + |S₁₃|² = 1 ------------ (7)

R₃C₃

=> |S₁₃|² + |S₁₃|² + 0 = 1

=> 2|S₁₃|² = 1

=> S₁₃ = 1/√2 ------------ (8)

R₃C₁

=> S₁₃ S₁₁* + S₁₃S₁₂*= 0

=> S₁₃ (S₁₁*+ S₁₂*) = 0

S₁₁* + S₁₂*= 0

S₁₁* = -S₁₂*

ie,  S₁₁ = -S₁₂ ------------------ (9)

Equating equation (6) and (7)

We get, |S₁₁|² =|S₂₂|²

S₁₁ = S₂₂ ------------------ (10)

Substitute eq (8) and (9) in eq (6)

We get,