H TYPE T JUNCTION (H PLANE TEE)

H TYPE TEE JUNCTION

An H type T junction its so in figure (A) it is called an  H type T Junction because the long axis of the b r is parallel to the plane of the magnetic lines of the force in the waveguide full stop again comma for simplicity, only  the E lines    are show in figure.It X indicates an E line Moving away from the observer.  Each dot indicates an E line is moving toward the observer.

In view (1) of figure(B),the signal fed into arm b and in phase outputs are obtained from the a and c and the output signal is obtained from the b arm because the fields add at the junction and induce E lines into the b arm. If 180 degree out of phase signals are fed into arms a and c, as shown in view (3),no output is obtained fro b arm because the opposing fields cancel at the junction .if a signal is fed into the a arm, as shown in view (4), outputs will be obtained from the b and c arms .the reverse is also true. If a signal is fed into the c arm, outputs will be obtained from  the a and b arms.

S MATRIX OF H TYPE TEE PLANE 

We know that,
When TE₁₀ mode is made to propagate into port 3 the two outputs at port 1 & port 2 will have a output equal in phase

Since it is a three port junction the s-matrix can be derived as follows.

Step 1: Scattering coefficient (plane of symmetry)

S23= S13 ------- (1)

the outputs at ports 1 and port 2  with an input at port 3 will be equal in phase

Step 2: If port 3 is perfectly matched to the junction

S33 = 0 -------- (2)

Step 3: From symmetric property

Sij = Sji

S12 = S21

S13 = S31

S23 = S32=S13 --------- (3)

Using values of equation 1, 2, 3 in S matrix, it becomes:

 --- (4)

Step 4: From unitary property  

i.e

• R1C1: |S11 |2 + |S12|2 + |S13|2 = 1 -------- (5)

R2C2: |S12|2 + |S22|2 + |S13|2 = 1 --------- (6)

R3C3: |S13|2 + |S13|2 = 1 --------- (7)

R3C1: S13.S11* + S13.S12* = 0 ---------- (8)

• Equating (5) & (6), we get,

• |S11 |2 + |S12|2 + |S13|2=|S12|2 + |S22|2 + |S13|2

               S11 = S22 ---------- (9)

• From equation (7) S13 =   --------- (10)

• From equation (8), S13 (S11* + S12*) = 0

Or S11 = -S12  or S12=-S11----------from (9) ------- (11)

• Using equation (9), (10) & (11) in equation (5) |S11|2 + |S11|2 +   = 1

Or 2|S11|2 =   or S11 =   --------- (12)

• S12=(-1/2)

S22=(1/2) ---------- (13)

• Substitute all these values in S-matrix

We know that [b] = [S] [a]

 ---------- (14)

 ---------- (15)

 ---------- (16)

 ---------- (17)

Case 1: a1=a2=0, a3≠ 0

i.e Input at Port 3 and no input at port1 and port 2

Put case 1 values in equation 15, 16, 17:

  H TYPE TEE JUNCTION WITH S MATRIX.