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Microwave Hybrid Circuits

Ahella Hegazy 185903Munya Alaini 185979

Introduction

A microwave circiut ordinarily consists of several microwave devices connected in some way to achieve the desired transmission of a microwave signal. The interconnection of two or more microwave devices may be regarded as a microwave junction. We shall be addressing the various microwave devices and further analysis that can be made with the help of the scattering matrix theory with respect to the relationships between input & output.

S-Parameters

S-Parameters

H,Y,Z cant be measured for the following reasons:

At microwave freq. it's not possiable to have open and short circuits.

Equipments are not availabe to measure voltage & current at microwave frequencies.

Active devices have stability issues.

Method of charatrization

The logical variables to use at the are travelling waves:

b1 = S11a1 + S12a2 b2 = S21a1 + S22a2

Waveguide Tees

E-plane

H-plane

Magic

Coupler

Circulator

Hybrid

E-PLANE TEE

A waveguide tee in which the axis of its side arm is parallel to the E-field of the main guide.

E-PLANE TEE

Two way transsmisson:

E-PLANE TEE

S11, S22 & S33 are zero, if E-plane is perfectly matched with the aid of screw tuners. When the waves are fed into port 3, the waves appearing at port 2 & 3 will be in the oppisate phase and same magnitude. Therefor, S13 = -S23

For a matched junction,

E-PLANE TEE

Symmetry property S12 = S21, S13 = S31 and S23 = S32 Zero property The sum of each term of any column (row) multiplied by the complex conjugate of the corresponding terms of any column(row) is zero. S11*S12 + S21*S22 + S31*S32 = 0 Unity property The sum of the products of each term of any one row (column) multiplied by its complex conjugate is unity S21*S21 + S31*S31 = 1 I S12*S12 + S32*S32 = 1 II S13*S13 + S23*S23 = 1 III

E-PLANE TEE

Diagnol elements are not all zero.

Hence,

Thus,

H-PLANE TEE

S13 = S23

H-PLANE TEE

S-matrix

H-PLANE TEE

Symmetry property S12 = S21, S13 = S31 and S23 = S32 We will assume that port 3 is perfectly matched so S33 = 0.

H-PLANE TEE

Unitary property [S][S*]=I

H-PLANE TEE

H-PLANE TEE

Using equation 1

H-PLANE TEE

Using equation 2

H-PLANE TEE

H-plane tee S-matrix

MAGIC TEES

MAGIC TEES

Characteristics

E-arm & H-arm are prefectly matched S33 = S44 = 0 Port 3 & 4 are isolated from each other S34 = S43 = 0 Input at E-arm, output at port 1 & 2 will be equal but out of phase S13 = -S23 Input H-arm, output at port 1 & 2 will be equal and in phase S14 = -S24

Magic tees

Symmetry property S12 = S21, S13 = S31 and S24 = S42

[S][S*] = I

Magic tees

S-matrix

MAGIC TEES

Applications

• Mixing
• Duplexing
• Isolator
• Power combiner

Hybrid Rings

Annular line of proper electrical length to sustain standing waves, to which four arms are connected at proper intervals by means of series or parallel junctions. Hybrid ring With series junctions

Hybrid Rings

Characteristics When a wave is fed into port 1, it will not appear at port 3 because the difference of phase shifts for the waves travelling in the clockwise and anticlockwise directions is 180. Thus the waves are cancelled at port 3. S imilarly the waves fed into port 2 will not emerge at port 4 and so on.

Directional couplers

Circulator

Thanks!

Munya Alaini & Ahella Hegazy