ECE 563 & TCOM 590 Microwave Engineering Microwave Passive Components October 21, November 4, 2004

Two-Port Device I1I1 +V1-+V1- +V2-+V2- I2I2 Network Matrices Low frequency circuits - use Z, Y, H parameters Z: V 1 = z 11 I 1 + z 12 I 2 Y: I 1 = y 11 V 1 + y 12 V 2 V 2 = z 21 I 1 + z 22 I 2 I 2 = y 21 V 1 + y 22 V 2 H: V 1 = h 11 I 1 + h 12 V 2 I 2 = h 21 I 1 + h 22 V 2

Network Matrices

E Y1 + E Y1 - E Y2 - E Y2 +

Network Matrices

Scattering Matrices for a 2 port a1+a1+ a1-a1- a2+a2+ a2-a2-

Scattering Matrices for an n port -

Physical Interpretation for a 2 port a1+a1+ a1-a1- a 2 + =0 a2-a2- Z L =Z TE Matched load

Scattering Matrices for an n port -

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Basic Properties of Scattering Matrix Elements (S parameters): Lossless System -

Basic Properties (continued) -

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Examples: Tee Junction Waveguide, coax, stripline, junction with 3 ports and used for power dividers, mixers, sampling junctions axis of side arm (2) is parallel to E of main guide [(1) to (3)]. Power fed at port 2 appears at (1) & (3) as = magnitude, opposite phase.

H Plane Tee Junction -

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Hybrid Tee -

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Directional Coupler 4 port microwave junction Power in 1 couples to port 2 with a fraction to port 4 and virtually none to 3 Power in 2 couples to port 1 with fraction to 3 and none to 4 All ports well matched so S ii =0

Directional Coupler -

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Directional Coupler (D/C) From this S matrix –Power coupled to port 4 is 90 o out of phase relative to power at port 2. (Same for power coupled to 3 compared to 1 for power in reverse direction. –Lines 1&2 and 3&4 are identical and any can be used as primary line while others serve as secondary –D/C with c 2 small(<<1): widely used for power moni- toring in forward and reverse directions. Reflections from imperfectly matched load or antenna. –D/C with c 2 significant fraction of unity used as power dividers

Directional Coupler Parameters

Balanced Amplifier Configuration (ref: Gonzalez, Microwave Transistor Amplifiers)

Branch Line Coupler (ref: Gonzalez, Microwave Transistor Amplifiers)

Branch-Line Coupler

(ref. Pozar, Microwave Electronics)

Lange Directional Coupler

Popular implementation of the quadrature hybrid in microstrip line form. The interdigital form of the microstrips permits a very compact geometric size and provides for tight coupling. Typically coupling values range between –5 and – 1 dB. Octave or more of bandwidth.

TEM Directional Couplers Pair of coupled transmission lines has coupling with wave induced on secondary line is in a direction opposite to that of primary

TEM Directional Coupler

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Coupled Coplanar Striplines Power on a coupled TEM-transmission line propagates as a composite of two possible modes: one even and one odd.

Coupled Coplanar Striplines -

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