An Introduction to Power Dividers & Couplers: Read Full Notes Here

By Himanshu Verma|Updated : April 6th, 2020

In this article, know all about Power Dividers & Couplers which is an important chapter in Microwave-Engineering. Read also the difference between power divider and a directional coupler.


These are passive components used for power division or power combining. In power division, an input signal is divided by coupler in two (or more) signals, equally or not.



5.1. Three Port Networks (T Junction)

It has two inputs with one output.

If component is passive (no anisotropic material), the network is reciprocal (Sij = Sji) and when all ports are also matched (Sij = 0), considering lossless one


Using the features of [S] for lossless and reciprocal network


To satisfy, above equation at least two parameters have to be zero means that three-port networks can not be reciprocal, lossless and matched all ports.

If the network is nonreciprocal with matching all port and satisfaction of energy conservation, such a device is known as Circulator relies on anisotropic materials.

byjusexamprep byjusexamprep

if only two ports of the network are matched, a lossless and reciprocal network can be physically realizable.

If the network is being lossy, network can be reciprocal and matched at all ports (Resistive Divider or Isolator). As an example, Ferrite Isolators are a two-port device having unidirectional transmission characteristics. Because [S] is not unitary, the isolator must be lossy. The isolators can be used between a high-power source and load to prevent possible reflections from damaging the source by absorbing reflected power.

5.1.1. T Junction Power Divider

This can be used for power division (or combining).

Lossless Divider: This suffers from the problem of not being matched at all ports and in addition does not have any isolation between two output ports. The fringing fields and higher-order modes at the discontinuity leading stored energy can be accounted by a lumped susceptance, B. The output line impedances Z1 and Z2 can be selected to provide various power decision.

Resistive Divider: Possible to match all ports simultaneously, the resistive (lossy) divider is used, but no isolation between two output ports due to being not lossless. Half of the supplied power is dissipated in resistors.

5.2. Four Port Networks (Directional Coupler)

It has two inputs and two outputs. After considering using the features of [S] matrix for reciprocal, matched and lossless network, the possible solutions are S14 = S23 = 0 means Directional Coupler. Using different phase references, Symmetrical or Anti-symmetrical Directional Coupler may be defined. The design parameters of directional coupler are


The coupling factor shows the fraction of input power to the output. The directivity is a measure of isolation ability for forward and backward waves. The ideal coupler has infinite directivity and isolation and also lossless. The directional property of the all directional coupler is produced through the use of two separate waves or wave components, which add in phase at the coupled port, and cancel in phase at the isolated port.

5.2.1. Waveguide Directional Coupler

Bethe Hole Coupler: Couple one waveguide to another through a single small hole in the common wall. Types of the parallel guides and skewed guides work properly only at the design frequency (narrow bandwidth in terms of its directivity).


Multi-Hole Coupler: Series of coupling holes are used to increase bandwidth as similar design to multi-section transformer. Making coupling coefficients proportional to binominal coefficients, maximally flat response can be obtained. Using Chebysev polynomial, different responses are possible.

5.2.2. Wilkinson Power Divider


It is a network with the useful property of being lossless when the output ports are matched, that is, only reflected power is dissipated. It is known that a lossy three-port network can be made having all ports are matched with isolation between the output ports. Wilkinson Power Divider can be made in microstrip or stripline form with arbitrary power division of N way Divider or Combiner. The even-odd mode technique is used for analysis.

5.2.3. Hybrid Coupler

It has C = 3 dB having types of the following. Quadrature Hybrid (90º Hybrid)

This is a 3 dB directional coupler (knows as Branch Line Hybrid) with a 90º phase difference in outputs (byjusexamprep). The even-odd mode technique can be applied for analysis. [S] matrix has a high degree of symmetry means any port can be used for input as given below



5.2.4. 180º Hybrid

It is a four-port network with a 180º phase shift byjusexamprep between two outputs (also may be in phase). It can be used as a combiner and has unitary symmetric scattering matrix as


It may be produces as the form of ring hybrid (rate race), tapered matching lines and hybrid waveguide junction (Magic T, (Rate Race)) in which symmetrically (or antisymmetrical) placed tuning ports (or irises) can be used for matching.

5.2.5. Coupled Line Directional Coupler


Coupled lines of two (or more) transmission lines are closed together, power can be coupled between the lines. Generally, TEM mode is assumed rigorously valid for striplines, but approximately valid for microstrips. Coupled Line Theory is based on types of excitations as even mode (strip currents are equal in amplitude with same directions) and odd mode (strip currents are equal in amplitude with opposite directions). Arbitrary excitation can be treated as a superposition of appropriate even and odd modes amplitudes. Moreover, design graphs are present for coupled lines.

Design Considerations:

- Although a single section coupled line has limited bandwidth due to byjusexamprep requirement, the bandwidth can be increased using multiple sections coupled line having close relations to multisection QWT.

- The assumption of the same velocity of propagation for even and odd modes in design, generally not satisfied for a coupled microstrip or non TEM lines. This gives poor directivity. By using a more effective dielectric constant (smaller phase velocity) for even mode, phase differences should be minimized. This also produces problems as the mismatching phase velocities for the multisection case and degrades coupler directivity. Increasing bandwidth can be obtained with low coupling limits.

5.2.6. Lange Coupler

To increase the coupling factor, Lange Coupler (several lines) with 90º phase difference between outputs is used as a 3 dB coupling ratio in an octave or more bandwidth can be achieved. The main disadvantage of it (a type of quadrature hybrid) is difficult to fabricate due to very narrow lines. Folded Lange coupler is also used for more easily analysis to model equivalent circuit.

5.3. Other Couplers

· Moreno Crossed Guide Coupler

· Schwinger Reversed-Phase Coupler

· Riblet Short Slot Coupler

· Symmetric Tapered Coupled Line Coupler

· Coupler with Apertures in Planar Lines

As an example of a device uses a directional coupler is Reflectometer isolate and sample the incident and reflected powers from a mismatch load as a heart of a scalar (or vectorial) network analyzer.


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