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Directional Couplers / Quadrature Hybrid Couplers

Directional couplers are implemented in a variety of constructions techniques (stripline, coaxial, lumped element) and packages (connectorized, solder pins, substrate carrier). What they all have in common is the ability to tap a sample of the input power without significantly affecting the original signal (with a noted exception). Generally, for well-designed devices the smaller the portion of the input power that the coupled power port extracts, the less profoundly the input signal is affected. For instance, a 30 dB coupler takes only 0.1% of the input power as a sample to Port 3 and passes the remaining 99.9% out Port 2 (assuming no mainline resistive loss). The opposite extreme is a [hybrid] 3 dB coupler that evenly divides the input power between Port 2 and Port 4.

Directional couplers are fundamentally 4-port devices, although many packaged designs bury the isolated port and its associated termination inside the package (or have it permanently attached to the outside and covered over with a heavy layer of epoxy paint). The following image illustrates the fundamental configuration for a directional coupler. Note that the coupled path is ¼ wavelength long, so there is a 90° phase shift between Port 1 and Port4, and between Port 2 and Port 3. I physical devices, the phase shift can be realized either with transmission line (for higher frequencies) or with lumped element inductors and capacitors.

Directional coupler ports

Directional Coupler / Bidirectional Coupler / Hybrid Coupler

An online calculator for power at the ports of a directional coupler is provided here. The same calculator is included in the RF Cafe Calculator Workbook and is available as a free download.

The directional coupler calculations presented below are textbook equations, where all four ports are assumed to be terminated in impedances that are exactly matched to the characteristic impedance of the coupler, and perfectly linear operation is also assumed. The "Directivity" term accounts for non-ideal isolation between the coupler input (Port 1) and the isolated port (Port 4). The "Mainline Loss" term exists to account for resistive losses in the coupler (a specification often provided by the manufacturer). Definitions of the terms are included.

Name Description
Port 1
Input Port
Incident Port
Main system signal input, PInputPort
Port 2
Output Port
Transmitted Port
Main system signal output, POutputPort
Port 3
Coupled Port
Forward Cpl'd Port
Power sampled from Port 1, PCoupledPort
Port 4
Isolated Port
Reverse Cpl'd Port
Power sampled from Port 2, PIsolatedPort
Coupling Factor Power transferred to the coupled port relative to Port 1.

RF Cafe: Coupling Factor*

This is S13=S31 in the forward direction and S24=S42 in the reverse direction, assuming all ports are terminated without reflection.
It will be a negative number expressed in dB.

Coupling Loss Amount of power lost to the coupled port (3) and to the isolated port (4). Assuming a reasonable directivity, the power transferred unintentionally to the isolated port will be negligible compared to that transferred intentionally to coupled port.

Coupling loss equation  *

(mainline loss not included)

Example (using easy numbers):
Assume that the coupling factor is -10 dB and the directivity is 20 dB. Intuitively, we know that -10 dB is equal to 1/10 in terms of power. Therefore, 10% of the input power is transferred to the coupled port and 90% is passed to the transmitted port. 20 dB of directivity means the power that leaks to the isolated port is 20 dB lower than what is present at the coupled port, so it is 30 dB lower than at the input port. 30 dB represents 1/1000 of the input power (0.1%), so the total lost due to coupling and non-infinite directivity is 10.1%. Therefore, 89.9% of the input power arrives at the transmitted port. To verify:

RF Cafe: Power coupler coupling loss equation

Mainline Loss Resistive loss due to heating (separate from coupling loss). This value is added to the theoretical reduction in power that is transferred to the coupled and isolated ports (coupling loss).
Directivity Power level difference between Port 3 and Port 4 (related to isolation). This is a measure of how independent the coupled and isolated ports are. Because it is impossible to build a perfect coupler, there will always be some amount of unintended coupling between all the signal paths.

RF Cafe: Power coupler directivity equation

Isolation Power level difference between Port 1 and Port 4 (related to directivity).

RF Cafe: Power coupler isolation equation

This is S14=S41 in the forward direction and S23=S32 in the reverse direction, assuming all ports are terminated without reflection.


Typical Uses for a Directional Coupler

The most common use for a directional coupler is to tap off a sample of the input power for use in signal monitoring circuits. That sample can be measured to determine the power level, frequency, and/or signal shape (modulation) and either presented for human viewing or can be integrated as part of a feedback loop that adjusts the output to stay within system specifications.

When monitoring the voltage standing wave ratio (VSWR) of the load at the transmitted port, both the coupled port and the isolated port outputs are used to sample the incident and reflected power, respectively. This configuration is referred to as a bidirectional coupler.

A special configuration of the directional coupler is referred to as a hybrid coupler, or a 3 dB coupler or a hybrid coupler or a "quadrature coupler," or a 3 dB hybrid coupler amongst other names. Regardless of what you call it, this coupler has the characteristics of dividing the input power into two paths the have equal powers when terminated properly. Phasing between the four ports remains the same as other directional couplers as shown in this figure.

Directional coupler port phase relationships

Coupler Port Phase Relationships

3 dB Hybrid Coupler


The hybrid coupler has a unique property that makes it very useful for amplifier design, and that is when two equal, but not necessarily 50 Ω (or 75 Ω ,or whatever the system impedance) loads are connected to Port 2 and Port 3, Port 1 will "see" the system impedance (50 Ω, eg) as long as that same 50 Ω is connected to Port 4. So, what that means is if you are designing a power amplifier with transistors that operate at, for example, 4.0 - j3.5 Ω input impedance and 1.5 - j2.5 Ω output impedance, a pair of them can be inserted between a set of quadrature couplers (Ports 2 and 3), with 50 Ω impedances at Port 1 and Port 4. Doing so eliminates the need to transform the transistor impedances to 50 Ω. The image below illustrates the hookup. Theoretically, and infinite number of these connections can be used. An added benefit of the balanced amplifier configuration is that both the IP3 and the P1dB is 3 dB greater than that of the individual devices. See this app note by Thomas Shafer.


Quadrature hybrid coupler connections for an amplifier

Quadrature Hybrid Coupler Hookup for an Amplifier


The same characteristic permits the hybrid coupler to be used as an attenuator. In this configuration, the signal input is on Port 1, and the output is taken on Port 4, the isolated port. Identical PIN diodes (and bias circuits) are connected to Port 2 and 3. When the diodes are turned off (usually requires a reverse bias to offset the negative portion of the RF voltage swing), Ports 2 & 3 "see 50 Ω, and no power is reflected into the isolated port (Port 4). When the diodes are shorted (fully biased on), all of the signal is reflected back into the coupler and exits out of the isolated port (Port 4). Attenuation is therefore maximum when the PIN diodes are reverse biased and minimum when they are forward biased. The attenuator can also be realized using a pair of couplers a la the amplifier circuit above, where the PIN diode circuits are in the place of the transistors.


Quadrature hybrid hookup for an attenuator

Quadrature Hybrid Hookup for an Attenuator


* Equation corrected to divide by Pin - thanks to Matt P. for pointing out the error.

Thanks to Christian D. for providing additional content to this article.

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