Directional coupler

RF directional coupler with three ports. From left to right: input, measuring connection for leading shaft, insulation connection, terminated with a terminating resistor, and output

Symmetrical power splitter, 3 dB through loss

Directional coupler English directional coupler count and as a special shape to also power divider English power splitter or inverse operation English power combiner are electrically passive components in the field of high-frequency technology , which serve a as a guided wave to divert or described electromagnetic power from a conductor structure - or to be coupled. In the case of an ideal directional coupler, this coupling occurs strictly selectively according to the direction in which the wave passes through the coupler.

The applications are, among other things, in the field of electrical measurement technology such as network analyzers or antenna technology, for example to determine the standing wave ratio . Further applications are power splitting in high-frequency amplifiers or, in the low-frequency range, the separation of received and transmitted audio signals in the form of hybrid circuits and in clinical imaging by magnetic resonance imaging (MRT) .

The technical structure depends heavily on the frequency range: For frequencies up to a few MHz, concentrated electronic components such as transformers and capacitors in the form of a bridge circuit are used, from a few 100 MHz up to a few 10 GHz, so-called line couplers, for example on electrical circuit boards , are used of striplines are used. In addition, combinations of waveguides are used up to the upper range of technically used frequencies in the range of a few THz .

Function description

Two symbols for directional couplers

Symmetrical power divider

The conditions at directional couplers are symbolically described by several gates and each with a wave entering a certain gate and a wave reflected at this gate . To differentiate between the individual shafts, which is synonymous with the performance , the gate number is also given as an index. The transmission or coupling factors between the incoming and reflected waves at a gate and the waves transmitted between the individual gates are expressed by the scattering parameters in the form of a matrix . The elements of this matrix represent factors with which the waves are reflected or transmitted. ${\displaystyle a}$ ${\displaystyle b}$

The first figure opposite shows two different directional coupler symbols with four or three ports, which are labeled with P _n . In the first case with four ports, there is a connection in the main branch between P ₁ to P ₂ or P ₃ to P ₄ . In addition, a wave arriving backwards at gate P ₂ is coupled to output P ₄ , and a wave arriving at P _{1 is} also output to gate P ₃ ; these coupling branches are indicated by crossed arrows in the middle. This shape represents the symmetrical shape of a forward coupler with four ports. In addition, there are also backward couplers in which the coupling branches exist between P ₁ and P ₄ or between P ₂ and P ₃ . Backward couplers are used in network analyzers , among other things .

The symmetrical form of a feedforward coupler with four ports can be transformed into a directional coupler with three ports by internally terminating port P ₄ with the line impedance , values ​​such as 50  Ω , as shown in the symbol below. This fourth, internally locked gate is then no longer shown in the symbol. The function is reduced to that of a power splitter: A wave arriving at port P ₁ is directed to both output ports P ₂ and P ₃ and thus divided between the two outputs in a certain ratio. With an ideal coupler, no power is lost through thermal losses or radiation, which means that the total power at the two output ports must correspond to the power supplied. In this example, the wave on port P ₃ is attenuated by the coupling factor of −10  dB ; the upper path has, asymmetrically, a clearly low insertion loss of just under approx. 0.5 dB. Applications are e.g. B. with measuring devices in which only a small part of the power transmitted between port 1 and 2 is decoupled at port 3 and sent to a measuring device such as a spectrum analyzer .

By selecting its parameters, a directional coupler can also be operated as a symmetrical power splitter, as shown in the adjacent figure. In the symmetrical case, the incoming wave at gate 1 is evenly distributed to both outputs, this corresponds to halving the power, which corresponds to an attenuation of 3 dB in each path. If a symmetrical power splitter is operated in reverse direction, the power of the two inputs P ₂ and P ₃ are output together at port P ₁ . In this case, there is a power combiner which, for example in larger transmission systems, combines the high frequency generated by individual amplifier stages into a common antenna signal.

parameter

Directional couplers are described by various parameters, which also determine the application. Since all parameters of the coupler are frequency-dependent , directional couplers with a large bandwidth are larger and more complex to manufacture. In the case of high-frequency couplers, the wave impedances are usually 50 Ω; in the area of ​​cable and satellite television, 75 Ω are common. The service is defined in the main branch. Another parameter at higher powers is the dielectric strength of the coupler.

In addition, couplers are described by the typical transmission factors that express the power ratios between the various ports. The factors are usually given in logarithmic form in decibels (dB).

Coupling factor

The coupling factor C specifies the value which power share of the main branch is transferred to the coupling branch. Using the example of the symmetrical forward directional coupler, one of the two coupling factors is given by:

${\displaystyle C_{3,1}=-10\log {\left({\frac {P_{3}}{P_{1}}}\right)}\quad {\rm {dB}}}$

Usual fixed values ​​of the coupling factor are −10 dB, −20 dB or −30 dB. Directional couplers with mechanically variable coupling factors are also common for applications in the upper power range; this enables coupling factors down to below −60 dB.

Insertion loss

Relationship between coupling factor and insertion loss

The insertion loss L indicates the level change from the input to the output of the main branch. The loss that arises from the coupling is also taken into account; this is referred to as coupling attenuation. Thus a 6 dB coupler has at least 1.3 dB and a 10 dB coupler at least 0.5 dB insertion loss. Using the example of the symmetrical directional coupler, the insertion loss in the main branch is given by:

${\displaystyle L_{i2,1}=-10\log {\left({\frac {P_{2}}{P_{1}}}\right)}\quad {\rm {dB}}}$

The coupling attenuation is given by:

${\displaystyle L_{c2,1}=-10\log {\left(1-{\frac {P_{3}}{P_{1}}}\right)}\quad {\rm {dB}}}$

The above relationships apply to ideal directional couplers and, as a good approximation, to real directional couplers. With real couplers, there are additional losses such as dielectric losses , which are expressed in heating, and undesired reflections at transition points. Since the sum of the output power must be the same as the power supplied, an ideal directional coupler without additional losses results in a simple relationship between the coupling factor and insertion loss, as shown in the diagram opposite. The following applies: The smaller the amount of the coupling factor, that is, the less power is coupled out, the lower the amount of insertion loss in the main branch. The following table shows the relationships as some corresponding numerical values:

Coupling factor [dB]	Insertion loss [dB]
3	3
6th	1.25
10	0.458
20th	0.0436
30th	0.00435

isolation

The isolation I of a symmetrical forward directional coupler is mostly unwanted crosstalk from the input port P ₁ directly to the port output P ₄ when the other two ports P ₂ and P ₃ are terminated with the line impedance and no reflections occur. The isolation is then given as:

${\displaystyle I_{4,1}=-10\log {\left({\frac {P_{4}}{P_{1}}}\right)}\quad {\rm {dB}}}$

Similarly, the isolation is defined as a mirror image of the other two ports if the two ports P ₁ and P ₄ are terminated with the line impedance:

${\displaystyle I_{3,2}=-10\log {\left({\frac {P_{3}}{P_{2}}}\right)}\quad {\rm {dB}}}$

The two insulation values ​​depend on the respective coupler and can also differ from one another. Ideally, the amount of insulation should be as high as possible; H. no signal transmission takes place via this path.

Directivity

The directivity D of a forward directional coupler is directly related to its isolation and the coupling factor via the following relationship:

${\displaystyle D_{3,4}=I_{4,1}-C_{3,1}\quad {\rm {dB}}}$

The magnitude of the directional effect should be as high as possible, which is also given to a good approximation in the area of ​​the center frequency. Of all the parameters, the directional effect is most dependent on the frequency and its value fluctuates, especially with broadband directional couplers. As a directional coupler, waveguides have the best directional effect due to their principle.

S parameters

In the case of a symmetrical and ideal directional coupler with four ports, the S-parameters can be represented as a matrix due to the symmetry on two, generally complex and frequency-dependent terms and . expresses the transmission coefficient, the coupling coefficient of the coupler: ${\displaystyle \tau }$ ${\displaystyle \kappa }$ ${\displaystyle \tau }$ ${\displaystyle \kappa }$

${\displaystyle \mathbf {S} ={\begin{bmatrix}0&\tau &\kappa &0\\\tau &0&0&\kappa \\\kappa &0&0&\tau \\0&\kappa &\tau &0\end{bmatrix}}}$

The zeros on the main diagonal are an expression of the freedom of reflection of the ideal directional coupler, the zeros on the opposite diagonal an expression of perfect isolation.

Physical structure

Coaxial cable

Function of a directional coupler

In the case of a coaxial cable , a parallel wire is carried along in the space between the inner and outer conductor, the length of which must not exceed λ / 4 of the wavelength to be measured. Both inductive and capacitive coupling occurs, the strength of which is determined by the distance. In an ideal directional coupler, inductive and capacitive coupling are exactly the same size.

A signal on line 1 (shown by the directional current arrow I green) has on line 2

• a common-mode inductive coupling component ( I _M , blue) which is opposite because of Lenz's rule .
• a push-pull capacitive coupling component ( I _C , red) that is not oriented.

At each of the two measuring resistors, the currents add up in the correct phase (constructive or destructive interference ) and generate voltages proportional to them, which are a measure of the flowing power. If the wave impedance of the coaxial cable corresponds to the impedance of the antenna ( standing wave ratio  = 1), no output signal appears at the right measurement output.

Line 2 must be terminated on both sides with relatively low resistances (≈100 Ω), the value of which depends on the geometric dimensions. This load leads to very low measuring voltages with short cable lengths. For this reason, two separate couplings ( lines 2a and 2b ) are often used, which are not loaded at the measurement output and therefore deliver higher voltage.

Waveguide

Directional coupler with waveguides

The illustration opposite shows the basic structure of a directional coupler made of waveguides . The two waveguides represent the two main branches, the coupling branches are realized by small bores that are arranged at intervals of λ / 4. Due to the defined distance between these connecting holes, the wave can only propagate in a certain direction due to interference. A waveguide is terminated by means of a wave sump .

Principle of a directional coupler made of waveguides with forward and backward waves

Microstrip technology

Directional coupler as stripline

In microwave technology, directional couplers for low power are manufactured using microstrip technology, as they are very cost-effective. There are a number of circuit concepts such as

• Tapered Line Coupler, translatable as a tapered line coupler
• Branch Line Coupler, in German about branch line coupler (e.g. 90 ° hybrid coupler )
• Lange coupler (consists of toothed stub lines)

which are chosen according to the requirements of the application. Tapered line and branch line couplers in particular are relatively easy to dimension and simulate. Particularly disadvantageous for the branch line coupler is the space required on the board, which increases in all directions with the wavelength of the center frequency.

Broadband directional coupler with several λ / 4 sections which are matched to neighboring frequency ranges due to their geometry

Bridge circuit with transformers

Basic circuit of a broadband directional coupler according to Sontheimer-Frederick

With the coaxial construction, the coupling is strongly frequency-dependent, which is why the necessary coupling length increases with the wavelength (lower shortwave range). Because this leads either to unwieldy dimensions or to very low voltages, a structure with current transformers (straight-through transformer) is used.

After Sontheimer-Frederick

Two identical current transformers are used to

• transform the current of the inner conductor in the ratio n: 1 with T1 and
• to transform the voltage between the inner and outer conductor in the ratio n : 1 with T2 .

This means that the impedance U / I is preserved. The coupling constant is calculated as C _3.1  = 20 · log ( n ). The two resistors R1 and R2 of the transformer T2 must have the same value as the characteristic impedance of the coaxial cable between P1 and P2.

Bruene Bridge

The "Bruene directional coupler" has a current transformer and two adjustable capacitors. The measured voltage is almost independent of the wavelength. The principle also works at only 50 Hz and is used in electricity trading to measure the direction of the transported energy (see picture).

Ring coupler

→ Main article : ring coupler

Ring couplers are characterized by their simplicity in construction. Directional couplers are often used as power dividers or in mixer circuits.

Wilkinson divider

→ Main article : Wilkinson divider

The Wilkinson divider is a simple design of a line-based power divider, usually built using microstrip technology.

Applications

Arrangement for additive mixing

Directional couplers are used, for example, in cable networks to connect a user exit. An additive mixing of several signal sources with correct impedance is also possible.

If HF rectifiers are attached to the two outputs of a directional coupler , the power of the forward and return waves can be determined separately with a DC voltage meter. The so-called standing wave ratio , i.e. the ratio of the forward to the returning wave, can be determined from the ratio of these voltages . From this, for example, conclusions can be drawn about the adaptation of the line to the impedance of the antenna and transmitter . Such devices are called standing wave measuring devices .

A component related to directional couplers is the circulator , which outputs the incoming power of a gate in a fixed direction of rotation exclusively at the adjacent connection. They are used in transmitting / receiving systems such as radar devices to separate the signals sent and received by the antenna ( diplexer ).

Parallel connection of eight power amplifiers using directional couplers.

In the figure above, the input signal is split symmetrically in the left half of the figure for the eight amplifiers shown in the middle of the figure. In the right half of the image, the eight amplified signals are combined to form its only transmission signal.

swell

1. ↑ a simple SWR / wattmeter (PDF; 144 kB)
2. ↑ Thomas H. Lee, Planar Microwave Engineering: A Practical Guide to Theory, Measurement, and Circuits, Cambridge University Press, 2004, ISBN 0-521-83526-7
3. ↑ Bruene directional coupler (PDF; 250 kB)
4. ↑ Bruene SWR measuring device
5. ↑ Bruene-SWR with improved accuracy

literature

• Jürgen Detlefsen, Uwe Siart: Basics of high frequency technology . 4th edition. Oldenbourg Verlag, 2012, ISBN 978-3-486-70891-2 .
• Herbert Zwaraber: Practical setup and testing of antenna systems . 9th edition. Hüthig Verlag, Heidelberg 1989, ISBN 3-7785-1807-0 .

Web links

Commons : Directional couplers and hybrids  - Collection of images, videos and audio files