62 High Frequency Electronics

High Frequency Design

90-DEGREE COUPLERS

Classic Designs for LumpedElement and Transmission Line 90-Degree Couplers

By Gary BreedEditorial Director

Couplers (or powerdivider/combiners)with outputs that

differ in phase by 90degrees are an importantpart of RF/microwavedesign. This tutorial pro-

vides an overview of various types of 90-degree combiners, using both lumped elementand transmission line structures. Our inten-tion is to introduce the subject to engineerswho may be unfamiliar with these couplers,and perhaps offer some reminders to experi-enced engineers who only occasionally usethem in their designs.

Introduction90-degree, or quadrature, couplers are

used in applications such as power amplifiers,antenna feed systems, phase shifters, modula-tors/demodulators, image-reject mixers, mea-surement systems, and many others. Usingthe mathematics of sine/cosine trigonometricrelationships, these circuits can provide isola-tion, reduce harmonic content, and improvelinearity (reduce distortion). An added valueof some couplers is the simplification of sys-tem design by simultaneously providingimpedance transformation. Also, becausethere are numerous coupler topologies, design-ers have a wide range of choices for electricalperformance, construction method, and physi-cal size.

Note that coupler descriptions are madewith the following convention: the commonport will be referred to as the input, and eachof the two 90-degree outputs will be referredto as an output or load. In other words, theywill be described as power dividers. This is for

convenience only, since the couplers are equal-ly valid as 90-degree power combiners, wherethe flow of power is in the opposite direction.

Delay LinesTransmission lines with an electrical

length of 90 degrees at the operating frequen-cy can provide the desired phase shift in someapplications. R-C (or R-L) equivalent circuitscan be used, as well [1] but they will haveadditional loss due to the resistive elements.Figure 1 shows these simple configurations.

These methods of obtaining the desiredphase relationship have two significant disad-

This tutorial reviews themost familiar options for

power division and com-bining with a 90-degree

phase difference

Figure 1 · Simple 90-degree power dividerscan be made with (a) a delay line, (b) R-Cequivalents.

Z0 l = 90º (λ/4)Z0

2

Z0 /_0º

Z0

R = |XC| = |Z0|

Z0 /_–45º

Z0 /_+45º

Z0 /_90º

(a)

(b)

From September 2007 High Frequency ElectronicsCopyright © 2007 Summit Technical Media, LLC

High Frequency Design

90-DEGREE COUPLERS

vantages. First, they require thatboth loads be essentially identical,and remain so over the frequency ofoperation. Second, there is no isola-tion between the ports. One of the fewpractical applications where thesewell-controlled characteristics existis a quadrature power divider at theoutput of a fixed-frequency localoscillator, with the two outputs fed tobuffer amplifiers with constant inputimpedances.

Two-Branch Quadrature HybridThe most common transmission

line structure for these applicationsis the two-branch hybrid [2] shown inFigure 2. In a 50-ohm system, thetransverse (vertically drawn) trans-mission lines are 50 ohms and thelongitudinal (horizontal) lines are35.4 ohms. All ports are 50 ohms, sothe load is also 50 ohms. At thedesign frequency, when all ports arematched, power is delivered to ports2 and 3 with a 90 degree phase shiftbetween the ports. No power is deliv-ered to the load.

Amplitude and phase accuracydeteriorate away from the design fre-quency, and the imbalance causespower to be delivered to the load. Theusable bandwidth depends on thedegree of precision required for the

user’s application. In many applica-tions, this type of coupler is consid-ered adequate for ±20 percent ormore frequency deviation. Cascadedsections can be used to obtain widerbandwidths up to an octave or more.

By varying the characteristicimpedances of the line sections, thiscoupler can be used to transformimpedance, maintaining the desired90-degree phase difference. This isuseful, for example, when driving orcombining outputs of devices in a bal-anced amplifier.

Figure 3 shows a reduced size ver-sion of the branch line coupler. Theline sections are replaced with equiv-alent combinations of shortened linesand shunt capacitors. Although theoccupied area is just 20 percent of thefull-size coupler, bandwidth is onlyslightly reduced. The transmissionline lengths shown are just one possi-ble solution, chosen for line sectionswith the same impedance, equal toZ0/√2. The capacitor values are thesums of the capacitances required forequivalence of each branch line

Branch line couplers may be con-structed using any transmission linetype—microstrip, stripline or coaxialcable. The method is chosen to suitthe frequency of operation and thepreferences of the user.

Coupled-Line DividersThe coupled line divider of Figure

4 is another common means ofobtaining quadrature outputs. Asshown in the figure, the topology maybe parallel lines or may include acrossover to place both outputs on thesame side of the coupler, which willbe more convenient for most applica-tions.

With λ/4 line sections, the outputsof the coupled ports 3 and 4 are as fol-lows [2, 3]:

S13 = –j√1 – K2

S14 = K

where K is the coupling coefficient.Equal voltage division is obtainedwhen K = 1/√2. With the requirementof strong coupling, these couplersmay be implemented as cascades oftwo couplers with 3 dB coupling coef-ficient, which are less critical in theirfabrication.

Another means of obtaining thedesired K is the Lange coupler, whichreplaces the individual lines of thecrossover version with a multipleinterdigital structure. The Lange cou-pler is popular because it reliablyprovides the proper coupling, butadditional crossover connections

Figure 2 · The two-branch quadrature hybrid. Thetransmission lines can any type: coaxial, microstrip(shown here) or stripline. Ports are all Z0.

Figure 3 · A reduced-size coupler, using short line sec-tions and shunt capacitors that are equivalent to theλλ/4 lines of the branch line hybrid.

64 High Frequency Electronics

Z0 / √2

Z0Z04 Branch Lines

l = 90º (λ/4)

Z0 / √2

2

1

4 3

2

34

1

INPUT

ISOLATED

OUTPUT

OUTPUT

Z0 = 50Ω

R0

70.7Ω λ/12

70.7Ω λ/1270.7Ω

λ/8

70.7Ω λ/8

66 High Frequency Electronics

High Frequency Design

90-DEGREE COUPLERS

result in a more complex and costlymanufacturing process.

The coupled-line divider haslumped-element equivalents, as well.Figure 5 shows two such implemen-tations. Fig. 5(a) replaces the trans-mission lines with a lowpass L-C net-work. These “lines” are uncoupled, sothe coupling is obtained using twotransformers. The transformers canalso provide an impedance transfor-mation for the selection of practicalcomponent values in the lowpass linesections. The author of Ref. [3] deter-mined that a three-section lumped-element lowpass network provided abandwidth equal to λ/4 coupled lines.

A simpler lumped element equiv-alent to the coupled-line divider isshown in Figure 5(b). Here, the cou-pling is provided in the inductors,

which are wound in interlaced (bifi-lar) manner, using a ferrite or ironpowder core to increase the magneticflux and achieve mutual couplingapproaching unity.

Port 1 or 2 may be the input, withthe other port terminated in the char-acteristic impedance. Ports 3 and 4are the quadrature outputs. Thevalue of L is selected for 50 ohmsreactance at the center frequency,while the capacitors have 100 ohmsreactance. This network may also beshown with each capacitor identifiedas “C/2” where the value of C has thesame 50 ohms reactance magnitudeas the inductor [4].

This simple circuit has a practicalbandwidth up to 50 percent of thecenter frequency, depending on thenecessary accuracy. A cascade of two

sections can provide an octave band-width. When cascading sections, iso-lating transmission line sections arerequired between the networks,which can also be implemented aslumped-element equivalents.

SummaryThese classic 90-degree, or

quadrature, couplers are key ele-ments in many RF and microwavesystems. For additional information,readers should note that the litera-ture includes a large number of refer-ences on this subject in the literature.With the exception of [3], the oneslisted here are recent works thathave concise summaries that are use-ful as introductory material. Thesereferences, in turn, include additionalreferences. Reference [4] includesselected reprints of seminal works onthis and other topics.

References1. W. Hayward, R. Campbell, R.

Larkin, Experimental Methods in RFDesign, American Radio RelayLeague, 2006, Chapter 9.

2. A. Grebennikov, RF andMicrowave Power Amplifier Design,McGraw-Hill, 2005, Chapter 5.

3. R. De Lillo, “Lumped-ElementHybrids for Wide-Band Antenna FeedNetworks,” Topics in Engineering,AIL Systems, Inc., Vol. IV, 1993.

4. J. Walker, D. Myer, F. Raab, C.Trask, eds., Classic Works in RFEngineering, Artech House, 2006,Chapter 6.

Figure 5 · These L-C couplers are derived from the coupled line divider: (a) uses transformer-coupled lowpass L-C sections, while (b) uses tightly-coupled inductances (M ≈≈ 1) to provide the coupling.

(a) (b)

Figure 4 · The basic coupled line structure (a) and a crossover configura-tion (b) that locates both coupled ports on the same side [2].