High Frequency Design From December 2007 High Frequency Electronics Copyright © 2007 Summit Technical Media, LLC COMBINERS & COUPLERS Power Combiners, Impedance Transformers and Directional Couplers By Andrei Grebennikov Infineon/DICE any RF applica- Transmission-Line Transformers This is the first of a multi- tions require and Combiners part article that provides a Mpower combiners The transmission-line transformers and textbook-style review of an or dividers, impedance combiners can provide very wide operating important group of RF transformers and direc- bandwidths and operate up to frequencies of 3 circuits used in applications tional couplers. In the GHz and higher [1, 2]. They are widely used in such as power amplifiers, case of combiners, it is matching networks for antennas and power antenna systems and critical, particularly at amplifiers in the HF and VHF bands, in mixer measurement systems higher frequencies, that circuits, and their low losses make them espe- the correct types are used cially useful in high power circuits [3, 4]. to achieve the desired power performance Typical structures for transmission-line trans- when combing individual active devices to formers consist of parallel wires, coaxial achieve higher power. cables or bifilar twisted wire pairs. In the lat- The methods for configuration of the com- ter case, the characteristic impedance can eas- biners or dividers differ, depending on the ily be determined by the wire diameter, the operating frequency, frequency bandwidth, insulation thickness, and, to some extent, the output power, and size requirements. Coaxial twisting pitch [5, 6]. For coaxial cable trans- cable combiners with ferrite cores are often formers with correctly chosen characteristic used to combine the output powers of power impedance, the theoretical high frequency amplifiers intended for wideband applica- bandwidth limit is reached when the cable tions. The device output impedance is usually length comes in order of a half wavelength, low at high power levels; so, to match this with the overall achievable bandwidth being impedance with a standard 50-ohm load, coax- about a decade. By introducing the low-loss ial-line transformers with specified high permeability ferrites alongside a good impedance transformation are used. For nar- quality semi-rigid coaxial or symmetrical strip row-band applications, the N-way Wilkinson cable, the low frequency limit can be signifi- combiners are widely used due to their simple cantly improved providing bandwidths of sev- practical realization. For microwaves, the size eral or more decades. of combiners should be very small and, there- The concept of a broadband impedance fore, the hybrid microstrip combiners (includ- transformer consisting of a pair of intercon- ing different types of the microwaves hybrids nected transmission lines was first disclosed and directional couplers) are commonly used and described by Guanella [7, 8]. Figure 1(a) to combine output powers of power amplifiers shows a Guanella transformer system with or oscillators. In this paper, a variety of differ- transmission line character achieved by an ent combiners, impedance transformers and arrangement comprising one pair of cylindri- directional couplers for application in RF and cal coils that are wound in the same sense and microwave transmitters is given with descrip- are spaced a certain distance apart by an tions of their schematics and operational prin- intervening dielectric. In this case, one cylin- ciples. drical coil is located inside the insulating 20 High Frequency Electronics High Frequency Design COMBINERS & COUPLERS Figure 1 · Schematic configura- tions of Guanella 1:1 and 4:1 trans- formers. cylinder and the other coil is located Figure 2 · Schematic configurations of a coaxial cable transformer. on the outside of this cylinder. For the currents flowing through both wind- ings in opposite directions, the corre- in the two times higher impedance currents—flowing in both transmis- sponding flux in the coil axis is negli- 2Z0 at the input and two times lower sion line inner and outer conductors gibly small. However, for the currents impedance Z0/2 at the output. By in phase, and in the same direction— flowing in the same direction through grounding terminal 4, such a 4:1 are suppressed, and the load may be both coils (common-mode), the latter impedance transformer provides balanced and floating above ground may be assumed to be connected in impedance matching of the balanced or balanced with a center tap ground- parallel, and a coil pair represents a source to the unbalanced load. In this ed load, thus operating as a balun [9, considerable inductance for such cur- case, when terminal 2 is grounded, it 10]. If the characteristic impedance of rents and acts like a choke coil. With performs as a 4:1 unun (unbalanced- the transmission line is equal to the terminal 4 being grounded, such a 1:1 to-unbalanced transformer). With a terminating impedances, the trans- transformer provides matching of the series-parallel connection of n coil mission is inherently broadband. If balanced source to unbalanced load pairs, each having the characteristic not, there will be a dip in the and is called a balun (balanced-to- impedance Z0, the input impedance is response at the frequency at which unbalanced transformer). In this equal to nZ0 and the output the transmission-line is a quarter- case, if terminal 2 is grounded, it rep- impedance is equal to Z0/n. Since wavelength long. resents simply a delay line. In a par- Guanella adds voltages that have A coaxial cable transformer with ticular case, when terminals 2 and 3 equal delays through the transmis- the physical configuration and equiv- are grounded, the transformer per- sion lines, such a technique results in alent circuit representation shown in forms as a phase inverter. A series- the so called equal-delay transmis- Figures 2(a) and 2(b), respectively, parallel connection of a plurality of sion-line transformers. consists of the coaxial line arranged these coil pairs can produce a match The simplest transmission-line is inside the ferrite core or wound between unequal source and load a quarter-wave transmission line around the ferrite core. Due to its resistances. whose characteristic impedance is practical configuration, the coaxial Figure 1(b) shows a 4:1 chosen to give the correct impedance cable transformer takes a position impedance (2:1 voltage) transmis- transformation. However, this trans- between the lumped and distributed sion-line transformer where the two former provides a narrow-band per- systems. Therefore, at lower frequen- pairs of cylindrical transmission line formance valid only around frequen- cies its equivalent circuit represents coils are connected in series at the cies for which the transmission line is a conventional polarity reversing input and in parallel at the output. odd multiples of a quarter wave- low-frequency transformer shown in For the characteristic impedance Z0 length. If a ferrite sleeve is added to Figure 2(c), while at higher frequency of each transmission line, this results the transmission line, common-mode it is a transmission line with the 22 High Frequency Electronics High Frequency Design COMBINERS & COUPLERS Figure 3 · Low frequency models of a 1:1 coaxial cable transformer. Figure 4 · Schematic configurations of the Ruthroff 1:4 impedance transformer. characteristic impedance Z0 shown in Figure 2(d). The advantage of such a transformer is that the parasitic interturn capacitance determines its characteristic ⎡ ⎛ 2l⎞ ⎤ impedance, whereas in the conventional wire-wound L = 2l ⎢ln⎜ ⎟ − 1⎥ nH (2) m ⎣ ⎝ ⎠ ⎦ transformer with discrete windings this parasitic capaci- r tance has a negative effect on the transformer frequency response performance. where l is the length of the coaxial cable in cm and r is the When RS = RL = Z0, the transmission line can be con- radius of the outer surface of the outer conductor in cm sidered a transformer with a 1:1 impedance transforma- [4]. tion. To avoid any resonant phenomena, especially for The use of high permeability core materials results in complex loads, which can contribute to the significant shorter transmission lines. If a toroid is used for the core, output power variations, as a general rule, the length l of the magnetizing inductance Lm is obtained by the transmission line is kept to no more than one-eighth λ A of wavelength min,or = πµ2 e Lm 4 n nH (3) Le λ l ≤ min (1) 8 where n is the number of turns, µ is the core permeabili- ty, Ae is the effective cross-sectional area of the core in λ 2 where min is the minimum wavelength in the transmis- cm , and Le is the average magnetic path length in cm sion line corresponding to the highest operating frequen- [11]. cy fmax. Considering the transformer equivalent circuit shown The low-frequency bandwidth limit of a coaxial cable in Fig. 2(a), the ratio between the power delivered to the 2 transformer is determined by the effect of the magnetiz- load PL and power available at the source Ps = Vs /8Rs ing inductance Lm of the outer surface of the outer con- when RS = RL can be obtained from ductor according to the equivalent low-frequency trans- 2 former model shown in Figure 3(a), where the transmis- P ()2ωL L = m (4) sion line is represented by the ideal 1:1 transformer [4]. P 2 + ()ω 2 S RLSm2 The resistance R0 represents the losses of the transmis- sion line. An approximation to the magnetizing induc- which gives the minimum operating frequency fmin for a tance can be made by considering the outer surface of the given magnetizing inductance Lm, taking into account the coaxial cable to be the same as that of a straight wire (or maximum decrease of the output power by 3 dB, as linear conductor), which, at higher frequencies where the skin effect causes the current to be concentrated on the R f ≥ S (5) min π outer surface, would have the self-inductance of 4 Lm 24 High Frequency Electronics High Frequency Design COMBINERS & COUPLERS Figure 5 · Schematic configura- tions of a 4:1 coaxial cable trans- former.