# POWER DIVIDERS AND DIRECTIONAL COUPLERS

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1 POWER DIVIDERS AND DIRECTIONAL COUPLERS A directional coupler is a passive device which couples part of the transmission power by a known amount out through another port, often by using two transmission lines set close enough together such that energy passing through one is coupled to the other. As shown in Figure, the device has four ports: input, transmitted, coupled, and isolated. The term "main line" refers to the section between ports and. On some directional couplers, the main line is P 3 Input Port Coupled Port The coupling factor is defined as: Coupling factor (db) ' &0 log P 3 where is the input power at port and P 3 is the output power from the coupled port (see Figure ). 3 8/4 Figure. Directional Coupler Transmitted Port P 4 Isolated Port designed for high power operation (large connectors), while the coupled port may use a small SMA connector. Often the isolated port is terminated with an internal or external matched load (typically 50 ohms). It should be pointed out that since the directional coupler is a linear device, the notations on Figure are arbitrary. Any port can be the input, (as in Figure 3) which will result in the directly connected port being the transmitted port, adjacent port being the coupled port, and the diagonal port being the isolated port. Physical considerations such as internal load on the isolated port will limit port operation. The coupled output from the directional coupler can be used to obtain the information (i.e., frequency and power level) on the signal without interrupting the main power flow in the system (except for a power reduction - see Figure ). When the power coupled out to port three is half the input power (i.e. 3 db below the input power level), the power on the main transmission line is also 3 db below the input power and equals the coupled power. Such a coupler is referred to as a 90 degree hybrid, hybrid, or 3 db coupler. The frequency range for coaxial couplers specified by manufacturers is that of the coupling arm. The main arm response is much wider (i.e. if the spec is -4 GHz, the main arm could operate at or 5 GHz - see Figure 3). However it should be recognized that the coupled response is periodic with frequency. For example, a 8/4 coupled line coupler will have responses at n8/4 where n is an odd integer. Common properties desired for all directional couplers are wide operational bandwidth, high directivity, and a good impedance match at all ports when the other ports are terminated in matched loads. These performance characteristics of hybrid or non-hybrid directional couplers are self-explanatory. Some other general characteristics will be discussed below. COUPLG FACTOR The coupling factor represents the primary property of a directional coupler. Coupling is not constant, but varies with frequency. While different designs may reduce the variance, a perfectly flat coupler theoretically cannot be built. Directional couplers are specified in terms of the coupling accuracy at the frequency band center. For example, a 0 db coupling ± 0.5 db means that the directional coupler can have 9.5 db to 0.5 db coupling at the frequency band center. The accuracy is due to dimensional tolerances that can be held for the spacing of the two coupled lines. Another coupling specification is frequency sensitivity. A larger frequency sensitivity will allow a larger frequency band of operation. Multiple quarter-wavelength coupling sections are used to obtain wide frequency bandwidth directional couplers. Typically this type of directional coupler is designed to a frequency bandwidth ratio and a maximum coupling ripple within the frequency band. For example a typical : frequency bandwidth coupler design that produces a 0 db coupling with a ±0. db ripple would, using the previous accuracy specification, be said to have 9.6 ± 0. db to 0.4 ± 0. db of coupling across the frequency range. P4 6-4.

2 LOSS 30 In an ideal directional coupler, the main line loss port to port ( - P ) due to power coupled to the coupled output port is: Insertion loss (db) ' 0 log & P 3 The actual directional coupler loss will be a combination of coupling loss, dielectric loss, conductor loss, and VSWR loss. Depending on the frequency range, coupling loss becomes less significant above 5 db coupling where the other Coupling db Insertion Loss - db Main Arm (Insertion) Loss - db Figure. Coupling Insertion Loss losses constitute the majority of the total loss. A graph of the theoretical insertion loss (db) vs coupling (db) for a dissipationless coupler is shown in Figure. ISOLATION Isolation of a directional coupler can be defined as the difference in signal levels in db between the input port and the isolated port when the two output ports are terminated by matched loads, or: Isolation (db) ' &0 log P 4 Isolation can also be defined between the two output ports. In this case, one of the output ports is used as the input; the other is considered the output port while the other two ports (input and isolated) are terminated by matched loads. Consequently: Isolation (db) ' &0 log P 3 P The isolation between the input and the isolated ports may be different from the isolation between the two output ports. For example, the isolation between ports and 4 can be 30 db while the isolation between ports and 3 can be a different value such as 5 db. If both isolation measurements are not available, they can assumed to be equal. If neither are available, an estimate of the isolation is the coupling plus return loss (see VSWR section). The isolation should be as high as possible. In actual couplers the isolated port is never completely isolated. Some RF power will always be present. Waveguide directional couplers will have the best isolation. If isolation is high, directional couplers are excellent for combining signals to feed a single line to a receiver for two-tone receiver tests. In Figure 3, one signal enters port P and one enters port P, while both exit port 3 P. The signal from port P to port P will experience 0 3 db of loss, and the signal from port P to port P will have 0.5 db loss. The internal load on the isolated port will dissipate the signal losses from port P and port P. If the 3 isolators in Figure 3 are neglected, the isolation measurement (port P to port P ) determines the amount of 3 power from the signal generator F that will be injected into the signal generator F. As the injection level increases, it may cause modulation of signal generator F, or even F Isolators (Section 6.7) P3 F + F 0 db P P F Figure 3. Two-Tone Receiver Tests 6-4.

3 injection phase locking. Because of the symmetry of the directional coupler, the reverse injection will happen with the same possible modulation problems of signal generator F by F. Therefore the isolators are used in Figure 3 to effectively increase the isolation (or directivity) of the directional coupler. Consequently the injection loss will be the isolation of the directional coupler plus the reverse isolation of the isolator. DIRECTIVITY Directivity is directly related to Isolation. It is defined as: Directivity (db) ' &0 log P 4 ' &0 log P 4 % 0 log P 3 P 3 where: P 3 is the output power from the coupled port and P 4 is the power output from the isolated port. The directivity should be as high as possible. Waveguide directional couplers will have the best directivity. Directivity is not directly measurable, and is calculated from the isolation and coupling measurements as: Directivity (db) = Isolation (db) - Coupling (db) HYBRIDS The hybrid coupler, or 3 db directional coupler, in which the two outputs are of equal amplitude takes many forms. Not too long ago the quadrature (90 degree) 3 db coupler with outputs 90 degrees out of phase was what came to mind when a hybrid coupler was mentioned. Now any matched 4-port with isolated arms and equal power division is called a hybrid or hybrid coupler. Today the characterizing feature is the phase difference of the outputs. If 90 degrees, it is a 90 degree hybrid. If 80 degrees, it is a 80 degree hybrid. Even the Wilkinson power divider which has 0 degrees phase difference is actually a hybrid although the fourth arm is normally imbedded. Applications of the hybrid include monopulse comparators, mixers, power combiners, dividers, modulators, and phased array radar antenna systems. AMPLITUDE BALANCE This terminology defines the power difference in db between the two output ports of a 3 db hybrid. In an ideal hybrid circuit, the difference should be 0 db. However, in a practical device the amplitude balance is frequency dependent and departs from the ideal 0 db difference. PHASE BALANCE The phase difference between the two output ports of a hybrid coupler should be 0, 90, or 80 degrees depending on the type used. However, like amplitude balance, the phase difference is sensitive to the input frequency and typically will vary a few degrees. The phase properties of a 90 degree hybrid coupler can be used to great advantage in microwave circuits. For example in a balanced microwave amplifier the two input stages are fed through a hybrid coupler. The FET device normally has a very poor match and reflects much of the incident energy. However, since the devices are essentially identical the reflection coefficients from each device are equal. The reflected voltage from the FETs are in phase at the isolated port and are 80E different at the input port. Therefore, all of the reflected power from the FETs goes to the load at the isolated port and no power goes to the input port. This results in a good input match (low VSWR)

4 If phase matched lines are used for an antenna input to a 80E hybrid coupler as shown in Figure 4, a null will occur directly between the antennas. If you want to receive a signal in that position, you would have to either change the hybrid type or line length. If you want to reject a signal from a given direction, or create the difference pattern for a monopulse radar, this is a good approach. 0E 80E Sum Difference Figure 4. Balanced Antenna Input OTHER POWER DIVIDERS Both in-phase (Wilkinson) and quadrature (90E) hybrid couplers may be used for coherent power divider applications. The Wilkinson's power divider has low VSWR at all ports and high isolation between output ports. The input and output impedances at each port is designed to be equal to the characteristic impedance of the microwave system. A typical power divider is shown in Figure 5. Ideally, input power would be divided equally between the output ports. Dividers are made up of multiple couplers, and like couplers, may be reversed and used as multiplexers. The drawback is that for a four channel multiplexer, the output consists of only /4 the power from each, and is relatively inefficient. Lossless multiplexing can only be done with filter networks. Coherent power division was first accomplished by means of simple Tee junctions. At microwave frequencies, waveguide tees have two possible forms - the H-Plane or the E-Plane. These two junctions split Figure 5. Power Divider power equally, but because of the different field configurations at the junction, the electric fields at the output arms are in-phase for the H-Plane tee and are anti-phase for the E-Plane tee. The combination of these two tees to form a hybrid tee allowed the realization of a four-port component which could perform the vector sum (E) and difference ()) of two coherent microwave signals. This device is known as the magic tee

5 POWER COMBERS Since hybrid circuits are bi-directional, they can be used to split up a signal to feed multiple low power amplifiers, then recombine to feed a single antenna with high power as shown in Figure 6. This approach allows the use of numerous less expensive and lower power amplifiers in the circuitry instead of a single high power TWT. Yet another approach is to have each solid state amplifier (SSA) feed an antenna and let the power be combined in space or be used to feed a lens which is attached to an antenna. (See Section 3-4) TYPICAL HYBRID SIGNAL ADDITION 0E- 6dB +40 db SOLID STATE AMPLIFIERS (SSAs) (Voltage Gain of 00) 0E- 9dB 0E+3dB 90E Output 90E, 70E s Cancel 90E+3dB 90E+34dB 80E Output 80E, 80E s Add SIGNAL PUT 0E- 3dB 90E- 3dB 90E- 6dB 90E- 6dB 80E- 9dB 90E+3dB 80E+3dB 90E+3dB 80E+34dB 80E+37dB 70E+40dB ANTENNA OUTPUT 80E- 9dB 80E+3dB 80E+34dB 80E- 6dB 80E- 9dB 80E+3dB 70E+37dB 70E- 9dB 70E+3dB 70E+34dB NOTE: All isolated ports of the hybrids have matched terminations. They have signals which are out of phase and cancel Figure 6. Combiner Network Sample Problem: If two watt peak unmodulated RF carrier signals at 0 GHz are received, how much peak power could one measure? A. 0 watts B. 0.5 watts C. watt D. watts E. All of these The phase error could be due to a hybrid being used to combine the same signal received from two aircraft antennas. A B A + B The answer is all of these as shown in Figure 7. If 80E out of phase, signals cancel and there is zero watts received If in phase, the signals add, so there would be watts received Any other phase relationship will produce a signal somewhere between 0 and watts. This shows signals that are 90E out of phase. Figure 7. Sinewaves Combined Using Various Phase Relationships 6-4.5

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