Experiment 9: Microwave Directional Couplers and Hybrids 1. Directional Couplers and Hybrids Directional couplers and hybrids are used in a variety of important applications at microwave frequencies. The way a directional coupler functions can be depicted as shown in Fig. 1. A signal is fed into one of the four ports. Ideally, part of the signal power emerges from the transmitted port. Ideally, the rest of the input power emerges from the coupled port. Again, ideally, no signal emerges from the isolated port. The direction from the input port to the transmitted port is considered to be the forward direction of signal propagation. If the input signal minus the transmitted signal emerges as shown in Fig.1a., then the coupler is denoted as a forward coupler. If the input signal minus the transmitted signal emerges as shown in Fig. 1b., then the coupler is denoted as a backward coupler. Directional couplers can be designed to send different portions of the input power to the coupled port, depending on the application for which they are designed. If the directional coupler is designed to lightly sample the input power, the coupled signal may be either 10 db or 20 db relative to the input signal strength. Such directional couplers are often used to sample (lightly couple) the signal strength of the input signal for applications like the network analyzer in the previous laboratory exercise (see Fig. 2. in the previous lab description). Input port Transmitted port Isolated port Coupled port Fig. 1a. Forward Directional Coupler Input port Transmitted port Coupled port Isolated port Fig. 1b. Backward Directional Coupler
Directional couplers also are available in 6dB and 3dB coupled signal strength. A 3dB directional coupler ideally sends one half the input power to the transmitted port and the other half of the power to the coupled port. Components that split half the power between the transmitted port and the coupled port are called hybrids. Depending on the intended application, these components may be designed so the transmitted and coupled signals are 90 o or 180 o different in phase. A 3dB directional coupler with a 90 o phase difference between the transmitted and the coupled signals is called a quadrature hybrid. The symbol used to represent a hybrid is shown in Fig. 2. Coupled signal Isolated signal (no signal) (1/2 input signal power) Input signal Transmitted signal (1/2 input signal power) Fig. 2. Symbol for hybrid Two of the more important applications where quadrature (90 o ) hybrids are employed are in power combining applications for power amplifiers and in mutiplexer or demultiplexer design. Fig. 3. depicts the use in combining the output from two lower power amplifiers to achieve greater output power from the combination than is possible from either of the individual power amplifiers. 90 o PA 0 o PA Fig. 3. Hybrids used to combine two power amplifiers Fig.. depicts a similar use of quadrature hybrids for passing a particular frequency band from a broader received band of frequencies. The configuration in Fig.. is a channel dropping configuration. Fig. 5. shows a demultiplexer that would separate signals received in the frequency range from f1 to f2 into two channels, one from f1 to f1 and one from. Hybrids can also be used to combine channels, therby creating a multiplexer.
90 o BPF BPF 0 o Fig.. Channel dropping configuration of the band pass filter pass band f1 to f1 f1 to f2 0 o BPF 90 o BPF f1 to f1 f1 to f1 0 o BPF 90 o BPF Fig. 5. Two channel demultiplexer
In this laboratory class, you will create and experimentally characterize two couplers. One will be a 20 db parallel line directional coupler. The other will be a 3dB directional coupler or hybrid. As you will see, each of these couplers ideally has a 90 o or quadrature relationship between the phase of the signals emerging from the transmitted and coupled ports, respectively. It can be shown [1] that for a coupled line region that is symmetric with respect to both the horizontal and vertical center lines through the coupled region, the signals emerging from the transmitted and coupled ports differ from each other in phase by 90 o. This result is true independent of the coupling strength. The parallel line directional coupler configuration is shown in Fig. 6. Input Port 1 Transmitted Port Coupled Region Coupled Port 2 3 Isolated Port Fig. 6. Parallel Line Directional Coupler The branch line quadrature hybrid schematic is shown in Fig. 7. Both of these coupler structures have symmetry along the length of the coupler on the substrate. As a result, both couplers can be represented symbolically as in Fig. 8. This symmetry and the linearity of the couplers enables the port couplers to be treated using by superimposing the responses to even and odd mode excitations as shown in Figs. 9a and 9b. The use of even and odd mode excitations, enables each port coupler to be decomposed into two, 2 port networks; each one corresponding to its appropriate excitation. The responses at each of the ports in Figs. 6 and 7 can be determined by appropriately combining the responses at each of the four ports for each coupler type. The results of this analysis for each coupler type are presented in the next sections.
1 2 3 Fig. 7. Branch Line Quadrature Hybrid Schematic 1 Vs 2 3 Fig. 8. View of Coupler Symmetry along Its Length 1 Vs/2 2 Vs/2 3 Fig. 9a. Even Mode Excitation Model 1 Vs/2 2 Vs/2 3 Fig. 9b. Odd Mode Excitation Model
Parallel Line Directional Coupler The signal emerging from the coupled port (port 2) in the coupler shown in Fig. 6. is given by the following expression [1] (1) The signal emerging from the transmitted port (port ) for that coupler is [1] (2) In these expressions where f is the operating frequency, L is the physical length of the coupled line region, and v is the phase velocity on the transmission line. Also, e and o are the characteristic impedances for the even and odd mode in (for this case) coupled microstrip. For a coupled microstrip coupled line structure, the values needed for e and o are determined by designing the coupler for a particular value of coupling at the center of the desired operating frequency band (k) using eqs. () and (5). (3) () (5) Here, is the characteristic impedance of the lines feeding the coupled line region in Fig. 6. The values for the actual line widths and lengths of the microstrip lines needed to obtain the desired behavior can be obtained from references [2 ]. For this analysis, it is assumed that the signal level emerging from the isolated port (port 3) and the reflected signal at the input port are both zero.
Branch Line Quadrature Hybrid Even and odd mode analysis of the branch line coupler leads to the following result for the S parameter matrix value at the mid band frequency value (6) More generally, the signals emerging at the various ports as a function of frequency can be determined by superimposing the responses for the even and odd mode networks at each port. The signals emerging at each port for the even and odd mode networks can be obtained using the following relationships for the ABCD matrices. (7) In (7), (8) L is the physical length of the horizontal and vertical line length denoted as lengths is Fig. 7. f is the operating frequency. v is the phase velocity for the microstrip line that can be determined from reference [2]. Also, YA is the admittance of the horizontal line shown with length. The parameter Ye,o is given by in Fig. 7. For the design in that figure (9) Using (7), (8), and (9) the A parameter can be found for both the even and odd mode signals. The ratio (1/A) gives the ratio of the output (at port ) to the input signal at port 1. By superimposing these results for the even and odd modes, the total signal emerging at port could be determined. Once this is known, the signal
emerging from port 3 can be found, by assuming that there is no reflection at the input and no signal emerging from the isolated port (perfect match and isolation assumptions). Laboratory Procedure 1. Obtain the pre cut copper pattern for the 20 db parallel line directional coupler. You will need to use the copper strip of the proper width to lay out the coupled lines with the spacing between them. Use the adhesive on these strips and solder these coupler contacts to the appropriate microstrip pigtails on the PCB. Take a picture of the coupler model that corresponds to the measurements you make on it. 2. Make sure to use the most appropriate calibration possible for the coupler measurements. In order to measure the input to transmitted, coupled, and isolated signals, you will have to perform three two port measurements while the unmeasured ports are terminated in 50 ohm loads. Take sufficient data over the 2 to GHz frequency range to capture all the important features of these signals. You will plot this data in db versus frequency. The directivity of a directional coupler or hybrid is defined by the following. (10) 3. Obtain the pre cut copper patterns needed to implement the branch line quadrature hybrid. Attach this to the circuit by trimming and pressing into place the copper strips. Then, solder these to the appropriate microstrip pigtails on the PCB. Take a picture of the circuit that corresponds to the hybrid you actually measure.. Make sure to use the most appropriate calibration possible for the hybrid measurements. Make measurements of signals emerging from the transmitted, coupled, isolated, and input ports versus frequency. You will ultimately need to plot these in db versus frequency for the 2 to GHz range. You will also have to plot all of these on the same plot versus frequency. Laboratory Report a. For the 20 db parallel line coupler, plot the transmitted, coupled, isolated, and reflected signals in db and the directivity versus frequency; first on separate plots for each quantity and finally all on the same graph. Show a photograph of the coupler you measured. Compare and discuss each of these quantities to the corresponding measurements you made on the commercial directional coupler you measured in the laboratory exercises when you first learned to use the network analyzer. Discuss how the value of coupling that is set at the middle frequency in the band of interest (here, 2 to GHz) determines the departure from the nominal coupling value over that frequency band.
b. For the quadrature hybrid, do similar plots and discussion (including directivity). Then compare results to those obtained for a commercially available quadrature hybrid. Discuss these results. References 1. L. Young ed., Advances in Microwaves, Section by R. Levy Directional Couplers, Academic Press, New York, NY, 1966, pp. 115 211. 2. R. Ludwig and P. Bretchko, RF Circuit Design, Theory and Applications, Prentice Hall, Upper Saddle River, NJ, 2000, pp. 6 69. 3. K. C. Gupta, R. Garg, and I. J. Bahl, Microstrip Line and Slotlines, Artech House, Dedham, MA, 1979.. B. C. Wadell, Transmission Line Design Handbook, Artech House, Boston, MA, 1991.