DIRECTIONAL COUPLERS

Transcription

1 DIRECTIONAL COUPLERS Ing. INICTEL Abstract This paper analyzes two types of Directional Couplers. First, magnetic coupling between a transmission line and a secondary circuit is studied. It is then shown that frequency independent samples of voltage and current on the transmission line yield a feasible way of obtaining separate readings of the forward and reflected waves. The second type of coupler takes advantage of the electrostatic and magnetic coupling existing between two parallel conductors. A simplified model of the coupler permits a straightforward analysis of the circuit. Expressions for the forward and reflected voltages are then readily obtained. In both cases, a peak detector circuit gives DC readings of the voltages. 1

2 A directional coupler D.C.) is a device that detects and separates the incident and reflected waves present in a transmission line, for instance, the one that links the radio transmitter with the antenna system. One type of D.C. that makes use of voltage and current coupling is shown in Fig. 1, where it is suggested that the device be placed somewhere along the transmission line, between the signal generator radio transmitter, for example) and the load Z L antenna). Usually, it is more comfortable to make the connection at the transmitter output. Consider an unbalanced line of length l, along with the circuit of Fig.1. If we call E x the transmission line voltage in the connection point to the secondary circuit and I x the current in the same point, we have: where: E f E b υ x ω E x = E f e j ωx/υ + E b e +j ωx/υ I x = E f e j ωx/υ E b e +j ωx/υ 1) = incident component of voltage = reflected component of voltage = velocity of propagation in the transmission line = characteristic impedance of the transmission line = position along the transmission line = angular frequency of the generator Figure 1. Unbalanced line and secondary circuit We have for the secondary mesh, with = I x : Therefore: If we make j ω = R + j ω ) I ) I = then the expression 3) becomes: j ω R + j ω 3) ω R 4) I = 5) Notice that for this condition and I are in phase and the frequency dependent term vanishes. Voltages in A and B will then be: E A = I R = R E B = I R = R Now, a frequency independent voltage sample may be obtained with the help of a capacitive divider, as is shown in Fig.. Then: 6) E C = E x + 7) INICTEL - Perú

3 or E C E x 8) if E c = E x + Figure. Capacitive divider The circuit for our coupler would become the one in Fig. 3. The following holds: E AC = E A E C = R E x 9) Substituting for E x and the expressions labeled as 1), we have: Ef E AC = R e j ωx/υ E ) b +j ωx/υ e E f e j ωx/υ + E b e +j ωx/υ) 10) If the following holds: ) 1 = R 11) the terms containing E f cancel each other and Also: E AC = E b e +j ωx/υ 1) E BD = E B E D = R E x 13) Substituting for E x and the expressions labeled as 1) and taking into account 11): E BD = E f e j ωx/υ 14) We thus have a directional coupler with readings of the incident and reflected waves. Capacitor can be made adjustable for calibration purposes and to assure good directivity. If required, DC voltages can be obtained to drive a galvanometer, rectifying and filtering voltages E AC for the reflected wave and E BD for the incident component. Figure 3. Basic coupler circuit topology One possible implementation of this directional coupler is shown in Fig. 4 on following page. INICTEL - Perú 3

4 D 1 D 4 : Germanium diodes 1N60, 1N34,... A practical implementation of Fig. 3 Figure 4. In Fig. 5 is shown a second type of D.C. that utilizes two parallel conductors with magnetic and electrostatic coupling. The main conductor is an extension of the transmission line that links the instrument with the generator at one end and with the load antenna) at the other. The second conductor coupled to the previous one is end terminated with a resistive load and a detector circuit, respectively. In these circuits readings from the incident or reflected waves can be selected by the switch. Figure 5. A C-M type directional coupler A relatively simple analysis of the coupler can be made utilizing the equivalent circuit of Fig. 6. Here, C represents the distributed capacitance between conductors; M is the mutual inductance of the system; R 1 and R are the end terminations of the secondary conductor and L is the self-inductance of this conductor. The transmission line current at the point where the device connects is I complex quantity) and E is the voltage on the line at that same point. The next calculations assume that the following inequality holds for R 1 and also for R ): ω L R 1 1 ω C 15) INICTEL - Perú 4

5 M 1 = M/ M = L/4 Figure 6. The directional coupler s equivalent circuit In Fig. 6: e 0 = j ω M 1 I j ω M 1 I + j ω L 4 j ω M I + j ω M j ω L 4 I + R 1 16) Substituting for M1 and M: e 0 = j ω M I + j ω L 4 + j ω L 4 j ω L 4 I j ω L 4 I + R 1 17) According to inequality 15), we can write: e 0 = j ω M I + j ω j ω I + R 1 18) e 0 j ω M I + R 1 j ω I 19) On the other hand: Also: e 1 = j ω M 1 I + j ω L 4 j ω M I + R 1 0) e 1 = +j ω M 1 I + j ω L 4 I j ω M + I R 1) Equating 0) with 1): R 1 + j ω L 4 ) j ω M 1 I j ω M I = R + j ω L ) I + j ω M 1 I j ω M ) 4 R 1 + j ω L ) 4 + j ω M = j ω M 1 I + R + j ω L ) 4 + j ω M I 3) or R 1 + j ω L ) = j ω M I + R + j ω L ) I 4) For the sake of inequality 15): R 1 j ω M I + I R 5) INICTEL - Perú 5

6 Also: with 0): or + I = + I = + I = E e 1 ) j ω 6) [ E R 1 + j ω L ) + j ω M 4 I + j ω L ] 4 I j ω 7) E + j ω M ) I j ω C R 1 + j ω L ) j ω C + j ω L ) 4 4 I j ω 8) From inequality 15) we get: Expression 6) becomes then: ω LC ω R 1 C 1 9) + I E + j ω M I ) j ω C 30) Solving for from the last expression: = E + j ω M ) I j ω C I 31) Substituting in 5): From 33) and according to 15): [E + j ω M I ) j ω C I ] R 1 = j ω M I + I R 3) j ω CR 1 E j ω M j ω CR ) 1 = I R 1 + R ) 33) I j ω CR 1 E j ω M I R 1 + R 34) On the other hand: 34) in 35): If: e 0 = e 0 = I R 35) R R + R 1 j ω M I + j ω CR 1 E) 36) R 1 = R = R and M = CR 1 37) From the equations for a transmission line e 0 = 1 j ω CR E I) 38) E = E f e j βx + E b e +j βx I = I f e j βx I b e +j βx 39) INICTEL - Perú 6

7 With β = ω/υ, and letting x = 0 generator side) E = E f + E b I = I f I b = E f E b 40) Then: Consequently: E I = E b 41) e 0 = j ω CR E b 4) From 5), 37) and 4): R = j ω CR I + 1 j ω CR E I) 43) = 1 j ω CR I + 1 j ω CR E 44) = 1 j ω CR E + I) 45) and according to 40): R = 1 j ω CR E f) 46) = j ω CR E f 47) Expressions 4) and 47) show us that we have separated the transmission line s incident and reflected waves. Conclusions Employing adequate circuit models two directional couplers have been studied. It has been shown that it is possible to obtain separate readings of the voltages for the incident and reflected components. This study helps the understanding of the principles of operation of actual devices in use at frequencies in the HF to UHF range. References 1 KUECKEN, JOHN A., Antennas and Transmission Lines, chapter 3, Howard W. Sams & Co., Inc., 1969 VARGAS PATRON, R., Lab Notes INICTEL - Perú 7