Coupled Helices 



By J. S. COOK, R. KOMPFNER and C. F. QUATE 



(Received September 21, 1955) 



An analysis of coupled helices is presented, using the transmission line 

 approach and also the field approach, with the objective of providing the 

 tube designer and the microwave circuit engineer with a basis for approxi- 

 mate calcidations. Devices based on the presence of only one mode of propa- 

 gation are briefly described; and methods for establishing such a mode are 

 given. Devices depending on the simultaneous presence of both modes, that 

 is, depending on the beat wave phenomenon, are described; some experi- 

 mental results are cited in support of the view that a novel and useful class of 

 coupling elements has been discovered. 



CONTENTS 



1. Introduction 129 



2. Theory of Coupled Helices 132 



2.1 Introduction 132 



2.2 Transmission Line Equations 133 



2.3 Solution for Synchronous Helices 135 



2.4 Non-Synchronous Helix Solutions 137 



2.5 A Look at the Fields 139 



2.6 A Simple Estimate of b and x 141 



2.7 Strength of Coupling versus Frequency 142 



2.8 Field Solutions 144 



. 2.9 Bifilar Helix 146 



2.10 Effect of Dielectric Material between Helices 148 



2.11 The Conditions for Maximum Power Transfer 151 



2.12 Mode Impedance 152 



3. Applications of Coupled Helices 154 



3.1 Excitation of Pure Modes 156 



3.1.1 Direct Excitation 156 



3.1.2 Tapered Coupler 157 



3.1.3 Stepped Coupler 158 



3.2 Low Noise Transverse Field Amplifier 159 



3.3 Dispersive Traveling Wave Tube 159 



3.4 Devices Using Both Modes 161 



3.4.1 Coupled Helix Transducer 161 



3.4.2 Coupled-Helix Attenuator 165 



4. Conclusion 167 



Appendix 



I Solution of Field Equations 168 



II Finding r I73 



III Complete Power Transfer 175 



127 



