Equivalent Circuit and Loss Invariant for Helicon Mode Semiconductor Devices

Abstract

A basic nonreciprocal two-port component in the HF range is considered consisting of two spatially orthogonal coils wound on an indium antimonide slab. A dc magnetic field is impressed perpendicular to the axes of the coils. Local helicon mode theory, assuming a single type of carrier, is used to derive the frequency-dependent network matrix of the device. From this matrix a broadband equivalent circuit is synthesized, which contains one gyrator. The resultant network structure is then analyzed to arrive at a loss invariant or figure of merit for the nonreciprocal device and the invariant is found to be frequency independent. This loss invariant is used to calculate the minimum possible insertion loss of an isolator formed by imbedding the helicon mode element in the most general lossless reciprocal circuit. The minimum loss is shown to be Minimum insertion loss = <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10 \log \left( 1 + \frac{1}{u^{2}} \right) dB</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</tex> is the tangent of the Hall angle in the InSb slab. Two-port experimental measurements were made (using a low-frequency embodiment of a microwave directional coupler) over the frequency band 5-15 MHz to verify the equivalent circuit and the value of the invariant. These data provided reasonable verification of the equivalent circuit, the invariant, and the minimum loss figure. A circuit for a minimum insertion loss isolator was constructed, and at fields of 2600 and 5600 gauss the measured minimum insertion loss at room temperature was found to be 2.8 and 1.5 dB, respectively. This data compares with the theoretically predicted figures of 3.1 and 1.0 dB. These results are all under infinite isolation conditions. A derivation is given to show the optimum benefits to be obtained by trading reduced isolation for improved insertion loss. Finally, the theory of invariance is employed to derive expressions for the minimum insertion loss of a helicon mode gyrator and three-port circulator.