A Methodology to Design Broadband Negative Inductors with Tight Tolerance for Microwave Applications

Introduction. Non-Foster elements (NFEs) mimic behavior of hypothetical negative inductors or capacitors in a certain frequency band. NFEs are used to compensate reactance of conventional inductors and capacitors that allows designing broadband microwave devices. To realize NFEs, active circuits referred to as negative impedance converters (NICs) are employed to convert the load impedance into the negative input impedance. The conversion error, caused by non-optimal choice of NIC parameters and non-idealities of NIC components, limits the accuracy and operating bandwidth of NFEs. The necessity to account for many factors, which indirectly and oppositely impact the final result, and unavailability of a universal design methodology complicate the design of NFEs significantly. As a result, broadband NFE characteristics differ from the target ones remarkably that limits practical applications.

Aim. Elaboration of a design methodology to compensate the Linvill’s NIC conversion error and realize high-accuracy broadband negative inductors.

Materials and methods. Influence of NIC constituent parameters on the negative inductor frequency characteristics is considered. The performed analysis and the identified relationships allowed us to propose a step-by-step methodology to design negative inductors having tight tolerance over a broad frequency band. The use of a transmission line section instead of a lumped inductor in the NIC load when realizing negative inductors of high absolute values is shown to be advantageous as this allows providing better tolerance and wider bandwidth.

Results. In order to demonstrate possibilities enabled by the proposed methodology, simulation results are presented for the GHz-range negative inductors with a set of inductance and tolerance values.

Conclusion. The results obtained show that the proposed methodology makes it possible to compensate the conversion error without any numerical optimization and therefore to reduce the deviation of the negative inductance from the target value in the given frequency range or to broaden the bandwidth for a given tolerable deviation of the negative inductance.

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