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## NGD-based Hilbert filter

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A particular application of the negative group delay (NGD) for a particular function of independent frequency phase shifter (PS) is developed in the present chapter. The independent frequency PS is a quadrature and unity magnitude PS which is known as Hilbert filter. An original circuit theory on analog Hilbert filter dedicated to the RF/microwave application is established in this chapter. The Hilbert filter can be assumed as an independent frequency quadrature PS with magnitude equal to unity. The identification methodology of the simplest lumped element-based topologies is presented. The proposed elementary cells are based on the NGD active cell constituted by a field effect transistor in cascade with a shunt RLC-series network. This NGD circuit is cascaded with a positive group delay (PGD) passive network in order to synthesize an Hilbert filter around the targeted operating frequency. The analytical expressions enable to establish the Hilbert filter designability characteristic condition between the topological parameters. The synthesis relations of the identified cells are established. The characteristics and properties are developed. Application example with the identified topology of LC and NGD cells in cascade is presented. The microwave Hilbert filter concept feasibility is demonstrated. Three proofs of concept (POCs) circuit operating around 2.45 GHz were synthesized and designed. After S-parameter simulations, transmission phase 90 + 10 flatness's are generated within the relative frequency better than 50% and +1 dB gain flatness's within 20% bandwidth. The identified Hilbert filter cells functioning are validated with simulations of SPICE environment designed circuits. As expected, typically narrow band Hilbert filters were obtained. The developed analog Hilbert filter topology is potentially useful for the RF/microwave transceiver system architecture designs notably for image intermediate frequency rejection.

Chapter Contents:

• Abstract
• Keywords
• 6.1 Introduction
• 6.2 Identification methodology of the NGD function-based Hilbert filter
• 6.2.1 General description of Hilbert filter basic topology
• 6.2.2 Basic configurations of PDG and NGD cells
• 6.2.3 S-parameter analysis
• 6.2.4 Identified Hilbert filter topologies implemented with PGD-NGD configuration
• 6.2.4.1 Hilbert filter topology with Z = 0
• 6.2.4.2 Hilbert filter with Y = 0
• 6.2.4.3 Hilbert filter with Z = Rp
• 6.2.4.4 Hilbert filter with Y = 1/Rp
• 6.2.4.5 Hilbert filter with Z = jX
• 6.2.5 Identified Hilbert filter topologies implemented with NGD-PGD configuration
• 6.2.5.1 Hilbert filter topology with Z = 0
• 6.2.5.2 Hilbert filter with Y = 0
• 6.2.5.3 Hilbert filter with Z = Rp
• 6.2.5.4 Hilbert filter with Y = 1/Rp
• 6.2.5.5 Hilbert filter with Z = jX
• 6.3 Analysis of LC-NGD cell-based NGD Hilbert filter topology
• 6.3.1 S-parameter analysis
• 6.3.1.1 Analysis of the LC-NGD cell
• 6.3.1.2 Synthesis formulation
• 6.3.1.3 Properties and characteristics of LC-NGD cascaded cell
• 6.3.2 Application examples
• 6.3.2.1 POC description
• 6.3.2.2 Feasibility principle validation results
• 6.4 Analysis of NGD-LC cell-based Hilbert filter topology
• 6.4.1 S-parameter analysis
• 6.4.1.1 Analysis of NGD-LC cell cascaded
• 6.4.1.2 Synthesis formulation
• 6.4.2 Application examples
• 6.4.2.1 Synthesis of the NGD-LC Hilbert filter prototype
• 6.4.2.2 Illustrative validation results
• 6.5 Conclusion
• References

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