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2022 | Buch

The Design of Gm-C Filters Kapitel lesen Erstes Kapitel lesen

Gm-C Filter Synthesis for Modern RF Systems

verfasst von: Vančo Litovski

Verlag: Springer Singapore

Buchreihe : Lecture Notes in Electrical Engineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

This book discusses synthesis of Gm-C filter for modern radio frequency systems. Analogue filters are an inevitable part of the chain of signal processing in modern radio and telecommunication systems. Among the technologies implemented for these purposes are the so-called Gm-C filters which are built of operational transconductance amplifiers and capacitors. This technology allows for integration of the filter into a CMOS system-on-chip so making it very attractive for application in low-power (battery operated) devices. The objective of this book is to achieve three goals: (1) to fully describe the circuit synthesis procedures for parallel, cascade, and a realization based on LC prototypes; (2) to make a thorough evaluation of the advantages and disadvantages of these methods and to recommend the “preferable” one; and (3) to create an extensive table of element values of cascaded Gm-C filters realizing the best-known low-pass filter functions. The book will influence the design community to embrace this technology even for non-communication applications.

Inhaltsverzeichnis

Frontmatter
Chapter 1. The Design of Gm-C Filters
Abstract
A short description of the motivation for the content of the book is given in this chapter. It is explained that filter design for modern RF systems, as such, is not in its prime mainly due to the fact that system designers are convinced that nothing else but Butterworth and Chebyshev happened in the last seventy years. Even so, conversion the transfer function into a circuit is very frequently done in a most unfavorable way. We claim that much more attention is to be devoted to filter design in this area. Namely, it is a pity to use so advanced and expensive modern integrated circuit technology for so decadent filter solutions as we are, not rarely, seeing around. This chapter also tries to set a framework for the location and type of filters in modern RF systems while giving a short overview of the Gm-C and two-phase solutions which will be offered in the sequel.
Vančo Litovski
Chapter 2. A Glimpse to the Active and Lumped Passive Integrated High Frequency Electronic Components
Abstract
High frequency active and lumped passive components intended to be implemented in integrated CMOS electronic filters are considered in this chapter. Gradually eliminating the ones which are losing feasibility for a given reason, we come to the Gm-C technology and the operational transconductance amplifier (OTA) as its fundamental circuit element. Short analysis of the structure and the properties of modern CMOS transconductance amplifiers will be given. In order to enable effective simulations intended for verification of the designed filters, linear macromodels of the OTA will be developed. The noise properties of the OTA will be considered in Chap. 7, while nonlinearities are out of the scope of this book since corrective circuits are used (within the filters designed by our methods) which do not allow large signals to occur (if no overdrive is present).
Vančo Litovski
Chapter 3. Parallel Realization of Gm-C Single- and Two-Phase Integrated Filters
Abstract
It is a common practice for the synthesis of electronic filters to be realized using cascade of cells. Here, however, we will start with the parallel realization so making a unique attempt to offer an alternative. The synthesis of parallel active network is simpler per se than any other since one needs only two (one second order and one first order) types of low-pass cells and, naturally, an adder circuit. That dramatically simplifies the computer program intended to do the synthesis. In this realization, starting from the input and arriving to the output, the signal is processed by a single cell and the summing. In that way, even in the case of high Q-factors of the poles, the value of the signal is not expected to reach extremely high value and produce nonlinear distortions.
Vančo Litovski
Chapter 4. Cascade Realization of Active Gm-C Circuits
Abstract
The cascade realization of filters is the “natural one” since a correspondence is usually established between the transfer function expressed in factored form and a cascade of second-order cells (with additional first-order cell in the case of odd order filters). Nevertheless, the mapping from a transfer function into a cascade of cells is facing obstacles which are related to the multiple combinations in the pole–zero pairing and multiple orders of extraction (order of the cells from the source to the load). In the case of Gm-C technology, an additional problem was observed and solved here for the first time. Since a Gm-C cell may have finite input impedance, it loads the previous one so changing its (and the overall) transfer function.
Vančo Litovski
Chapter 5. Use of LC-to-Gm-C Transformation for Synthesis of Gm-C Single- and Two-Phase Integrated Filters
Abstract
The abundance of synthesis solutions for passive LC filters of many kinds suggests the idea to accommodate these circuits for production in CMOS. The main obstacle for that is the inductive component being it a simple inductor or a transformer. Solutions were found in the past to simulate both the inductor and transformer by a connection of operational amplifiers and capacitors. That idea was elaborated in this chapter allowing synthesis on active Gm-C filters based on existing passive LC prototypes. Of course, that idea was here extended to two-phase circuits to allow fully automatic synthesis of this kind of solutions. Illustrative examples demonstrate that no limits on the types of transmission zeros and the order of the filter may exist if the RM software for filter design is used.
Vančo Litovski
Chapter 6. Synthesis of Analog Gm-C Hilbert Transformer and Its Implementation for Band-Pass Filter Design
Abstract
In conjunction with the problem of synthesis high frequency, selective, linear phase, arithmetically symmetrical band-pass filters implemented as CMOS integrated circuits using OTAs and capacitors only is considered. To that end, complex (two-phase) systems are adopted which are driven by two sinusoidal signals mutually shifted in phase by π/2. Solutions to two problems are offered. New maximally flat approximation algorithm of constant output phase difference of two all-pass networks is developed and implemented. In that way, the so-called Hilbert transformer of any order is synthesized by a newly proposed method. Then, starting with a low-pass prototype, a complex (two phase) solution is proposed in order to preserve arithmetical symmetry of the filter’s frequency domain response. For both the Hilbert transformer and the complex filter, parallel physical realization in a form of Gm-C structure is used. Study of the result obtained was performed on several circuits using SPICE simulation.
Vančo Litovski
Chapter 7. Implementation Issues
Abstract
To get a realistic filter design, one has to verify the temporary results against: element value variation (coming from Ambiental changes, aging or design errors) and imperfections of the built-in components. The first goal is achieved below by Monte Carlo simulation of the circuit with a given maximum tolerance value, while for the second, a simplified macromodel of the transconductor is used and the output capacitance varied. To complete the study, we are trying to answer to the question of selection of the filter architecture among parallel, cascade, and LC-to-Gm-C paradigms. Criterions will include the complexity of the circuit and the spread of the element values. To all that one may add questions related to the choice of the nominal transconductance since it may seriously affect the complete design and the noise properties of the architectures. Thorough analyses brought us to a conclusion that when all aspects are introduced one may rely first on the cascade solution as will be shown by a synthesis of 10 MHz passband width two-phase Gm-C filter.
Vančo Litovski
Chapter 8. Element Values of Cascaded Gm-C and Two-Phase Gm-C Filters

There are many possibilities to conform to a set of requirements imposed to a filter design. By choosing the Gm-C concept, only one of the doubts is resolved. Within that technology, as it was demonstrated in the previous chapter, variants exist offering corresponding advantages and disadvantages. Further, one needs to find out the approximation type and the complexity of the solution. Among the seemingly unlimited number of variants of solutions to the transfer function approximation problem, a set was chosen considered to be the most representative and of much usefulness. In this chapter, we will adopt the cascade structure as the most convenient one and produce tables of element values of Gm-C circuits synthesized from different transfer functions and different complexities. The set of design requirements, e.g., passband attenuation, stopband attenuation, and maximum group delay error, will be limited in order to keep the size of the chapter acceptable.

Vančo Litovski
Backmatter
Metadaten
Titel
Gm-C Filter Synthesis for Modern RF Systems
verfasst von
Vančo Litovski
Copyright-Jahr
2022
Verlag
Springer Singapore
Electronic ISBN
978-981-16-6561-5
Print ISBN
978-981-16-6560-8
DOI
https://doi.org/10.1007/978-981-16-6561-5

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