Continuous-Time Integrated Filters | 22 | v2

ABSTRACT

All modern signal-processing systems include various types of electrical ﬁlters that the designer has to realize in an appropriate technology. The literature contains many well-deﬁned ﬁlter design techniques [1-3], and computer programs are available, which help the designer ﬁnd the appropriate transfer function that describes the required ﬁlter characteristics mathematically. The reader may also refer to Section I in this book and the other chapters of this section (Section II). Once the ﬁlter’s transfer function is obtained, implementation methods must be found that are

compatible with the technology selected for the design of the total system. In some situations, considerations of power consumption, frequency range, signal level, or production numbers may dictate discrete (passive or active) ﬁlter realizations. Often, however, as much as possible of the total system must be fully integrated in microelectronic form, so that the ﬁlters can be implemented in the same technology. Often, digital (Section III) or sampled-data (Chapter 18) implementations are suitable for realizing

the ﬁlter requirements. However, in modern communications applications, the required frequency range is so high that digital or sampled-data circuitry is inappropriate or too expensive so that continuous-time (c-t) ﬁlters are necessary. In addition, ﬁlters in many signal-processing situations must interface with the ‘‘real world,’’ where the input and output signals take on continuous values as functions of the continuous variable time, i.e., they are c-t signals. In these situations c-t antialiasing and reconstruction ﬁlters are often required. Because the performance of the total ﬁlter system is of relevance and not just the performance of the intrinsic ﬁlter, the designer may have to consider if it might not be preferable to implement the entire system in the c-t domain rather than as a digital or sampled-data system. At least at low frequencies the latter methods have the advantages of very high accuracy, better signalto-noise ratio, and little or no parameter drifts, but they entail a number of problems connected with

analog-to-digital (A=D) and digital-to-analog (D=A) conversion (see Chapter 10 of Analog and VLSI Circuits), sample-and-hold, switching, antialiasing, and reconstruction circuitry. Traditionally, c-t ﬁlters were implemented as discrete designs. Well-understood procedures exist for

deriving passive LC ﬁlters (Section I) from a given transfer function with prescribed complex natural frequencies, e.g., [1, Chapter 2], [2], [3, Chapter 13]. To date no practical methods exist for building highquality, i.e., low-loss, inductors on an integrated circuit (IC) chip.* The required complex natural frequencies must, therefore, be realized by using gain, i.e., as we saw earlier in this section, by embedding an operational ampliﬁer (op-amp; see Chapter 16 of Fundamentals of Circuits and Filters) in an RC feedback network [1,3]. Since op-amps, resistors, and capacitors can be implemented on an integrated circuit, it appears that with active RC networks the problem of monolithic ﬁlter design is solved in principle: all active devices and any necessary capacitors and resistors can be integrated together on one silicon chip. Although this conclusion is correct, the designer needs to consider four other factors that are important in integrated c-t ﬁlter design and perhaps are not immediately obvious. The ﬁrst item concerns the most important design task for achieving commercially practical designs:

integrated ﬁlters must be electronically tunable, preferably by an automatic tuning scheme. Because of its importance, we shall devote a separate section, Section 16.4, to this topic. The second item deals with the economics of practical implementations of active ﬁlters: in discrete designs, the cost of components and stocking them usually necessitate designing the ﬁlter with a minimum number of active devices. One, two, or possibly three op-amps per pole pair are used and the smallest number of different (if possible, all identical) capacitors. In integrated realizations, capacitors are determined by processing mask dimensions and the number of different capacitor values is unimportant, as long as the element spread is not excessive. Further, active devices frequently occupy less chip area than passive elements so that it is often preferable to use active elements instead of passive ones.y Also, the designer should remember that in IC technology it is not easy to generate accurate absolute component values, but that ratios of like components, such as capacitor ratios, can be realized very precisely. The third observation pertains to the fact that ﬁlters usually have to share an integrated circuit with other, possibly switched or digital, systems so that the ac ground lines (power supply and ground wires) are likely to contain switching transients and generally are noisy. Measuring the analog signals relative to ac ground, therefore, may result in designs with poor signal-to-noise ratio and low power-supply rejection. The situation is remedied in practice by building continuous-time ﬁlters in fully differential, balanced form, where the signals are referred to each other as V¼V þV as shown in Figure 16.4b through d. An additional advantage of this arrangement is that the signal range is doubled (for an added 6 dB of signal-to-noise ratio) and that the even-order harmonics in the nonlinear operation of the active devices cancel. All ﬁlters in this chapter are understood, therefore, to be designed in fully differential form. Finally, we point out that communication circuitry is often required to operate at hundreds of megahertz or higher, where op-amp-based active RC ﬁlters will not function because of the op-amps’ limited bandwidth. Today, c-t ﬁlters integrated in bipolar, CMOS, or BiCMOS technology are no longer academic curiosities

but a commercial reality (see Ref. [5] for some recent advances in the ﬁeld). In the following we discuss the main methods that have proven to be reliable. First, we presentMOSFET-C ﬁlters, whose design methods resemble most closely the standard active RC procedures discussed in Chapters 11-14; they can, therefore, be most readily understood by the reader without requiring further background. Next, we introduce the transconductance-C (also referred to as gm-C) technique, which is currently the predominant method for

c-t integrated ﬁlters. Designs based on transconductors lead to ﬁlters for the higher operating frequencies that are important for modern communication systems.