State-space synthesis of biquads based on the MOSFET square law

Abstract

This paper presents a design methodology for implementing integrators and biquads based on the square-law relationship between gate voltage and drain current in a saturated MOS transistor. The resulting circuit architecture is suitable for implementation in BiCMOS or CMOS VLSI technology.

Externally linear integrators

“…Other circuits using the quadratic characteristics of MOS-FET's to make ELIN integrators are described elsewhere [7], [37].…”

Design of Square-Root Domain Filters

“…Based on the idea of Adams, Frey [2,3] further rewrote a set of nonlinear differential equations resulted from state-space as KCL nodal equations, yielding a novel class of circuits termed Exponential State Space (ESS) filters, moreover, Tsividis [4] had embedded it in as forming part of a broader branch of structures classified as Externally Linear Internally Nonlinear (ELIN) networks. Due to the characteristics of high-frequency operation, tuneability, and extended dynamic range under low power supply voltages, many researchers have devoted themselves to developing log-domain filters [5][6][7][8][9][10][11][12][13][14][15].…”

“…Furthermore, Toumazou et al [8] and Germanovix et al [9] presented log-domain filters in terms of MOSFET circuits that operate in weak inversion, however, its operation is restricted only in kilo hertz range. Hence, in order to improve the problems of the above method, Eskiyerli et al [10] and Yu et al [11] adopted MOSFETs operated in saturation region to implement log domain filters, respectively. Although their methods are able to reduce fabrication cost, the operation frequencies are only approximately two megahertz's and supply voltages are as high as five volts.…”

Design of Current-Mode Square-Root Domain Band-Pass Filter with Reduced Voltage

“…As a result, the problems of the above methods are solved and enhanced via adopting MOSFETs which operated in saturation region to implement log-domain filters-reducing fabrication cost while also lessening drawbacks such as high power supply voltage, high power consumption and low operation frequency. The methods are according to those of Eskiyerli et al [10,14], Yu et al [11,12] and Lopez-Martin [13]. For this reason, these filters are also known as square-root domain filters.…”