General current-mode analysis method for translinear filters

Abstract

Abstract-Log-domain or translinear filters are regarded as being a promising alternative in the area of low-voltage filter design. To date, most publications have reported on synthesis of translinear filters. Although synthesis is more powerful than analysis, it must go together with a generally applicable analysis method in the same domain. In this paper, a general currentmode analysis method is proposed. By using a current-mode approach, we stay close to the existing theory on static translinear circuits, which might be beneficial in developing a general, possibly more powerful synthesis method.

An instantaneous and syllabic companding translinear filter

“…For example, the capacitance current I cap flowing through the capacitance C shown in Fig. 1(a), is given by [8] I cap = CU T _ I out I out (1) where UT is the thermal voltage, Iout is the collector current, and the dot represents differentiation with respect to time. Clearly, I cap is nonlinearly related to I out , thus expressing the instantaneous companding inherently present.…”

“…In fact, TL filters can be described completely in terms of currents [8]. As a consequence, they can be regarded as an extension of the TL principle toward dynamic transfer functions.…”

A wide-tunable translinear second-order oscillator

“…1. Assuming a bipolar transistor, it follows [1]: (4) , , , and being the capacitance value, the thermal voltage , the collector current, and the capacitance current, respectively. The dot again represents differentiation with respect to time.…”

“…R ECENTLY, both an analysis method and a synthesis method for dynamic translinear circuits were proposed by the authors [1], [2]. The dynamic translinear principle can be regarded as a generalization of the well-known "static" translinear principle, formulated by Gilbert in 1975 [3].…”

“…They implement a second-order differential equation, which ideally equals (1) and being the oscillator signal and the angular frequency, respectively. The dot represents differentiation with respect to time.…”