Miller Theorem for Weakly Nonlinear Feedback Circuits and Application to CE Amplifier

Abstract

The paper presents the derivation of Miller formulas for weakly nonlinear feedback networks. The expressions found are simple and compact and constitute a generalization of the wellknown linear case.As an application example, the formulas are applied to a common-emitter amplifier to straightforwardly derive the closed-form expressions of second-and third-harmonic distortion factors. The results found, validated by Spectre simulations with a VBIC bipolar model, allow to understand in depth the contribution of each nonlinear element.

Operator o and analysis of harmonic distortion

“…Second, the symbol o used in both (2) and (3) does not mean the same. Concerning (2), it is impossible to define the operator o mathematically, relying upon its descriptive definition given in [3][4][5]. But, the situation seems to be better in the case of Meyer and Stephens definition because, as shown in [1], their o operator can be identified with the convolution operation.…”

Analysis and Optimization of SFDR in Differential Active-RC Filters

“…In differential op amps, the second-order nonlinearities can be ignored. By substituting the blocker phasors corresponding to and , into (14), the component generated at the output of each stage can be calculated for as (15) Equation (15) can be expressed more concisely as where is defined as (17) and is the linear voltage gain of the th stage. Applying Kirchhoff's current law (KCL) at the output nodes of both stages of Fig.…”

“…The filter is assumed to be weakly nonlinear, which means that the input signals are small enough so that the distortion terms higher than third-order can be neglected, without introducing a noticeable error. This assumption enables us to use linear techniques in the distortion analysis [12]- [15]. The output distortion is expressed in terms of level of individual op amps in the filter, which is modeled and discussed in Section III, where a linearity model for Miller-compensated op amps is also given.…”

Miller Equivalents and Their Applications

“…In the above examples, it is observed that the most laborious part is to determine the transfer function A V , A I , Z E or Y E (equations (11), (12), (13), (17), (18) and (19)). Depending on the ratio or parameter to be found out, appropriate Miller equivalents applied to particular elements judiciously will give the result with less number of steps and thus faster as shown in Example 1.…”

“…Nayaka [12] utilizes Miller's theorem for analysis of high-frequency voltage amplifier where the approximate value of gain is taken as A/ √ 2 instead the mid-band gain value A, to obtain more appropriate results. Recently, Palumbo et al [13] have extended the use of Miller's theorem and derived generalized Miller formulae for weakly nonlinear networks and applied it to analyze the harmonic distortion of bipolar transistor in CE configuration.…”