03-03-2012, 03:38 PM
Non linear analog circuits and its equalization techniques
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INTRODUCTION
The confluence of Moore’s law and the maturation of the art of analog integrated circuit (IC) design has created a flurry of recent research and development work on digitally intelligent analog circuits. Exploiting high-density on-chip digital processing, the approach represents a trendy alternative to conventional hard-labored analog design methodology, in which the inescapable trade-off between linearity, circuit bandwidth, complexity, and power dissipation has limited the scaling progress of precision analog circuits in the past.
This trend is most observable in the area of analog-to-digital converters (ADCs), in which the readily available output bits provide a convenient digital means to infer component errors of the constituent imperfect analog circuits, and to devise correction schemes to mitigate the effect of these imperfections, all performed naturally in the digital domain. On a parallel path, although treating a continuous-time radio frequency (RF) circuit is considerably more difficult than treating a discrete-time baseband ADC, the potential benefit and adaptability that can be harvested from such treatment seems to well offset the initial design effort involved. As a result, similar design approaches are making quick inroads in the RF and soon even millimeter- wave sectors.
Why Non-linear Circuits?
Electrical devices (amplifiers, computers) are built from nonlinear components. In order to understand the design of these devices, a fundamental understanding of nonlinear circuits is necessary. Moreover, nonlinear circuits is where the “real engineering” comes in. That is, there are no hard and fast rules to analyze most nonlinear circuits -you have to use your brain! But, to make your life easy we will start with some systematic methods to analyze op-amp nonlinear circuits. This chapter is organized as follows: first we will talk about what makes a circuit nonlinear. Next, we will see a very useful nonlinear circuit -the negative resistance converter. Then we will see an application of the negative resistance converter: the oscillator.
Equillibrium Point:
The above expression means an equilibrium point is defined when the derivative of the function is zero. This makes sense physically. Equilibrium is when nothing changes, mathematically, the derivative has to be zero at equilibrium since derivative means rate of change. Next we will classify equilibrium points as stable or unstable. It is easier to see the classification with an example. Let us use our negative resistance converter circuit from figure 8. The i-v graph is reproduced below, but now I have added other information:
Limitations of Digital Technology
The amplifier and filter front-end of the mixed signal system are problem dependent. Sometimes the amplifier can also be used as a filter, like in the case of accelerometers, due to their noisy nature [10]. In this case, the anti-alias filter is mixed with the amplifier, since the effect is to limit the pass band of the sensor response. With strain gauges, the excitation is composed of few frequencies, and generally the acquisition system excites the sensor with a pure sinus [11]. The design of the anti-alias filter is dependent also on the used converter. The closest to the Nyquist rate the converter works, the higher the complexity of the anti-alias filter. For amplifiers and anti-alias circuits, discrete implementations are common and readily available in the literature [12]. However, the silicon realization of these circuits is not as simple. Although a high gain amplifier can be achieved, its use to build an amplifier with linear and controlled gain is a hard task. Linear resistors and capacitors take to much area, and the other option is to use non-linear components like the MOS channel (as a resistor) or gate (as a capacitor). Besides that, there is also some non-ideal behavior in the operational amplifiers themselves, like limited gain and pass band.