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Operational Amplifiers
Published in Michael Olorunfunmi Kolawole, Electronics, 2020
The differentiator generates an output signal proportional to the first derivative of the input with respect to time. An ideal differentiator circuit is shown in Figure 4.18a. At node A, in time domain, v− = v+ = 0, and iR + ic = 0, we can write vo(t)R︸iR+Cdvi(t)dt︸iC=0
The Frequency Domain: Describing the Human Operator
Published in Richard J. Jagacinski, John M. Flach, Control Theory for Humans, 2018
Richard J. Jagacinski, John M. Flach
The picture changes again (Fig. 14.5) when performance is measured with a second-order (acceleration) control system [YP = 4/(jω)2]. With this plant, the frequency response of the human seems to show increasing gain with increasing frequency (up to a point). Also, note that the phase response is positive at some frequencies. That is, the controller is generating phase lead. This is characteristic of differentiation. A differentiator has a frequency response, jω, that is the inverse of an integrator; that is, gain increases 20 db/decade with frequency and there is a constant phase shift of +90°. Similarly, a lead, (TLjω + 1), is the inverse of a lag. A lead resembles a unity gain at low frequencies and resembles a differentiator at high frequencies. The human describing function in Figure 14.5 appears to consist of a gain, a time delay, and lead, or differentiation at high frequencies.
Introduction to microelectronic circuits, power electronic devices, and power converters
Published in Sergey E. Lyshevski, and Applied Mechatronics, 2018
The operational differentiator performs the differentiation of the input signal. The current through the input capacitor is C1du1(t)dt (see Figure 4.9). That is, the output voltage is proportional to the derivative of the input voltage with respect to time, and u0(t)=−R2C1du1(t)dt.
Search of Optimal s-to-z Mapping Function for IIR Filter Designing without Frequency Pre-warping
Published in IETE Journal of Research, 2021
Shalabh K. Mishra, Dharmendra K. Upadhyay, Maneesha Gupta
Nowadays most of the communication systems work in the digital domain, and therefore filters are mostly used in the digital domain. Unlike the analog filter, the digital filters are composed of delays, multipliers and adder circuits in place of resistors, inductors, and capacitors [7,8]. Digital filters are extensively used in control theory, speech processing, radar, telecommunication systems, biomedical signal processing, etc [9–11]. Digital filters have some important merits over their analog counterparts, such as superior performance-to-cost ratio, resistance to manufacturing variations or aging, and not drifting with temperature or humidity, system flexibility, and programmability. There are mainly two topologies for digital filter designing, named as IIR (infinite impulse response) and FIR (finite impulse response). Both of the designs have their own advantages and disadvantages. In conventional IIR filter designing, filters with the desired specifications are designed in analog domain first and then transferred into digital domain using appropriate analog-to-digital (s-to-z) mapping functions. Several s-to-z mapping functions are available in literature such as bilinear, Al-alaoui, Schneider, etc [12,13]. The transfer function of the digital differentiator is also an s-to-z mapping function [14–19].
Global adaptive HOSM differentiators via monitoring functions and hybrid state-norm observers for output feedback
Published in International Journal of Control, 2018
Victor Hugo Pereira Rodrigues, Tiago Roux Oliveira
(Tracking control × pure differentiation problem): In the results of Theorem 7.1, we are interested in the global-exact differentiation applied to tracking problem by means of output feedback, rather than pure differentiation simply. Reminding that ρ is the relative degree of the plant, the differentiator gain must be an upper bound for the ρth derivative of the output error e(t). Consequently, the implementation of demands to dominate unknown terms with unknown bounds, which are time-varying and can grow with the unmeasured state variables as well. On the other hand, the pure differentiation of any exogenous signal f(t) is a particular scenario, where the differentiator gain can be exclusively designed as a class function of the switching index k in order to majorise the higher derivatives of f(t), which are assumed uniformly bounded by unknown constants. As discussed in the introductory section, the latter problem has already been handled by Efimov and Fridman (2011). The differentiation of signals with unbounded higher derivatives was introduced in Levant and Livne (2012) and, more recently, in Moreno (2017). However, in both publications, a known time-varying upper bound for the higher derivatives of f(t) are assumed known to be applied as the differentiator gain.
Two New Third-Order Quadrature Sinusoidal Oscillators
Published in IETE Journal of Research, 2023
Ajishek Raj, Data Ram Bhaskar, Pragati Kumar
Third-order quadrature sinusoidal oscillators (TOQSOs), on the other hand, though utilize a minimum of three capacitors, have certain advantageous features as compared to their second-order counterparts in terms of accuracy, Q-factor, and distortion [12]. As a result, TOQSOs have also been designed with different active blocks including OTAs. TOQSOs presented in the literature have been designed using several approaches. Since the proposed work deals with the realization of TOQSOs, in the following, we present a brief overview of the reported realization techniques used to realize TOQSOs cited in [13–53]. In the first approach, a cascade connection of low pass filter (second-order) and an integrator in a loop with unity feedback has been used to obtain TOQSOs with different properties [13–28]. The second technique utilizes a cascade of second-order high pass filter with a differentiator in a loop to get TOQSO [26,27]. In the third technique, a lossy integrator is cascaded with two lossless integrators to obtain TOQSOs [29–31]. In the fourth approach, two lossy integrators and one lossless integrator with unity feedback have been used to realize TOQSO circuits [32–36]. A cascade connection of three lossy integrators in a unity feedback loop has also been used to realize TOQSO [37]. Table 1 presents the various features of previously reported TOQSOs. However, none of the realized TOQSOs with the above-mentioned approaches have fully independent control of CO and FO. This feature of an oscillator is desirable for realizing voltage-controlled oscillators (VCOs) as the FO can be adjusted without disturbing CO and can also be used to stabilize the amplitude of output signals.