Gain-sensitivity Product Research Articles

Research on error compensation in the process of geomagnetic sensor measurement

The geomagnetic sensor is a kind of highly sensitive sensor, which is easy to be interfered with by the outside in the process of measurement. To solve this problem, the author uses the least square method to estimate the gain value and sensitivity product value of the amplification circuit of the geomagnetic sensor and explores the solution of the bias voltage of the geomagnetic sensor by using the ellipsoid fitting model. By analyzing the error sources of the geomagnetic sensors in the measurement process, the error compensation model covering various error factors is constructed. All parameters of the error compensation model are obtained by fitting the experimental data of the turntable. After several experiments with different attitude angles, the validity of the compensation model is verified, and the measurement accuracy of the roll angle is improved, which meets the requirements of roll angle measurement.

Component value selection for active filters based on minimization of GSP and E12 compatible using Grey Wolf and Particle Swarm Optimization

The component value selection for active analogue filter design is an important issue to improve the performances and to make compatible with existing parameters value. The Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) are efficient intelligent evolutionary algorithms for solving optimization problems. Both techniques are used to minimize the total design error of a 4th order Butterworth low pass active filter. This would be realized with component values which are compatible with E12 series. In addition, stability of filter is guaranteed by minimization of gain sensitivity product. By considering the minimization of Gain Sensitivity Product (GSP), the sixteen variables of objective function are reduced to eight variables which speed up the iteration process. The simulation results prove the efficiency of algorithms for the design of analogue active filter by optimizing the component values based on E12 compatible with minimization of GSP by minimising the design error.

A note on general gain-sensitivity product and complementary transformation

It is shown that the general gain-sensitivity product Gamma /sup T//sub A/ does not change after performing complementary transformation in a linear feedback system with a single op amp.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Slew-induced distortion of single-amplifier active filters using the gain-sensitivity product concept

The Volterra-Wiener series is used to obtain an analytical formula for slew-induced distortion (SID) in single-amplifier active filters. It is shown that the relative change of the transfer function caused by SID depends on the parameters of the operational amplifier (OA) and on the method of frequency compensation applied to it. This change also depends on the transfer function to be realized, on the amplitude of the input signal and on the gain-sensitivity product (GSP). It is shown that reducing the GSP also reduces the SID. The corresponding relationship was verified experimentally.

Nonlinear sensitivity in a single-loop feedback circuit

A nonlinear sensitivity criterion is defined for the single-loop feedback circuits in terms of the Volterra-Wiener series. It is shown that, when the input-signal amplitude is sufficiently small, this sensitivity approaches the linear definition for the change in amplifier gain. The result is applied to a single-amplifier filter whose dynamic range is limited by slew-induced distortion. It is demonstrated that, for such circuits, the nonlinear sensitivity is closely related to the gain-sensitivity product.

Erratum: Design of twin-T single amplifier building block with prescribed values of capacitors and minimum gain-sensitivity product

Erratum: Design of twin-T single amplifier building block with prescribed values of capacitors and minimum gain-sensitivity product

Design of twin-T single amplifier building block with prescribed values of capacitors and minimum gain-sensitivity product

Equations are supplied for the design of a widely known active filter building block, namely the twin-T single-amplifier building block (TT-SABB), when used as a frequency rejection network in its standard form. Through the proposed equations, the required value of pole and zero frequency and pole Q are realised by assigning free preferred values to the capacitors and then computing the resistor values for minimum gain-sensitivity product.

Sensitivity minimization of networks with operational amplifiers and parasitics

A computational method is described which calculates network sensitivity to the influence of parasitics by simulating only the ideal network. For active networks, a similar sensitivity is defined with respect to the deviations from ideal behavior of operational amplifiers. It is shown that this sensitivity is equivalent to the gain-sensitivity product and depends only on the passive elements and the topology. The procedure was applied to known active networks and, in every case considered, minimization resulted in networks with smaller sensitivities. Compensation for nonideal behavior of the operational amplifiers is outlined. A Monte Carlo simulation is performed on the well-known STAR network and it is shown that optimization can lead to considerable improvement, even in the case of well-designed networks.

Dual‐amplifier expansion and the design of very‐low‐frequency (VLF) hybrid integrated active filters

AbstractThe problem of designing very‐low frequency (VLF) active filters in hybrid‐integrated form is discussed. It is shown that a class of single‐amplifier second‐order filters exists with which VLF active filters can be built while at the same time satisfying the constraints imposed by hybrid‐integrated circuit technology (i.e. limited resistor and capacitor values). However, with decreasing pole frequency, the gain required of the single amplifier becomes excessive, the gain‐sensitivity product (GSP) intolerably high. A solution to the problem is to introduce a second amplifier into the circuit and to distribute the required gain between the two amplifiers. This ‘dual‐amplifier expansion’ (DAX) significantly reduces the GSP, enhances the stability of the filter response, and reduces the susceptibility of the filter characteristics to nonideal amplifier effects. On the other hand DAX may not be arbitrarily introduced into a single‐amplifier circuit without taking the effect of the limited gain‐bandwidth product of the two amplifiers into account. It is shown that the degree by which the gain may be distributed between them is limited by the gain‐bandwidth product ratio of the two amplifiers. Much can be improved in this respect by proper frequency compensation of the two amplifiers. It is shown that a combination of the so‐called T‐compensation and the single‐pole single‐capacitor compensation produces results that are close to those obtainable with ideal amplifiers with unlimited bandwidth.

Active-filter pole displacement due to nonideal operational amplifiers

The effect of nonideal operational-amplifier output impedance on active-filter pole displacement or pole variation, respectively, is discussed and compared with the effects of finite amplifier gain and gainbandwidth product. The analysis shows that the pole variation is mainly dependent on three factors: the gain-sensitivity product, the pole frequency rated with the gain-bandwidth product, and the amplifier output resistance RA as compared to the network impedance level R∞. The influence of the amplifier output impedance on the total pole shift can be varied, within some practical and technological limits, by the choice of the impedance level R∞. The results have been verified experimentally.

Reducing nonideal op-amp effects in active filters by minimizing the gain-sensitivity product (GSP)

It is shown that the effects of finite amplifier gain and gain-bandwidth product, and of the Variations of these quantities, on the transfer characteristics of an active filter can be expressed in terms of the gain-sensitivity product (GSP). To minimize these effects, it is sufficient, in most practical cases, to minimize the GSP with respect to the pole <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> . Among other things, the expressions obtained also demonstrate the influence of the op-amp frequency compensation on the poles of an active filter. Experimental results comparing the pole variation of active filters with and without minimized GSP, coincide accurately with the theoretical results obtained in the paper. It is shown that considerable improvement in pole and transfer-characteristic stability of active filters can be expected by minimizing the GSP.

Optimising two commonly used active-filter building blocks using the complementary transformation

In the paper, the minimisation of the gain-sensitivity product (g.s.p.) for two important active-filter types that are finding widespread use in voiceband communication systems, in the form of hybrid-integrated filter building blocks, is considered. The first comprises a twin I for zero realisation: this is incorporated in the positive-feedback loop of a single operational amplifier and is referred to as the twin-T s.a.b.b. The known conditions for minimum g.s.p. for the twin-T s.a.b.b. are briefly recapitulated and expanded. The second comprises a differential scheme for zero realisation, and combines positive and negative feedback. It is referred to as the single-amplifier biquad (s.a.b.). The paper shows that the two circuits are closely related by the complementary transformation, and that conditions for minimum g.s.p. in both cases are identical

Design of a Highly Selective Bridge Amplifier with Zero Gain Sensitivity Product

Design procedure of a very highly selective bridge amplifier using a new bridge type RC rejection filter is given. Under unbalanced (non-null) condition of the bridge circuit, it is shown that even with a moderate forward gain exceedingly high values of Q can be obtained. It is shown that by modifying this bridge circuit zero gain sensitivity can be obtained maintaining the very high Q-values at low forward gain. Experimental verification of the gain insensitivity properties is given using a circuit which realises a stable Q of 500 at 1000 Hz.

Active filter realization of biquadratic transfer function

The realization of quadratic transfer functions by an active band-pass filter is described. The hybrid-integrated circuit used consists of a three-terminal passive network, connected to a high-gain inverting amplifier. A design procedure for minimizing the gain–sensitivity product is given. By interchanging two connections between the passive network and the amplifier, the band-pass is converted into a band-stop characteristic. A pair of such circuits may be cascaded to generate a generalized biquadratic transfer function. Parasitic singularities due to each circuit are eliminated through pole-zero cancellation between the cascaded filters. In this manner, a wide range of transfer functions is realizable. A low-pass or a notch filter can be obtained by adding an isolating stage.

Design of active RC filters with zero gain-sensitivity product

A root locus with respect to the active parameter for any second-order active RC filter is circular with center on the real axis. It is shown that for any pole pair <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> and pole frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_0</tex> , the circular root locus centered at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2Q \omega_0</tex> on the real axis and of radius <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}\sqrt{4Q^{2}-1}</tex> exhibits zero <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -sensitivity and zero gain-sensitivity product (GSP) with respect to the active parameter. Furthermore, realization techniques to achieve zero <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -sensitivity and zero GSP for prescribed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_0</tex> are outlined. Experimental results agree closely with the theoretical expectations.

A class of stable active filters using unity-gain voltage followers

A new class of active filters using a single unity-gain amplifier is introduced and shown to have a gain-sensitivity product and a maximum spread of component values lower than those for the corresponding Sallen and Key circuits by a factor of Q.

Gain-sensitivity product-a figure of merit for hybrid-integrated filters using single operational amplifiers

It is shown that a different measure of performance must be used to evaluate hybrid-integrated active filters from that used to evaluate active filters in discrete form. Where sensitivity was previously found to be an adequate and useful measure for Q stability of discrete active filters, the gain-sensitivity product gives an accurate measure of Q stability for hybrid-integrated circuits. Where negative feedback filter schemes were found to be preferable with respect to Q stability when realized in discrete form, positive feedback schemes with their very much lower gain- sensitivity product may be preferable in hybrid-integrated filter circuits. In addition, they require low-gain amplifiers than can be used up to higher frequencies. Q-stability measurements of hybrid- integrated positive feedback, or Sallen-Key-type circuits, which were realized with tantalum thin-film resistors and capacitors combined with beam-leaded operational amplifier chips agree very accurately with the predictions derived from gain-sensitivity calculations.