Operational Amplifier Gain-bandwidth Research Articles

Sampled data simulation of linear and nonlinear circuits

In this paper, an efficient, accurate, stable, and explicit method for transient analysis of lumped linear time invariant circuits is given. The method formulates a set of finite difference equations in the analog domain for sampled data simulation of the circuit. The solution of these equations gives the network response at fixed and equally spaced discrete instants of time. The fixed-time interval between each solution can be chosen arbitrarily and does not depend on the circuit time constants. The transient solution at each time point requires one matrix/vector multiplication and vector addition only. The algorithm is a general computer oriented formulation method that can be applied to any linear circuit. In addition to linear time invariant circuits, the method can be applied to a restricted class of time varying and/or nonlinear circuits. It is directly applicable to linear networks containing periodically clocked ideal switches, for example, switched capacitor and switched current circuits. In these networks, the circuit is linear inside each phase and changes its topology at fixed discrete instants of time. All nonlinear elements allowed in analysis must be clocked, such that their characteristics change only at discrete instants of time. For example, clocked digital circuits, such as, ideal comparators, A/D and D/A blocks are allowed. In particular, the method is applied to the simulation of oversampled delta-sigma modulators. The method can be used to study the effect of clock feed through, finite switch resistance, and finite gain bandwidth of operational amplifiers on the performance of these modulators. In addition, the algorithm can be used for analysis of continuous time delta-sigma modulators. Examples of simulation results are given.

Active and passive analog filter design: an introduction

This text introduces the theory and design of active and passive analog filters and emphasizes modern trends and applications. It includes an introduction to OTA (operational transconductance amplifier) and switched-capacitor filters. The book is designed to lead smoothly from basic background circuit theory into the details of modern analog filter theory. The treatment not only covers a study of the basic filter structures, but also introduces advanced topics including sensitivity, operational amplifier gain bandwidth effects and compensation. Its complete coverage of modern approximation allows students to study all types and enables comparative studies of different filter realizations because of the use of computers in filter design. Many computer methods are introduced, emphasizing design and applications. Special features of the text include detailed discussion of filter design tables; treatment of effects and compensation methods; modern active filter techniques; and a variety of end-of-chapter problems.

Compensation improvements in RC-active integrators

The gain and phase errors in high quality integrator circuits are discussed, and the relative merits of inverting and noninverting structures are established. It is shown that the normally positive gain and phase errors in noninverting integrators can be reduced to zero or negative values. Analytical and experimental evidence is presented to demonstrate that the sensitivity to uniform changes in the operational amplifier gain-bandwidth products in two-integrator loop structures can be forced to zero.

Biquadratic SC filters with small GB effects

The effects of proper switch phasing in SC filters to yield low gain-bandwidth (GB) product dependence is discussed. A figure of merit for comparing GB effects in SC networks based upon the topology dependent effective GB matrices has been introduced. Motivated by this consideration, two general biquadratic switched-capacitor filter structures are presented. These circuits are stray-insensitive, have small <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> sensitivities, and are easy to apply. A significant feature of these biquads is their reduced dependence on the operational amplifier GB product. Filter center frequencies up to the 50-kHz range are feasible for op amps with typical values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GB/2 \pi = 10^{6}</tex> Hz, making these circuits attractive for high-frequency applications. The advantages of the proposed structures are demonstrated by an example. Results enabling the designer to determine the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> deviations for different values of GB are presented. A comparison of theoretical and experimental results shows good agreement.

A Comparison of Three Active Analogue Band-Pass Filter Circuits

This tutorial paper outlines the design procedure and compares the response of three different forms of active band-pass filter circuit, which are designed to meet the same basic filter specification. The paper shows in particular how the response varies with the spread of operational amplifier gain-bandwidth product; this spread exists, in practice, amongst operational amplifiers of any given type.

Integrator design for high-frequency active filter applications

The combined effects of deviation from ideal in integrator magnitude and phase on the performance of integrator-based active filters is investigated. The limitations of using the integrator Q -factor as a measure of integrator performance are discussed. Conditions for minimizing the operational amplifier gain bandwidth product effects on integrator-based active filters are established which are dependent only upon the characteristics of the integrators. Inverting and noninverting integrators for use in active filters which are independent of first-order and second-order operational amplifier time constant effects and require no amplifier matching are introduced. These new integrators are compared with existing actively compensated configurations directly and in a filter structure. Experimental results are presented which confirm the theoretical development.

Predistortion design of active filters to compensate for finite gain-bandwidth

The effects of finite operational amplifier gain-bandwidth have only been considered relatively recently. Previous work centred around calculation of the shift in polo positions—or, equivalently, the ω0 and Q—due to known amplifier characteristics. The presumption is that the ideal design values are known. This paper takes the inverse approach. Assuming that the desired values of ω0 and Q are known, along with the operational amplifier characteristics, it presents a procedure for deriving the ideal values of ω0 and Q which will result in a shift to the design values. The method is, therefore, one of pro-distortion. The technique involves polynomial coefficient matching and the solution of a set of non-linear equations. The technique is developed for both single and multiple amplifier circuits, and a number of examples of each are presented. The paper concludes with experimental results proving the efficacy of the method.

Effects of finite operational amplifier gain-bandwidth product on a switched-capacitor amplifier

The effects of the finite operational amplifier gain-bandwidth product GB on the performance of an inverting switched-capacitor amplifier are presented. Limitations of the GB and the clock frequency fc=1/T as well as GB.T are determined.

Active compensation of opamps

A novel active compensation method for the finite gain bandwidth of operational amplifiers, when used in voltage-controlled voltage source structures, is given. In this method, a universal active compensation scheme is proposed which can be used with operational amplifier voltage-controlled voltage sources, when looked upon as a general threeport active building block. It is shown that phase shifts contributed by imperfect operational amplifiers are virtually eliminated over an extended frequency range. Experimental resnits are presented.

An active-RC filter for high-Q and high-frequencies with zero-Q and zero-frequency-sensitivity to amplifier gain-bandwidth product

A double integrator active-RC filter is described, in which both Q and frequency sensitivity to the operational-amplifier gain-bandwidth product are made zero by active-compensation techniques. The circuit can be used for high-Q high-frequency applications.

Compensation of some operational-amplifier based RC-active networks

Means of compensating for the finite gain bandwidth of operational amplifiers, when used in voltage-controlled voltage source and inverting integrator blocks, are described and are shown to virtually eliminate excess phase shifts over a prescribed frequency range. As applied to integrators, the compensating technique simultaneously reduces gain (period) and phase errors. The methods should prove of maximum advantage where trimming of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> elements is difficult or expensive as in thin-film realizations. It is shown that the overall temperature stability of the compensated network can be significantly improved.

Operational amplifier integrators for the measurement of the delay times of microwave transistors

A simple low frequency technique for the measurement of subnanosecond delay times with an operational amplifier connected as a summing integrator is described. Previous integrator theory is extended to incorporate second-order effects. The operational amplifier gain-bandwidth product is shown to set a limit to the sensitivity of the integrator. For a gain-bandwidth product of 1 GHz the smallest measurable delay time is estimated to be about 5 ps, which is small enough for measurements on the fastest microwave transistors. Expressions for the delay times of transistors are derived from the hybrid-/spl pi/ model. Examples of measured delay times of microwave transistors are given and the results are compared with theoretical predictions.

Comparison of a class of active filters with respect to the operational-amplifier gain-bandwidth product

Abstracr-A class of positive-feedback active RC filters which realize high stable Q's is presented. This class generalizes the earlier circuits of Tarmy and Ghausi and of Moschytz. The performance of the circuits presented is analyzed using a one-pole rolloff model for the operational amplifier. The Q and wO variations due to one-pole rolloff are tabulated for different filters. It is shown that the positive-feedback filters have lower Q sensitivity to the gain-bandwidth product than the state-variable filter. The theoretical behavior of the circuit Q is experimentally verified.