Operational amplifiers, active filters, and control systems
Operational amplifiers
An operational amplifier often referred to as op-amp, is used to provide a basis for realizing a transfer function with prescribed poles and zeros in a relatively straightforward manner. It usually has two input terminals, one of them is inverting, and the other one is noninverting, and it has one output terminal.
For an operational amplifier to be called ideal it has to fulfill the following four assumptions:
1. The operational amplifier acts as a voltage-controlled voltage source described by the following input-output relation:
V0 = A (V2 - V1).
2. The open-loop voltage gain will have a constant value that is very large compared to unity. This property is also referred to as virtual ground.
3. The impedance between the two input terminals is infinitely large, and similarly, the impedance between each one of them and the ground is also large. Implying the input terminal currents are zero.
4. The output impedance should be zero.
In most cases of an open-loop system, operational amplifiers are not used.
It is usually implemented in a feedback circuit as an amplifier component in which the feedback controls the closed-loop transfer function of the circuit.
Let us assume a circuit where the noninverting input terminal of the operational amplifier is grounded and the impedances, Z1(s) and Z2(s), represent the input element and the feedback element of the circuit, respectively. And, let Vin(s) and Vout(s) represent the Laplace transforms of the input and output voltage signals, respectively. Then using the ideal model we can easily construct the model for the feedback circuit.
The closed-loop transfer function of the feedback circuit will be represented as follows:
T(s) = Vout(s)/Vin(s) = -Z2(s)/Z1(s).
Active filters
Filters designed using operational amplifiers are known as active filters. By connecting different versions of a basic circuit in series, it is possible to synthesize an overall transfer function with arbitrary real poles, and arbitrary real zeros.
In contrast to passive LC filters, active filters have an advantage as they do not need an inductor. And, in contrast to digital filters, active filters provide the advantage of continuous-time operation and reduced complexity. Though, it also comes with a disadvantage. It lacks the computing power and flexibility that is offered by digital filters.
Control systems
A control system is used to attain accurate control over the plant so that the output of the plant remains close to the desired response. It can be achieved by modifying the plant input.
There are two types of control systems, they are as follows:
1. Open-loop control
Open-loop control modifies the plant input directly from the target response.
2. Closed-loop control
Closed-loop control modifies the plant input using feedback. The closed-loop control is also known as a single degree of freedom or 1-DOF structure. Some other important factors to keep in mind for closed-loop control are:
- The effect of distortion due to the nonlinear behavior of the plant is reduced by F(s).
- The sensitivity of the closed-loop system T(s) is reduced by a factor that is equal to the return difference.
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