 | This article needs additional citations for verification .(December 2019) |
A state variable filter is a type of active filter in electronic circuits. It consists of one or more integrators, connected in some feedback configuration. It is essentially used when precise Q factor is required, as other multi-order filters are unable to provide. [1] The most common implementation sums the input signal with its integral and its double integral, another is an MDAC based implementation.
The example given below can produce simultaneous lowpass, highpass, and bandpass outputs from a single input. [2] This is a second-order (biquad) filter. Its derivation comes from rearranging a high-pass filter's transfer function, which is the ratio of two quadratic functions. The rearrangement reveals that one signal is the sum of integrated copies of another. That is, the rearrangement reveals a state-variable-filter structure. By using different states as outputs, different kinds of filters can be produced. In more general state-variable-filter examples, additional filter orders are possible with more integrators (i.e., more states).
The signal input is marked Vin; the LP, HP and BP outputs give the lowpass, highpass, and bandpass filtered signals respectively. [3] [4]
For simplicity, we set:
Then:
The pass-band gain for the LP and HP outputs is given by:
It can be seen that the frequency of operation and the Q factor can be varied independently. This and the ability to switch between different filter responses make the state-variable filter widely used in analogue synthesizers.
Values for a resonance frequency of 1 kHz are Rf1 = Rf2 = 10k, C1 = C2 = 15nF and R1 = R2 = 10k.
State variable filters are frequently used for modifying frequency response in audio signal processing. At low Q settings they are often used in parametric equaliser circuits, and at high or variable Q settings to create resonant filter modules in analog synthesizers. For manual control of frequency, Rf1 and Rf2 in the section above may be replaced by a dual potentiometer; and for voltage control, the devices U2 and U3 may be replaced by voltage controlled amplifiers or operational transconductance amplifiers.
An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential that is typically 100,000 times larger than the potential difference between its input terminals. The operational amplifier traces its origin and name to analog computers, where they were used to perform mathematical operations in linear, non-linear, and frequency-dependent circuits.
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter.
A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter in the context of audio engineering. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices. They can also be used in conjunction with a low-pass filter to produce a band-pass filter.
A negative-feedback amplifier is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal. The applied negative feedback can improve its performance and reduces sensitivity to parameter variations due to manufacturing or environment. Because of these advantages, many amplifiers and control systems use negative feedback.
Image response is a measure of performance of a radio receiver that operates on the superheterodyne principle.
In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them.
The Sallen–Key topology is an electronic filter topology used to implement second-order active filters that is particularly valued for its simplicity. It is a degenerate form of a voltage-controlled voltage-source (VCVS) filter topology.
A voltage-controlled filter (VCF) is an electronic filter whose operating characteristics can be set by an input control voltage. Voltage controlled filters are widely used in synthesizers.
A Colpitts oscillator, invented in 1918 by American engineer Edwin H. Colpitts, is one of a number of designs for LC oscillators, electronic oscillators that use a combination of inductors (L) and capacitors (C) to produce an oscillation at a certain frequency. The distinguishing feature of the Colpitts oscillator is that the feedback for the active device is taken from a voltage divider made of two capacitors in series across the inductor.
The asymptotic gain model is a representation of the gain of negative feedback amplifiers given by the asymptotic gain relation:
In electronics, a frequency multiplier is an electronic circuit that generates an output signal and that output frequency is a harmonic (multiple) of its input frequency. Frequency multipliers consist of a nonlinear circuit that distorts the input signal and consequently generates harmonics of the input signal. A subsequent bandpass filter selects the desired harmonic frequency and removes the unwanted fundamental and other harmonics from the output.
A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies. The oscillator is based on a bridge circuit originally developed by Max Wien in 1891 for the measurement of impedances. The bridge comprises four resistors and two capacitors. The oscillator can also be viewed as a positive gain amplifier combined with a bandpass filter that provides positive feedback. Automatic gain control, intentional non-linearity and incidental non-linearity limit the output amplitude in various implementations of the oscillator.
Delta-sigma modulation is a method for encoding analog signals into digital signals as found in an analog-to-digital converter (ADC). It is also used to convert high-bit-count, low-frequency digital signals into lower-bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter (DAC).
This article illustrates some typical operational amplifier applications. A non-ideal operational amplifier's equivalent circuit has a finite input impedance, a non-zero output impedance, and a finite gain. A real op-amp has a number of non-ideal features as shown in the diagram, but here a simplified schematic notation is used, many details such as device selection and power supply connections are not shown. Operational amplifiers are optimised for use with negative feedback, and this article discusses only negative-feedback applications. When positive feedback is required, a comparator is usually more appropriate. See Comparator applications for further information.
A Q meter is a piece of equipment used in the testing of radio frequency circuits. It has been largely replaced in professional laboratories by other types of impedance measuring devices, though it is still in use among radio amateurs. It was developed at Boonton Radio Corporation in Boonton, New Jersey in 1934 by William D. Loughlin.
A charge amplifier is an electronic current integrator that produces a voltage output proportional to the integrated value of the input current, or the total charge injected.
Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected.
In electronics, a differentiator is a circuit that is designed such that the output of the circuit is approximately directly proportional to the rate of change of the input. A true differentiator cannot be physically realized, because it has infinite gain at infinite frequency. A similar effect can be achieved, however, by limiting the gain above some frequency. The differentiator circuit is essentially a high-pass filter.
An active differentiator includes some form of amplifier, while a passive differentiator is made only of resistors, capacitors and inductors.
Prototype filters are electronic filter designs that are used as a template to produce a modified filter design for a particular application. They are an example of a nondimensionalised design from which the desired filter can be scaled or transformed. They are most often seen in regard to electronic filters and especially linear analogue passive filters. However, in principle, the method can be applied to any kind of linear filter or signal processing, including mechanical, acoustic and optical filters.
In electronics, a transimpedance amplifier (TIA) is a current to voltage converter, almost exclusively implemented with one or more operational amplifiers. The TIA can be used to amplify the current output of Geiger–Müller tubes, photo multiplier tubes, accelerometers, photo detectors and other types of sensors to a usable voltage. Current to voltage converters are used with sensors that have a current response that is more linear than the voltage response. This is the case with photodiodes where it is not uncommon for the current response to have better than 1% nonlinearity over a wide range of light input. The transimpedance amplifier presents a low impedance to the photodiode and isolates it from the output voltage of the operational amplifier. In its simplest form a transimpedance amplifier has just a large valued feedback resistor, Rf. The gain of the amplifer is set by this resistor and because the amplifier is in an inverting configuration, has a value of -Rf. There are several different configurations of transimpedance amplifiers, each suited to a particular application. The one factor they all have in common is the requirement to convert the low-level current of a sensor to a voltage. The gain, bandwidth, as well as current and voltage offsets change with different types of sensors, requiring different configurations of transimpedance amplifiers.
