Active Filters And Their Applications Computer Science Essay

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A filter is a device that passes electric signals at certain ranges of frequencies or frequency while preventing the passage of other signals. Filters of some sort are essential to the operation of most electronic circuits. It is therefore like an interesting challenge to anyone involved in electronic circuit design to have the ability to develop filter circuits capable of meeting a given set of specifications. But unfortunately, many in the electronics field are uncomfortable with the subject of filters, whether due to a lack of familiarity with it, or a problem to grapple with the mathematics involved in a complex filter design.

Filter circuits are used in a wide variety of applications. In the field of telecommunication, band-pass filters are used in the audio frequency range (0 kHz to 20 kHz) for modems and speech processing. High-frequency band-pass filters (several hundred MHz) are used for channel selection in telephone central offices. Data acquisition systems mostly require anti-aliasing low-pass filters as well as low-pass noise filters in their preceding signal conditioning stages. System power supplies often use band-rejection filters to suppress the 60-Hz line frequency and high frequency transients. In addition, there are filters that do not filter any frequencies of a complex input signal, but just add a linear phase shift to each frequency component, thus contributing to a constant time delay. These are called all-pass filters.

At high frequencies (> 1 MHz), all of these filters usually consist of passive components such as inductors (L), resistors (R), and capacitors (C). They are then called LRC filters.

In the lower frequency range (1 Hz to 1 MHz), however, the inductor value becomes very large and the inductor itself gets quite bulky, making economical production difficult. In these cases, active filters become important. Active filters are circuits that use an operational amplifier (op amp) as the active device in combination with some resistors and capacitors to provide an LRC-like filter performance at low frequencies.

In circuit theory, a filter is an electrical network that alters the amplitude and/or phase characteristics of a signal with respect to frequency. Ideally, a filter will not add new frequencies to the input signal, nor will it change the component frequencies of that signal, but it will change the relative amplitudes of the various frequency components and/or their phase relationships. Filters are mostly used in electronic systems to accept signals in certain frequency ranges and reject signals in other frequency ranges. Such a filter has a gain which depends on signal frequency. Consider a situation where a useful signal at frequency f1 has been contaminated with an unwanted signal at f2. If the contaminated signal is passed through a circuit that has very low gain at f2 compared to f1, the undesired signal can be removed, and the useful signal will remain. Note that in the case of this simple example, we are not concerned with the gain of the filter at any frequency other than f1 and f2. As long as f2 is sufficiently attenuated relative to f1, the performance of this filter will be satisfactory. In general, however, a filter's gain may be specified at several different frequencies, or over a band of frequencies. Since filters are defined by their frequency-domain effects on signals, it makes sense that the most useful analytical and graphical descriptions of filters also fall into the frequency domain. Thus, curves of gain versus frequency and phase versus frequency are commonly used to illustrate filter characteristics, and the most widely-used mathematical tools are based in the frequency domain. The frequency-domain behaviour of a filter is described in terms of its transfer function or network function in form of a mathematical expression.

The transfer function defines the filter's response to any arbitrary input signal, but we are most often concerned with its effect on continuous sine waves. Magnitude of the transfer function is very important when considered as a function of frequency, which indicates the effect of the filter on the amplitudes of sinusoidal signals at various frequencies. Knowing the transfer function magnitude (or gain) at each frequency helps us in determining how well the filter can distinguish between signals at different frequencies. The transfer function magnitude versus frequency is called the amplitude response or sometimes, mostly in audio applications, the frequency response. Similarly, the phase response of the filter gives the amount of phase shift introduced in sinusoidal signals as a function of frequency. Since a change in phase of a signal also represents a change in time, the phase characteristics of a filter become especially important when dealing with complex signals where the time relationships between signal components at different frequencies are critical.


Active filters use amplifying elements, especially operational amplifiers, with resistors and capacitors in their feedback loops, to synthesize the required filter characteristics. Active filters can have high input impedance, low output impedance, and virtually any arbitrary gain. They are also usually easier in design than passive filters. Possibly their most important attribute is that they lack inductors, thereby reducing the problems associated with those components. Still, the problems of accuracy and value spacing also affect capacitors, although to a lesser degree. Performance at high frequencies is limited by the gain-bandwidth product of the amplifying elements, but within the amplifier's operating frequency range, the op amp-based active filter can achieve very good accuracy, provided that low-tolerance resistors and capacitors are used. Active filters will generate noise due to the amplifying circuitry, but this can be minimized by the use of low-noise amplifiers and careful circuit design.

Active filters have become a viable alternative for controlling harmonic levels in industrial and commercial facilities. However, there are many different filter configurations that can be employed and there is no standard method for rating the active filters. This paper describes the active filter operation characteristics and develops standard ratings that can be used for filtering different types of nonlinear loads. Limitations of the active filters are also described.

The active filter uses power electronic switching to generate harmonic currents that cancel the harmonic currents from a nonlinear load. The active filter configuration investigated in this paper is based on a pulse-width modulated (PWM) voltage source inverter that interfaces to the system through a system interface filter. In this configuration, the filter is connected in parallel with the load being compensated. Therefore, the configuration is often referred to as an active parallel filter.

The voltage source inverter used in the active filter makes the harmonic control possible. This inverter uses dc capacitors as the supply and can switch at a high frequency to generate a signal which will cancel the harmonics from the nonlinear load. The active filter does not need to provide any real power to cancel harmonic currents from the load. The harmonic currents to be cancelled show up as reactive power. Reduction in the harmonic voltage distortion occurs because the harmonic currents flowing through the source impedance are reduced. Therefore, the dc capacitors and the filter components must be rated based on the reactive power associated with the harmonics to be cancelled and on the actual current waveform (rms and peak current magnitude) that must be generated to achieve the cancellation. The current waveform for cancelling harmonics is achieved with the voltage source inverter and an interfacing filter. The filter consists of a relatively large isolation inductance to convert the voltage signal created by the inverter to a current signal for cancelling harmonics. The rest of the filter provides smoothing and isolation for high frequency components. The desired current waveform is obtained by accurately controlling the switching of the insulated gate bipolar transistors (IGBTs) in the inverter. Control of the current waveshape is limited by the switching frequency of the inverter and by the available driving voltage across the interfacing inductance. The driving voltage across the interfacing inductance determines the maximum di/dt that can be achieved by the filter. This is important because relatively high values of di/dt may be needed to cancel higher order harmonic components. Therefore, there is a trade off involved in sizing the interface inductor. A larger inductor is better for isolation from the power system and protection from transient disturbances. However, the larger inductor limits the ability of the active filter to cancel higher order harmonics.


In applications that use filters, the amplitude response is generally of greater interest than the phase response. But in some applications, the phase response of the filter is important. An example of this might be where a filter is an element of a process control loop. Here the total phase shift is of concern, since it may affect loop stability. Whether the topology used to build the filter produces a sign inversion at some frequencies can be important.

It might be useful to visualize the active filter as two cascaded filters. One is the ideal filter, embodying the transfer equation; the other is the amplifier used to build the filter. This is illustrated in Figure 1. An amplifier used in a closed negative-feedback loop can be considered as a simple low-pass filter with a first-order response. The gain rolls off with frequency above a certain breakpoint. In addition, there will be, in effect, an additional 180° phase shift at all frequencies if the amplifier is used in the inverting configuration.

Filter design is a two-step process. First, the filter response is chosen; then, a circuit topology is selected to implement it. The filter response refers to the shape of the attenuation curve. Often, this is one of the classical responses such as Butterworth, Bessel, or some form of Chebyshev. Although these response curves areusually chosen to affect the amplitude response, they will also affect the shape of the phase response. For the purpose of the comparisons in this discussion, the amplitude response will be ignored and considered essentially constant.

Filter complexity is typically defined by the filter "order," which is related to the number of energy storage elements (inductors and capacitors). The order of the filter transfer function's denominator defines the attenuation rate as frequency increases. The asymptotic filter roll off rate is -6n dB/octave or -20n dB/decade, where n is the number of poles. An octave is a doubling or halving of the frequency; a decade is a tenfold increase or decrease of frequency. So a first-order (or single-pole) filter has a roll off rate of -6 dB/octave or -20 dB/decade. Similarly, a second-order (or 2-pole) filter has a roll off rate of -12 dB/octave or -40 dB/decade. Higher-order filters are usually built up of cascaded first- and second-order blocks. It is, of course, possible to build third- and, even, fourth-order sections with a single active stage, but sensitivities to component values and the effects of interactions among the components on the

frequency response increase dramatically, making these choices less attractive.

Which Approach is best- Active, Passive, or Switched- Capacitor?

Each filter technology offers a unique set of advantages and disadvantages that makes it a nearly ideal solution to some filtering problems and completely unacceptable in other applications. Here are quick look at the most important differences between active, passive, and switched-capacitor filters.

Accuracy: Switched-capacitor filters have the advantage of better accuracy in most cases. Typical centre-frequency accuracies are normally on the order of about 0.2% for most switched-capacitor ICs, and worst-case numbers range from

0.4% to 1.5% (assuming, of course, that an accurate clock is provided). In order to achieve this kind of precision using passive or conventional active filter techniques requires the use of either very accurate resistors, capacitors, and sometimes inductors, or trimming of component values to reduce errors. It is possible for active or passive filter designs to achieve better accuracy than switched-capacitor circuits, but additional cost is the penalty. A resistor-programmed switched-capacitor filter circuit can be trimmed to achieve better accuracy when necessary, but again, there is a cost penalty.

Cost: No single technology is a clear winner here. If a single pole filter is all that is needed, a passive RC network may be an ideal solution. For more complex designs, switched-capacitor filters can be very inexpensive to buy, and take up very little expensive circuit board space. When good accuracy is necessary, the passive components, especially the capacitors, used in the discrete approaches can be quite expensive; this is even more apparent in very compact designs that require surface-mount components. On the other hand, when speed and accuracy are not important concerns, some conventional active filters can be built quite cheaply.

Noise: Passive filters generate very little noise (just the thermal noise of the resistors), and conventional active filters generally have lower noise than switched-capacitor ICs. Switched-capacitor filters use active op amp-based integrators as their basic internal building blocks. The integrating capacitors used in these circuits must be very small in size, so their values must also be very small. The input resistors on these integrators must therefore be large in value in order to achieve useful time constants. Large resistors produce high levels of thermal noise voltage; typical output noise levels from switched-capacitor filters are on the order of 100 μV to 300 μVrms over a 20 kHz bandwidth. It is interesting to note that the integrator input resistors in \ switched-capacitor filters are made up of switches and capacitors, but they produce thermal noise the same as "real" resistors.

(Some published comparisons of switched-capacitor vs. op amp filter noise levels have used very noisy op amps in the op amp-based designs to show that the switched-capacitor filter noise levels are nearly as good as those of the op ampbased filters. However, filters with noise levels at least 20 dB below those of most switched-capacitor designs can be built using low-cost, low-noise op amps such as the LM833.)

Although switched-capacitor filters tend to have higher noise

levels than conventional active filters, they still achieve dynamic ranges on the order of 80 dB to 90 dB-easily quiet enough for most applications, provided that the signal levels applied to the filter are large enough to keep the signals "out of the mud".

Thermal noise isn't the only unwanted quantity that switchedcapacitor filters inject into the signal path. Since these are clocked devices, a portion of the clock waveform (on the order of 10 mV p-p) will make its way to the filter's output. In many cases, the clock frequency is high enough compared to the signal frequency that the clock feed through can be ignored, or at least filtered with a passive RC network at the output, but there are also applications that cannot tolerate this level of clock noise.

Offset Voltage: Passive filters have no inherent offset voltage. When a filter is built from op amps, resistors and capacitors, its offset voltage will be a simple function of the offset voltages of the op amps and the dc gains of the various filter stages. It's therefore not too difficult to build filters with submillivolt offsets using conventional techniques. Switched-capacitor filters have far larger offsets, usually ranging from a few millivolts to about 100 mV; there are some filters available with offsets over 1V! Obviously, switched-capacitor filters are inappropriate for applications requiring dc precision unless external circuitry is used to correct their offsets.

Frequency Range: A single switched-capacitor filter can cover a centre frequency range from 0.1 Hz or less to 100 kHz or more. A passive circuit or an op amp/resistor/ capacitor circuit can be designed to operate at very low frequencies, but it will require some very large, and probably expensive, reactive components. A fast operational amplifier is necessary if a conventional active filter is to work properly at 100 kHz or higher frequencies.

Tunability: Although a conventional active or passive filter can be designed to have virtually any center frequency that a switched-capacitor filter can have, it is very difficult to vary that center frequency without changing the values of several components. A switched-capacitor filter's center (or cutoff) frequency is proportional to a clock frequency and can therefore be easily varied over a range of 5 to 6 decades with no change in external circuitry. This can be an important advantage in applications that require multiple center frequencies.

Component Count/Circuit Board Area: The switched-capacitor approach wins easily in this category. The dedicated, single-function monolithic filters use no external components other than a clock, even for multipole transfer functions, while passive filters need a capacitor or inductor per pole, and conventional active approaches normally require at least one op amp, two resistors, and two capacitors per second-order filter. Resistor-programmable switched-capacitor devices generally need four resistors per second-order filter, but these usually take up less space than the components needed for the alternative approaches.

Aliasing: Switched-capacitor filters are sampled-data devices, and will therefore be susceptible to aliasing when the input signal contains frequencies higher than one-half the clock frequency. Whether this makes a difference in a particular application depends on the application itself. Most switched-capacitor filters have clock-to center-frequency ratios of 50:1 or 100:1, so the frequencies at which aliasing begin to occur are 25 or 50 times the center frequencies. When there are no signals with appreciable amplitudes at frequencies higher than one-half the clock frequency, aliasing will not be a problem. In a low-pass or bandpass application, the presence of signals at frequencies nearly as high as the clock rate will often be acceptable because although these signals are aliased, they are reflected into the filter's stopband and are therefore attenuated by the filter. When aliasing is a problem, it can sometimes be fixed by adding a simple, passive RC low-pass filter ahead of the switched-capacitor filter to remove some of the unwanted high-frequency signals. This is generally effective when the switched-capacitor filter is performing a low-pass or band pass function, but it may not be practical with high-pass or notch filters because the passive anti-aliasing filter will reduce the passband width of the overall filter response.

Design Effort: Depending on system requirements, either type of filter can have an advantage in this category. WEBENCH Active Filter Designer makes the design of an active filter easy. You can specify the filter performance (cutoff frequency, stopband, etc.) or the filter transfer function, compare multiple filters, and get the schematic/BOM implementation of the one you choose. In addition, online simulation enables further performance analysis. The procedure of designing a switched capacitor filter is supported by filter software from a number of vendors that will aid in the design of LMF100-type resistor-programmable filters. The software allows the user to specify the filter's desired performance in terms of cutoff frequency, a passband ripple, stopband attenuation, etc., and then determines the required characteristics of the second-order sections that will be used to build the filter. It also computes the values of the external resistors and produces amplitude and phase vs. frequency data.


Active filters could have wide applications for controlling harmonic currents from non -linear loads. The best performance is obtained for loads such as PWM type ASDs and switch mode power supplies, where the current waveform does not have abrupt changes that are difficult for the active filter to follow. Guidelines for rating the active filters are presented. Capacitor switching transients should not be a major problem for the active filter inverter and controls. However, the interface filter capacitor could experience high transient voltages that may exceed the capabilities of the capacitor and surge suppressors. The capacitor switching transients could also cause overload of the anti-parallel diodes in the inverter bridge. Other devices in customer facilities can also have problems with these transients and many utilities are making efforts to control substation capacitor switching transients.