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- Electronic filter
- Active Filter Design
- Design of analog filters : passive, active RC, and switched capacitor
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A short summary of this paper. An elementary example would be a signal having only low-frequency and high-frequency components. A low-pass ftlter would permit only the low frequencies to be transmitted, the high frequencies being suppressed or attenuated. The converse is true for passing the high frequencies while suppressing the low frequencies by means of a high-pass ftlter.
Other ftlters may be designed to pass a range of frequencies about a given selected frequency, rejecting frequencies outside the selected band. Conversely, a ftlter may be designed to reject a narrow band of frequencies while accepting all other frequencies outside the selected band. It may be said that electrical and electronic ftlter networks have become an indispensable part of electronic and modern communication systems. The fundamental principles of electrical wave ftlters were outlined by Wagner in Germany and Campbell in the USA around the year Since those early beginnings, the state-ofthe-art has encompassed many new ideas and techniques associated with modern network theory and feedback analysis.
Examples include the work of Bode and Black on the stability of amplifiers and that of Darlington in the application of modern network theory to electrical ftlters. The choice of a particular type of ftlter from the large range of ftlters must be influenced by several factors, some of which are: complexity, ease of tuning, economics, compatability with existing circuitry and whether or not power supplies may be required.
By referring to figure 1. Furthermore, at frequencies close to or within the microwave range, only waveguide or coaxial cable type ftlters are possible. Mention must be made of digital filtering techniques since such ftlters are becoming widely used and of increasing importance.
Digital ftlters far exceed the analogue circuits where high-order ftlters and multiplexing are required, since tuning may be simply achieved by adjusting the coefficients of a mathematical algorithm. A disadvantage is that the ftltering of high frequencies is limited by the time delays within the circuitry, but improvements are being made with the introduction of faster semiconductor materials such as gallium arsenide.
Other types of filters are the piezo-crystal type which presents very stable resonant frequencies, very high Q-factors and small power losses; the surface acoustic wave SAW type used in the majority of TV receivers and, fmally, mechanical filters, a popular type being based on the principle of magnetostriction. This book will concentrate almost wholly on the R-C types with a brief mention of the passive types and their op-amp, gyrator equivalents.
Advantages of active over passive circuitsIntroduction types are that expensive and bulky coils are eliminated, circuit gain may be realised, and high input and low output impedances give the amplifier good isolating properties which are useful when cascading networks to produce higherorder fJJ. The main disadvantages are that a power supply is required, that above about 50 kHz the op-amp has a considerably reduced gain although more expensive devices are available to the designer for frequencies up to kHz and that the circuit sensitivities to component changes are worse than the passive counterparts.
At high frequencies, coils are of considerably improved quality, cheaper and physically much smaller, thereby making the passive L-C circuit a more viable proposition at such frequencies. Component qualityClearly it is of paramount importance to select good-quality components having a high stability over the dynamic working range. Care must therefore be taken in the choice of op-amps, resistors and capacitors when constructing active fJJ. The op-amp is considered in chapter 3 where the important user design data is gain-bandwidth product, slew rate and whether internal or external compensation is to be employed.
The types of resistors used are: carbon-composition, carbon-film and metalfilm. Carbon-film resistors are more stable than the composition type and have very good temperature coefficients of resistance with good ageing characteristics. They exhibit better temperature stability and ageing characteristics than the carbon film type. Choice of type of capacitor may be made from film polyester types , mica, ceramic or electrolytic depending on factors such as frequency range, temperature stability and cost.
Film types should be considered for fJJ. Mica capacitors are more expensive than the film types but possess far superior properties such as temperature coefficient, where a few parts in a million may be achieved.
These capacitors may be used well into the VHF region. Ceramic capacitors have greater dielectric constants than the ftlm and mica types and may be constructed to provide positive or negative temperature coefficients. This property makes these devices particularly useful for temperature compensation of active and passive circuits. They also exhibit minimum parasitic inductance and power dissipation over a range from low audio to high radio frequencies which make them attractive at radio frequencies.
Aluminium electrolytic capacitors are usually employed as by-pass devices or for non-precision timing applications at low frequencies and are in general unsuitable for active or passive circuits.
The tantalum form, however, may be used at low frequencies where low selectivity ftlters are required. Filter responsesThere are five basic forms of ftlter-response and these are shown in figure 1. From a consideration of the gain and phase responses in figure 1.
For example, the low-and high-pass ftlters must involve not only the pass and stopband information, but also the type of response -whether Butterworth or Chebyshev. Basic fdter theoryA ftlter may be considered to be composed of lumped elements as shown in figure 1. In order to plot the gain and phase responses, it is necessary to select values for w and to insert these values into the appropriate equations 1.
Experience shows that usually three well-chosen values for w are sufficient to enable reasonable response curves to be drawn when considering reasonably simple ftlter structures.
Since we are considering the denominator expression of H jw , the phase angle will be negative as shown in figure 1. The gain and phase responses for the circuit are shown in figure 1. We may summarise the performance of any order n of filter having the maximally flat Butterworth characteristic shown in figure 1. Magnitude and frequency scalingIn example 1. The process of referring components and also frequency to the value unity is referred to as nonnalising the circuit.
Correctly applied, this scaling technique may significantly simplify the analysis and synthesis of electrical networks. In example 1. Clearly the values of inductance and capacitance must change because of the influence of the actual design data. Wn The normal low-pass filter will be tuned to the fundamental component w0 , all other components 3w0 , 5w0 etc. There is another type of filter, however, which is used to reproduce, ideally, at its output terminals, an exact replica of the input waveform such as that described by equation 1.
The problem arises when such a complex waveform is applied as the input signal to a filter. The fundamental along with all the significant harmonics must show the correct relative amplitude relationship at the output of the filter to maintain the original input signal. Furthermore, the various frequency components should not be displaced in time relative to one another.
Filters designed around a constant delay for a given range of frequencies are called Bessel or Thomson filters and are not considered in this book. Consider the response diagram shown in figure 1. Should the phase response be non-linear, then clearly the phase delay for each frequency would be different and output distortion would occur.
Most filters have non-linear phase response characteristics, with the result that waveform distortion will occur for complex input signals. Finally it should be mentioned that in amplitude modulated signals where the carrier is associated with side-bands, then the carrier, which is affected by the phase delay, could be delayed differently from the side-bands which are affected by what is called group-delay.
This again could produce a distorted output signal. The steps involved in any successful filter design may be summarised as follows: a Specification of a suitable filter characteristic -for example, attenuation, phase shift, size, weight etc. The second step usually involves what is often described as 'the approximation technique'. The filter specification, in the form of pass-band gain, transition bandwidth, stop-band attenuation and cut-off frequency, is normally given in the frequency domain.
The selection of a realisable mathematical relationship which approximates to the given specification usually involves considerable algebraic manipulation. Two of the most popular relationships are considered here in a simplified form. The student is referred to the Bibliography for books covering the theory in greater detail. From the outset it should be noted that almost all filter circuits are derived from the equivalent low-pass prototype. A typical idea! The requirements of the specification are that all frequencies below We cutoff are passed with no attenuation and above We are stopped with infmite attenuation.
An 'actual' magnitude characteristic is shown in figure 2. It should be stressed at this point that the technique applied to filter design is one of choosing a fllter response characteristic which closely approximates to the ideal and which finally results in a circuit realisation that contains a manageable number of components.
After the circuit has been realised using nominal component values to ascertain the correctness of the design, it is desirable to introduce tolerances within the components to assess whether or not the original speciication will still be met in a practical design..
J 0 Figure 2. The Butterworth approximationThe Butterworth characteristic takes the form described by the equation 2. Obviously the quality of the approximation depends on F w 2 which must be defmed so as to make the approximation as accurate as possible.
Being unity, there are no ripples in the pass-band of the Butterworth response. This is often referred to as the maximally flat condition. Insertion into equation 2. From equation 2. Calculate the order of the filter and the roots of the Butterworth polynomial. An alternative approximation, called the Chebyshev approximation, spreads the zeros ofF w 2 across the pass band and constrains H jw to attain its maximum value at a number of points within the pass band.
It will be seen that the ripple factor e affects the way the response behaves in the pass band. Depending on the order of the filter, pass-band ripples occur having equal heights and variable frequency, the ripple height or width being determined by the ripple factor.
These features are shown in figure 2. The specification for a Chebyshev filter is given by AMIN Note that this fourth-order Chebyshev circuit satisfies the requirements better than the previously considered sixth-order Butterworth circuit, at the expense of some pass-band ripple.
This result should be compared with the data given in table 2. It should again be noted that we have also obtained important design coefficients which will later be used in the design of filters having specified ripple widths. Table 2. ConclusionsWe may conclude that the Chebyshev response gives a superior pass-band response, particularly if the ripple width is not too large, than does the Butterworth response.
Active Filter Design
This paper will explain the basic concepts underlying the operation of the switched capacitor, as well asthe use of switched-capacitors to realize compact and versatile circuits already familiar to theundergraduate student of electronics. One set of example circuits include easily tunable active filters;specific examples of filter designs that incorporate switched-capacitors will be developed, and the use of acommercially available switched-capacitor integrated circuit, the MF10, to implement the designs will beshown. Another example circuit is an instrumentation amplifier that is more compact and has a higherCMRR than the conventional realization. Linear Technology's LTC serves as the vehicle for thiscircuit. By demonstrating the utility of the modern switched-capacitor IC in these two importantelectronic functions, it is hoped that instructors and students in engineering technology will include thestudy of the switched-capacitor in advanced electronics courses.
design: active RC and switched capacitor - Google Books Modern filter design: Active RC and switched capacitor -. IEEE Xplore Get PDF 68K - Wiley Online.
Design of analog filters : passive, active RC, and switched capacitor
Switched-capacitor SC filters have been researched extensively and the design techniques are well documented. These filters require linear capacitors and additional processing steps to realize floating capacitors beyond those needed for digital CMOS design. VLSI design of digital ICs usually cannot economically afford these additional processing steps if mixed signal design is needed. Moreover, with the advent of 3V logic ICs, the signal swings available from analog ICs will be smaller and as such, the dynamic range available will be directly affected. Further, the logic gate design demands lower threshold voltages affecting the switch performance in SC filters.
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This 1st-Order low pass type filter, consists simply of a passive RC filter connected to the input of an inverting operational amplifier. An engineer who wants to design a custom filter may have trouble obtaining precision inductive components and tuning the filter to a active and passive analog filter design solution manual pdf specific corner frequency requires considerable expertise. Advantages and dis-advantages with the existing Signal Processing Toolbox are.