A keen knowledge of filter designs requires years of study and contains more design variables than meet the eye. This introduction will provide basic concepts.
Many suppressor companies claim EMI/RFI filtering when in reality their products contain only an "X" or "Y" capacitor, or worse an unapproved device. Requirements for X and Y capacitors are found in the following documents: IEC 384-14, UL 1414 and CSA 22.2.
Class "X" capacitors are used where a short circuit in the capacitor will not cause a dangerous electrical shock hazard. They are rated X1 (most demanding in terms of peak voltage) and X2. This class is used in line to line or line to neutral installations.
Class "Y" capacitors are used where a short in the capacitor may cause electrical shock hazard. There are four sub classes. Y1 is the most rigorous, must endure an 8kV pulse, and is constructed with double insulation. These capacitors normally install between line and ground.
There are a large number of capacitor manufacturers who offer a line of X and Y capacitors. Our lab testing shows marked differences among manufacturers in dv/dt response time, actual value and consistency.
Effective filters for today's electronic circuits generally require more sophisticated filter designs than a simple capacitor.
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Filter Characteristics and Design
A filter may be considered to be a combination of capacitors, coils and resistors in a circuit that will impede or pass certain frequencies. |
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a) |
The "shape factor" of a filter is the ratio of its bandpass 60 dB down from the midband value to its bandpass 6 dB down. The steeper the skirts, the smaller the shape factor. (See figure 5) |
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When the inductive reactance (XL) in ohms of a coil equals the capacitance reactive (XC) in ohms of a capacitor in a circuit condition known as resonance occurs.
XL = XC or 2πfL = 1 / (2πfC)
Where
f = frequency in Hz
L
= Inductance in H
C = capacitance in Farads
Figure 6 shows a series resonant circuit and a parallel resonant circuit.
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Inductive reactance is directly proportional to frequency while capacitive reactance is inversely proportional. The frequency at which a coil and capacitor will resonate is found by the formula:
ƒ = 1 / (2π√LC)
At any frequency where the XL of a coil equals the XC of a capacitor, the secondary will appear as a low inpedance circuit to this frequency. Thus this one frequency produces significant current in the secondary. With high current flowing, relatively high amplitude voltage will be developed across the reactances.
In a parallel-resonant circuit, the same voltage is across both the coil and capacitor. However, current lags the source voltage by 90° in the coil and leads by 90° in the capacitor. Since the two currents are 180° out of phase, a "fly wheel effect" of currents occurs where current flowing down out of the coil must equal the current flowing into the capacitor. |
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c) |
A term often applied to inductor/capacitor circuits is " Q ". The symbol Q can be considered to mean Quality. A coil with no resistance or other losses would be a perfect inductor and would have an infinitely high Q. Since a coil without losses is impossible, the Q of a coil will always have some finite value. Q value of a coil is the ratio of reactance to resistance or
QL = XL / R = 2πfL / R
Where
R = resistance in Ohms
f = frequency in Hz
L = inductance in Henrys
At higher frequencies, however, electrons flowing in a wire or coil travel near the surface. This increased resistance, known as "skin effect", is one cause of a lower Q value in a coil. This effect can be reduced by: (using larger wire, silver plating the wire, using fewer turns while increasing core permeability or using "Litz" or multi stranded insulated wire.
Capacitors also have a Q value. The formula used for capacitors is
QC = XC / R = 1 / (2πfCR)
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d) |
In industrial measurement and control applications the most common requirement is for a "low-pass" filter. This filter passes low frequency AC or signals and attenuates or "strips off" high frequencies. A simple low pass filter consists of a coil and capacitor sized to provide "cutoff" at a desired frequency. (See the Constant -K Low pass filter in Figure 7 ). |
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This filter is called constant K because the product of XL times XC is constant at all frequencies. L and C falues may be computed using the formulas
L = R / (πƒC)
C = 1 / (πƒCR)
Where
L = inductance in Henrys
C = capacitance in Farads
R = Impedance, of both source and load in Ohms
ƒC = cut off frequency
Simple filter designs assume source and load impedances to be equal. In practice this is rarely the case and filter design must accommodate variations in source and load impedance.
The higher the Q of the reactances, the sharper the cutoff. For sharper cutoff more sections are used. A balanced constant-K low pass filter may be constructed as on Fig 15 above.
For a sharper cutoff than a constant-K filter provides, an M-derived filter may be used. The M may be considered to be a ratio of the cutoff frequency to the frequency of infinite attenuation (zero output). In a low pass filter, M will be between 0 and 1 in value. An M value of 1 will provide the same curve as a constant-K filter. (See Figures 8, 9) |
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Practical filters are made up in sections. There are three very basic configurations. Variations of these will be seen to accommodate source or load impedance matching as well as two line or multi-line applications. (See Figure 9 below) |
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Effective filter designs require consideration of a large number of variables and generally present a challenge even to veteran designers. Design calculations rarely exactly match actual derived designs due to losses, impedance imbalances manufacturer's variations and tolerances etc.
Veteran designers provide extensive testing under a variety of conditions in order to properly profile actual filter response. Understanding filter response to variations of source and load impedance is particularly important. |
