Manufacturing Concepts - Inductors - Assignment Example

Manufacturing Concepts (inductors) "0.72 mH" inductor of a two-way crossover 2nd order Butterworth An inductoris a passive electrical component usually a coil of wire which tends to oppose changes in electrical current. It stores energy in a magnetic field and generates a voltage which is directly proportional to its inductance L and change in current with time. Its inductance is rated in terms of henries (H). Physically the inductor can be viewed as having two major parts the winding and the core material. Its inductance is dependent on core size, material, shape, winding resistance and number of loops. The core material varies with the desired application of the inductor. A filter is one area where inductors are applied. According to Winder (1997), filters are used to control the output energy of a circuit at a given range of frequencies. This report will focus on a 0.72mH inductor used for a two-way, second order crossover Butterworth filter. The general design of this kind of a filter has inductors and capacitors in a ladder network as shown below.Fig 1:High pass and low pass 2nd order Butterworth 2-way crossover Filter (ApICSLLc 2011) The two circuits are coupled to form a 2-way crossover filter giving two outputs suitable for high and low frequency ranges as required in loudspeaker and tweeter scenario. The components in the filter can be calculated from the known impedance values of the speakers to be driven by the circuit and a known slope (6dB or 12dB per octave). In a 12dB crossover filter, we use these formulas: C = 1 / (2 * π * Z * d * f ) and L = ( Z * d ) / ( 2 * π * f ) Where C = capacitance in farads, L = inductance of the coil in Henrys, f = frequency in hertz, Z = (actual) impedance of the speaker in ohms and D=damping factor (1.414 for Butterworth) (Elliot, 2004). A typical inductor as used in the filter is as shown below: Fig. 2. a) Structure, (b) Equivalent circuit (University of Colorado, 2011) Using this design, certain product specifications have to be followed for it to operate effectively as follows: Inductance drop is a design concern in our filter as it may cause audible distortion. This is specified in percentages commonly 10% and 20% and is caused by bias current determined by the magnetic properties of the core (Vishay Intertechnology Inc, 2011). Magnetic flux density stored is dependent on the core and the space around it. When it goes beyond a certain maximum value it reduces the cores permeability causing a drop in inductance. Kuphaldt ( 2010), this applies to ferrite cores and powdered-iron cores but not air-cores By use of an air-core, core losses are eliminated leaving us with only conductor losses, usually copper losses. In such a case our inductor could be modeled to an equivalent RL circuit. Fig. 3. Equivalent Circuit of a real inductor (University of Colorado, 2011) The inductance L must be equal to the one specified in our case its 0.72mH or 720µ this is determined by the turns ratio core area and gap length. Using the figure 2 above inductance is given by L= n2/Rg= µo Ac n2/ lg where Ac is the core cross-sectional area, µo the permeability of air, lg the air gap length and n- Number of turns in the winding (University of Colorado, 2011) The winding resistance R should be in such a way that saturation doesn’t occur when the highest possible peak current is applied. This resistance is equivalent to the specified copper loss given by Pcu=Irms2R. The resistance of the winding usually specified in terms of its maximum rating and expressed in ohms must be kept at minimum to reduce power losses. To achieve this, the inductor should be wound with the highest possible gauge wire which could be heavy alternatively a small one with significant resistance could be used as far as it’s suitable to operate with. Taking the design shown in figure 2 above an whose equivalent circuit is as shown in part b two design specifications arise; Reluctance of the core given by Rc= lc /( µc Ac ) and the air-gap reluctance given by Rg= lg /( µ0 Ac ), these terms define the core, where lc represents its magnetic path length and µc its permeability. The magnetic property of the inductor is given by ni=Φ (Re+Rg) but Rg dominates Re . In general the inductor properties are determined by the size air gap (McLyman, 1988). Other specifications: Maximum flux density; this depends on the peak current through the winding which is supposed to be operated at maximum magnetic flux but at a lesser value than the one that would cause saturation in flux density. This property depends on the turns ratio n and air gap lg length as follows nImax=BmaxAcRg=bmaxlg/ µ0. Winding area; the area available for the coil to be wound through is called the window/winding area. This is determined by the conductor cross-sectional area (Aw) and the number of turns n. With the window area being given by WA and the window utilization factor/fill factor Ku, from these four factors mentioned here, the design should be in such a way that WA Ku≥ n Aw. The fill factor lies between 0 and 1 depending on conductor shape, winding technique and insulation. Low voltage inductors have a filling factor of about 0.5. Winding resistance: this is given by R= ρ lW /AW, symbols, ρ represents the resistivity of the conductor, lW its length and AW cross-sectional area. Copper is the most the commonly used material for this with a resistivity of 1.724x10-6 Ω-cm. the total winding length is given by the product of its Mean-Length-per-Turn (MLT) and the number of turns to give a resistance of, R= ρnMLT/AW where MLT is determined from the core design. Other specifications are: inductor must have a current rating (RMS current or DC current), which defines the maximum temperature rise that it will have at maximum ambient temperature. This defines the power losses that will be experienced in the inductor hence its heat dissipation in the windings. If for instance the filter is to be in a cabinet, the heat from the inductor will be of great concern hence it should be minimized by use of low resistance winding or a large inductor. Operation at high frequency may cause self resonance in the inductor (its distributed capacitance equates to its inductance) making it to be purely resistive, with the highest impedance at the SRF point .For a filter this may fall into its pass band (Elliot, 2004). Above the SRF frequencies the inductor impedance is capacitive and its Q factor is equal to zero which could completely change the operational mode of our filter. Self-Resonant-Frequency (MHz) is used to define of the inductor rating whose minimum should be way above the maximum frequency of operation. Additionally, the inductor’s distributed capacitance should be as low as possible for us to have a high SRF point. The magnetic flux density in the inductor can be affected by stray magnetic fields existing around it. This may be due to cross-coupling from other inductors, which can lead to unfavorable fluctuations in its inductance and hence audible distortion in the filter. The inductors in the circuit therefore should be shielded from such fields. One of the ways of achieving this is by mounting the inductors at right angles to each other and keeping them at a ‘safe distance’ from ferrous materials such as the loudspeaker coil. Materials used versus the design specification. To achieve the desired specifications suitable materials must be chosen. The ones used for the filter’s inductor are: Copper is used for the core winding material: this is because it has a low resistivity hence it gives a low winding resistance suitable for the inductor to prevent excessive heat dissipation (due to power loss) especially if the circuit is to be in a cabinet. It also allows a high current rating necessary to accommodate the peak winding current and it’s a good conductor of heat. The core material of this inductor should not only a platform for holding terminals in place just like any other, but also it has to observe the uniqueness of its application such as; it should have a relatively high inductance stability at specified temperatures of operation thus a low thermal coefficient of expansion is necessary and low core losses, high frequency operation as in the filter requires low inductance values hence high permeability is not required. A suitable material matching these design characteristics are the ceramic cores which give us the ceramic-core/ air-core inductor. Chosen Manufacturing Process To manufacture these inductors especially for the ladder network, accuracy is important and so is consistency. Traditionally the complete inductor would be manufactured at once, with raw materials being shaped by hand to give the desired characteristics. This posed the challenge of repeatability and consistency. To overcome it the patented Microfusion technology by GH group is used. Additionally, in this method since multiple systems run the same process, the time required to calibrate or perform maintenance practices is reduced (GH Induction Atmospheres, 2011). To ensure there is minimal mechanical noise which can be picked up by the amplifier. For this reason the coils are impregnated with a suitable varnish by dipping them into it for about an hour before draining and drying them. This report covers most of the specifications considered for an inductor to be used in a filter, a couple of issues have been neglected though, which include detailed insulation requirements, conductor eddy current losses, temperature rise in the filter, round off of number of turns, etc. Reference list: ApICSLLC 2011, Filter Design, Ohio, viewed 27 April 2011, < http://www.apicsllc.com/apics/Misc/filter2.htm> Elliot, R (2004), ‘Design of Passive Crossovers’, in Elliot Sound Products, viewed 27 April 2011, < http://sound.westhost.com/lr-passive.htm >. GH Induction Atmospheres 2011, Microfusion Technology, Inductive Heating, viewed 6 May 2011, < http://www.inductionatmospheres.com/induction- heating/microfusion.html >. Kuphaldt, T 2010, ‘Transformers’, in Lessons In Electric Circuits, viewed 5 May 2011, < http://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_9.html > McLyman, C. W. T.1988, ‘Transformer and Inductor Design Handbook’, 2nd edn., Marcel Dekker, Inc., New York, p.16-18. University of Colorado 2011, Filter Inductor Design, Department of Electrical, Computer, and Energy Engineering, viewed 5 May 2011, < ecee.colorado.edu/~ecen4517/materials/Inductor.pdf>. Vishay Intertechnology Inc 2011, Inductors101, USA, viewed 5 May 2011, < http://www.newark.com/pdfs/techarticles/vishay/Inductors101.pdf>. Winder, S 1997, ‘Analog and digital filter design’, 2nd edn, Newness, New York. Read More