FERRITE CORE INDUCTOR VALUE VARIATION WITH NUMBER OF TURNS AND DIAMETER OF COPPER WIRE,LENGTH AND DIAMETER OF CORE
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1 FERRITE CORE INDUCTOR VALUE VARIATION WITH NUMBER OF TURNS AND DIAMETER OF COPPER WIRE,LENGTH AND DIAMETER OF CORE PRJ. NO. 073 PRESENTED BY: OMWENGA EDWIN NYAKUNDI F17/8280/2004 SUPERVISOR : MR. OGABA EXAMINER: MR. DHARMADHIKARY
2 PRESENTATION OUTLINE OBJECTIVE DEFINATION OF TERMS APPLICATIONS OF FERRITE PROCEDURE RESULTS ANALYSIS CONCLUSION FUTURE WORK QUESTIONS
3 OBJECTIVE To perform experiments and derive equation for inductance variation with number of turns and diameter of copper wire, length and diameter of core.
4 DEFINATION OF TERMS Equations and units for B and H Inside magnetic materials the vector field quantities B, H are sometimes not parallel, so it is useful to represent the material contribution separately. In the SI system the equation for flux density is written as: Β= µ 0 (H+M) (1) Β= µ 0 Н + B i also written B = µ 0 Н+J (2) M = χh and also B i = µ 0 χh (3) B = µ 0 H (1 + χ) = µ 0 µ r H = µh (4)
5 During magnetization process energy barriers have to be overcome. Therefore the magnetization will always lag behind the field forming a hysteresis loop. B H Figure 1 representing hysteresis loop
6 PERMEABILITY The ratio of flux density and applied field is called absolute permeability. B/H = µ o (1 + M/H) = µ o µ r = µ absolute (5) Since there are several versions of µ r depending on conditions, the index r is generally removed and replaced by the applicable symbol for example: Initial permeability (µ i ) Effective permeability (µ e ) Amplitude permeability (µ a ) Incremental permeability (µ ) Complex permeability (µ' s, µ'' s or µ' p, µ'' p )
7 LOSS FACTOR tan δ m The loss factor (tan δ m /µ i ) is used to describe the magnetic losses: Hysteresis losses Eddy current losses Residual losses This gives the formula: tan δ m = tan δ h + tan δ f + tanδ r (6) frequency Figure 2
8 INDUCTIVE INTERACTION BETWEEN CONDUCTORS Currents flowing through conductors create magnetic fields (Ampere s Law) Magnetic fields varying with time create induced electric fields (Faraday s Law) Induced electric fields exert forces upon the electrons in the conductors and cause electric voltage (Electric Potential) drops.
9 FERRITES FOR TELECOMMUNICATIONS Most important applications are in: Filter inductors Pulse and matching transformers Other applications of ferrite are : Power conversion (S.M.P.S) Interference suppression
10 APPROXIMATION FORMULA FOR INDUCTANCE An approximation of inductance for any coil of wire can be found with this formula: L = N 2 µa/l c (7)
11 FACTORS THAT AFFECT INDUCTANCE Number of turns Diameter of core Length of core Diameter of wire
12 PROCEDURE An R L series connection V S = (V R 2 + V L 2 ) 1/2 (8) V R = I (R+r) (9) L = (V L /V R ) ((R+r)/ (2πf)) (10)
13 RESULTS A comparison of inductor value with variation on number of turns at 50 khz l c =0.82mm SWG= 19 D=6.11mm R=10(Ω) f=50 khz N r(ω) No. of V s (mv) V L (mv) V R (mv) I(mA) L(µH) layers
14 A comparison of inductor value with variation on diameter of wire at 50 khz l c = 32mm D=6.11mm R=10(Ω) f=50 khz, SWG d (mm) N r (Ω) V s (mv) V L (mv) V R (mv) I(mA) L(µH)
15 A comparison of inductor value with variation on length of core at 50 khz N=40 SWG= 19 D=6.11mm R=10(Ω) f=50 khz l c (mm) r (Ω) No of V s (mv) V L (mv) V R (mv) I(mA) L(µH) layers
16 A comparison of inductor value with variation on diameter core at 50 khz N=40 SWG= 19 l c =41.00mm R=10(Ω) f=50 khz D(mm) r (Ω) V s (mv) V L (mv) V R (mv) I(mA) L(µH)
17 ANALYSIS GRAPHS 90 A CURVE OF INDUCTANCE VALUE VERSUS NUMBER OF TURNS INDUCTANCE (µh) NUMBER OF TURNS
18 160 A CURVE OF INDUCTANCE VALUE VERSUS DIAMETER OF WIRE INDUCTANCE (µh) DIAMETER OF WIRE(m) x 10-4
19 100 A CURVE OF INDUCTANCE VALUE VERSUS LENGTH OF CORE INDUCTANCE (µh) LENGTH OF CORE (m)
20 80 A CURVE OF INDUCTANCE VALUE VERSUS DIAMETER OF CORE INDUCTANCE (µh) DIAMETER OF CORE(m) x 10-3
21 EQUATIONS Equation relating the inductance value with number of turns: L = x 10-9 N (11) Equation relating the inductance value with diameter of wire: L = x d (12) Equation relating the inductance value with length of core: L = x 10-7 l c (13) Equation relating the inductance value with diameter of core: L = x D (14)
22 Equation relating the inductance value with number of turns, diameter of wire, length of core and diameter of core is given as: L = (1.977 x N d l c D ) 1/4 (15)
23 CONCLUSION This chapter summarizes the major contributions of this work and identifies areas that merit future study. CONTRIBUTION An equation for ferrite core inductor value calculation is developed. The equation relates inductance to number of turns and diameter of copper wire, length and diameter of core. Since inductance vary with the stated parameters; graphs are available that relate the inductance with each parameter. FUTURE WORK The inductance of the ferrite core inductor will depend crucially on the following factors: The geometry of the magnetic core. The amount of air gap in the magnetic circuit. The properties of the core material (especially permeability and hysteresis). The operating temperature of the core. Whether the core is laminated to reduce eddy current. These parameters will provide a definite and more accurate formula for inductance for the ferrite core inductor.
24 QUESTIONS
25 END
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