Magnetics calculations for transformer designs.xls
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Magnetics Design Equations Field Strength Air Core Inductance H=(0.4*pi*N*Ip)/Le Lo=(4*pi*N^2*10^-9)/C1 H= 1.2566371 Oersted Lo= 1.256637E-08 N= 1 Number of turns N= 1 Number of tu Ip= 1A C1= 1 cm^-1 Le 1 cm Flux Density Number of turns B=(E*10^8)/(4.44*f*N*Ae) N=SQRT((L*10^9)/Al)) B= 4265.6293 Gauss N= 12 Number of tu E= 100 Volts(rms) L= 1 Henries f= 5.50E+05 Hertz Al= 2725 Inductance f N= 6 Number of turns Ae= 0.16 cm^2 Effective Core Parameters Effective Permeability C1=sum(L)/A cm^-1 ue=Le/(Le/ui+L) C1= 1 cm^-1 L 1 cm ue= 0.5 effective pe A 1 cm^2 Le= 1 Effective pa ui= 1 initial perm C2=sum(L)/A^2 cm^-3 L= 1 Air gap leng C2= 1 cm^-3 L= 1 cm A= 1 cm^2 Q factor Q=2*pi*f*Ls/Rs Le=C1^2/C2 cm Le= 1 cm Q= 6.2831853072 C1= 1 cm^-1 f= 1 Hertz C2= 1 cm^-3 Ls= 1 Henries Rs= 1 Ohms Ae=C1/C2 cm^2 Ae= 1 cm^2 Q= 0.1591549431 C1= 1 cm^-1 f= 1 Hertz C2= 1 cm^-3 Lp= 1 Henries Rp= 1 Ohms Ve=C1^3/C2^2 cm^3 Ve= 1 cm^3 C1= 1 cm^-1 C2= 1 cm^-3 Application Enter Core Material Properties Here =J RMS Load Pow Ae (cm^2) 0.243 Affective Area * E(volts) Ie (cm) 5.2 Magnetic Path Length Load impedan
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Interactive spreadsheet for transformer designs.
Transcript of Magnetics calculations for transformer designs.xls
Magnetics Design Equations
Field Strength Air Core InductanceH=(0.4*pi*N*Ip)/Le Lo=(4*pi*N^2*10^-9)/C1
H= 1.2566371 Oersted Lo= 1.256637E-08N= 1 Number of turns N= 1 Number of turnsIp= 1 A C1= 1 cm^-1Le 1 cm
Flux Density Number of turnsB=(E*10^8)/(4.44*f*N*Ae) N=SQRT((L*10^9)/Al))
B= 4265.6293 Gauss N= 12 Number of turnsE= 100 Volts(rms) L= 1 Henriesf= 5.50E+05 Hertz Al= 2725 Inductance factorN= 6 Number of turnsAe= 0.16 cm^2
Effective Core Parameters Effective PermeabilityC1=sum(L)/A cm^-1 ue=Le/(Le/ui+L)C1= 1 cm^-1L 1 cm ue= 0.5 effective permeabilityA 1 cm^2 Le= 1 Effective path length
ui= 1 initial permeabilityC2=sum(L)/A^2 cm^-3 L= 1 Air gap lengthC2= 1 cm^-3L= 1 cm A= 1 cm^2 Q factor
Q=2*pi*f*Ls/RsLe=C1^2/C2 cmLe= 1 cm Q= 6.2831853072C1= 1 cm^-1 f= 1 HertzC2= 1 cm^-3 Ls= 1 Henries
Rs= 1 OhmsAe=C1/C2 cm^2Ae= 1 cm^2 Q= 0.1591549431C1= 1 cm^-1 f= 1 HertzC2= 1 cm^-3 Lp= 1 Henries
Rp= 1 OhmsVe=C1^3/C2^2 cm^3Ve= 1 cm^3C1= 1 cm^-1C2= 1 cm^-3
Application ConsiderationsEnter Core Material Properties Here =J RMS Load PowerAe (cm^2) 0.243 Affective Area * E(volts)Ie (cm) 5.2 Magnetic Path Length Load impedance
Al (nH/N^2) 1175 Nanohenries/Turn^2 * Lowest Operating FrequencyBsat 2800 Saturation Flux density for material chosen Highest Operating FrequencyHsat 12.6 Saturation Flux intensity for material chosen Midband Frequency
Peak currentPeak voltage
Flux Density Saturation Test Loss calculationsBpeak 2531.0576 Gauss Low Frequency Loss
Mid Band LossFlux intensity Saturation Test * dc current High Frequency LossHpeak 11.377257
Original spreadsheet work by Fabian Hartery, B.Eng
For the design of transformer magnetics and core selection as derived fromFair-Rite Soft Ferrites Data BookDexter Magneticshttp://www.fair-rite.com/newfair/pdf/Fair-Rite_Catalog_16th_Edition_Rev_03_2012.pdf
InductanceL=N^2/Al
L= 0.0132110092 HenriesN= 6 Number of turnsAl= 2725 Inductance factor
L=10^-9*ui*((4*pi*N^2)/C1)
L= 0.0090477868 Henriesui= 5000 initial permeabilityN= 12 Number of turnsC1= 1 cm^-1
L=10^-9*ui*((4*pi*N^2)/C1) Henries
L= 1.256637E-08 Henriesue= 1 effective permeabilityN= 1 Number of turnsC1= 1 cm^-1
AttenuationLoss=20log(abs(Zs+Zl+Zsc)/Zs+Zl) dB
Loss= 3.5218251811 dBZs= 1 OhmsZl= 1 OhmsZsc= 1 Ohms
Application Considerations500 watts
158.11388301 Vrms Shunt inductance to load ratio 9 ratio Wire gauge resistance50 ohms Suggested shunt inductance 1.30E-04 Henries
Lowest Operating Frequency 550000 Hertz Number of turns= 1.05273E+01Highest Operating Frequency 750000 Hertz Expected pri resistance 1 ohms
650000 Hertx Expected sec winding resistance 0.25 ohms4.472135955 amps
223.60679775 4.00E-04
0.053288 dB *determined by shunt inductance0.107901 dB *determined by winding resistance when loss of shunt inductance is neglible
*determined by leakage losses
Wire gauge resistance
