SMPS switch mode power supply design spreadsheet

AC/DC Power supply design - 3Phase, 8.1kW

Version:	3g	2003			Project "Raptor"

	PFC	Calculates Boost PFC main components, voltages and currents.
	PFC_Ind	Calculates Boost inductor, number of turns, core and copper loss.
	DC_DC	Calculates Power Transformer turn ratio, output ind. value, etc.
	PWR_Tr	Calculates Power Transformer no. of turns, core and copper loss.
	Out_Ind	Calculates Output Inductor number of turns, core and copper loss.
	Losses	Calculates losses for all stages, max. case temp., efficiency, etc.
	PFC_Loops	Calculates the values for current and voltage loops.
	DC_DC_Loops	Estimates the compensation network for DC/DC stage.
	Other	Estimates parameters for other inductors, bas bars, shunts
	Sat_Ind	Calculates a magnetic snubber.
	Ind	Calculates a generic inductance.
	Ind_K	Calculates the coupling coefficients for a Spice model.


This Excel spreadsheet file contains design calculation for a SMPS with the following specifications:

	Pout=		8,100	W	(3 kW to 15 kW)
	Vin=		180-264	Vac	(176 to 456 Vac)
	Voutn=		54.00	Vdc	(12 to 360 Vdc)
	Ioutn=		150	A	(10 to 800 A)
	Switching Frequencies:	PFC=	120	kHz	(25 to 200 kHz)
		DC/DC=	140	kHz	(50 to 500 kHz)

Input data can be changed to design a similar power supply.

Nominal Conditions:
	1	Nominal AC Input Voltage
	2	25°C Ambient Temperature
	3	Full Power (Nominal DC Output Voltage x Nominal Output Current)


In BLUE color are data that you MUST ENTER.

In PINK color are data that are calculated by the spreadsheet, or copied from another page. DO NOT
MODIFY DATA IN PINK COLOR.

In RED color are data calculated by the spreadsheet. DO NOT MODIFY DATA IN RED COLOR.

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Power Factor Cerrection design

Input data	Vinm=		Vrms	Minimum AC Input Line Voltage
	Vinn=		Vrms	Nominal AC Input Line Voltage
	Vinx=		Vrms	Maximum AC Input Line Voltage
	fpfc=		kHz	PFC Switching Frequency
	fline=		Hz	Line Frequency
	PF=			Estimated Input Power Factor @ Full Load
	Ppfcn=	8,709	W	Nominal Output Power, PFC Stage
	Vidb=	1.13	V	Voltage drop, one diode Input Bridge @ Iinnpk
	Vidb=		V	Voltage drop, one diode Input Bridge @ Iinnpk	copy from above cell
	Effpfcn=	97.49	%	Nominal PFC Efficiency
	Effpfc=		%	PFC Efficiency, initial estimation	copy from above cell
	dth=		ms	Hold-Up Time, average @ nominal conditions
	Irpfc=		%	Boost Ind max pk to pk ripple current	from Iravgx
	dV=		V	Average DC Boost Voltage above the line pk
	Ddcn=	88.12	%	Nominal DC/DC Stage Duty Cycle
	Ddcx=	93.06	%	Max available DC/DC Stage Duty Cycle

Intermediate	Vinfm=	103.9	Vrms	Minimum AC Input Phase Voltage
data	Vinfn=	138.6	Vrms	Nominal AC Input Phase Voltage
	Vinfx=	152.4	Vrms	Maximum AC Input Phase Voltage
	Vrdcm=	220.5	V	Low line dip rectified voltage
	Vrdcx=	373.4	V	High line peak rectified voltage
	Vravgm=	240.8	V	Low line avg rectified voltage
	Vravgn=	321.9	V	Nominal line avg rectified voltage
	Vravgx=	354.3	V	High line avg rectified voltage
	Dpfcx=	0.4082		Max avg PFC Duty Cycle
	Dpfcn=	0.2091		Nom avg PFC Duty Cycle
	Irpkx=	38.84	Apk	Low line peak rectified current
	Irpkn=	29.06	Apk	Nominal line peak rectified current
	Ibclf+=	1.89	A	Boost Capacitor, 6xfline, peak charging current
	Ibclf-=	3.46	A	Boost Capacitor, 6xfline, peak discharging current

Output data	Vba=	407.0	Vdc	Average Boost Voltage, 90% Load
	Vbm=	406.6	Vdc	Minimum Boost Voltage
	Iba=	21.40	A	Average PFC output current
	Lbc=	56.34	µH	PFC Boost Inductor, calculated
	Lb=		µH	PFC Boost Inductor, chosen
	Cbc=	2,346	µF	Boost Capacitor, min for the required hold-up time
	Cb=		µF	Boost Capacitor, chosen	0.98204
	Iinx=	30.11	Arms	Max rms Input Phase Current @ low line
	Iinn=	22.58	Arms	Nom rms Input Phase Current @ nominal line
	Iinm=	20.53	Arms	Min rms Input Phase Current @ high line
	Iravgx=	37.09	Aavg	Max avg rectified current
	Iravgn=	27.75	Aavg	Nom avg rectified current
	Iravgm=	25.21	Aavg	Min avg rectified current
	Ibpkx=	44.41	Apk	Boost Ind, Switch and Diode max avg pk current
	Ibpkn=	32.76	Apk	Boost Ind, Switch and Diode nom avg pk current
	Ibpkm=	27.33	Apk	Boost Ind, Switch and Diode min avg pk current
	Iblppx=	14.63	App	Boost Ind max pk to pk ripple current
	Iblppn=	10.02	App	Boost Ind. nom pk to pk ripple current

	Iblacx=	4.22	Arms	Boost Ind max avgd rms ripple current
	Iblacn=	2.89	Arms	Boost Ind nom avgd rms ripple current

	Ibswx=	23.9	Arms	Switch avg rms current at low line
	Ibswn=	12.76	Arms	Switch avg rms current at nominal line

	Ibdx=	28.72	Arms	Boost Diode avg rms current at low line
	Ibdn=	24.82	Arms	Boost Diode avg rms current at nominal line

	Vbpp=	0.63	Vpp	Boost Voltage ripple, peak to peak, full load
	Ibclf=	1.69	Arms	Boost Capacitor, 6xfline, ripple current
	Ibchfx=	18.53	Arms	Boost Capacitor, max HF ripple current
	Ibchfn=	11.59	Arms	Boost Capacitor, nom HF ripple current

	Ibctx=	18.60	Arms	Boost Capacitor, max total ripple current
	Ibctn=	11.71	Arms	Boost Capacitor, nom total ripple current



Electrolytic capacitors are ±20% nominal tolerance, and considered to have -10% "REAL" capacitance

PFC Inductor design

Input data	Lb=	56.0	uH	Inductance
	Ibpkx=	44.4	Apk	Inductor maximum peak current
	Ibppx=	14.6	App	Max peak to peak current
	Iravgn=	27.8	Aavg	Nom avg rectified current
	Iblacn=	2.9	Arms	Boost Ind nom avgd rms ripple current
	fpfc=	120	kHz	PFC Switching Frequency
	Icd=		A/mm²	Current density
	Smp=		mm	Safety margin, Pri/HF winding, mm
	Sms=		mm	Safety margin, Sec/LF winding, mm
	Whm=		mm	Min winding height, mm
	Wwm=		mm	Min winding width, mm
	Ht=		mm	Core height or "C" dimension
	Ltm=		mm	Min turn length
	le=		mm	Magnetic path length
	Ae=		mm²	Magnetic core area, effective
	Am=		mm²	Magnetic core area, minimum
	Vm=		mm³	Magnetic volume
	ur=			u, ungapped core, no DC bias
	Bmax=		T	Maximum flux density @130°C
	uh=		%	Permeability @ Hpk
	ncpfc=			Number of core sets

Intermediate	Ltm=	88.5	mm	Min turn length, ncpfc sets
data	Ltn=	122.5	mm	Average turn length, ncpfc sets
	Aet=	350	mm²	Magnetic core area, effective, ncpfc sets
	Amt=	346	mm²	Magnetic core area, minimum, ncpfc sets
	Vmt=	43,100	mm³	Magnetic volume, ncpfc sets
	Vc=	31,089	mm³	Copper volume
	Vt=	74,189	mm³	Total inductor volume
	ALc=	11.1	nH/T²	AL, coil only
	ALo=	143.0	nH/T²	AL, ungapped core, no DC bias, one set
	ALot=	143.0	nH/T²	AL, ungapped core, no DC bias, ncpfc sets
	AL=	97.3	nH/T²	AL, ungapped core, bias @ Hpk, ncpfc sets
	ALg=	97.2	nH/T²	Required core AL, gapped, bias @ Hpk
	L0=	6.38	uH	Inductance, no cores
	Lb0=	88.77	uH	Zero bias inductance, no gap, test value

Output data	Nbmin=	7.2		Minimum Number of turns
	Nb=			Number of turns, chosen	> 1.2 x Nbmin
	Bpk=	0.30	T	Actual peak flux density	OK
	Gap0=	0.00	mm	Core gap, no fringe effect
	Gap=	0.00	mm	Core gap, closer to real
	dBpk=	49	mT	Half of max B peak to peak variation
	Hpksi=	7,237	A/m	Magnetizing Force, SI
	Hpku=	91	Oe	Magnetizing Force, USA


	PFC Inductor Core Loss

Intermediate	P3=	16	mW/cm³	Philips Ferrite 3F3 material
data	Pml=	130	mW/cm³	Allied Signal MicroLite 245 material
	Pm60=	109	mW/cm³	Magnetics MPP 60u material
	Pm125=	191	mW/cm³	Magnetics MPP 125u material
	Pk=	264	mW/cm³	Magnetics Kool-Mu material
	Ppl=	326	mW/cm³	Allied Signal PowerLite material
	Phf=	540	mW/cm³	Magnetics High Flux 60u material
	P18=	931	mW/cm³	Micrometals Iron Powder 18 material
	Rthm=	5.53	°C/W	Rth, toroid, open wound, natural convection

Output data	P3=	0.7	W	3F3
	Pml=	5.6	W	MicroLite 245
	Pm60=	4.7	W	MPP 60u
	Pm125=	8.2	W	MPP 125u
	Pk=	11.4	W	Kool-Mu
	Ppl=	14.1	W	PowerLite
	Phf=	23.3	W	High Flux 60u
	P18=	40.1	W	Iron Powder 18
	dT3=	4	°C	Core Temperature Rise, 3F3
	dTml=	31	°C	Core Temperature Rise, MicroLite 245
	dTm60=	26	°C	Core Temperature Rise, MPP 60u
	dTm125=	46	°C	Core Temperature Rise, MPP 125u
	dTk=	63	°C	Core Temperature Rise, Kool-Mu
	dTpl=	78	°C	Core Temperature Rise, PowerLite
	dThf=	129	°C	Core Temperature Rise, High Flux 60u
	dT18=	222	°C	Core Temperature Rise, Iron Powder 18


	PFC Inductor Copper Loss

Intermediate	Dpenm=	0.230	mm	Penetration depth, mm
data	Dpen=	9.0	mil	Penetration depth, mil
	Sml=	84	mil	Safety margin, LF winding, mil
	Smh=	84	mil	Safety margin, HF winding, mil
	Ww=	1.319	inch	Winding width, available
	Ltl=	4.823	inch	Average turn length, LF winding
	Lth=	4.823	inch	Average turn length, HF winding
	Wal=	1.150	inch	Winding width, LF winding
	Waf=	1.150	inch	Winding width, HF winding
	Dlf1=	6.2	mil	Thickness, LF winding (required by current density)
	Dlfc=		mil	Thickness, LF, chosen
	Dlf2=	10.9	mil	Thickness, LF winding (winding height limited)
	Alf=	5.20	mm²	Cross section area, LF winding
	Dhf=	1.218	mm	Diameter, HF winding wire	x 1
	Dhfc=	0.178	mm	Diameter, HF winding wire, chosen
	Ahfc=	5.195	mm²	Cross section area, HF winding, chosen
	Qs=	0.77		Layer thickness/penetration depth, HF winding
	Pb=	24.0		Number of layers per winding portion
	Frb=	23.65		Rac/Rdc ratio, HF winding
	Tc=		°C	Actual copper temperature

Output data	Pbicrl=	11.4	W	Core Power Loss, Kool-Mu
	Pgap=		W	Gap related loss
	Rdclf=	17.30	mOhm	DC resistance, low frequency winding
	Rdchf=	14.14	mOhm	DC resistance, high frequency winding
	Rachf=	354.4	mOhm	AC resistance, high frequency winding
	Pbilfl=	13.3	W	Low frequency winding copper loss
	Pbihfl=	3.0	W	High frequency winding copper loss
	Pbitcpl=	16.3	W	Total Copper Loss
	Pbitl=	27.7	W	Inductor total loss
	Rth=	4.1	°C/W	Rth, toroid, open wound, natural convection
	dT3=	114	°C	Temperature Rise, natural convection	For comparison only !


We suggest using class H(180°C) for Power Magnetics (Boost Inductor, Power Transformer
and Output Inductor).

The operating core temperature is assumed to be 100°C for core loss calculation.
Minimum loss would be at 80-90°C.
Maximum core operating temperature should be <160°C (Tc=200°C-40°C margin).

The accuracy of the formulas for core loss is expected to be ±10%.
The accuracy of the formulas for temperature rise is expected to be ±30%.

Temperature rise is for natural convection cooling.
For forced (fan) cooling the temperature rise could be 1/2 to 1/3, depending on airflow.

DC/DC Converter design

Input data	Vba=	407	Vdc	Average Boost Voltage
	Vbm=	407	Vdc	Minimum Boost Voltage
	Iba=	21.4	A	Average PFC output current
	fdc=		kHz	Switching Frequency, DC/DC Converter
	Voutn=		Vdc	Nominal DC Output Voltage
	Voutx=	59.400	Vdc	Maximum DC Output Voltage
	Ioutn=		Adc	Nominal Output Current
	Ioutx=	165.00	Adc	Maximum Output Current
	Ddch=		%	Duty Cycle head-room @ Maximum Output Voltage
	Dicx=		%	Max available PWM IC Duty Cycle	Due to PWM IC
	Effdc=	93.48	%	DC/DC Efficiency
	Effdc=		%	DC/DC Efficiency, initial estimation	copy from above cell
	Irdc=		%	Ripple Current, Output Ind., Nom. Output, pk-pk, % from avg
	Im=		%	Magnetizing current, primary, pk-pk, max, % from avg
	tsw=		ns	Voltage Rise and Fall times for bridge switches
	Rdson=	0.152	Ohm	Actual MOSFET(s) Rds ON
	Coer=	595	pF	MOSFET output capacitance @ Vba
	VF=	1.71	V	Diode(s) forward voltage at operating current
	Vrpn=		mVrms	Output Maximum Ripple Voltage, Nominal Output
	Ilss=		%	Minimum load for Soft Switch
	kp=			1 for Hard Switching, 2 for Phase Shift
	ks=			1 for Center Tap, 2 for Current Doubler
	N=	0.1667		Actual Secondary to Primary Turn Ratio

Intermediate	Pomax=	8,100	W	Maximum Output Power, DC/DC Stage
data	tdc=	7.14	us	Switching Period, DC/DC Converter
	Iavg=	25.0	A	Average primary current
	Irdcpk=	3.9	A	Primary pk-pk ripple current reflected from sec.
	Impk=	7.4	A	Primary pk-pk magnetizing current
	Idppx=	11.3	App	Primary total pk-pk current
	Itpk=	30.6	A	Peak Current Bridge Switch
	Ibchfx=	8.7	Arms	DC input Capacitor, max HF ripple current
	Vt=	3.79	V	Average Voltage drop, Bridge Switches @ Nominal Output
	Ddcx1=	97.4	%	Maximum Available Duty Cycle	Due to dV/dt + IC
	Nm=	0.1654		Minimum Secondary to Primary Turn Ratio
	Ilopk=	161.6	Apk	Output Inductor Peak Current
	Ilopp=	23.1	App	Output Inductor Ripple, Peak to Peak
	Irpr=	6.7	Arms	Output Inductor Ripple, RMS


Output data	Iprrms=	25.2	Arms	RMS Current, Transformer Primary
	Iscrms=	75.1	Arms	RMS Current, Transformer Secondary	Eq. end to end - Idc
	Loc=	1.40	uH	Output Inductor, calculated
	Lo=		uH	Output Inductor, chosen
	Comin=	758	uF	Minimum Output Capacitor (Zero ESR)
	C401=	2,952	uF	Output Capacitor(s), chosen
	Resrx=	0.7	mOhm	Maximum Output Capacitor ESR (Infinite capacitance)
	ESR1=	9.3	mOhm	Output Capacitor(s) ESR, chosen
	RLoad=	0.360	Ohm	Load Resistance
	Vrp2=	60.5	mVrms	Output ripple voltage, first stage filter
	Attn2m=	12.1		Required second stage filter attenuation
	Llkg=	1.34	uH	Leakage inductance for soft switch
	tdlk=	154.9	ns	Dead time due to leakage inductance
	Ddcn=	88.12	%	Nominal DC/DC Stage Duty Cycle
	Ddcx=	93.06	%	Max available DC/DC Stage Duty Cycle	Due to dV/dt & Llkg

High Frequency Power Transformer design

Input data	Nm=	0.165		Minimum Secondary to Primary Turn Ratio
	Vbn=	407	Vdc	Nominal Average DC Boost Voltage
	Vbx=		Vdc	Maximum Boost Voltage
	Vt=	3.79	V	Max voltage drop, Bridge Switches
	fdc=	140	kHz	Switching Frequency, DC/DC Converter
	tdc=	7.14	us	Switching Period, DC/DC Converter
	Impk=	7.4	A	Peak magnetizing current
	Ddcn=	88.1	%	Nominal DC/DC Stage Duty Cycle
	Iprrms=	25.2	Arms	RMS Current, Transformer Primary
	Iscrms=	75.1	Arms	RMS Current, Transformer Secondary	Eq. end to end - Idc
	Ioutn=	150.00	Adc	Nominal Output Current
	ks=	1		1 for Center Tap, 2 for Current Doubler
	Icd=		A/mm²	Current density
	Smp=		mm	Safety margin, Pri/HF winding, mm
	Sms=		mm	Safety margin, Sec/LF winding, mm
	Whm=		mm	Min winding height, mm
	Wwm=		mm	Min winding width, mm
	Ht=		mm	Core height or "C" dimension
	Ltm=		mm	Min turn length
	le=		mm	Magnetic path length
	Ae=		mm²	Magnetic core area, effective
	Am=		mm²	Magnetic core area, minimum
	Vm=		mm³	Magnetic volume
	ur=			u, ungapped core, no DC bias
	Bmax=		T	Maximum flux density @130°C
	uh=		%	Permeability @ Hpk
	nctr=			Number of core sets

Intermediate	Ltm=	95.5	mm	Min turn length, nctr sets
data	Ltn=	122.9	mm	Average turn length, nctr sets
	Aet=	420	mm²	Magnetic core area, effective, nctr sets
	Amt=	411	mm²	Magnetic core area, minimum, nctr sets
	Vmt=	52,000	mm³	Magnetic volume, nctr sets
	Vc=	33,487	mm³	Copper volume
	Vt=	85,487	mm³	Total transformer volume
	ALc=	11.9	nH/T²	AL, primary coil only
	ALo=	7,724	nH/T²	AL, ungapped core, no DC bias
	ALot=	7,724	nH/T²	AL, ungapped core, no DC bias, nctr sets
	Llk=		uH	Primary leakage inductance
	Cpri=		pF	Primary capacitance

Output data	Npmin=	6.5		Minimum Number of turns, Primary
	Np=			Primary Number of turns, chosen	> 2 x Npmin
	Nsc=	2.0		Secondary Number of turns, calculated
	Ns=			Secondary Number of turns, chosen	2 x Ns end to end
	Bpk=	0.13	T	Actual peak flux density, steady state	OK
	kw=			1 for 4 portions, 2 for 8 portions	8 winding portions
	N=	0.1667		Actual Secondary to Primary Turn Ratio
	Lm=	170	uH	Magnetizing inductance
	Idcpk=	5.0	A	Maximum DC current
	AL=	1,179	nH/T²	Core Al, ungapped, bias @ Hpk
	Gap0=	0.19	mm	Core gap, no fringe effect	x 2
	Gap=	0.21	mm	Core gap, closer to real
	dB=	127	mT	Half of B peak to peak variation


	Power Transformer Loss

Intermediate	Pcld=	209	mW/cm³	Philips Ferrite 3F3 material
data	Dpenm=	0.213	mm	Penetration depth, mm
	Dpen=	8.4	mil	Penetration depth, mil
	Smp=	147	mil	Safety margin primary, mil
	Sms=	122	mil	Safety margin secondary, mil
	Ww=	1.319	inch	Winding width, available
	Ltn=	4.840	inch	Average turn length
	Wp=	1.025	inch	Primary winding width
	kfr=			1 for copper foil, 2 for round wire
	Cs=		mil	Copper foil thickness
	Dp=	6.4	mil	Thickness, primary (required by current density)

	Dpc=	5.0	mil	Thickness, primary, chosen
	Qp=	0.60		Layer thickness/depth penetration, primary
	Pp=	3.0		Number of layers per winding portion, primary
	Frp=	1.12		Rac/Rdc ratio, primary
	Ap=	3.3	mm²	Cross section area, primary
	Ws=	1.075	inch	Secondary winding width
	Ds=	18.0	mil	Thickness, secondary (required by current density)
	Dsc=		mil	Thickness, secondary, chosen
	Qs=	2.39		Layer thickness/depth penetration, secondary
	Pbs=	1.0		Number of layers per winding portion, secondary
	Frs=	2.35		Rac/Rdc ratio, secondary
	As=	13.9	mm²	Cross section area, secondary
	Wff=	80.7	%	Winding height, fill factor
	Tc=		°C	Actual copper temperature

Output data	Ptcrl=	10.9	W	Core Power Loss, 3F3
	Pgap=		W	Gap related loss
	Rdcp=	11.1	mOhm	DC Primary resistance
	Racp=	12.5	mOhm	AC Primary resistance
	Rdcs=	0.9	mOhm	DC Secondary resistance	end to end
	Racs=	2.1	mOhm	AC Secondary resistance
	Ptpl=	8.0	W	Primary copper loss
	Ptsl=	16.7	W	Secondary copper loss
	Ttcu=	24.7	W	Total Copper loss
	Pttl=	35.6	W	Power Transformer total loss
	Rth=	3.8	°C/W	Rth, toroid, open wound, natural convection
	dT3=	136	°C	Core Temperature Rise, 3F3


The coupling coefficient between primary and secondary is assumed to be 1.

We suggest using class H(180°C) for Power Magnetics (Boost Inductor, Power Transformer
and Output Inductor).

For ferrites cores (Philips 3F3, Magnetics R, Siemens N87):
Guaranteed Curie temperature: 200°C.
Saturation flux density: 0.33@100°C, 0.30@130°C, 0.27@160°C.
The operating core temperature is assumed to be 100°C for core loss calculation.
Minimum loss would be at 80-90°C.
Maximum core operating temperature should be <160°C (Tc=200°C-40°C margin).

The accuracy of the formulas for core loss is expected to be ±10%.
The accuracy of the formulas for temperature rise is expected to be ±30%.

Temperature rise is for natural convection cooling.
For forced (fan) cooling the temperature rise could be 1/2 to 1/3, depending on airflow.

Output Inductor design

Input data	Lo=	1.43	uH	Inductance
	Iopkx=	161.6	Apk	Inductor maximum peak current
	Ioppx=	23.1	App	Max peak to peak current
	Iodcx=	150.0	Aavg	Max avg current
	Ioacx=	6.7	Arms	Max AC rms ripple current
	fdc=	280	kHz	Frequency for B variation
	Icd=		A/mm²	Current density
	Smp=		mm	Safety margin, Pri/HF winding, mm
	Sms=		mm	Safety margin, Sec/LF winding, mm
	Whm=		mm	Min winding height, mm
	Wwm=		mm	Min winding width, mm
	Ht=		mm	Core height or "C" dimension
	Ltm=		mm	Min turn length
	le=		mm	Magnetic path length
	Ae=		mm²	Magnetic core area, effective
	Am=		mm²	Magnetic core area, minimum
	Vm=		mm³	Magnetic volume
	ur=			u, ungapped core, no DC bias
	Bmax=		T	Maximum flux density
	uh=		%	Permeability @ Hpk
	ncoin=			Number of core sets

Intermediate	Ltm=	75.5	mm	Min turn length, ncoin sets
data	Ltn=	103.9	mm	Average turn length, ncoin sets
	Aet=	237	mm²	Magnetic core area, effective, ncoin sets
	Amt=	237	mm²	Magnetic core area, minimum, ncoin sets
	Vmt=	23,300	mm³	Magnetic volume, ncoin sets
	Vc=	16,675	mm³	Copper volume
	Vt=	39,975	mm³	Total inductor volume
	ALc=	10.9	nH/T²	AL, coil only
	ALo=	121	nH/T²	AL, ungapped core, no DC bias, one set
	ALot=	121	nH/T²	AL, ungapped core, no DC bias, ncoin sets
	AL=	89	nH/T²	AL, ungapped core, bias @ Hpk, ncoin sets
	ALg=	89.4	nH/T²	Required core AL, gapped, bias @ Hpk
	L0=	0.17	uH	Inductance, no cores
	Lo0=	2.11	uH	Zero bias inductance, no gap, test value

Output data	Nbmin=	1.0		Minimum Number of turns
	Nb=			Number of turns, chosen	> 1.2 x Nbmin
	Bpk=	0.24	T	Actual peak flux density	OK
	Gap0=	0.00	mm	Core gap, no fringe effect
	Gap=	0.00	mm	Core gap, closer to real
	dBpk=	17	mT	Half of max B peak to peak variation
	Hpksi=	6,098	A/m	Magnetizing Force, SI
	Hpku=	77	Oe	Magnetizing Force, USA


	Output Inductor Core Loss

Intermediate	P3=	5	mW/cm³	Philips Ferrite 3F3 material
data	Pml=	22	mW/cm³	Allied Signal MicroLite 245 material
	Pm60=	35	mW/cm³	Magnetics MPP 60u material
	Pm125=	57	mW/cm³	Magnetics MPP 125u material
	Pk=	114	mW/cm³	Magnetics Kool-Mu material
	Ppl=	190	mW/cm³	Allied Signal PowerLite material
	Phf=	107	mW/cm³	Magnetics High Flux 60u material
	P18=	258	mW/cm³	Micrometals Iron Powder 18 material
	Rthm=	7.7	°C/W	Rth, toroid, open wound, natural convection

Output data	P3=	0.1	W	3F3
	Pml=	0.5	W	MicroLite 245
	Pm60=	0.8	W	MPP 60u
	Pm125=	1.3	W	MPP 125u
	Pk=	2.6	W	Kool-Mu
	Ppl=	4.4	W	PowerLite
	Phf=	2.5	W	High Flux 60u
	P18=	6.0	W	Iron Powder 18
	dT3=	1	°C	Core Temperature Rise, 3F3
	dTml=	4	°C	Core Temperature Rise, MicroLite 245
	dTm60=	6	°C	Core Temperature Rise, MPP 60u
	dTm125=	10	°C	Core Temperature Rise, MPP 125u
	dTk=	20	°C	Core Temperature Rise, Kool-Mu
	dTpl=	34	°C	Core Temperature Rise, PowerLite
	dThf=	19	°C	Core Temperature Rise, High Flux 60
	dT18=	46	°C	Core Temperature Rise, Iron Powder 18


	Output Inductor Copper Loss

Intermediate	Dpenm=	0.150	mm	Penetration depth, mm
data	Dpen=	5.9	mil	Penetration depth, mil
	Sml=	52	mil	Safety margin, LF winding, mil
	Smh=	52	mil	Safety margin, HF winding, mil
	Ww=	1.004	inch	Winding width, available
	Ltl=	4.091	inch	Average turn length, LF winding
	Lth=	4.091	inch	Average turn length, HF winding
	Wal=	0.900	inch	Winding width, LF winding
	Waf=	0.900	inch	Winding width, HF winding
	Dlf1=	43.1	mil	Thickness, LF winding (required by current density)
	Dlfc=		mil	Thickness, LF, chosen
	Dlf2=	66.9	mil	Thickness, LF winding (winding height limited)
	Alf=	34.84	mm²	Cross section area, LF winding
	Dhf=	5.715	mm	Diameter, HF winding wire	x 1
	Dhfc=	1.524	mm	Diameter, HF winding wire, chosen
	Ahfc=	34.84	mm²	Cross section area, HF winding, chosen
	Qs=	10.14		Layer thickness/penetration depth, HF winding
	Po=	4.0		Number of layers per winding portion
	Fro=	111.51		Rac/Rdc ratio, HF winding
	Tc=	125.0	°C	Actual copper temperature

Output data	Poicrl=	2.6	W	Core Power Loss, Kool-Mu
	Pgap=		W	Gap related loss
	Rdclf=	0.3	mOhm	DC resistance, low frequency winding
	Rdchf=	0.3	mOhm	DC resistance, high frequency winding
	Rachf=	33.2	mOhm	AC resistance, high frequency winding
	Poilfl=	6.7	W	Low frequency winding copper loss
	Poihfl=	1.5	W	High frequency winding copper loss
	Poitcpl=	8.2	W	Total Copper Loss
	Poitl=	10.8	W	Inductor total loss
	Rth=	5.8	°C/W	Rth, toroid, open wound, natural convection
	dT3=	62	°C	Temperature Rise, natural convection	For comparison only !


We suggest using class H(180°C) for Power Magnetics (Boost Inductor, Power Transformer
and Output Inductor).

The operating core temperature is assumed to be 100°C for core loss calculation.
Minimum loss would be at 80-90°C.
Maximum core operating temperature should be <160°C (Tc=200°C-40°C margin).

The accuracy of the formulas for core loss is expected to be ±10%.
The accuracy of the formulas for temperature rise is expected to be ±30%.

Temperature rise is for natural convection cooling.
For forced (fan) cooling the temperature rise could be 1/2 to 1/3, depending on airflow.

Pwer Supply Losses calculations

Input data	Vinn=	240.0	Vrms	Nom AC Input Line Voltage
	Iinn=	22.58	Arms	Nom rms Input Phase Current @ nom line
	Irpkn=	29.06	Apk	Nom line peak rectified current
	Iravgn=	27.75	Aavg	Nom avg rectified current
	Ibpkn=	32.76	Apk	Boost Ind, Switch and Diode nom avg pk current
	Ibacn=	2.89	Arms	Boost Ind ripple nom rms current
	PF=	0.9517		Estimated Input Power Factor @ Full Load
	Voutn=	54.00	Vdc	Nominal DC Output Voltage
	Ioutn=	150.00	Adc	Nominal Output Current
	Pomax=	8,100	W	Maximum Output Power, DC/DC Stage
	Iaux=		mA	Auxiliary Power Supply current
	Tamb=		°C	Maximum Ambient Temperature

Output data	Pin=	8,932	W	Input Active Power
	Ppfc=	8,709	W	Maximum Output Power, PFC Stage
	Pinl=	114.5	W	Total Input Stage power loss
	Ppfcl=	109.5	W	Total PFC Stage power loss
	Pdcl=	240.2	W	Total DC/DC Stage power loss
	Poutl=	324.8	W	Total Output Stage power loss
	Paul=	43.5	W	Auxiliary circuits power loss
	Pm=	101.1	W	Total Magnetics loss
	Ps=	557.8	W	Total Semiconductors Loss
	Ptl=	832.5	W	Total Power Loss
	Effpfc=	97.49	%	PFC (+ Input Stage, + Aux) Efficiency
	Effdc=	93.48	%	DC/DC (+ Output Stage) Efficiency
	Eff=	90.68	%	Total Efficiency


	Input Stage Loss Evaluation

Input data	Rif=		mOhm	DC Resistance, Input Fuses
	Ricm1=	5.29	mOhm	DC Resistance, Input CM Inductor 1	1mH (*3)
	Ricm2=	5.29	mOhm	DC Resistance, Input CM Inductor 2	1mH (*3)
	Ridm=	7.10	mOhm	DC Resistance, Input DM Inductor(s)	30uH (*3)
	Rbinlf=	14.60	mOhm	PCB AC Input path, low frequency
	Vidb=	1.12	V	Voltage drop, one diode Input Bridge @ Irpkn	RURP3060, typ
	Visb=	1.13	V	Voltage drop, one SCR Input Bridge @ Irpkn	TYN640, max
	Rdthjc=		°C/W	Input diodes junction to case thermal resistance
	Rdthcs=		°C/W	Input diodes case to heat sink thermal resistance
	Rsthjc=		°C/W	Input SCRs junction to case thermal resistance
	Rsthcs=		°C/W	Input SCRs case to heat sink thermal resistance
	Tidjx=		°C	Input diodes maximum junction temperature
	Tidj=		°C	Input diodes actual junction temperature
	Tisjx=		°C	Input SCRs maximum junction temperature
	Tisj=		°C	Input SCRs actual junction temperature

Output data	Pif=	2.6	W	Power loss, input fuses	3*JLLN45
	Picm1=	8.1	W	Power Loss, Input CM Inductor 1	all 3 windings
	Picm2=	8.1	W	Power Loss, Input CM Inductor 2	all 3 windings
	Pidm=	10.9	W	Power Loss, Input DM Inductor(s)	all 3 inductors
	Pbinlf=	22.3	W	Power loss, PCB, input stage	3 x 1/3
	Pidb=	31.0	W	Power Loss, Input Diode Bridge	3*RURP3060
	Pisb=	31.5	W	Power Loss, Input SCR Bridge	3*TYN640
	Pinu=	114.5	W	Total Input Stage power loss
	Tdc=	133	°C	Case temperature, diodes
	Tsc=	116	°C	Case temperature, SCRs
	Tdh=	118	°C	Diodes heat sink temperature
	Tsh=	111	°C	SCRs heat sink temperature
	Ridthsx=	2.18	°C/W	Max. Diodes Heat sink Thermal Resistance
	Ridths=		°C/W	Chosen Diodes Heat sink Thermal Resistance
	Risthsx=	1.95	°C/W	Max. SCRs Heat sink Thermal Resistance
	Risths=		°C/W	Chosen SCRs Heat sink Thermal Resistance


	PFC Stage Loss Evaluation

Input data	Vba=	407.0	Vdc	Average Boost Voltage
	fpfc=	120	kHz	PFC Switching Frequency
	Iba=	21.40	A	Average PFC output current
	Iba=		A	Average PFC output current	Copy from above cell
	Ibswn=	12.8	Arms	Switch rms current at nom line
	Ibpkon=	22.7	Apk	SW turn ON, Diode turn OFF pk current, nom avg
	Ibpkoff=	32.8	Apk	SW turn OFF, Diode turn ON pk current, nom, avg
	kf=			1 for Hard SW, 2 for Soft SW	Soft switching
	dIf/dt=		A/us	Turn-ON current slope, max, should be chosen <	3178
	Lsnb=	1.91	uH	Boost snubber inductor	required
	dVd/dton=		kV/us	SS turn ON dV/dt for MOSFET drain voltage <	-240
	nd=	2		Number of boost diodes	1/2*RHRG3060CC
	Vbd=	1.21	V	Diode forward voltage @ peak line current	1/2*RHRG3060CC
	Vbdfr=		V	Diode forward recovery voltage
	tfrx=		ns	Diode forward recovery time
	Irrpk=	6.7	A	Boost diode pk reverse recovering current	1/2*RHRG3060CC
	trrx=	107.5	ns	Boost diode reverse recovering time	1/2*RHRG3060CC
	ta=	33.6	ns		1/2*RHRG3060CC
	tb=	73.9	ns		1/2*RHRG3060CC
	Rthjc=		°C/W	Boost diode(s) junction to case thermal resistance
	Rthcs=		°C/W	Boost diode(s) case to heat sink thermal resistance
	Tjbdx=		°C	Boost diode(s) maximum junction temperature
	Tjbd=	127	°C	Boost diode(s) junction temperature	same htsk with BT
	Tjbd=		°C	Boost diode(s) junction temperature	Copy from above cell
	nt=			Number of transistors
	Rdso=		Ohm	MOSFET Rdson, max @25°C
	Rds=	0.048	Ohm	Actual MOSFET(s) Rds ON	SPW47N60C3
	Vgsth=		V	Gate Threshold Voltage
	Vx=		V	Vds voltage @ t3
	gfs=		S	Forward Transconductance
	Q3=		nC	Gate charge t1s -> t2s
	Cisu=		pF	Ciss @ Vds=Vba & Vgsth<Vgs<Vgsp
	Coer=		pF	MOSFET output capacitance @ Vba
	rg=		Ohm	Transistor intrinsic gate resistance
	Ls=		nH	Source inductance
	Vgson=		V	Effective gate ON voltage
	Vgsoff=		V	Effective gate OFF voltage
	Vgst1s->2s	4.36	V	Vgs from t1s to t2s
	Vgst1s->2s		V	Vgs from t1s to t2s	Copy from above cell
	Vgst3b=	4.49	V	Vgs when Id=Idiode
	Vlsta=	0.60	V	Voltage across Ls during turn-on, t2s->t3s
	t:2s->3a=	113.7	ns	time from Id starting to rise to Id reaching the Idiode
	t:1s->2s	38.4	ns	time from Vds starting to drop to Vds=Vx	Soft switching
	dVd/dton=	-10.0	kV/us	Turn ON dV/dt for MOSFET drain voltage
	Vsaton=	1.1	V	Vdrain after turn-on
	Icossf=	-2.5	A	Coss current during voltage falling	SPW47N60C3
	Rswonc=	17.0	Ohm	Gate turn ON resistor	Determined by dV/dt
	Rswon=		Ohm	Gate turn ON resistor, chosen	>Rswonc
	Rswoff=		Ohm	Gate turn OFF resistor, chosen
	Csf=	0	pF	Optimum Boost snubber capacitor	required
	Csf=		pF	Boost snubber capacitor	required
	Vsatoff=	1.6	V	Vdrain before turn-off
	Vgst3r=	4.57	V	Vgs @ t3r, before Vds begins to rise	Soft switching
	t:3r->2r=	9.3	ns	time from Vds=Vx to Vds=Vb	Soft switching
	dVd/dtoff=	41.2	kV/us	Turn OFF dV/dt for MOSFET drain voltage
	Icossr=	10.43	A	Coss current during voltage rising
	Icsf=	0.49	A	Csf current during voltage rising
	Icht3r->2r=	0.00	A	Internal channel current
	Vgst2r=	4.30	V	Vgs @ t2r, after Vds reach Vb	Soft switching
	dId/dt=	-2,657	A/us	Turn-OFF current slope (internal channel !)
	t:2r->1r=	12.3	ns	time from Ichannel going from Id to zero
	Vlsoff=	-7.97	V	Voltage across Ls during turn-off
	Rthjc=		°C/W	MOSFET(s) junction to case thermal resistance
	Rthcs=		°C/W	MOSFET(s) case to heat sink thermal resistance
	Tjbtx=		°C	MOSFET(s) Maximum junction temperature
	Tjbt=		°C	MOSFET(s) actual junction temperature
	Resrlf=		mOhm	ESR@100Hz, Boost Capacitors
	Resrhf=		mOhm	ESR@100kHz, Boost Capacitors
	Rspfc=	5.0	mOhm	PFC shunt resistor
	Rbpfchf=	4.3	mOhm	PCB PFC path high frequency
	Pbitl=	27.7	W	Boost Inductor total loss

Output data	Pt5=	7.8	W	Conduction Loss in MOSFET(s)
	Pt1->2=	3.9	W	Turn ON Switching Loss in MOSFET(s)	Soft switching
	Pt2a->2b=	1.1	W	MOSFET turn ON Switching Loss due to the diode
	Pt2->2b=	0.0	W	Turn ON Switching Loss in the diode
	Pt4=	9.9	W	Turn OFF Switching Loss in MOSFET(s)
	Pt5=	7.5	W	Transistor Capacitance discharge Loss
	Ptr=	30.2	W	Total Losses Main Switch(s)
	Pdc=	25.9	W	Conduction losses in the Boost Diode(s)
	Pdoff=	1.5		Switch turn OFF losses in the Boost Diode(s)	Forward recovery
	Pd=	27.4	W	Total Losses Main Diode
	Pdsn=	2.7	W	Snubber diodes losses
	Pbs=	60.4	W	Total PFC Stage Semiconductors Loss
	Tcbtx=	122	°C	MOSFET(s) max allowable case temperature
	Thpfcx=	115	°C	MOSFET(s) heat sink max allowable temperature
	Tcbd=	121	°C	Boost diode case temperature	same htsk with BT
	Rths	1.07	°C/W	PFC heat sink Thermal Resistance
	Pish=	3.9	W	Power loss, PFC Shunt
	Pbpfclf=	3.6	W	Power loss, PCB PFC path high frequency
	Pbo=		W	Total PFC Stage Other Losses
	Pesrlf=	0.1	W	Boost Capacitors low frequency Loss
	Pesrhf=	8.9	W	Boost Capacitors high frequency Loss
	Pbt=	109.5	W	Total PFC Stage Loss


	DC/DC Stage Loss Evaluation

Input data	Rdso=		Ohm	MOSFET Rds, max @25°C
	Rdsd=	0.152	Ohm	MOSFET(s) Rds ON Resistance @125°C	2*IRFP31N50L
	Rthjc=		°C/W	MOSFET(s) junction to case thermal resistance
	Rthcs=		°C/W	MOSFET(s) case to heat sink thermal resistance
	Tj=		°C	MOSFET(s) Maximum junction temperature
	Tja=		°C	MOSFET(s) actual junction temperature
	Coer=		pF	MOSFET output capacitance @ Vba
	Ibchfx=	8.67	Arms	DC input Capacitor, max HF ripple current
	Ibchfx=		Arms	DC input Capacitor, max HF ripple current	Copy from above cell
	Resrin=		mOhm	ESR@100kHz, Boost Capacitors
	Rdcm=		mOhm	DC Resistance, DC/DC CM Inductor
	Rbdcp=	28.07	mOhm	PCB DC/DC path primary
	Pttl=	35.6	W	Power transformer total loss

Output data	Pdc=	192.7	W	Conduction Loss in Phase Shift Bridge Transistors
	Psw=	9.6	W	Switching Loss in Phase Shift Bridge Transistors
	Ptr=	202.3	W	Total Losses Bridge Switches
	Tc=	115	°C	Case temperature
	Th=	97	°C	Heat sink temperature
	Rths	0.23	°C/W	PS Bridge Heat sink Thermal Resistance
	Pcin=	2.0	W	Power Loss, Input Capacitor
	Pcin=	0.3	W	Power Loss, DC/DC CM Inductor
	Pbdcp=	17.8	W	Power loss, PCB DC/DC path primary
	Pdctot=	240.2	W	Total DC/DC Stage power loss


	Output Stage Loss Evaluation

Input data	Rbdcslf=	0.3	mOhm	PCB DC/DC path secondary, low frequency
	Rbdcshf=	1.5	mOhm	PCB DC/DC path secondary, high frequency
	Rocm=		mOhm	DC Resistance, Output CM Inductor
	Rodm=		mOhm	DC Resistance, Output DM Inductor
	Rosh=	0.28	mOhm	DC Resistance, Output Shunt
	Rbdco=	0.76	mOhm	PCB DC/DC path output
	Roc=		mOhm	DC Resistance, Output Connector
	Poitl	10.8	W	Output Inductor(s) total loss
	nrd=			Number of Rectifier diodes
	Ddcn=	88.12	%	Nominal DC/DC Stage Duty Cycle
	Ddcn=		%	Nominal DC/DC Stage Duty Cycle	Copy from above cell
	Vfr=	1.07	V	Diode forward voltage @ Tja
	Rthjc=		°C/W	Output Diode(s) junction to case thermal resistance
	Rthcs=		°C/W	Output Diode case to heat sink thermal resistance
	Tj=		°C	Output Diode Maximum junction temperature
	Tja=		°C	Output Diode actual junction temperature
	Tc=		°C	Output diode case temperature
	nod=			Number of OR-ing diodes
	Vfo=	0.64	V	OR-ing diode forward voltage @ Tja	1/2*203CNQ100
	Rthjc=		°C/W	OR-ing Diode junction to case thermal resistance
	Rthcs=		°C/W	OR-ing Diode case to heat sink thermal resistance
	Tj=		°C	OR-ing Diode Maximum junction temperature
	Tja=		°C	OR-ing Diode actual junction temperature
	Resro=	9	mOhm	ESR Output Capacitor	4 x 820uF/63V
	PLmin=		W	Power loss R Load min
	Psnb=		W	Power loss Clamping

Output data	Pbdcs=	10.0	W	Power loss DC/DC path secondary
	Psatind=		W	Power loss saturable inductors
	Pocm=	4.5	W	Power Loss, Output CM Inductor
	Podm=	1.1	W	Power Loss, Output DM Inductor
	Posh=	6.3	W	Power Loss, Output Shunt
	Rbdco=	17.2	W	Power loss PCB DC/DC path output
	Poc=	0.2	W	Power loss output connector
	P1=	160.3	W	Conduction Loss in Output Diodes
	P3=	8.0	W	Switching Loss in Output Diodes
	Prd=	168.3	W	Total Losses Output Diodes
	Pod=	95.8	W	DC losses OR-ing Diode
	Tc=	106	°C	Case temperature, Output Diodes
	Th=	89	°C	Heat sink temperature, Output Diodes
	Rths	0.23	°C/W	Heat sink Thermal Resistance, Output Diodes
	Tc=	126	°C	Case temperature, OR-ing Diode
	Th=	116	°C	Heat sink temperature, OR-ing Diode
	Rths	0.69	°C/W	Heat sink Thermal Resistance, OR-ing Diode
	Pco=	0.41	W	Power Loss Output Capacitor
	Potot=	324.8	W	Total Output Stage power loss


Semiconductors with 175°C maximum junction temperature are considered to operate at 145°C
junction temperature in the worst case.

Semiconductors with 150°C maximum junction temperature are considered to operate at 125°C
junction temperature in the worst case.

PFC Voltage and Current Loops design

Input data	Vinm=	180	Vrms	Minimum AC Input Line Voltage
	Vinn=	240	Vrms	Nominal AC Input Line Voltage
	Vinx=	264	Vrms	Maximum AC Input Line Voltage
	fpfc=	120	kHz	PFC switching frequency
	fline=	60	Hz	Line Frequency
	Ppfc=	8,709	W	Maximum Output Power, PFC Stage
	Cb=	2,952	uF	Boost Capacitor, chosen
	Vba=	407	V	Average boost voltage
	Vbpp=	0.6	Vpp	Boost Voltage ripple, peak to peak
	Lb=	56.0	uH	PFC boost inductor
	Iravgx=	37.1	Arms	Max avg rectified current
	Iravgn=	27.8	Arms	Nom avg rectified current
	Ibpkx=	44.4	Apk	Boost Ind., Switch and Diode max pk current
	Vspfc=		mV	Peak voltage, PFC shunt, nominal conditions
	Iacpkx=		uA	Maximum peak Iac @ Maximum line
	Vs=		Vpp	Slope voltage, peak to peak	5.4
	Vvea=		Vpp	Vvea=1.5V to 5V. At 5V full power.
	V3thd=		%	Third harmonic contribution to THD
	V3vff=		%	Third harmonic contribution to THD due to Vff
	V3vao=	0.9	%	Third harmonic contribution to THD due to Vvao
	Rvi=		k
	Rff1=		k
	Rff2=		k
	Rff3=		k
	Rpk1=		k
	Ilim=		%	Percentage above nominal
	Plim=		%	Input power percentage above nominal

Output data	Rspfcc=	5.0	mOhm	PFC shunt resistor
	Rspfc=		mOhm	PFC shunt resistor, chosen
	Pspfc=	3.9	W	PFC shunt, nominal power
	Pspfc=	6.9	W	PFC shunt, maximum power
	Rvacc=	1,245	k	Multiplier Iac set resistor
	Rvac=		k	Multiplier Iac set resistor, chosen
	Iacl=	226	uA	Iac at low line
	Iml=	453	uA	Multiplier current limit at low line. Should be >	68
	Impk=	68	uA	Multiplier current at peak low line
	Vffm=	3.40	V	Multiplier Vrms input at low line
	Vffn=	4.54	V	Multiplier Vrms input at nominal line
	Vffx=	4.99	V	Multiplier Vrms input at high line
	Gff=	0.289
	fp=	64	Hz	Vff double pole frequency
	Cff1=	25	nF
	Cff2=	123	nF
	Vspfcx=	194	mV	Peak voltage, PFC shunt, low line
	Rmoc=	2.47	k	Resistor, multiplier output
	Rmo=		k	Resistor, multiplier output, chosen
	dVs/dt	0.648	V/us	Timing capacitor voltage slope
	dVspfc/dt=	0.036	V/us	Shunt voltage downslope
	Gca=	17.83		Gain, current amplifier
	Rci=Rmo=	2.49	k
	Rcz=	44.4	k
	fci=	19.1	kHz	Current loop crossover frequency, should be =	19.1
	Cczp=	593	pF
	Ccz=		pF
	Ccpc=	59	pF
	Ccp=		pF
	Gva=	0.2002
	Cvf=	6.8	nF
	fvi=	89.0	Hz
	Rvf=	263.0	k
	Rpk2=	0.385	k
	Rvd=	7.13	k


The reference designators are those used by Unitrode in its application notes.

DC/DC Converter voltage loops design

Input data	CTtr=			Current Transformer turn ratio
	Rcsh=		Ohm
	RampL=		mV	Ramp valley voltage	No load
	RampH=		mV	Ramp peak voltage	No load


Output data	CT=	0.0300		Current Transducer gain



	Output Voltage Loop

Input data	RLoad=	0.360	Ohm	Load Resistor
	Voutn=	54.00	V	Nominal DC Output Voltage
	Lo=	1.43	uH	Output Inductor, chosen
	C401=		uF	Output Capacitor (before CM/DM Inductor)
	C402=		uF	Output Capacitor (after CM/DM Inductor)
	ESR1=		mOhm	C401 ESR
	ESR2=		mOhm	C402 ESR
	Attn2m=	12.1		Minimum second stage filter attenuation
	Attn2=			Second stage filter attenuation, chosen
	P_Gain		A/V	Power Stage Gain (average current mode)
	D_Gain		dB	DC Gain of the Voltage Error Amplifier
	fr=	280	kHz	Ripple Frequency in the Output Capacitor
	fc=	5	kHz	Crossover Frequency
	R401=		k	Scale amplifier input resistors
	R801=		k	Scale amplifier feedback resistors
	R802=		k	Error amplifier input resistor

Output data	Z1=	9.3	mOhm	C401/ESR1 impedance @ fr
	Z2=	18.5	mOhm	C402/ESR2 impedance @ fr
	f1=	5.3	Hz	Pole, DC Gain of Error Amplifier
	f2=	99.8	Hz	Pole, Load Resistance/Output Capacitors
	f3=	99.8	Hz	Zero, Rzo*Czo
	f4=	5.8	kHz	Zero, ESR*Output capacitor
	f5=	5.8	kHz	Pole, Rzo*Cpe
	f6=	44	kHz	Pole, L1ESR(CE1)
	f7=	44	kHz	Zero, RzfCpe(Rzo)
	L406=	125.5	nH	Inductor of the second stage output filter
	Rslope=	10.00	Meg	Error amplifier feedback resistor
	Czo=	2.99	nF	Rzo series with Czo feedback network
	Rzo=	533	k	Rzo series with Czo feedback network
	Cpe=	51.2	pF	Rzf series with Cpe feedback network
	Rzf=	62.1	k	Rzf series with Cpe feedback network


	Output Current Loop

Input data	Rosh=		mOhm	Output Shunt Resistor


Output data



A differential scale amplifier, followed by a error amplifier is assumed to be used.

Other power supply components design

	CM 3Ph Inductor
	3 x 0.8mH/30A, core Magnetics ZJ-43825-TC

Input data	Nb=			Number of turns
	Ltn=		mm	Average turn length
	Ltt=	556.5	mm	Total wire length
	Alf=		mm2	Cross section area
	Tc=		°C	Copper temperature

Output data	Rcm=	5.29	mOhm	DC resistance Tc


	DM Inductor
	10.8uH/30A, core Micrometals T106-52

Input data	Nb=			Number of turns
	Ltn=		mm	Average turn length
	Ltt=	747.0	mm	Total wire length
	Alf=		mm2	Cross section area
	Tc=		°C	Copper temperature

Output data	Rdm=	7.10	mOhm	DC resistance Tc


	Resistance of PCBs traces

Input data	Rbinlf=		mOhm	PCB AC Input path, low frequency	@ 100Hz
	Rbpfchf=		mOhm	PCB PFC path high frequency	@ 100kHz
	Rbdcp=		mOhm	PCB DC/DC path primary	@ 100kHz
	Rbdcslf=		mOhm	PCB DC/DC path secondary, low frequency	@ 100Hz
	Rbdcshf=		mOhm	PCB DC/DC path secondary, high frequency	@ 100kHz
	Rbdco=	0.60	mOhm	PCB DC/DC path output	@ 100Hz
	Tpcb=		°C	PCB temperature

Output data	Rbinlf=	14.60	mOhm	PCB AC Input path, low frequency	@ 100Hz
	Rbpfchf=	4.33	mOhm	PCB PFC path high frequency	@ 100kHz
	Rbdcp=	28.07	mOhm	PCB DC/DC path primary	@ 100kHz
	Rbdcslf=	0.25	mOhm	PCB DC/DC path secondary, low frequency	@ 100Hz
	Rbdcshf=	1.53	mOhm	PCB DC/DC path secondary, high frequency	@ 100kHz
	Rbdco=	0.76	mOhm	PCB DC/DC path output	@ 100Hz


	Energy Stored

Input data	Vba=	407.0	V	Average Boost Voltage, 90% Load
	Ccb=	2,952	uF	Boost Capacitor, chosen

Output data	Ecb=	244	J	Energy stored in PFC electrolytic capacitors

Saturable Inductor design

Input data	Vr=	136	V	Reverse voltage across the rectifier diode
	If=	75	A	Forward current in the rectifier diode
	trr=		ns	Reverse recovery time of the rectifier diode
	fdc=	140	kHz	Frequency for B variation
	Ae=		mm²	Magnetic core area
	le=		mm	Magnetic path length
	Vm=	381	mm³	Magnetic Volume
	Vt=		mm³	Total core volume
	AL0=		nH/T²	AL, ungapped core, no DC bias
	ur=			Relative permeability, ungapped core, no DC bias
	Bmax=		mT	Maximum flux density @ 100degC

Intermediate	Ft=	10.3	uWb	Total Flux
data	Pmt=	1,239	mW/cm³	Core loss, Toshiba MT, 50kHz to 300kHz
	Pms=	1,778	mW/cm³	Core loss, Toshiba MS, 50kHz to 300kHz
	Pas=	1,793	mW/cm³	Core loss, Allied Signal 2714AS, 50kHz to 300kHz
	P3=	3,517	mW/cm³	Core loss, Philips 3F3, 50kHz to 300kHz
	P85=	4,636	mW/cm³	Core loss, Fair-Rite 85 Material, 20kHz to 100kHz
	Rth=	71.1	K/W	Rth, toroid, open wound, natural convection

Output data	Np=	1.8		Minimum number of turns
	Nr=			Number of turns, chosen
	Hpko=	5,085	A/m	Magnetizing Force, SI
	Hpko=	64	Oe	Magnetizing Force, USA
	Pmt=	0.5	W	Core Loss, Toshiba MT
	Pms=	0.7	W	Core Loss, Toshiba MS
	Pas=	0.7	W	Core Loss, AlliedSignal 2714AS
	P3=	1.3	W	Core Loss, 3F3
	P85=	1.8	W	Core Loss, Fair-Rite 85 Material
	dTmt=	33	°C	Core Temperature Rise, Toshiba MT
	dTms=	48	°C	Core Temperature Rise, Toshiba MS
	dTas=	48	°C	Core Temperature Rise, AlliedSignal
	dT3=	95	°C	Core Temperature Rise, 3F3
	dT85=	125	°C	Core Temperature Rise, Fair-Rite


The operating core temperature is assumed to be 100°C
Minimum loss would be at 80-90°C
Maximum core operating temperature should be <140°C
The accuracy of the formulas is expected to be ±20%

General Purpose Inductor design

Input data	L=		uH	Inductance
	Ipkx=	41.5	Apk	Inductor maximum peak current
	Ippx=		App	Max peak to peak current
	Idcx=		Aavg	Max avg current
	Iacx=	3.2	Arms	Max AC rms ripple current
	f=		kHz	Frequency for B variation
	Icd=		A/mm²	Current density
	Smp=		mm	Safety margin, Pri/HF winding, mm
	Sms=		mm	Safety margin, Sec/LF winding, mm
	Whm=		mm	Min winding height, mm
	Wwm=		mm	Min winding width, mm
	Ltm=		mm	Min turn length
	Ltn=		mm	Average turn length
	Am=		mm²	Magnetic core area, minimum
	Ae=		mm²	Magnetic core area, effective
	le=		mm	Magnetic path length
	Vm=		mm³	Magnetic volume
	Vt=	8,340	mm³	Total volume
	ALo=		nH/T²	AL, ungapped core, no DC bias
	ur=	1,558		u, ungapped core, no DC bias
	Bmax=		T	Maximum flux density
	uh=		%	Permeability @ Hpk

Output data	L0=	20.2	uH	Zero bias, no gap Inductance
	Lb=	20.0	uH	Peak current bias, no gap Inductance
	L=	1.5	uH	Peak current bias, gapped Inductance
	Nomin=	1.7		Minimum Number of turns
	No=			Number of turns, chosen	> 1.2 x Nomin
	Bpk=	0.25	T	Actual peak flux density	OK
	AL=	5,000	nH/T²	Core Al, ungapped, bias @ Hpk
	ALg=	375	nH/T²	Required core AL, gapped, bias @ Hpk
	ue=	116		Required relative permeability, gapped core
	Gap0=	0.45	mm	Core gap, no fringe effect
	Gap=	0.49	mm	Core gap, closer to real
	dB=	28	mT	Half of B peak to peak variation
	Hpk=	1,272	A/m	Magnetizing Force, SI
	Hpk=	16	Oe	Magnetizing Force, USA


	Inductor Core Loss

Intermediate	P3=	4	mW/cm³	Philips Ferrite 3F3 material
data	Pml=	35	mW/cm³	Allied Signal MicroLite 245 material
	Pm60=	31	mW/cm³	Magnetics MPP 60u material
	Pm125=	53	mW/cm³	Magnetics MPP 125u material
	Pk=	87	mW/cm³	Magnetics Kool-Mu material
	Ppl=	124	mW/cm³	Allied Signal PowerLite material
	Phf=	130	mW/cm³	Magnetics High Flux 60u material
	P18=	278	mW/cm³	Micrometals Iron Powder 18 material
	Rthm=	13.4	°C/W	Rth, toroid, open wound, natural convection

Output data	P3=	0.0	W	3F3
	Pml=	0.3	W	MicroLite 245
	Pm60=	0.3	W	MPP 60u
	Pm125=	0.4	W	MPP 125u
	Pk=	0.7	W	Kool-Mu
	Ppl=	1.0	W	PowerLite
	Phf=	1.1	W	High Flux 60u
	P18=	2.3	W	Iron Powder 18
	dT3=	0	°C	Core Temperature Rise, 3F3
	dTml=	4	°C	Core Temperature Rise, MicroLite 245
	dTm60=	4	°C	Core Temperature Rise, MPP 60u
	dTm125=	6	°C	Core Temperature Rise, MPP 125u
	dTk=	10	°C	Core Temperature Rise, Kool-Mu
	dTpl=	14	°C	Core Temperature Rise, PowerLite
	dThf=	15	°C	Core Temperature Rise, High Flux 60
	dT18=	31	°C	Core Temperature Rise, Iron Powder 18


This worksheet calculates a inductor (number of turns and core loss).
The operating core temperature is assumed to be 100°C.
Minimum loss would be at 80-90°C.
Maximum core operating temperature should be <140°C.
The accuracy of the formulas is expected to be ±10% for core loss, and ±25% for temperature rise.

Coupled Inductor PSpice model extraction

Input data	f=		kHz	Measurement frequency
	L1=		uH	L1 Inductance @ f
	L2=		uH	L2 Inductance @ f
	L3=		uH	L3 Inductance @ f
	Q1=			L1 Quality factor @ f
	Q2=			L2 Quality factor @ f
	Q3=			L3 Quality factor @ f
	L(1+2)=		uH	L1 + L2 Inductance (Magnetic fields aiding)
	L(1-2)=		uH	L1 - L2 Inductance (Magnetic fields opposing)
	L(2+3)=		uH	L2 + L3 Inductance (Magnetic fields aiding)
	L(2-3)=		uH	L2 - L3 Inductance (Magnetic fields opposing)
	L(3+1)=		uH	L3 + L1 Inductance (Magnetic fields aiding)
	L(3-1)=		uH	L3 - L1 Inductance (Magnetic fields opposing)

Intermediate	M12=	6.7	uH	L1--L2 Mutual Inductance
data	M23=	0.0	uH	L2--L3 Mutual Inductance
	M31=	0.0	uH	L3--L1 Mutual Inductance

Output data	K12=	0.499		L1--L2 Coupling coefficient
	K23=	0.000		L2--L3 Coupling coefficient
	K31=	0.000		L3--L1 Coupling coefficient
	R1=	8.50	mOhm	L1 Equivalent series resistor @ f
	R2=	2.19	mOhm	L2 Equivalent series resistor @ f
	R3=	0.06	mOhm	L3 Equivalent series resistor @ f


Input data	f=		kHz	Measurement frequency
	L1=		uH	L1 Inductance @ f
	L2=		uH	L2 Inductance @ f
	L3=		uH	L3 Inductance @ f
	Q1=			L1 Quality factor @ f
	Q2=			L2 Quality factor @ f
	Q3=			L3 Quality factor @ f
	L(1+2)=		uH	L1 + L2 Inductance (Magnetic fields aiding)
	L(1-2)=		uH	L1 - L2 Inductance (Magnetic fields opposing)
	L(2+3)=		uH	L2 + L3 Inductance (Magnetic fields aiding)
	L(2-3)=		uH	L2 - L3 Inductance (Magnetic fields opposing)
	L(3+1)=		uH	L3 + L1 Inductance (Magnetic fields aiding)
	L(3-1)=		uH	L3 - L1 Inductance (Magnetic fields opposing)

Intermediate	M12=	6.6	uH	L1--L2 Mutual Inductance
data	M23=	0.0	uH	L2--L3 Mutual Inductance
	M31=	0.0	uH	L3--L1 Mutual Inductance

Output data	K12=	0.496		L1--L2 Coupling coefficient
	K23=	0.000		L2--L3 Coupling coefficient
	K31=	0.000		L3--L1 Coupling coefficient
	R1=	11.39	mOhm	L1 Equivalent series resistor @ f
	R2=	2.45	mOhm	L2 Equivalent series resistor @ f
	R3=	0.06	mOhm	L3 Equivalent series resistor @ f


Input data	f=		kHz	Measurement frequency
	L1=		uH	L1 Inductance @ f
	L2=		uH	L2 Inductance @ f
	L3=		uH	L3 Inductance @ f
	Q1=			L1 Quality factor @ f
	Q2=			L2 Quality factor @ f
	Q3=			L3 Quality factor @ f
	L(1+2)=		uH	L1 + L2 Inductance (Magnetic fields aiding)
	L(1-2)=		uH	L1 - L2 Inductance (Magnetic fields opposing)
	L(2+3)=		uH	L2 + L3 Inductance (Magnetic fields aiding)
	L(2-3)=		uH	L2 - L3 Inductance (Magnetic fields opposing)
	L(3+1)=		uH	L3 + L1 Inductance (Magnetic fields aiding)
	L(3-1)=		uH	L3 - L1 Inductance (Magnetic fields opposing)

Intermediate	M12=	6.5	uH	L1--L2 Mutual Inductance
data	M23=	0.0	uH	L2--L3 Mutual Inductance
	M31=	0.0	uH	L3--L1 Mutual Inductance

Output data	K12=	0.505		L1--L2 Coupling coefficient
	K23=	0.000		L2--L3 Coupling coefficient
	K31=	0.000		L3--L1 Coupling coefficient
	R1=	28.94	mOhm	L1 Equivalent series resistor @ f
	R2=	3.55	mOhm	L2 Equivalent series resistor @ f
	R3=	0.06	mOhm	L3 Equivalent series resistor @ f


Input data	f=		kHz	Measurement frequency
	L1=		uH	L1 Inductance @ f
	L2=		uH	L2 Inductance @ f
	L3=		uH	L3 Inductance @ f
	Q1=			L1 Quality factor @ f
	Q2=			L2 Quality factor @ f
	Q3=			L3 Quality factor @ f
	L(1+2)=		uH	L1 + L2 Inductance (Magnetic fields aiding)
	L(1-2)=		uH	L1 - L2 Inductance (Magnetic fields opposing)
	L(2+3)=		uH	L2 + L3 Inductance (Magnetic fields aiding)
	L(2-3)=		uH	L2 - L3 Inductance (Magnetic fields opposing)
	L(3+1)=		uH	L3 + L1 Inductance (Magnetic fields aiding)
	L(3-1)=		uH	L3 - L1 Inductance (Magnetic fields opposing)

Intermediate	M12=	6.5	uH	L1--L2 Mutual Inductance
data	M23=	0.0	uH	L2--L3 Mutual Inductance
	M31=	0.0	uH	L3--L1 Mutual Inductance

Output data	K12=	0.506		L1--L2 Coupling coefficient
	K23=	0.000		L2--L3 Coupling coefficient
	K31=	0.000		L3--L1 Coupling coefficient
	R1=	195.65	mOhm	L1 Equivalent series resistor @ f
	R2=	13.86	mOhm	L2 Equivalent series resistor @ f
	R3=	0.01	mOhm	L3 Equivalent series resistor @ f


This worksheet calculates the coupling coefficients for a magnetic structure with three coupled inductors.

The calculation is based on measuring the inductances of any combination of two inductors connected in
series, with fields aiding and opposing.

The calculated coupling coefficients and equivalent series resistors, together with measured inductances can
now be used to generate a Spice model.

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