LLC Circuit Calculation Guide | GREEN Digital Power

Input Operating Condition Parameters

Rated output voltage: Vout
Rated output current: Iout
Rated input voltage: Vin:
Rated operating frequency: fr
Inductance ratio (Lm/Ls): KL, default 6.0. A larger KL reduces magnetizing current, a smaller one adapts better to load changes; reasonable range is 4~7
Resonant quality factor: Q, default 0.35. Reasonable range at full load is 0.2~0.5, which secures gain at both heavy and light loads.

Input voltage ripple factor: dVin, generally default dVin=0.05 LLC bridge factor: KQ=0.5 for half-bridge (100~2000W), KQ=1 for full-bridge (above 2000W)

Determine the transformer primary/secondary turns ratio n

n = KQ*Vin/Vout

Calculate the primary-side equivalent load impedance Re

Re = 8*n*n*Vout/(3.14*3.14*Iout)

Calculate resonant inductor Lr, resonant capacitor Cr, and transformer magnetizing inductance Lm

01Cr = 1/(2*3.14*Q*fr*Re),

02Lr = 1/(Cr*(2*3.14*fr)^2)),

Lm = KL*Lr

Calculate peak and RMS magnetizing currents Im_pk, Im_rms, and peak and RMS resonant currents Ir_pk, Ir_rms

Im_pk = KQ*Vin/(4*fr*Lm),

Im_rms = Im_pk/1.732

Ir_rms =（Im_rms^2 + (1.1*Iout/n)^2)^0.5,

Ir_pk = 1.414*Ir_rms

Resonant Inductor Parameter Design

Calculate the resonant inductor core AP value, select the core size accordingly, and obtain the core cross-sectional area Ae and winding turn length ML

AP=10^4*Lr_pk*Ir_rms /(2*Ku*fr*KQ*dBmax*J), AP unit is cm^4,

Recommended constant values: Ku=0.25, dBmax=0.2, J=500 A/cm^2

Calculate the winding turns N_L

N_Lr>=(Lr*Ir_pk)/(Ae*dBmax)

Calculate the winding cross-sectional area

S_Lr= Ir_rms/5.0

Calculate the winding DC resistance

Rls = 2.1×10^(-8)*N_Lr*ML/(S_Ls×10^(-6) )

Transformer Parameter Design

Calculate the transformer AP value, select the core size accordingly, and obtain the core cross-sectional area Ae and winding turn length ML

AP=10^4*Vout*Iout*1.05/(2*Ku*fr*KQ*dBmax*J), AP unit is cm^4

Ku: window factor (share of the total window area taken by primary winding copper), default 0.25
dBmax: flux density swing, default 0.3
J: current density, default 500 A/cm^2

Calculate the transformer primary turns Np and secondary turns Ns

Ns >= Vout/(2*fr*Ae*dBmax), round to integer Np = Ns*n

Calculate the primary/secondary winding cross-sections Sp, Ss and resistances Rp, Rs

Sp = Ir_rms/5.0, unit is mm^2. To reduce skin effect, wind with 0.1mm-diameter multi-strand copper wire.

Rp = 2.1×10^(-8)*Np*ML/(Sp×10^(-6) )

Ss = n*Sp, unit is mm^2. To reduce skin effect, wind with 0.2mm-thick copper foil.

Rs = 2.1×10^(-8)*Ns*ML/(Ss×10^(-6) )

Recommended Core Parameters for Common Transformers and Resonant Inductors in 150W~3kW LLC Circuits (Table 1)

Core Model	Material	Loss/cm3 50kH0.1T	Main Dimensions (mm)	Max Flux Bmax(T)	Core Area Ae (cm^2)	Magnetic Path Length	Window Area Ae (cm^2)	AP Value cm^4	Core Volume Ve (cm^3)	Length per Turn ML (m)
ATQ1704	PC95	30mW	171718	0.35	0.46	34.0	0.36	0.16	1.40	0.041
ATQ2716	PC95	30mW	271622	0.35	1.35	48.6	0.6	0.78	6.61	0.053
PQ2620	PC95	30mW	262019	0.35	1.18	46.3	0.6	0.71	5.50	0.053
PQ2625	PC95	30mW	262519	0.35	1.18	55.5	0.8	0.94	6.53	0.053
PQ3220	PC95	30mW	322226	0.35	1.70	55.5	0.80	1.36	9.40	0.063
PQ3225	PC95	30mW	322522	0.35	1.61	60.6	1.17	1.89	9.76	0.063
PQ3525	PC95	30mW	352526	0.35	1.69	60.5	1.08	2.00	10.2	0.072
PQ3530	PC95	30mW	353026	0.35	1.69	74.6	1.80	3.20	12.0	0.072
PQ4040	PC95	30mW	404028	0.35	2.00	102	3.30	6.60	20.5	0.082
PQ5040	PC95	30mW	504032	0.35	3.28	95.4	3.09	9.84	29.7	0.101

Theoretical Calculation of LLC Transformer, Resonant Inductor, Resonant Capacitor and Resonant Current for 150W~3000W AC-DC Power Supplies (Table 2)

Output Power	200W	200W	300W	400W	600W	800W	1000W	1200W	1800W	2800W
Bridge Factor KQ	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	1
Resonant Frequency fr	180k	100k	100k	100k	100k	100k	100k	100k	90k	90k
Input Voltage Vin	400	400	400	400	400	400	400	400	400	400
Output Voltage Vout	20	20	30	50	50	50	50	50	50	50
Inductance Ratio KL	6	6	6	6	6	6	6	6	6	6
Quality Factor Q	0.35	0.35	0.35	0.35	0.35	0.35	0.35	0.35	0.35	0.35
Transformer Turns Ratio n	10	10	6.67	4	4	4	4	4	4	8
Resonant Inductor Lr	50.2μH	90.3μH	60.2μH	45.2μH	30.1μH	22.6μH	18.1μH	15.1μH	11.1μH	28.7μH
Magnetizing Inductance Lm	301.0μH	541.8μH	361.2μH	270.9μH	180.6μH	135.5μH	108.4μH	90.3μH	66.9μH	172.0μH
Resonant Capacitor Cr	15.6nF	28.0nF	42.1nF	56.1nF	84.1nF	112.2nF	140.2nF	168.3nF	280.5nF	109.1nF
Magnetizing Current Im_rms	0.533A	0.533A	0.799A	1.066A	1.598A	2.131A	2.664A	3.197A	4.795A	3.729A
Resonant Current Ir_rms	1.222A	1.222A	1.833A	2.444A	3.667A	4.889A	6.111A	7.333A	11.000A	8.556A

n = KQ*Vin/Vout,

Cr = 1/(2*3.14*Q*fr*Re), Re = 8*n*n*Vout/(3.14*3.14*Iout) Lr = 1/(Cr*(2*3.14*fr)^2)), Lm = KL*Lr Im_pk = KQ*Vin/(4*fr*Lm), Im_rms = Im_pk/1.732 Ir_rms =（Im_rms^2 + (1.1*Iout/n)^2)^0.5, Ir_pk = 1.414*Ir_rms

Verification of fr, Q, KL and Currents under Actual Transformer/Resonant Inductor/Resonant Capacitor for 150W~3000W AC-DC Power Supplies (Table 3)

	200W	300W	600W	800W	1000W	1200W	1800W	2800W
Bridge Factor KQ	0.5	0.5	0.5	0.5	0.5	0.5	0.5	1
Input Vin	400	400	400	400	400	400	400	400
Output Voltage Vout	30	30	50	50	42	60	50	50
Transformer Turns Ratio n	7.5	7	3	4.2	5.3	3.4	4	8
Resonant Inductor Lr	50μH	50μH	35μH	25μH	15μH	15μH	12μH	25μH
Magnetizing Inductance Lm	330μH	300μH	220μH	140μH	100μH	90μH	70μH	200μH
Resonant Capacitor Cr	15nF	39nF	94nF	112nF	112nF	164nF	270nF	132nF
Inductance Ratio KL	6.6	6	6.3	5.6	6.7	6	5.8	8
Resonant Frequency fr	183.8kHz	114.0kHz	87.7kHz	95.1kHz	122.8kHz	101.5kHz	88.4kHz	87.6kHz
Quality Factor Q	0.228	0.244	0.515	0.271	0.234	0.276	0.3	0.241
Magnetizing Current Im_rms	0.476A	0.844A	1.495A	2.168A	2.351A	3.161A	4.664A	3.295A
Resonant Current Ir_rms	1.087A	1.784A	4.647A	4.718A	5.472A	7.201A	10.944A	8.375A

fr = 1/(2*3.14*(Lr*Cr)^0.5) Q = (Lr/Cr)^0.5/(n*n*Vout*Vout/Po) Im_rms = KQ*Vin/(4*fr*Lm)/1.732 Ir_rms =（Im_rms^2 + ((1.1*Po/Vout)/n)^2)^0.5

Note: A larger KL reduces magnetizing current, a smaller one adapts better to load changes; reasonable range is 4~7. Reasonable Q is 0.2~0.5, which secures gain at both heavy and light loads.

Theoretical Calculation of LLC Resonant Inductor Parameters for 150W~3000W AC-DC Power Supplies (Table 4)

Power Pout	200W	200W	300W	400W	600W	800W	1000W	1200W	1800W	2800W
Resonant Frequency fr	180k	100k	100k	100k	100k	100k	100k	100k	90k	90k
Resonant Current Ir_rms	1.222A	1.222A	1.833A	2.444A	3.667A	4.889A	6.111A	7.333A	11.000A	8.556A
Inductance Lr	50.2μH	90.3μH	60.2μH	45.2μH	30.1μH	22.6μH	18.1μH	15.1μH	11.1μH	28.7μH
Theoretical Inductor AP_Ls	0.036	0.065	0.09	0.13	0.18	0.25	0.30	0.38	0.60	1.0
Recommended Inductor Spec	ATQ1704	ATQ1704	PQ2620	PQ2620	PQ2620	PQ2620	PQ3220	PQ3220	PQ3220	PQ3220
Core Area Ae	0.46	0.46	1.18	1.18	1.18	1.18	1.7	1.7	1.7	1.7
Core AP Value	0.16	0.16	0.71	0.71	0.71	0.71	1.36	1.36	1.36	1.36
Core Turn Length ML	0.041	0.043	0.053	0.053	0.053	0.053	0.063	0.072	0.072	0.072
Winding Turns N_Lr	20	34	14	14	14	14	10	10	12	22
Winding Cross-Section S_Ls	0.244	0.244	0.366	0.488	0.733	0.977	1.222	1.466	2.2	1.711
DC Resistance R_Ls	0.07Ω	0.13Ω	0.042Ω	0.03Ω	0.04Ω	0.016Ω	0.01Ω	0.01Ω	0.01Ω	0.02Ω

AP_Ls = 10^4*Lr*Ir_rms*Ir_rms*1.4/(Ku*dBmax*J), Ku=0.6, dBmax=0.1, J=500 N_Lr>=(Lr*Ir_rms*1.4)/(Ae*10^-4*dBmax), round to integer; Np = Ns*n

S_Ls = Ir_rms/5.0, unit is mm^2;

R_Ls = 2.1×10^(-8)*Np*ML/(Sp×10^(-6) )

Theoretical Calculated Values of LLC Transformer Parameters for 150W~3000W AC-DC Power Supplies (Table 5)

Output Power Pout	200W	200W	300W	400W	600W	800W	1000W	1200W	1800W	2800W
Bridge Factor KQ	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	1
Resonant Frequency fr	180k	100k	100k	100k	100k	100k	100k	100k	90k	90k
Input Voltage Vin	400	400	400	400	400	400	400	400	400	400
Output Voltage Vout	30	30	30	50	50	50	50	50	50	50
Transformer Minimum AP	0.2333	0.56	0.84	1.12	1.68	2.24	2.8	3.36	5.6	4.3556
Recommended Transformer Spec	ATQ2716	ATQ2716	PQ3525	PQ3525	PQ3530	PQ3530	PQ4040	PQ4040	PQ5040	PQ5040
Core Area Ae	1.29	1.29	1.85	1.85	1.85	1.85	2	2	3.28	3.28
Core Turn Length ML	0.053	0.053	0.063	0.063	0.072	0.072	0.082	0.082	0.101	0.101
Primary Turns Np	20	27	20	20	20	20	20	20	12	24
Secondary Turns Ns	3	4	3	5	5	5	5	5	3	3
Primary Winding Sp	0.1645	0.2468	0.3702	0.4936	0.7404	0.9872	1.234	1.4808	2.2214	1.7278
Secondary Winding Ss	1.645	2.468	2.468	1.9744	2.9616	3.9488	4.936	5.9232	8.8856	13.8224
Primary Resistance Rp	0.0426	0.1353	0.0715	0.0536	0.0408	0.0306	0.0279	0.0233	0.0115	0.0295
Secondary Resistance Rs	0.0004	0.0014	0.0016	0.0034	0.0026	0.0019	0.0017	0.0015	0.0007	0.0005
Actual Flux Swing dB_T	0.215	0.287	0.27	0.27	0.27	0.27	0.25	0.25	0.282	0.282

AP=10^4*Pout*1.05/(2*Ku*fr*KQ*dBmax*J), AP unit is cm^4, Ku=0.25, dBmax=0.3, J=500 A/cm^2 n=KQ*Vin/Vout; Ns >=Vout/(2*fr*Ae*dBmax), round to integer; Np = Ns*n Sp = Ir_rms/5.0, unit is mm^2; Rpr = 2.1×10^(-8)*Np*ML/(Sp×10^(-6) ) Ss = n*Sp, unit is mm^2; Rse = 2.1×10^(-8)*Ns*ML/(Ss×10^(-6) ) dB_T = KQ*Vin/(2*Ae*fr*Np)

Theoretical Thermal Loss Calculation of Power Devices in the LLC Converter

Item	Parameter	200W	300W	400W	600W	800W	1000W	1200W	1800W	2800W
Input Voltage V	Vin	400	400	400	400	400	400	400	400	400
Output Voltage V	Vout	30	30	50	50	50	50	50	50	50
Output Current A	Iout	6.7	10	8	12	16	20	24	36	56
Half-Bridge or Full-Bridge	KQ	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	1.0
Resonant Frequency Hz	fr	100k	100k	100k	100k	100k	100k	100k	90k	90k
Inductance Ratio	KL	6	6	6	6	6	6	6	6	6
Resonant Quality Factor	Q	0.35	0.35	0.35	0.35	0.35	0.35	0.35	0.35	0.35
Magnetizing Current	Imag	0.533	0.533	0.799	1.066	1.598	2.131	2.664	3.197	4.795
Resonant Current	Ir_rms	1.222	1.222	1.833	2.444	3.667	4.889	6.111	7.333	11.000
Recommended Transformer Spec		ATQ2716	PQ3525	PQ3525	PQ3530	PQ3530	PQ4040	PQ4040	PQ5040	PQ5040
Transformer Core Area	Ve_T	1.29	1.85	1.85	1.85	1.85	2	2	3.28	3.28
Transformer Turns Ratio	n
Transformer Volume	Ve_T	7.1	12	12	14.8	14.8	20.5	20.5	32	32
Transformer Primary Resistance	Rr	0.1353	0.0715	0.0536	0.0408	0.0306	0.0279	0.0233	0.0115	0.0295
Transformer Secondary Resistance	Rs	0.0014	0.0016	0.0034	0.0026	0.0019	0.0017	0.0015	0.0007	0.0005
Transformer Flux Swing (mT)	dB_T	287	270	270	270	270	250	250	282	282
Resonant Inductor Spec		ATQ1704	PQ2620	PQ2620	PQ2620	PQ2620	PQ3220	PQ3220	PQ3220	PQ3220
Resonant Inductor Resistance	R_Ls	0.13	0.042	0.03	0.04	0.016	0.01	0.01	0.01	0.02
Resonant Inductor Flux Swing (mT)	dB_Ls	100	100	100	100	100	100	100	100	100
Resonant Inductor Volume	Ve_L	1.22	5.5	5.5	5.5	5.5	9.4	9.4	9.4	9.4
Switch On-Resistance	Ron_pr	0.3	0.18	0.12	0.15	0.15	0.08	0.075	0.060	0.045
Switch Fall Time	tf_pr	10ns	10ns	10ns	30ns	30ns	57ns	25ns	4ns	4ns
Rectifier On-Resistance	Ron_se	0.025	0.0125	0.0125	X	X	X	0.004	0.0033	0.0024
Rectifier Fall Time	tf_se	65ns	65ns	65ns	X	X	X	65ns	110ns	168ns
Transformer Copper Loss	Pcu_T	0.3539	0.2556	0.4354	0.5906	0.9843	1.5804	2.1197	1.4648	8.9298
Transformer Core Loss	Pcore_T	4.4158	8.3807	8.3807	10.3362	10.3362	11.7658	11.7658	21.9574	21.9574
Total Switch Loss	Pmos_pr	0.9386	0.5806	0.8699	2.048	4.416	4.794	6.135	6.536	22.332
Total Rectifier Loss	Pmos_se	2.354	2.92	2.68	11.52	15.36	19.2	7.906	16.678	35.908
Resonant Inductor Copper Loss	Pcu_L	0.233	0.0753	0.1209	0.2868	0.2576	0.2868	0.4484	0.6453	2.904
Resonant Inductor Core Loss	Pcore_L	0.417	1.881	1.881	1.881	1.881	3.215	3.215	2.956	2.956
Overall LLC Conversion Efficiency	Eff	95.84%	95.51%	96.53%	95.75%	96.01%	96.08%	97.44%	97.28%	96.72%

Transformer turns ratio n=KQ*Vin/Vout Transformer copper loss: Pcu_T = Ir_rms^2*Rp*1.2 + (n*Ir_rms)^2*Rs*1.2 Transformer core loss: Pcore_T = K*fr^a*dB_T^b*Ve_T, with K=1.6×10^-9, a=1.22, b=2.55 Resonant inductor copper loss: Pcu_L = Ir_rms^2*R_Ls*1.2 Resonant inductor core loss: Pcore_L = K*fs^a*dB_L^b*Ve_L, with K=1.6×10^-9, a=1.22, b=2.55 Primary switch loss: P_mos_pr = 4*KQ*(P_turn_on_pr+P_turn_off_pr +P_on_pr) P_turn_on_pr = 0 P_turn_off _pr= 0.2*KQ*Vin*Imag*tf_pr*fr P_on_pr = Ir_rms*Ir_rms*Ron_pr

Secondary synchronous rectifier loss: P_mos_se = 2*(P_on_se + P_turn_on_se+ P_turn_off_se);

P_turn_on_se = 0

P_turn_off_se = 0.3*Vout*Iout*tf_se*fr,

P_on_se = 0.7*Iout*Iout*Ron_se. Note: if Ron_se=X, then P_mos_se=1.2*Iout*0.8 Overall LLC conversion efficiency: Eff = Vout*Iout/(Vout*Iout+Pcore_T+Pcu_T+Pcu_L+Pcore_L+Pmos_se+Pmos_pr)