* Z:\home\khalils\Downloads\files\data\raw_asc\364a537fc926_llc_5th_eq_vo-omega.asc
* Generated by LTspice 26.0.1 for Windows.
R1 Vo 0 {RL}
C1 Vo 0 {Cf}
B1 0 Vo I={ks} * I(V_Its_sns)
B2 0 Vo I={kc} * I(V_Itc_sns)
Vfb N012 0 AC 1
E1 N008 0 V_omega 0 {Irc * Lr}
E2 0 N013 V_omega 0 {Irs * Lr}
L1 N008 N009 {Lr}
B3 N007 N011 V=2* {ks} * V(Vo)
L2 N013 N014 {Lr}
B4 N019 N017 V= 2 * {kc} * V(Vo)
R2 N011 0 {Rs}
R3 0 N017 {Rc}
V_Its_sns N001 N002 0
B5 N005 N009 V={Omega_s * Lr} * I(V_Irc_sns)
B6 N014 N015 V={Omega_s * Lr} * I(V_Irs_sns)
C2 N003 N005 {Cr}
B7 N003 N005 I={Omega_s * Cr } * V(Vrc_sns)
B8 N003 N005 I={Vrc * Cr } * V(V_omega)
C3 N015 N016 {Cr}
B9 N015 N016 I={Omega_s * Cr} * V(Vrs_sns)
B10 N015 N016 I={Vrs * Cr } * V(V_omega)
B11 N002 N007 V={krs} * I(V_Itc_sns)
B12 N023 N019 V= {krc} * I(V_Its_sns)
V_Itc_sns N021 N023 0
E3 Vrs_sns 0 N005 N003 1
E4 Vrc_sns 0 N015 N016 1
L3 N004 N006 {Lm}
B13 N010 N006 V={Omega_s * Lm} * I(V_Imc_sns)
L4 N020 N022 {Lm}
B15 N020 N018 V={Omega_s * Lm} * I(V_Ims_sns)
V_Imc_sns N021 N022 0
V_Ims_sns N001 N004 0
V_Irs_sns N003 N001 0
V_Irc_sns N016 N021 0
B14 0 N010 V={Ims * Lm} * V(V_omega)
B16 N018 0 V={Imc * Lm} * V(V_omega)
E5 V_omega 0 N012 0 {2*pi*F0}
* .param Lr = 360n
* .param Lm = 2.1u
* .param Cr = 110n
* .param n = 5
* .param Cf = 50u
* .param RL = 1
* .param Vg = 50
.param Lr = 14u
.param Lm = 60u
.param Cr = 30n
.param n = 4
.param Cf = 660u
.param RL = 2.3
.param Vg = 400
.param F0 = 1/(2*pi*sqrt(Lr*Cr))
.param Z0 = sqrt(Lr/Cr)
.param Req = 8* (n**2) * RL/(pi**2)
.param Qeq = Z0 / Req
.param fs = 1.2* F0
.param Omega_s =2*pi*fs
.param Xeq = Omega_s*Lr - 1/Omega_s/Cr
.param Ln = Lm/Lr
.param fn = fs/F0
.param Its = (2*Vg/pi/Req) * Ln * (fn**2) * (Ln + 1 - 1/(fn**2)) / ((fn**2) * ((Ln + 1 - 1/(fn**2))**2) + (Qeq*Ln*((fn**2) -1))**2)
.param Itc = (2*Vg/pi/Req) * (Ln**2) * fn * Qeq * (1 - (fn**2)) / ((fn**2) * ((Ln + 1 - 1/(fn**2))**2) + (Qeq*Ln*((fn**2) -1))**2)
.param Ims = Itc * Req / Omega_s / Lm
.param Imc = - Its * Req / Omega_s / Lm
.param Irs = Its + Ims
.param Irc = Itc + Imc
.param Vrs = Irc / Omega_s / Cr
.param Vrc = - Irs / Omega_s / Cr
.param ks = (2*n/pi) * Its/sqrt((Its**2) + (Itc**2))
.param kc = (2*n/pi) * Itc/sqrt(Its**2 + Itc**2)
.param Vo = (pi/4/n) * Req * sqrt(Its**2 + Itc**2)
.param Rs = (4*n*Vo/pi) * (Itc**2) / ((Its**2 + Itc**2)**1.5)
.param Rc = -(4*n*Vo/pi) * (Its**2) / ((Its**2 + Itc**2)**1.5)
.param krs = -(4*n*Vo/pi) * (Its * Itc) / ((Its**2 + Itc**2)**1.5)
.param krc = krs
* 5th order LLC small signal model control to output transfer function
.ac dec 100 10 100k
* Here 1V Vfb = F0, the frequency \nis proportional to Vfb value.\nd_omega/d_vfb = 2*pi*F0
.backanno
.end

* LTspice schematic (.asc):
Version 4
SHEET 1 3236 1600
WIRE 496 112 96 112
WIRE 736 112 576 112
WIRE -80 176 -144 176
WIRE 96 176 96 112
WIRE 96 176 0 176
WIRE 160 176 96 176
WIRE 320 176 240 176
WIRE -400 192 -496 192
WIRE -272 192 -320 192
WIRE -272 208 -272 192
WIRE -384 240 -512 240
WIRE -240 240 -336 240
WIRE -144 240 -144 176
WIRE -144 240 -240 240
WIRE 320 240 320 176
WIRE 736 272 736 112
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WIRE -240 304 -336 304
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WIRE 1392 544 1344 544
WIRE 320 560 320 464
WIRE -1056 592 -1056 544
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WIRE -1472 656 -1472 608
WIRE -1296 656 -1296 608
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WIRE 320 704 -464 704
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WIRE 736 736 736 704
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WIRE 880 800 880 768
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WIRE -1184 848 -1184 816
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WIRE -48 1280 -240 1280
WIRE 96 1280 32 1280
WIRE 160 1280 96 1280
WIRE 320 1280 320 1200
WIRE 320 1280 240 1280
WIRE 96 1344 96 1280
WIRE 496 1344 96 1344
WIRE 736 1344 736 1136
WIRE 736 1344 576 1344
FLAG -464 736 0
FLAG -1472 848 0
FLAG 880 800 0
FLAG 1392 544 Vo
IOPIN 1392 544 Out
FLAG -272 208 0
FLAG -496 192 Vrs_sns
FLAG -272 1248 0
FLAG -480 1232 Vrc_sns
FLAG -1184 608 V_omega
IOPIN -1184 608 In
FLAG -1184 848 0
SYMBOL res 1328 592 R0
SYMATTR InstName R1
SYMATTR Value {RL}
SYMBOL cap 1216 624 R0
SYMATTR InstName C1
SYMATTR Value {Cf}
SYMBOL bi2 880 624 R0
SYMATTR InstName B1
SYMATTR Value I={ks} * I(V_Its_sns)
SYMBOL bi2 992 592 R0
SYMATTR InstName B2
SYMATTR Value I={kc} * I(V_Itc_sns)
SYMBOL voltage -1472 640 R0
WINDOW 123 24 124 Left 2
WINDOW 39 0 0 Left 2
SYMATTR Value2 AC 1
SYMATTR InstName Vfb
SYMATTR Value ""
SYMBOL e -1056 576 R0
SYMATTR InstName E1
SYMATTR Value {Irc * Lr}
SYMBOL e -1056 736 R0
SYMATTR InstName E2
SYMATTR Value {Irs * Lr}
SYMBOL ind -976 560 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 5 56 VBottom 2
SYMATTR InstName L1
SYMATTR Value {Lr}
SYMBOL bv 736 384 R0
SYMATTR InstName B3
SYMATTR Value V=2* {ks} * V(Vo)
SYMBOL ind -976 896 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 5 56 VBottom 2
SYMATTR InstName L2
SYMATTR Value {Lr}
SYMBOL bv 736 1008 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Left 2
SYMATTR InstName B4
SYMATTR Value V= 2 * {kc} * V(Vo)
SYMBOL res 720 576 R0
SYMATTR InstName R2
SYMATTR Value {Rs}
SYMBOL res 720 720 R0
SYMATTR InstName R3
SYMATTR Value {Rc}
SYMBOL voltage 480 112 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 -32 56 VBottom 2
SYMATTR InstName V_Its_sns
SYMATTR Value 0
SYMBOL bv -672 544 R90
WINDOW 0 -32 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName B5
SYMATTR Value V={Omega_s * Lr} * I(V_Irc_sns)
SYMBOL bv -784 880 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 -32 56 VBottom 2
SYMATTR InstName B6
SYMATTR Value V={Omega_s * Lr} * I(V_Irs_sns)
SYMBOL cap -336 288 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName C2
SYMATTR Value {Cr}
SYMBOL bi2 -400 416 R270
WINDOW 0 32 40 VTop 2
WINDOW 3 -32 40 VBottom 2
SYMATTR InstName B7
SYMATTR Value I={Omega_s * Cr } * V(Vrc_sns)
SYMBOL bi2 -400 544 R270
WINDOW 0 32 40 VTop 2
WINDOW 3 -32 40 VBottom 2
SYMATTR InstName B8
SYMATTR Value I={Vrc * Cr } * V(V_omega)
SYMBOL cap -400 1136 R270
WINDOW 0 32 32 VTop 2
WINDOW 3 0 32 VBottom 2
SYMATTR InstName C3
SYMATTR Value {Cr}
SYMBOL bi2 -336 1008 R90
WINDOW 0 -32 40 VBottom 2
WINDOW 3 32 40 VTop 2
SYMATTR InstName B9
SYMATTR Value I={Omega_s * Cr} * V(Vrs_sns)
SYMBOL bi2 -336 880 R90
WINDOW 0 -32 40 VBottom 2
WINDOW 3 32 40 VTop 2
SYMATTR InstName B10
SYMATTR Value I={Vrs * Cr } * V(V_omega)
SYMBOL bv 736 256 R0
SYMATTR InstName B11
SYMATTR Value V={krs} * I(V_Itc_sns)
SYMBOL bv 736 1152 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Left 2
SYMATTR InstName B12
SYMATTR Value V= {krc} * I(V_Its_sns)
SYMBOL voltage 480 1344 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 -32 56 VBottom 2
SYMATTR InstName V_Itc_sns
SYMATTR Value 0
SYMBOL e -416 192 R270
SYMATTR InstName E3
SYMATTR Value 1
SYMBOL e -416 1232 R270
SYMATTR InstName E4
SYMATTR Value 1
SYMBOL ind 304 224 R0
SYMATTR InstName L3
SYMATTR Value {Lm}
SYMBOL bv 320 480 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Left 2
SYMATTR InstName B13
SYMATTR Value V={Omega_s * Lm} * I(V_Imc_sns)
SYMBOL ind 304 1104 R0
SYMATTR InstName L4
SYMATTR Value {Lm}
SYMBOL bv 320 1072 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Left 2
SYMATTR InstName B15
SYMATTR Value V={Omega_s * Lm} * I(V_Ims_sns)
SYMBOL voltage 144 1280 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 -32 56 VBottom 2
SYMATTR InstName V_Imc_sns
SYMATTR Value 0
SYMBOL voltage 144 176 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 -32 56 VBottom 2
SYMATTR InstName V_Ims_sns
SYMATTR Value 0
SYMBOL voltage -96 176 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 -32 56 VBottom 2
SYMATTR InstName V_Irs_sns
SYMATTR Value 0
SYMBOL voltage -64 1280 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 -32 56 VBottom 2
SYMATTR InstName V_Irc_sns
SYMATTR Value 0
SYMBOL bv 320 656 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Left 2
SYMATTR InstName B14
SYMATTR Value V={Ims * Lm} * V(V_omega)
SYMBOL bv 320 896 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Left 2
SYMATTR InstName B16
SYMATTR Value V={Imc * Lm} * V(V_omega)
SYMBOL e -1296 640 R0
SYMATTR InstName E5
SYMATTR Value {2*pi*F0}
TEXT 1664 -104 Left 2 !* .param Lr = 360n\n* .param Lm = 2.1u\n* .param Cr = 110n\n* .param n = 5\n* .param Cf = 50u\n* .param RL = 1\n* .param Vg = 50\n \n.param Lr = 14u\n.param Lm = 60u\n.param Cr = 30n\n.param n = 4\n.param Cf = 660u\n.param RL = 2.3\n.param Vg = 400\n \n.param F0 = 1/(2*pi*sqrt(Lr*Cr))\n.param Z0 = sqrt(Lr/Cr)\n.param Req = 8* (n**2) * RL/(pi**2)\n.param Qeq = Z0 / Req\n.param fs = 1.2* F0\n.param Omega_s =2*pi*fs\n \n.param Xeq = Omega_s*Lr - 1/Omega_s/Cr\n \n.param Ln = Lm/Lr\n.param fn = fs/F0\n \n.param Its = (2*Vg/pi/Req) * Ln * (fn**2) * (Ln + 1 - 1/(fn**2)) / ((fn**2) * ((Ln + 1 - 1/(fn**2))**2) + (Qeq*Ln*((fn**2) -1))**2)\n.param Itc = (2*Vg/pi/Req) * (Ln**2) * fn * Qeq * (1 - (fn**2)) / ((fn**2) * ((Ln + 1 - 1/(fn**2))**2) + (Qeq*Ln*((fn**2) -1))**2)\n \n.param Ims = Itc * Req / Omega_s / Lm\n.param Imc = - Its * Req / Omega_s / Lm\n \n.param Irs = Its + Ims\n.param Irc = Itc + Imc\n \n.param Vrs = Irc / Omega_s / Cr\n.param Vrc = - Irs / Omega_s / Cr\n \n.param ks = (2*n/pi) * Its/sqrt((Its**2) + (Itc**2))\n.param kc = (2*n/pi) * Itc/sqrt(Its**2 + Itc**2)\n \n.param Vo = (pi/4/n) * Req * sqrt(Its**2 + Itc**2)\n \n.param Rs = (4*n*Vo/pi) * (Itc**2) / ((Its**2 + Itc**2)**1.5)\n.param Rc = -(4*n*Vo/pi) * (Its**2) / ((Its**2 + Itc**2)**1.5)\n \n.param krs = -(4*n*Vo/pi) * (Its * Itc) / ((Its**2 + Itc**2)**1.5)\n.param krc = krs
TEXT -216 -24 Left 2 ;5th order LLC small signal model control to output transfer function
TEXT 1112 984 Left 2 !.ac dec 100 10 100k
TEXT -1536 400 Left 2 ;Here 1V Vfb = F0, the frequency \nis proportional to Vfb value.\nd_omega/d_vfb = 2*pi*F0