* Z:\home\khalils\Downloads\files\data\raw_asc\364a537fc926_llc_5th_eq_vo-omega.asc
* Generated by LTspice 26.0.1 for Windows.
* .param Lr = 360n
* .param Lm = 2.1u
* .param Cr = 110n
* .param n = 5
* .param Cf = 50u
* .param RL = 1
* .param Vg = 50
* 5th order LLC small signal model control to output transfer function
* Here 1V Vfb = F0, the frequency \nis proportional to Vfb value.\nd_omega/d_vfb = 2*pi*F0
B14 0 N010 V={Ims * Lm} * V(V_omega)
B5 N005 N009 V={Omega_s * Lr} * I(V_Irc_sns)
R2 N011 0 {Rs}
V_Irs_sns N003 N001 0
B6 N014 N015 V={Omega_s * Lr} * I(V_Irs_sns)
L3 N004 N006 {Lm}
C3 N015 N016 {Cr}
E1 N008 0 V_omega 0 {Irc * Lr}
L4 N020 N022 {Lm}
B4 N019 N017 V= 2 * {kc} * V(Vo)
B15 N020 N018 V={Omega_s * Lm} * I(V_Ims_sns)
C2 N003 N005 {Cr}
B9 N015 N016 I={Omega_s * Cr} * V(Vrs_sns)
B10 N015 N016 I={Vrs * Cr } * V(V_omega)
E5 V_omega 0 N012 0 {2*pi*F0}
L2 N013 N014 {Lr}
V_Imc_sns N021 N022 0
B16 N018 0 V={Imc * Lm} * V(V_omega)
E2 0 N013 V_omega 0 {Irs * Lr}
R3 0 N017 {Rc}
B7 N003 N005 I={Omega_s * Cr } * V(Vrc_sns)
B2 0 Vo I={kc} * I(V_Itc_sns)
E4 Vrc_sns 0 N015 N016 1
B3 N007 N011 V=2* {ks} * V(Vo)
R1 Vo 0 {RL}
V_Itc_sns N021 N023 0
B13 N010 N006 V={Omega_s * Lm} * I(V_Imc_sns)
E3 Vrs_sns 0 N005 N003 1
B1 0 Vo I={ks} * I(V_Its_sns)
B11 N002 N007 V={krs} * I(V_Itc_sns)
C1 Vo 0 {Cf}
Vfb N012 0 AC 1
B12 N023 N019 V= {krc} * I(V_Its_sns)
V_Its_sns N001 N002 0
V_Ims_sns N001 N004 0
B8 N003 N005 I={Vrc * Cr } * V(V_omega)
L1 N008 N009 {Lr}
V_Irc_sns N016 N021 0
.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
.ac dec 100 10 100k
.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
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WIRE 96 1344 96 1280
WIRE 496 1344 96 1344
WIRE 736 1344 736 1136
WIRE 736 1344 576 1344
IOPIN 1392 544 Out
IOPIN -1184 608 In
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 ind 304 224 R0
SYMATTR InstName L3
SYMATTR Value {Lm}
SYMBOL bi2 880 624 R0
SYMATTR InstName B1
SYMATTR Value I={ks} * I(V_Its_sns)
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 bi2 992 592 R0
SYMATTR InstName B2
SYMATTR Value I={kc} * I(V_Itc_sns)
SYMBOL bv 736 384 R0
SYMATTR InstName B3
SYMATTR Value V=2* {ks} * V(Vo)
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 ind 304 1104 R0
SYMATTR InstName L4
SYMATTR Value {Lm}
SYMBOL res 1328 592 R0
SYMATTR InstName R1
SYMATTR Value {RL}
SYMBOL ind -976 896 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 5 56 VBottom 2
SYMATTR InstName L2
SYMATTR Value {Lr}
SYMBOL e -416 1232 R270
SYMATTR InstName E4
SYMATTR Value 1
SYMBOL ind -976 560 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 5 56 VBottom 2
SYMATTR InstName L1
SYMATTR Value {Lr}
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 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 res 720 576 R0
SYMATTR InstName R2
SYMATTR Value {Rs}
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 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 cap 1216 624 R0
SYMATTR InstName C1
SYMATTR Value {Cf}
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 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 -1056 576 R0
SYMATTR InstName E1
SYMATTR Value {Irc * Lr}
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 320 480 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 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 cap -400 1136 R270
WINDOW 0 32 32 VTop 2
WINDOW 3 0 32 VBottom 2
SYMATTR InstName C3
SYMATTR Value {Cr}
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 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 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 res 720 720 R0
SYMATTR InstName R3
SYMATTR Value {Rc}
SYMBOL bv 736 256 R0
SYMATTR InstName B11
SYMATTR Value V={krs} * I(V_Itc_sns)
SYMBOL e -1056 736 R0
SYMATTR InstName E2
SYMATTR Value {Irs * Lr}
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 e -1296 640 R0
SYMATTR InstName E5
SYMATTR Value {2*pi*F0}
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 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 -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 -416 192 R270
SYMATTR InstName E3
SYMATTR Value 1
SYMBOL cap -336 288 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName C2
SYMATTR Value {Cr}
FLAG -464 736 0
FLAG -1472 848 0
FLAG 880 800 0
FLAG 1392 544 Vo
FLAG -272 208 0
FLAG -496 192 Vrs_sns
FLAG -272 1248 0
FLAG -480 1232 Vrc_sns
FLAG -1184 608 V_omega
FLAG -1184 848 0
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