* Z:\home\khalils\Downloads\files\data\raw_asc\04a3a49d6e19_rhpz_small_signal_verification.asc
* Generated by LTspice 26.0.1 for Windows.
* AVERAGE OUTPUT CURRENT: \nSMALL SIGNAL MODEL
* AVERAGE OUTPUT CURRENT: \nEXACT NONLINEAR EXPRESSION
* AVERAGE OUTPUT CURRENT: \nCONVENTIONAL SMALL SIGNAL MODEL\n(e.g. CHRISTOPH BASSO)
* INPUT BUS VOLTAGE\nCONVERTER OUTPUT VOLTAGE\nCOUPLED INDUCTOR/TRANSFORMER TURNS RATIO (SECONDARY:PRIMARY)\nINDUCTOR CHARGING VOLTAGE\nINDUCTOR DISCHARGING VOLTAGE AS REFLECTED BACK TO PRIMARY SIDE\nSTEADY-STATE VALLEY CURRRENT\nMAGNETIZING INDUCTANCE\nSWITCHING FREQUENCY\nSWITCHING PERIOD
* INPUT PARAMETERS -- SYSTEM STEADY-STATE OPERATING CONDITIONS
* INDUCTOR CURRENT CHARGING SLOPE\nINDUCTOR CURRENT DISCHARGING SLOPE\nCONVENIENT VARIABLE SUBSTITUTION FOR A DENOMINATOR TERM FOUND IN EVERY COEFFICIENT\nCOEFFICIENT: adg*iv[n]^2\nCOEFFICIENT: bdg*iv[n-1]^2\nCOEFFICIENT: cdg*iv[n]*iv[n-1]\nCOEFFICIENT: ddg*iv[n]\nCOEFFICIENT: edg*iv[n-1]\nCONSTANT : fdg, APPEARS IN STEADY-STATE AVERAGE CURRENT COMPUTATION
* COMPUTED PARAMETERS -- SYSTEM VARIABLES AND COEFFICIENTS
* iv[n]
* iv[n-1]
* SYSTEM INPUT SOURCES
* STIMULUS GENERATION FOR VALLEY CURRENTS\ni[n] and i[n-1]
* AVERAGED CURRENT STEADY STATE OUTPUT
* SMALL SIGNAL MODELS COMPARED WITH EXACT NONLINEAR EXPRESSION
* FIR FILTER COEFFICIENTS FOR\nLTI SMALL-SIGNAL MODEL
* SYSTEM PARAMS RE-FACTORED\nINTO COMPATIBLE QUANTITIES\nUSED IN C. BASSO RHPZ EQN.
* VERIFICATION OF DISCRETE TIME SMALL SIGNAL ANALYTICAL MODEL FOR SWITCH-MODE INDUCTOR:
* TRANSFER FUNCTION OF VALLEY CURRENT TO AVERAGE OUTPUT CURRENT EXPRESSED AS FIR FILTER
* COMPARED TO CHRISTOPHE BASSO'S CONTINUOUS-TIME APPROXIMATION OF THE RIGHT-HALF PLANE ZERO
* DC term "fcg" maintained throughout\nthe discrete model term to see \nDC agreement with conventional \nRHPZ expression
* INVERSE ZERO-ORDER-HOLD FUNCTION
V1 iv0 0 {iv} AC 1
B3 k0 0 V=2*adg*iv + cdg*iv +ddg
B4 k1 0 V=2*bdg*iv +cdg*iv + edg
B10 IooChk 0 V=Iinf
B2 Ioo 0 V=(adg+bdg+cdg)*V(iv0)*V(iv0) + (ddg+edg)*V(iv0) + fdg
B1 idg_irm_ss 0 V=V(k0)*V(iv0) + V(k1)*V(iv1) + fdg
B13 idg_izoh 0 V=V(idg_irm_ss) Laplace=s*Tsw/(1 - exp(-s*Tsw))
B5 iv1 0 V=V(iv0) Laplace=exp(-s*Tsw)
B6 idg_irm 0 V=adg*V(iv0)*V(iv0) + bdg*V(iv1)*V(iv1) + cdg*V(iv0)*V(iv1) + ddg*V(iv0) + edg*V(iv1) + fdg
B7 <idgbasso> 0 V=V(Ioo) Laplace=(1 - s/wrhpz)
.param Vin 18.75
.param Vout 5.25
.param N 3.5
.param Vcg {Vin}
.param Vdg {N*Vout}
.param iv 7.5
.param Lm 17.0u
.param Fsw 130k
.param Tsw {1/Fsw}
.param mc {Vcg/Lm}
.param md {Vdg/Lm}
.param dencom {(mc*mc + 2*mc*md + md*md)}
.param adg {-(1/(2*Tsw))*((2*mc + md)/dencom)}
.param bdg {(1/(2*Tsw))*((md)/dencom)}
.param cdg {(1/(Tsw))*((mc)/dencom)}
.param ddg {(mc*mc)/dencom}
.param edg {mc*md/dencom}
.param fdg {(Tsw/2)*md*mc*mc/dencom}
.ac oct 500 10 {6.1*Fsw}
.param Dc {Vdg/(Vdg+Vcg)}
.param Dp {1-Dc}
.param wrhpz ro*Dp*Dp/(Dc*Lm)
.param Iinf {(adg+bdg+cdg)*iv*iv + (ddg+edg)*iv + fdg}
.param ro {Vdg/Iinf}
.backanno
.end

* LTspice schematic (.asc):
Version 4
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LINE Normal -368 -400 -1216 -400 2
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SYMBOL bv -1680 1440 R0
WINDOW 3 -127 197 Left 2
SYMATTR Value V=2*adg*iv + cdg*iv +ddg
SYMATTR InstName B3
SYMBOL bv -1664 1888 R0
SYMATTR InstName B1
SYMATTR Value V=V(k0)*V(iv0) + V(k1)*V(iv1) + fdg
SYMBOL bv -1376 1440 R0
WINDOW 3 -69 198 Left 2
SYMATTR Value V=2*bdg*iv +cdg*iv + edg
SYMATTR InstName B4
SYMBOL bv -176 1888 R0
SYMATTR InstName B6
SYMATTR Value V=adg*V(iv0)*V(iv0) + bdg*V(iv1)*V(iv1) + cdg*V(iv0)*V(iv1) + ddg*V(iv0) + edg*V(iv1) + fdg
SYMBOL bv -768 864 R0
SYMATTR InstName B2
SYMATTR Value V=(adg+bdg+cdg)*V(iv0)*V(iv0) + (ddg+edg)*V(iv0) + fdg
SYMBOL voltage -1184 224 R0
WINDOW 123 24 124 Left 2
WINDOW 39 0 0 Left 2
SYMATTR Value2 AC 1
SYMATTR InstName V1
SYMATTR Value {iv}
SYMBOL bv 976 1888 R0
SYMATTR InstName B13
SYMATTR Value V=V(idg_irm_ss) Laplace=s*Tsw/(1 - exp(-s*Tsw))
SYMBOL bv -928 1888 R0
SYMATTR InstName B7
SYMATTR Value V=V(Ioo) Laplace=(1 - s/wrhpz)
SYMBOL bv -896 224 R0
SYMATTR InstName B5
SYMATTR Value V=V(iv0) Laplace=exp(-s*Tsw)
SYMBOL bv -1056 864 R0
SYMATTR InstName B10
SYMATTR Value V=Iinf
FLAG -1424 1792 idg_irm_ss
FLAG -1664 2048 0
FLAG -896 768 Ioo
FLAG -768 1024 0
FLAG -1856 1344 k0
FLAG -1680 1600 0
FLAG -1520 1344 k1
FLAG -1376 1600 0
FLAG -1184 384 0
FLAG -1104 176 iv0
FLAG -896 384 0
FLAG -816 176 iv1
FLAG 32 1792 idg_irm
FLAG -176 2048 0
FLAG -736 1792 <idgbasso>
FLAG -928 2048 0
FLAG -1056 1024 0
FLAG -1184 768 IooChk
FLAG 976 2048 0
FLAG 1056 1792 idg_izoh
TEXT -1680 2136 Left 3 ;AVERAGE OUTPUT CURRENT: \nSMALL SIGNAL MODEL
TEXT -1216 -704 Left 2 !.param Vin 18.75\n.param Vout 5.25\n.param N 3.5\n.param Vcg {Vin}\n.param Vdg {N*Vout}\n.param iv 7.5\n.param Lm 17.0u\n.param Fsw 130k\n.param Tsw {1/Fsw}
TEXT -1216 -272 Left 2 !.param mc {Vcg/Lm}\n.param md {Vdg/Lm}\n.param dencom {(mc*mc + 2*mc*md + md*md)}\n.param adg {-(1/(2*Tsw))*((2*mc + md)/dencom)}\n.param bdg {(1/(2*Tsw))*((md)/dencom)}\n.param cdg {(1/(Tsw))*((mc)/dencom)}\n.param ddg {(mc*mc)/dencom}\n.param edg {mc*md/dencom}\n.param fdg  {(Tsw/2)*md*mc*mc/dencom}
TEXT -200 2136 Left 3 ;AVERAGE OUTPUT CURRENT: \nEXACT NONLINEAR EXPRESSION
TEXT -1208 552 Left 2 !.ac oct 500 10 {6.1*Fsw}
TEXT -944 2136 Left 3 ;AVERAGE OUTPUT CURRENT: \nCONVENTIONAL SMALL SIGNAL MODEL\n(e.g. CHRISTOPH BASSO)
TEXT -960 1544 Left 2 !.param Dc {Vdg/(Vdg+Vcg)}\n.param Dp {1-Dc}\n.param wrhpz ro*Dp*Dp/(Dc*Lm)
TEXT -960 1480 Left 2 !.param Iinf {(adg+bdg+cdg)*iv*iv + (ddg+edg)*iv + fdg}\n.param ro {Vdg/Iinf}
TEXT -920 -704 Left 2 ;INPUT BUS VOLTAGE\nCONVERTER OUTPUT VOLTAGE\nCOUPLED INDUCTOR/TRANSFORMER TURNS RATIO (SECONDARY:PRIMARY)\nINDUCTOR CHARGING VOLTAGE\nINDUCTOR DISCHARGING VOLTAGE AS REFLECTED BACK TO PRIMARY SIDE\nSTEADY-STATE VALLEY CURRRENT\nMAGNETIZING INDUCTANCE\nSWITCHING FREQUENCY\nSWITCHING PERIOD
TEXT -1216 -416 Left 2 ;INPUT PARAMETERS -- SYSTEM STEADY-STATE OPERATING CONDITIONS
TEXT -544 -280 Left 2 ;INDUCTOR CURRENT CHARGING SLOPE\nINDUCTOR CURRENT DISCHARGING SLOPE\nCONVENIENT VARIABLE SUBSTITUTION FOR A DENOMINATOR TERM FOUND IN EVERY COEFFICIENT\nCOEFFICIENT: adg*iv[n]^2\nCOEFFICIENT: bdg*iv[n-1]^2\nCOEFFICIENT: cdg*iv[n]*iv[n-1]\nCOEFFICIENT: ddg*iv[n]\nCOEFFICIENT: edg*iv[n-1]\nCONSTANT   :  fdg, APPEARS IN STEADY-STATE AVERAGE CURRENT COMPUTATION
TEXT -1216 32 Left 2 ;COMPUTED PARAMETERS -- SYSTEM VARIABLES AND COEFFICIENTS
TEXT -1104 200 Left 2 ;iv[n]
TEXT -816 200 Left 2 ;iv[n-1]
TEXT -1216 592 Left 2 ;SYSTEM INPUT SOURCES
TEXT -1208 456 Left 2 ;STIMULUS GENERATION FOR VALLEY CURRENTS\ni[n] and i[n-1]
TEXT -1216 1088 Left 2 ;AVERAGED CURRENT STEADY STATE OUTPUT
TEXT -1232 2368 Left 2 ;SMALL SIGNAL MODELS COMPARED WITH EXACT NONLINEAR EXPRESSION
TEXT -1680 1688 Left 2 ;FIR FILTER COEFFICIENTS FOR\nLTI SMALL-SIGNAL MODEL
TEXT -952 1664 Left 2 ;SYSTEM PARAMS RE-FACTORED\nINTO COMPATIBLE QUANTITIES\nUSED IN C. BASSO RHPZ EQN.
TEXT -1232 -848 Left 3 ;VERIFICATION OF DISCRETE TIME SMALL SIGNAL ANALYTICAL MODEL FOR SWITCH-MODE INDUCTOR:
TEXT -1224 -808 Left 2 ;TRANSFER FUNCTION OF VALLEY CURRENT TO AVERAGE OUTPUT CURRENT EXPRESSED AS FIR FILTER
TEXT -1224 -784 Left 2 ;COMPARED TO CHRISTOPHE BASSO'S CONTINUOUS-TIME APPROXIMATION OF THE RIGHT-HALF PLANE ZERO
TEXT -2128 1816 Left 2 ;DC term "fcg" maintained throughout\nthe discrete model term to see \nDC agreement with conventional \nRHPZ expression
TEXT 960 2104 Left 2 ;INVERSE ZERO-ORDER-HOLD FUNCTION