This document describes a simplified SPICE behavioral model for a saturable transformer. It provides an overview of the model concepts and parameters that characterize the saturable core and ideal transformer components of the model. These include BSAT, RLOSS, LM, and BEXP for the core, and N, RP, RS, and LP for the transformer. The document also provides examples of simulations using the model to demonstrate its hysteresis behavior under different excitation conditions.

1. Saturable transformer model Simplified SPICE Behavioral Model Bee Technologies Inc. All Rights Reserved Copyright (C) Bee Technologies Corporation 2012

2. Contents Model Overview Concept of the Model Parameter Settings of Saturable Core Saturable core SUBCKT using LTspiceIV <<-- Netlist is not open(If you buy this model , you can show netlist) Saturable Core Parameter Setting (Example) 5.1 Curve fitting: RLOSS 5.2 Curve fitting: LM 5.3 Curve fitting: BEXP 6. Dynamic Magnetizing Curves Characteristics 7. Basic Ideal Transformers and Their Parameters 7.1 Parameter settings of 1:1 ideal transformer 7.2 Parameter settings of 2:1 ideal transformer 7.3 Parameter settings of 1:2 ideal transformer 8. Saturable transformer SUBCKT Using LTspiceIV <<-- Netlist is not open(If you buy this model , you can show netlist) 9. 1:1 Saturable transformer model (Example) 10. 1:1 Saturable transformer model (Example) (Phase reverse) 11. 2:1 Saturable transformer model (Example) 12. 1:2 Saturable transformer model (Example) 13. 1:2 Saturable transformer model (Example) (Center tap) 14. Application Circuit Example: Flyback converter Library Files and Symbol Files Location Library Files Index Simulation Index All Rights Reserved Copyright (C) Bee Technologies Corporation 2012

3. This Saturable Transformer Simplified SPICE Behavioral Model is for users who require the model of the core loss and hysteresis as a part of their system. The model focuses on the hysteresis loop behavior in their operation area, which user can shape the B-H curve. 1) Model Overview All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Saturation Flux Density B S H (A-turns/m) B (Teslas) Coercive Field H C Remanent Flux Density B r Saturation Field H S Figure 1 , Hysteresis Loop and Magnetic Properties.

4. 2) Concept of the Model The Saturable core is characterized by parameters: BSAT, RLOSS, LM and BEXP, which represent the Flux density vs. Magnetic field characteristics of the Saturable core. The Ideal transformer is characterized by parameters: N, R P , R S and L P . Saturable Core Simplified SPICE Behavioral Model [Model parameters: BSAT, RLOSS, LM and BEXP] Ideal Transformer Simplified SPICE Behavioral Model [Model parameters: N, R P , R S and L P ] All Rights Reserved Copyright (C) Bee Technologies Corporation 2012

5. 3) Parameter Settings of Saturable Core BSAT  The saturation flux density (in teslas). e.g. 100mT, 350mT, 500mT Value = <BSAT> RLOSS  The resistor RLOSS represents a loss when a voltage is applied. e.g. 0.5 Ω , 1 Ω , 100K Ω Value = <RLOSS> LM  Magnetizing inductance of the core inductor (in henry). e.g. 1uH, 5uH, 50uH Value = <LM> BEXP  The exponent in the expression for coupling factor K C . e.g. 2, 4, 8 Value = <BEXP> From the Saturable Core specification, the model is characterized by setting parameter BSAT, then adjust the parameters RLOSS, LM and BEXP to shape the dynamic magnetic curve. All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Model Parameters: B-H Curve test points Figure 2 , Saturable core model (Default parameters).

6. 4) Saturable core SUBCKT using LTspiceIV All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 3 , Saturable core subcircuit SPICE compatible, the key parameters are shown in bold. Information of Netlist

7. 5) Saturable Core Parameter Setting (Example) Material: NC-2H Manganese Zinc Ferrite Cores with B S = 500(mT) B r = 140(mT) H C = 15.9(A/m) Conditions: F = 10(KHz) T C = 23(  C) All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 4 , Dynamic Magnetization Curves. Specification   The data is provided in the datasheet Input the parameter BSAT=500m

8. 5.1) Curve fitting: RLOSS Condition: F=10KHz, Vin=80V P Parametric sweep: RLOSS=0.5 Ω , 1 Ω , 100K Ω All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 0.5 Ω --- 1 Ω --- 100K Ω --- Figure 5 , The magnetizing line difference, RLOSS. H (A-turns/m) B (Teslas)

9. 5.2) Curve fitting: LM Condition: F=10KHz, Vin=80V P Parametric sweep: LM=1uH, 5uH, 50uH All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 1uH --- 5uH --- 50uH --- Figure 6 , The magnetizing line difference, LM . H (A-turns/m) B (Teslas)

10. 5.3) Curve fitting: BEXP Condition: F=10KHz, Vin=80V P Parametric sweep: BEXP=2, 4, 8 All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 2 --- 4 --- 8 --- Figure 7 , The magnetizing line difference, BEXP. H (A-turns/m) B (Teslas)

11. 6) Dynamic Magnetizing Curves Characteristics - Evaluation Circuit and Setting Sine wave excitation Square wave excitation Condition: F=10KHz, Vin=80V P , T C =23°C .tran 0 200u 100u 10n .lib score.sub All Rights Reserved Copyright (C) Bee Technologies Corporation 2012

12. 6) Dynamic Magnetizing Curves Characteristics - Simulation Result The saturable core model is completed with both sine and square wave (above) excitation as shown in these LTspiceIV simulations. All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 8 , Sine wave excitation Figure 9 , Square wave excitation

13. 7) Basic Ideal Transformers and Their Parameters The relationship between the Voltage and current are defined as equations below. V P is the primary voltage. V S is the secondary voltage. I P is the primary current. I S is the secondary current. N P is the turns number of primary winding. N S is the turns number of secondary winding. All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 10 , Symbol of basic ideal transformer with The voltage to current relationships. N P N S I P I S V P V S 1 : N + - + - (7.2) (7.3) (7.1) N is the turns ratio of Ideal transformer (above).

14. 7.1) Parameter settings of 1:1 ideal transformer LP  Inductance of primary winding (in henry). e.g. 100uH, 250uH, 500uH Value = <LP> N  is the turns ratio of Ideal transformer. e.g. 0.1, 0.5, 1 Value = <N> RP  A series resistance of primary winding (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RP> RS  A series resistance of secondary winding (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RS> All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Model Parameters: Figure 11 , 1:1 Ideal transformer (Default parameters). Figure 12 , 1:1 Phase reverse ideal transformer (Default parameters).

15. 7.2) Parameter settings of 2:1 ideal transformer LP  Inductance of primary winding (in henry). e.g. 100uH, 250uH, 500uH Value = <LP> N  is the turns ratio of Ideal transformer. e.g. 0.1, 0.5, 1 Value = <N> RP1  A series resistance of primary winding 1 (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RP1> RP2  A series resistance of primary winding 2 (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RP2> RS  A series resistance of secondary winding (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RS> All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Model Parameters: Figure 13 , 2:1 Ideal transformer (Default parameters).

16. 7.3) Parameter settings of 1:2 ideal transformer LP  Inductance of primary winding (in henry). e.g. 100uH, 250uH, 500uH Value = <LP> N  is the turns ratio of Ideal transformer. e.g. 0.1, 0.5, 1 Value = <N> RP  A series resistance of primary winding (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RP> RS1  A series resistance of secondary winding 1 (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RS1> RS2  A series resistance of secondary winding 2 (in ohm). e.g. 1m Ω , 10m Ω , 100m Ω Value = <RS2> All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Model Parameters: Figure 14 , 1:2 Ideal transformer (Default parameters). Figure 15 , 1:2 Center tap ideal transformer (Default parameters).

17. 8) Saturable transformer SUBCKT Using LTspiceIV All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 17 , Saturable transformer equivalent circuit. Figure 16 , Saturable transformer symbol, the key parameters are shown in bold. Information of Netlist

18. Condition: F=10KHz, V IN =50V P , V OUT =5V P , R OUT =10 Ω .tran 0 2500u 0 50n .lib tfmr1.sub 9) 1:1 Saturable transformer model (Example) - Simulation Circuit and Setting All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Saturable transformer model Primary current Output Voltage 1 : {N} Secondary current

19. 9) 1:1 Saturable transformer model (Example) - Simulation Result All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Input voltage Output voltage Input Current Output Current Figure 18 , The Input–Output Characteristics of 1:1 Saturable transformer.

20. Condition: F=10KHz, V IN =50V P , V OUT =5V P , R OUT =10 Ω .tran 0 2500u 0 50n .lib tfmr1_rev.sub 10) 1:1 Saturable transformer model (Example) - Simulation Circuit and Setting (Phase reverse) All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 1 : {N}

21. 10) 1:1 Saturable transformer model (Example) - Simulation Result (Phase reverse) All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 19 , The Input–Output Characteristics of 1:1 Saturable transformer (Phase reverse). Input voltage Output voltage Input Current Output Current

22. Condition: F=10KHz, V IN =25V P , V OUT =5V P , R OUT =10 Ω .tran 0 2500u 0 50n .lib tfmr2prim.sub 11) 2:1 Saturable transformer model (Example) - Simulation Circuit and Setting All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 1 : {N}

23. 11) 2:1 Saturable transformer model (Example) - Simulation Result All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 20 , The Input–Output Characteristics of 2:1 Saturable transformer. Input voltage 1 Input Current 1 Output voltage Output Current Input voltage 2 Input Current 2

24. Condition: F=10KHz, V IN =50V P , V OUT1 =V OUT2 =5V P , R OUT =10 Ω .tran 0 2500u 0 50n .lib tfmr2.sub 12) 1:2 Saturable transformer model (Example) - Simulation Circuit and Setting All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 1 : {N}

25. 12) 1:2 Saturable transformer model (Example) - Simulation Result All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Input voltage Output voltage 1 Input Current Output Current 1 Figure 21 , The Input–Output Characteristics of 1:2 Saturable transformer. Output voltage 2 Output Current 2

26. Condition: F=10KHz, V IN =50V P , V OUT1 =V OUT2 =5V P , R OUT =10 Ω .tran 0 2500u 0 50n .lib tfmr2_ct.sub 13) 1:2 Saturable transformer model (Example) - Simulation Circuit and Setting (Center tap) All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 1 : {N}

27. 13) 1:2 Saturable transformer model (Example) - Simulation Result (Center tap) All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Figure 22 , The Input–Output Characteristics of 1:2 Saturable transformer (Center tap). Input voltage Output voltage 1 Input Current Output Current 1 Output voltage 2 Output Current 2

28. Condition: F=40KHz, V IN =24V, V OUT =5V, R L =5 Ω , C L =200uF, L P =500uH .tran 0 10m 0 100n startup .lib tfmr1_rev.sub 14) Application Circuit Example: Flyback converter - Simulation Circuit and Setting All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 1 : {N}

29. 14) Application Circuit Example: Flyback converter - Simulation Result All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Secondary voltage of transformer Output voltage= 5Vdc Figure 23 , Flyback converter with Saturable transformer model. Output ripple voltage Secondary current of transformer V RIPPLE Input voltage= 24Vdc

30. Library Files and Symbol Files Location All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 … \Simulations C:\Program Files\LTC\LTspiceIV\lib\sub C:\Program Files\LTC\LTspiceIV\lib\sym Copy/Paste into Copy/Paste into Copy the library files (.lib) from the folder …\Simulations \.lib\, then paste into the folder C:\Program Files\LTC\LTspiceIV\lib\sub Copy the symbol files(.asy) from the folder …\Simulations \.asy\, then paste into the folder C:\Program Files\LTC\LTspiceIV\lib\sym

31. Library Files Index All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Model Library Symbol Saturable Core……....................................................... 1:1 Saturable transformer model………………….......... 1:1 Saturable transformer model (Phase reverse)……. 2:1 Saturable transformer model..…………….………… 1:2 Saturable transformer model..…….………………… 1:2 Saturable transformer model (Center tap)……....... score.sub tfmr1.sub tfmr1_rev.sub tfmr2prim.sub tfmr2.sub tfmr2_ct.sub SCORE.asy TFMR1.asy TFMR1_REV.asy TFMR2PRIM.asyTFMR2.asy TFMR2_CT.asy

32. Simulation Index All Rights Reserved Copyright (C) Bee Technologies Corporation 2012 Simulations Folder name Curve fitting: RLOSS…………………………………………........ Curve fitting: LM………………………………………………........ Curve fitting: BEXP………………………………………………… Dynamic Magnetizing Curves Characteristics…….................... 1:1 Saturable transformer model (Example)…………………….. 1:1 Saturable transformer model (Example) (Phase reverse)… 2:1 Saturable transformer model (Example)..…………….…….. 1:2 Saturable transformer model (Example)..…….…………….. 1:2 Saturable transformer model (Example) (Center tap)……... Application Circuit Example: Flyback converter……………….... Curve fitting Curve fitting Curve fitting Sat_Core Sat_Trans1 Sat_Trans2 Sat_Trans3 Sat_Trans4 Sat_Trans5 Appl