SPICE modeling of Magnetic Core from Datasheet

Vittorio Carboni

Department of Electronics and Automatic, University of Ancona 1999/2000

SPICE simulations and analisys by Ing. Cristoforo Baldoni

1. Switching  power supply: Choice of ferrite

2. Simplified calculation of the transformer

3. Transformer for Flyback converter: Calculation example

4. Transformer for Forward converter :Calculation example

5. Windings: Supports, wires and insulation

 

On what

How

With what

Skin and proximity effects

6. Let’ s complete the design of the flyback transformer

Primary

Secondary

Conclusions

7. Appendix

8. SPICE modeling of ETD49 N67 core from datasheet

9. Bibliography

 

1. Switching  power supply: Choice of ferrite

The first step in the design of the transformer is the choice of the ferrite as physical form,  type of material and dimensions. It’s a very important choice that characterizes the project as all subsequent calculations based on it. An error of assessment may lead, at the end of designing, to realize, for example, that the dimensions are not suitable: this means start again with considerable lost of time and resources.

The ferrites are characterized by very low losses at high frequencies, they are made with alloys of iron oxides and other metals such as zinc and manganese. The material is pulverized together with insulating oxides and then modeled using techniques typical of ceramics. This allows to make ferrites with a great variety of shapes and sizes and tolerances very restricted about magnetic and mechanically characteristics. They, also, can be machined with precision after the operation of the cooking.

The ferrites typically have a density of the saturation flux between 3 and 5 kGauss, also the presence of oxides increases its specific resistivity at very high levels thus allowing to reduce losses due to eddy currents. The available shapes include bars, toroids, EE EI and UI cores. The Curie temperature TC, namely the temperature at which the material loses its ferromagnetic properties, is between 100 and 300 ° C, depending on the type of material; the phenomenon is reversible, reducing the temperature to below the TC material regains its properties.

For low to medium power transformers E-Series is the best choice. As the acronym suggests, the magnetic core is composed of two elements in the shape of E. The two pieces forming the magnetic circuit, are slipped into the holder of the windings and locked in place with the clips and / or bonded with Araldite or other epoxy adhesives. The three contact surfaces of the half-cores are machined so as to reduce the roughness and therefore contain to negligible size the not intentional air gap . In some cases the air gap is desired, this can be obtained realizing the central column of the half-core shorter than outer ones.

figure1

Figure 1 – Example of assembling of a kit composed of the support for the windings, a pair of ferrites of ETD type and a pair of fastening clips. (FERRITES and Accessories, Siemens Matsushita Components)

It’s possible choose from a catalog of half-cores with air gap calibrated. For the ferrite type ETD49, for example, we can have 4 values of the air gap: 0.20 +- 0.02 mm, 0.50 +- 0.05 mm, 1.00 +- 0.05, 2.00 +- 0.05 mm.

Coupling a half-core with air gap with another without, or also with air gap, also of different value, it is possible to obtain numerous combinations.

The ferrites of series E and ETD are widely used, so are easy to find. The catalog Siemens Matsushita indicates that the materials available for the E-series are different and coded with the initials N27, N67, N87, N49, N30, T37. The choice of material to use is correlated with the switching frequency: the type N27 is suitable for power applications in a frequency band of switching up to 100KHz, N67 is suitable for similar application, but the frequency range is between 100KHz and the 300KHz. Table 1 shows the possible applications for different materials. The E series has the classical central square column, other families in the same series are available for special applications such as the best known:

ETD stands for Economic Transformer Design, with circular cross-section of the center column

EFD stands for Economic Flat Design transformer for applications with space vertical content.

table1

Table 1 – Some parameters for the type ferrites ETD (FERRITES and Accessories, Siemens Matsushita Components).

Table 2 – Maximum permissible temperature rise for different materials (FERRITES and Accessories, Siemens Matsushita Components).

Table 3 – Thermal resistance for different types and sizes of ferrite (FERRITES and Accessories, Siemens Matsushita Components).

The most important parameters for a correct choice of the ferrite are:

1. Maximum power (Ptrans)

2. Type of converter (Forward, Flyback, Push-Pull)

3. Switching frequency and maximum permissible temperature

4. maximum volume

To make the choice you might consider that the manufacturer, as a rule, always indicates the limit values, so if it is not pressing the issue of costs, it is a good idea to choose on the table, the type immediately above the one that delivers the requested power. This will avoid,later in the phase of winding, to discover that the number of turns calculated, with the wire section calculated does not enter for lack of space in the throat of the support of the windings. This precaution is especially recommended if the transformer should be wrapped in accordance with the safety standards (minimum distances between the different layers of the windings, using wire with double insulation etc..).

It follows an example of calculation of a switching transformer in [1]; the approach to this type of  calculation is in many passages forcibly empirical, in many other simplified. On the other hand a completely theoretical discussion would result in a significant waste of resources without the benefits of improved performance.

SPICE modeling of a JFET from Datasheet

In this article we’ ll see how to find the parameters used to describe the mathematical behaviour of JFET (Junction Field Effect Transistors).The syntax for the N-channel model is:

model ModelName NJF( par1=a par2=b………parn=x)

while for the P-channel model is:

model ModelName PJF( par1=a par2=b………parn=x)

Where par1 par2… parn are the parameters that allow us to model the equations of the JFET transistor.

The main parameters for modeling the JFET are listed below in this table:

 

ParametersDescriptionUnitsDefault Value
AFFlicker noise exponentno unit dimension1.0
ALPHAIonization coefficient1/V1e-006
BETATransconductance coefficientA/V^20.0001
BETATCEBETA exponential temperature coefficient%/°C-0.5
CGDZero-bias gate-drain p-n capacitanceF1e-012
CGSZero-bias gate-source p-n capacitanceF1e-012
FCForward-bias depletion capacitance coefficientno unit dimension0.5
ISGate p-n saturation currentA1e-014
ISRGate p-n recombination current parameterA0
KFFlicker noise coefficientno unit dimension1e-018
LAMBDAChannel-length modulation1/V1e-006
MGate p-n grading coefficientno unit dimension0.5
NGate p-n emission coefficientno unit dimension1.0
NREmission coefficient for ISRno unit dimension2.0
PBGate p-n potentialV1.0
RDDrain ohmic resistanceOhm1.0
RSSource ohmic resistanceOhm1.0
VKIonization knee voltageV1.0
VTOThresold voltageV-2.0
VTOTCVTO temperature coefficientV/°C-0.0025
XTIIS temperature coefficientno unit dimension3.0

SPICE modeling of a BJT from Datasheet

BJT bipolar transistors require a certain number of parameters to get a good model.The syntax for this model is:

.model ModelNameNPN (par1=a par2=b………parn=x)

for PNP case:

.model ModelNamePNP (par1=a par2=b………parn=x)

where par1 par2…….parn are the parameters that allow to model equations of the BJT.

The main parameters for a reasonable modeling of the behavior of the component are summarized in the following table:

ParametersDescriptionUnitsDefault Value
ISTransport saturation currentA1e-16
XTIIS temperature effect exponentno unit dimension3.0
EGBandgap voltage (barrier height)eV1.11
VAFForward Early voltageVInfinite
BFIdeal maximum forward betano unit dimension100
ISEBase-emitter leakage saturation currentA0
NEBase-emitter leakage emission coefficientno unit dimension1.5
IKFCorner for forward-beta high-current roll-offAInfinite
NKHigh-current roll-off coefficientno unit dimension0.5
XTBForward and reverse beta temperature coefficientno unit dimension0
BRIdeal maximum reverse betano unit dimension1.0
ISCBase-collector leakage saturation currentA0
NCBase-collector leakage emission coefficientno unit dimension2.0
IKRCorner for reverse-beta high-current roll-offAInfinite
RCCollector ohmic resistanceOhm0
CJCBase-collector zero-bias p-n capacitanceF0
MJCBase-collector p-n grading factorno unit dimension0.33
VJCV0.75
FCForward-bias depletion capacitor coefficientno unit dimension0.5
CJEBase-emitter zero-bias p-n capacitanceF0
MJEBase-emitter p-n grading factorno unit dimension0.33
VJEBase-emitter built-in potentialV0.75
TRIdeal reverse transit timesec1e-8
TFIdeal forward transit timesec0
ITFTransit time dependency on IcA0
XTFTransit time bias dependence coefficientno unit dimension0
VTFTransit time dependency on VbcVInfinite
RBZero-bias (maximum) base resistanceOhm0

SPICE modeling of a Diode from Datasheet

Modeling in SPICE& a diode is not a trivial work. Although the operation of the diode is quite simple, extract a model from datasheet takes some time.Every component has its own syntax defined in SPICE , in the case of the diode:

.model ModelName D (par1=a par2=b………parn=x)

where par1 par2 …. parn are characteristic parameters of diode.

we can sum up the set of main parameters in the following table:

ParameterDescriptionUnitDefault value
BVReverse breakdown knee voltageVInfinite
CJOZero-bias p-n capacitanceF0
EGBandgap voltageeV1.11
FCForward-bias depletion capacitance coefficientno unit dimension0.5
IBLVLow-level reverse breakdown knee correntA0
IBVReverse breakdown knee correntA1e-10
IKFHigh-injection knee currentAInfinite
ISSaturation correntA1e-14
ISRRecombination current parameterA0
Mp-n grading coefficientno unit dimension0.5
NEmission coefficientno unit dimension1.0
NREmission coefficient for ISRno unit dimension2.0
RSParasitic resistanceOhm0
TTTransit timesec0
VJp-n potentialV1.0
XTIIS temperature exponentno unit dimension3.0

All these parameters are used by SPICE to describe the behavior of the diode in the different situations of signal, for example in direct polarization in DC that, forward current will be:

ID = IS*(e^(VD/(N*Vt))-1)

where VD is the forward voltage, Vt = k * T / q is the thermal voltage equal to 0.026 V at 27 degrees Celsius.

The so-called recombination current is instead calculated as

Irec = ISR*(e^(VD/(N*Vt))-1).

Other equations from the given parameters describing the capacitance of the junction, its evolution with temperature and more.

At this point we have to derive the various parameters from the datasheet of the component. Assume we want to model a silicon diode 1N4148. The extraction of the parameters of the table from the values reported in the datasheet, is not immediate for almost none of the parameters.look at the values of our interest in datasheet:

data1

From the table we can get BV which is equal to VRM, in other cases reported as Vbr, or in the case of Zener diode Vz.

data2

From this second table we see that the maximum leakage current at 25 degrees is Ir = 5 uA.We can take IBV as equal to 10 times Ir. Usually for this type of diodes the value of IBV is around 100uA. For Zener diodes Ir can be called Izk, or in other cases as Ibr.

CJO can be directly equal to the value specified in the datasheet as Cj or Ctot, in this case is 4pF.