# Single Transistor Forward Converter

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## How to use the program

Reference: The shapes of current and voltage curves are calculated using Faraday's Law. They do not represent an incremental simulation like it is done normally by programs like P-Spice. In the calculations the forward voltages of the diodes are considered with VF = 0.7V, and the transistors are interpreted as ideal switches.
• The values of all input fields can be changed.
• If an input field is left empty, a default value is chosen. This value is displayed after leaving the input field in question.
• The switch mode power supply operates within a certain input range i.e. between Vin_min and Vin_max.
Note:
• For the european mains of 230V +/-10% and behind the rectifier and the smoothing (with a voltage ripple of 10%) the input voltage range is between Vin_min = 250V and Vin_max = 360V.
• For wide range Switch Mode Power Supplies the input voltage range of the mains is from 100Vac -10% (Japan) to 240Vac +6% (Great Britain). In this case, the DC input range of the power supply is from Vin_min =110V to Vin_max =360V.
• For use of a power factor pre-regulator the input voltage range is normally from Vin_min =360V to Vin_max =400V.
• The program needs the output values Vout and Iout.
• The switching frequency  f  is the operating frequency of the transistor.
• If the field "proposal" is activated for the inductor L, a value for L and the corresponding current ripple ΔIL is proposed. These values are laid out such that ΔIL = 0.4Iout with Vin_max as the input voltage.
• If the field "proposal" for the input field "N1/N2" is activated, the turns ratio N1/N2 is proposed. This suggestion is chosen such that the required output voltage can be achieved using Vin_min as an input voltage.
• If you do not agree with our proposals, you can change N1/N2 or L as well as ΔIL. The field "proposal" is then deactivated automatically.
• The value Vin is the value for the calculation of the current and voltage diagrams on the right side of the display. Vin must lie between Vin_min and Vin_max.

## Application

The Single Transistor Forward Converter belongs to the primary switched converter family since there is isolation between input and output. It is suitable for output powers up to several hundred Watts.

## Function principals Illustration 1: Single Transistor Forward Converter

For the following analysis it will be assumed that the transistor is simplified as an ideal switch and the diode has no forward voltage drop. In the program itself, the diode will take into account a forward voltage drop VF = 0.7V.

The forward converter transfers the energy during the on-time of the transistor. During this time the voltage V1 is equal to the input voltage Vin. The winding N2 is in the same direction as N1. When the transistor is on the voltage V2 at N2 is given by V2 = Vin·N2/N1. The voltage V2 charges the output capacitor Cout through the inductor L.

During the off-time of the transistor, N1 and N2 are without current. The inductor L draws its current through the diode D3. At this time the value of the voltage V3 is equal to zero.

During the off-time of the transistor, the magnetic flux of the transformer has to be reduced to zero. The transformer core is demagnetized with N1' via D1 to Vin. N1' is therefore wound in the opposite direction to N1 and has an equal number of turns. Therefore the demagnetisation needs the same time interval as the on-time of the transistor. For this the minimum off-time has to be as long as the on-time. This means that the maximum duty cycle t1/T for this converter may never be higher than 50%.

During the off-time, the voltage at N1' is equal to the input voltage Vin. This voltage will be transformed back to the primary winding N1 such that V1 = -Vin. Due to this the transistor drain-source voltage steps up to Vds > 2Vin when the transistor is turned off.

The voltage V3 is therefore a pulse-width-modulated voltage which jumps between zero and Vin· N2/N1. The Low-Pass filter, formed by the inductor and the output capacitor, produces the average value of V3. For continuous mode (IL never becomes zero) this leads to: Due to the fact that the duty cycle t1/T may not be greater than 50%, it follows for the turns ratio that: In the program, this value is multiplied by a factor of 0.95, so that the proposed value for N1/N2 includes a small margin which guarantees the demagnetisation of the core, when the input voltage is minimal, (remember: at minimum input voltage the duty cycle reaches its maximum).

For the calculation of the inductor L, the same rules as for the Buck Converter can be used. One also distinguishes between discontinuous and continuous mode, depending on whether or not the inductor current falls to zero during the off-time of the transistor.

During continuous operation: The output voltage depends only on the duty cycle and the input voltage, it is load independent. The inductor current IL has a triangular shape and its average value is determined by the load. The change in inductor current ΔIL is dependent on L and can be calculated with the help of Faraday's Law.
During continuous mode, with Vout = Vin · (N2/N1) ·t1/T and a chosen switching frequency  f  it can be shown that: The change in inductor current is load independent. The output current Iout is taken to be the average value of the inductor current IL.

At low load current, namely if Iout < ΔIL/2, the inductor current IL falls to zero during every switching cycle. This mode is called discontinuous mode (see illustration 2). For this mode the calculations above are not valid.

In that moment, when the inductor current becomes zero, the voltage V3 jumps to the value of Vout. The diode-junction capacitance forms a resonant circuit with the inductance, which is activated by the voltage jump across the diode D3. The voltage V3 then oscillates and fades away.  Continuous Mode Discontinuous Mode

Illustration 2: Operating modes of the Single Transistor Forward Converter

## Tips

• The larger the chosen value of the inductor L, the smaller the current ripple ΔIL. However this results in a physically larger and heavier inductor.
• The higher the chosen value of the switching frequency  f , the smaller the size of the inductor. However the switching losses of the transistor also become larger as  f  increases.
• The smallest possible physical size for the inductor is achieved when ΔIL = 2Iout at Vin_max. However, the switching losses at the transistors are at their highest in this state.
• Choose ΔIL so that it is not too big. The suggestions proposed by us have adequately small current ripple along with physically small inductor size. With a larger current ripple, the voltage ripple of the output voltage Vout becomes clearly bigger while the physical size of the inductor decreases marginally.
• It is best not to alter the turns ratio N1/N2 proposed by us.

## Mathematics used in the program

The following parameters must be entered into the input fields:

Vin_min, Vin_max, Vout, Iout and  f

Using these parameters, the program produces a proposal for N1/N2 and L: (the factor of 0.95 is taken into account to allow for the fact that the duty cycle t1/T = 0.5 cannot be completely reached).  VF = 0.7 (Diode Forward-voltage)

ΔIL = 0.4Iout
For the calculation of the curve-shapes, and also for the calculation of "ΔIL for Vin_max", two cases have to be distinguished, i.e. continuous mode and discontinuous mode:  From this it follows that:

1. For ΔIL< 2Iout the converter is in continuous mode and it follows that: ,  2. For ΔIL> 2Iout the converter is in discontinuous mode and it follows that: ,  Main page | How to use the program | Function principals | Mathematics used in the program | Help for HF transformer Top of page | Application            | Tips              | Literature Notes                | Help for choking coils