# Flyback Inductor & Transformer Theory

Flyback circuits repeat a cycle of two or three stages; a charging stage, a discharging stage, and in some applications idle time following a complete discharge. Charging creates a magnetic field. Discharging action results from the collapse of the magnetic field. The typical flyback transformer application is a unipolar application. The magnetic field flux density varies up in down in value ( 0 or larger ) but keeps the same ( hence unipolar ) direction.

#### Charging Stage:

The flyback transformer ( or inductor ) draws current from the power source. The current increases over time. The current flow creates a magnetic field flux that also increases over time. Energy is stored within the magnetic field. The associated positive flux change over time induces a voltage in the flyback transformer ( or inductor ) which opposes the source voltage. Typically, a diode and a capacitor are series connected across a flyback transformer winding ( or inductor ). A load resistor is then connected across the capacitor. The diode is oriented to block current flow from the flyback transformer ( or source ) to the capacitor and the load resistor during the charging stage. Controlling the charging time duration (known as duty cycle) in a cycle can control the amount of energy stored during each cycle. Stored energy value, E = ( I x I x L ) / 2, where E is in joules, I = current in amps, L = inductance in Henries. Current is defined by the differential equation V(t) = L x di/dt. Applying this equation to applications with constant source voltage and constant inductance value one obtains the following equation; I = Io + V x t / L , where I = currents in amps, Io = starting current in amps, V = voltage in volts across the flyback transformer winding ( or inductor ), L = inductance in Henries, and t = elapsed time in seconds. Note that increasing L will decrease the current. Stored energy will consequently decrease because effects of the current squared decrease will more than offset the effects of the inductance increase. Also be aware that the flyback transformer ( or inductor ) input voltage is less than the source voltage due to switching and resistive voltage drops in the circuit.

#### Discharge Stage:

The current ( which creates the magnetic field ) from the source is then interrupted by opening a switch, thereby causing the magnetic field to collapse or decrease, hence a reversal in the direction of the magnetic field flux change ( negative flux change over time ). The negative flux change induces a voltage in the opposite direction from that induced during the charging stage. The terms flyback or kickback originate from the induced voltage reversal that occurs when the supply current is interrupted. The reversed induced voltage(s) tries to create ( induce ) a current flow. The open switch prevents current from flowing through the power supply. With the voltage reversed, the diode now permits current flow through it, hence current flows into the capacitor and the load across the capacitor. If current can flow, then the resulting flow of current is in the direction, which tries to maintain the existing magnetic field. The induced current cannot maintain this field but does slow down the decline of the magnetic field. A slower decline translates to a lower induced flyback voltage. If current cannot flow, the magnetic field will decline very rapidly and consequently create a much higher induced voltage. In effect, the flyback action will create the necessary voltage needed to discharge the energy stored in the flyback transformer or inductor. This principle, along with controlling the duration of the charging stage, allows a flyback inductor to increase or decrease the voltage without the use of a step-up or step-down turns ratio. In the typical flyback circuit, the output capacitor clamps the flyback voltage to the capacitor voltage plus the diode and resistive voltage drops. For a sufficiently large & fully charged capacitor, the clamping capacitor voltage can be treated as a constant value. The equations V(t) = L x di/dt, and I = Io + V x t / L can also be applied to the discharge stage. Use the inductance value of the discharging winding and the time duration of the discharging stage. The time will either be the cycle time minus the charging time ( no idle time ), or the time it takes to fully discharge the magnetic field thereby reaching zero current. The cycle time equals the period which equals 1 / frequency.

#### Idle Stage:

This stage occurs whenever the flyback transformer ( or inductor ) has completely discharged its stored energy. Input and output current ( of the transformer or inductor ) is at zero value.

## OTHER PRINCIPLES OF OPERATION

#### Equal Ampere-Turns Condition:

A magnetic field is created by the current flow through the winding(s). The current creates a magnetizing force, H, and a magnetic field flux density B. A core dependent correlation will exist between B and H. B is not usually linear with H. By definition H is proportional to the product of the winding turns and the current flowing through the winding, hence ampere-turns. In classical physics, the magnetic field flux cannot instantaneously change value if the source of the field ( the current flow ) is removed. When the source current is removed from the flyback transformer ( or inductor ) the charging stage ends and the discharge stage begins. The value of the magnetic field will be the same for both stages at that point in time ( cannot instantaneously change to another value ). The same magnetic core is used for both stages, hence if the magnetic field is the same, then the magnetizing force, H, must be the same. Consequently the ampere-turns at the end of the charging stage must equal the ampere-turns at the start of the discharge stage. If there are multiple outputs then the total amperes turns of all outputs at the start of the discharge stage must equal the ampere-turns at the end of the charging stage. The same condition applies at the start of the charging stage. The total ampere-turns of all outputs at the start of the charging stage must equal the ampere-turns at the end of the discharge stage. Note that there are zero ampere-turns at both the start and end of an idle stage when an idle stage exists.

#### Zero Average Voltage:

During steady state operation, the average voltage across the charging winding must equal the average voltage across the discharge winding, or equivalently, the volt-seconds of the charging stage must equal the volt-seconds of the discharge stage. If not, flux density increases over time and the core saturates. Assuming a 1:1 turns ratio, then from V1 x t1 = V2 x t2 one can obtain t1 / t2 = V2 / V1 for both continuous and discontinuous modes of operation. For continuous mode operation, t1 + t2 = 1 / operating frequency.

#### Zero Average Voltage:

Power out cannot exceed power in. Sum up output power ( V x I ) of each output at maximum steady state load plus allowances for parasitic output power losses ( diode and resistive losses ). Divide power in watts by operating frequency. The result is the energy in Joules that must be discharged each cycle into the output storage capacitor during steady state operation. It is also the amount of energy that must be added to the flyback transformer ( or inductor ) during the charging stage. The energy being transferred equals ( Ipeak x Ipeak â Imin. x Imin. ) x L /2. If operating in the continuous mode, the stored energy will exceed the energy being transferred because the starting level of stored energy is above zero ( Imin. > 0 ). The flyback transformer ( or inductor ) must be designed to handle the peak stored energy, Ipeak x Ipeak x L / 2. The power source will have to supply the transferred energy plus the parasitic switching and resistive losses of the charging circuit, plus some power allowance for transient conditions. Take this value and divide by the power supply voltage. The result will be the average input current.