Flyback Converter - Duty Cycle and Lp Sizing
Flyback converter calculator for isolated DC-DC designs - returns duty cycle, primary inductance, and output capacitor values from Vin, Vout, and turns ratio.
Flyback Converter
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What Is Flyback Converter?
A flyback converter calculator solves the steady-state design equations for an isolated DC-DC switching converter that stores energy in the magnetizing inductance of a coupled inductor and releases it through a secondary winding. This flyback converter calculator handles the duty cycle, primary and secondary currents, primary inductance, secondary inductance, and output capacitor from a few input values.
- • Sizing an isolated 5 V USB supply from a 12 V battery rail: Pick the primary inductance and output capacitor for a 5 W isolated flyback that drops 12 V to 5 V with a 1:2 step-down turns ratio.
- • Teaching isolated switching converters: Walk students through the duty-cycle equation, primary ripple current, and secondary-side capacitor sizing in a power-electronics course.
- • Verifying an off-line adapter design: Confirm the duty cycle and Lp of a mains-to-low-voltage flyback before committing to a transformer vendor and controller IC.
- • Choosing between flyback and forward topologies: Estimate the primary peak current and output capacitor for a multi-watt isolated rail, then decide whether the flyback converter calculator stays in CCM at full load.
A flyback converter is one of the basic isolated PWM switching topologies. The transformer provides galvanic isolation and acts as a coupled inductor; energy flows into the magnetizing inductance while the switch is on, then out through the secondary winding and rectifier diode while the switch is off. Compared with the boost converter and buck converter in the same calculator family, this topology trades a separate output inductor for a gapped transformer, so the secondary voltage is set by the turns ratio and the duty cycle rather than by the input voltage alone.
When the input rail is below Vout and you do not need isolation, Boost Converter Calculator solves the simpler non-isolated step-up with the same CCM framework.
How Flyback Converter Works
The flyback converter calculator applies volt-second balance to the magnetizing inductance in continuous conduction mode and charge balance to the output capacitor. Both balances come from averaging the inductor voltage and capacitor current over one switching period, which is why the flyback converter calculator returns a closed-form duty cycle without solving differential equations.
- Vin: DC input voltage feeding the primary winding.
- Vout: Target DC output voltage on the secondary side after the rectifier.
- Ns/Np: Secondary-to-primary turns ratio. Less than 1 for step-down, greater than 1 for step-up.
- D: Switch duty cycle, the fraction of each period the transistor is on.
- f: Switching frequency in hertz, set by the controller IC.
- Pout: Output power delivered to the load in watts.
D = Vout / (Ns/Np * Vin + Vout) gives the duty cycle directly. With D known, Iout = Pout / Vout, Rload = Vout / Iout, and ILp_avg = Pout / (Vin * D) because ILp only flows while the switch is closed. The primary inductance Lp = (Vin * D) / (f * dILp) comes from the chosen ripple budget, the secondary inductance referred to the secondary terminals is Ls = Lp * (Ns/Np)^2 from the same core, and the secondary peak current equals the primary peak divided by the turns ratio.
Worked example: 12 V to 5 V isolated USB supply, 5 W at 100 kHz
Vin = 12 V, Vout = 5 V, Ns/Np = 0.5, f = 100 kHz, Pout = 5 W, primary ripple 30 percent, output ripple 5 percent.
D = 5 / (0.5 * 12 + 5) = 0.4545. Iout = 1 A, ILp_avg = 0.917 A, Lp = (12 * 0.4545) / (100000 * 0.275) = 198 uH, Ls = 198 * 0.5^2 = 49.6 uH, Co = (1 * 0.4545) / (100000 * 0.25) = 18 uF.
Output duty cycle 45.5 percent, primary inductance 198 uH, secondary inductance 49.6 uH, required output capacitor 18 uF.
The 1:2 step-down turns ratio leaves headroom on the controller, the 198 uH primary keeps ripple inside the 30 percent budget, and the 49.6 uH referred secondary is what the same core presents at the secondary terminals.
According to Texas Instruments (SLVA478), in continuous conduction mode a flyback converter obeys Vout/Vin = (Ns/Np) * D/(1-D) and the primary inductance Lp = (Vin * D) / (fs * dILp) keeps the ripple current inside the chosen budget.
The output capacitor is sized from the same RC charge-balance idea used in the boost output stage, so Capacitor Charge Time Calculator reuses that RC analysis on a different stage of the converter.
Key Concepts Explained
Four concepts describe how the calculator handles an isolated switching converter.
Continuous conduction mode (CCM)
The magnetizing current never returns to zero during a switching period. CCM is the assumption behind the closed-form duty-cycle equation.
Turns ratio Ns/Np
The secondary-to-primary turns ratio. With Ns/Np below 1 the converter steps down and the secondary current is larger; above 1 the converter steps up.
Magnetizing inductance Lp
The inductance seen at the primary winding, set by the core gap. Lp together with the ripple fraction sets the peak primary current and the energy stored per cycle.
Energy transfer cycle
While the switch is on, current ramps up in the primary and stores 0.5 * Lp * Ipp^2 of energy in the gap. While the switch is off, the same energy transfers to the secondary through the rectifier diode into the output capacitor.
If the magnetizing current is allowed to touch zero before the next switch turn-on, the converter enters DCM, where the duty-cycle equation changes because part of the period has no current flow. If your load is so light that DCM becomes likely, raise the primary inductance or the switching frequency so the average primary current stays comfortably above half of its peak-to-peak ripple.
When you just need to drop Vin without isolation, Buck Converter Calculator returns the matching duty cycle and inductor value for the simpler non-isolated step-down.
How to Use This Calculator
Six numbered steps walk through a typical design pass for a 12 V to 5 V, 1:2 step-down, 100 kHz, 5 W flyback.
- 1 Enter the input voltage: Type the DC supply voltage feeding the primary winding. A 12 V battery rail is 12 V, a 24 V industrial bus is 24 V.
- 2 Enter the target output voltage: Type the DC voltage you need on the secondary side after the rectifier. USB rails are 5 V, isolated sensor supplies are 3.3 V, 5 V, or 24 V.
- 3 Choose the turns ratio: Pick Ns/Np from your transformer design. Common values are 0.5 for 2:1 step-down and 1.0 for 1:1 transfer.
- 4 Set the switching frequency: Type the switching frequency the controller IC will run at. Off-line controllers commonly run at 65 to 130 kHz.
- 5 Enter the load power: Type the output power delivered to the load in watts. This sets the load current and average primary current.
- 6 Set the ripple fractions: Choose a primary ripple fraction around 0.3 for CCM and an output ripple fraction between 0.01 and 0.05.
For a 12 V to 5 V isolated USB supply at 5 W with a 1:2 turns ratio and 100 kHz, the calculator returns a duty cycle near 45 percent, a primary inductance near 200 uH, and an output capacitor near 18 uF.
Benefits of Using This Calculator
Five benefits show where the flyback converter calculator saves time in an isolated switching-converter design.
- • Solve duty cycle directly: Gives a numeric duty cycle the moment you enter Vin, Vout, and the turns ratio.
- • Pick a transformer Lp: Returns a primary inductance from the ripple budget and switching frequency for vendor catalog searches.
- • Pick an output capacitor: Returns the minimum secondary-side capacitance from the ripple voltage budget.
- • Verify the operating mode: Shows the average and peak primary current so you can confirm the flyback converter calculator stays in CCM at full load.
- • Teach isolated converter design: Walks students through the duty-cycle equation, primary ripple current, and output capacitor sizing.
The same formulas are also the starting point for choosing a controller IC, because the maximum duty cycle, current sense threshold, and current-mode control loop all depend on these numbers.
To back-calculate the equivalent load resistance from Vout and Pout, Ohm's Law Calculator applies the V = IR relationship directly.
Factors That Affect Your Results
Four factors drive the values the calculator returns. They explain why the same input voltages give different Lp and Co at different switching frequencies and ripple budgets.
Switching frequency
A higher frequency shrinks the primary inductance and the output capacitor by the same ratio. Going from 100 kHz to 200 kHz halves both Lp and Co for the same ripple budgets.
Primary ripple fraction
A larger ripple fraction lets the inductor be smaller but increases RMS conduction losses. CCM designs usually sit between 0.2 and 0.4.
Output ripple fraction
A tighter ripple budget forces a larger output capacitor. For analog rails 0.01 is common; for digital-only loads 0.05 is fine.
Turns ratio Ns/Np
Changing the turns ratio changes the duty cycle, average primary current, and secondary peak current all at once. A larger Ns/Np drives the duty cycle lower because the denominator Ns/Np * Vin + Vout grows faster than Vout.
- • The model assumes continuous conduction mode. At light load the magnetizing current may touch zero before the next switch turn-on, and the closed-form transfer function no longer holds.
- • The model treats the converter as lossless. Switch on-resistance, diode forward drop, transformer winding resistance, and leakage inductance are not included, so subtract these drops from Vout before sizing the transformer.
Snubber design also matters in a real flyback. The leakage inductance between primary and secondary windings causes a voltage spike on the switch at turn-off; an RC snubber across the primary winding absorbs that spike.
According to MIT OpenCourseWare 6.622 Power Electronics, the flyback converter stores energy in the magnetizing inductance of a gapped transformer during the switch on-time and releases it through a secondary winding during the off-time, so it acts like a buck-boost with galvanic isolation.
According to All About Circuits flyback converter article, the flyback output capacitor in continuous conduction mode must satisfy Co = (Iout * D) / (fs * dVout) because the secondary diode is reverse-biased during the switch on-time and the load is supplied by Co alone.
Active-PFC front ends often use a flyback as the first isolated stage, so Power Factor Calculator covers the related AC-side PF and kVAR sizing.
Frequently Asked Questions
Q: How is the duty cycle of a flyback converter calculated?
A: In continuous conduction mode the duty cycle is D = Vout / (Ns/Np * Vin + Vout), where Vin is the DC input voltage, Vout is the target output voltage, and Ns/Np is the turns ratio. The expression comes from volt-second balance on the magnetizing inductance.
Q: How do you choose the turns ratio of a flyback transformer?
A: Pick Ns/Np so the duty cycle stays between 0.2 and 0.7 at the nominal input voltage. Most 12 V to 5 V adapters land near Ns/Np = 0.5.
Q: How do you size the primary inductance of a flyback converter?
A: The required primary inductance is Lp = (Vin * D) / (f * dILp), where Vin is the input voltage, D is the duty cycle, f is the switching frequency, and dILp is the peak-to-peak primary ripple current.
Q: How is the output capacitor of a flyback converter calculated?
A: The required output capacitance is Co = (Iout * D) / (f * dVout), where Iout is the load current, D is the duty cycle, f is the switching frequency, and dVout is the allowed peak-to-peak output ripple voltage.
Q: What is the difference between CCM and DCM in a flyback converter?
A: In continuous conduction mode the magnetizing current never falls to zero, so Vout = Vin * (Ns/Np) * D / (1 - D) holds. In DCM the magnetizing current touches zero each cycle and the transfer function changes.
Q: Why does a flyback converter need a coupled inductor?
A: A flyback converter uses a gapped transformer (a coupled inductor) instead of a separate output inductor. The coupled inductor also provides the galvanic isolation that the boost and buck topologies cannot offer.