How this instrument works
A flyback converter is the simplest isolated switch-mode topology: one transistor, one two-winding coupled inductor doing double duty as a transformer, and one diode carry the whole design. While the switch is on, the primary winding sees Vin and current in it ramps up, storing energy in the core's magnetic field — the secondary diode sits reverse-biased, so nothing reaches the output yet. When the switch opens, the field collapses, polarity across both windings flips, that diode starts conducting, and the stored energy pours into the output capacitor. Nothing crosses from primary to secondary while the switch is closed, which is why this is called energy-storage transfer rather than direct transfer — a forward converter, by contrast, conducts current straight through its transformer during the on-time and needs a separate reset winding to keep its core from walking into saturation.
Duty cycle here falls out of volt-second balance on the primary winding, the same steady-state rule that governs every switching regulator: what an inductor's current gains during the on-time it must give back during the off-time, or that current would ramp away indefinitely rather than settling into a repeating pattern. During the on-fraction D, the primary sees Vin driving current up; during the off-fraction (1 − D), the secondary discharges into the load at Vout, scaled by the turns ratio n — more secondary turns for every primary turn means each slice of off-time returns a larger figure to that balance, so a bigger n needs more on-time to balance the same Vin. Setting Vin·D equal to n·Vout·(1 − D) and solving for D gives D = n·Vout ⁄ (Vin + n·Vout), where turns ratio behaves like a lever a designer pulls to keep duty cycle inside a controller's comfortable range.
The formula assumes continuous conduction mode, an ideal switch, and a lossless diode — real hardware only approximates all three. At light load, the transformer's stored energy can fully discharge before the next switching cycle starts, tipping the converter into discontinuous conduction, where duty cycle also depends on load current and magnetizing inductance rather than on Vin, Vout, and n alone. Diode forward drop eats into the reflected voltage too, so a bench measurement typically needs a percent or two more duty cycle than this sheet predicts to hold the same output. Controller ICs built for offline flyback supplies — TinySwitch, TOPSwitch, and UC3843-family parts among them — usually cap maximum duty cycle well below 100%, often between 50% and 80%, specifically so the transformer core gets a full reset window before the next on-time begins.
- Enter Input voltage — the DC rail feeding the primary-side switch, such as a rectified mains bus or a battery pack.
- Enter Output voltage — the regulated DC rail the secondary winding and diode deliver to the load.
- Enter Turns ratio, Ns ⁄ Np — secondary turns divided by primary turns, taken from the transformer's datasheet or a direct count.
- Read Duty cycle, % — the share of each switching period the controller must hold the primary switch closed to sustain that output.
- Compare the result against your PWM controller's maximum duty-cycle limit before finalizing a transformer design.
Worked example — 12 V to 5 V with a 1:1 transformer
A small isolated auxiliary supply steps a 12 V input down to a 5 V logic rail through a transformer wound 1:1, so Turns ratio, Ns ⁄ Np is entered as 1. With Input voltage at 12 V and Output voltage at 5 V, the formula gives D = (1 × 5) ⁄ (12 + 1 × 5) = 5 ⁄ 17 = 0.294117647059, which reads out as Duty cycle, % = 29.4117647059 — call it 29.4% on the bench. The controller has to hold its switch closed for just over a quarter of every switching period to keep that 5 V rail in regulation.
Raise the turns ratio to 2 — twice as many secondary turns as primary turns — while holding the same 12 V input and 5 V output, and duty cycle climbs to (2 × 5) ⁄ (12 + 2 × 5) = 10 ⁄ 22 = 45.4545454545%. Doubling the winding ratio very nearly doubles the required on-time, which is exactly why transformer winding counts and PWM controller duty-cycle limits get chosen together rather than one after the other.
Questions
Why isn't flyback duty cycle simply Vout divided by Vin, like a buck converter?
Because a flyback stores energy in a transformer instead of passing current straight through an inductor, so the turns ratio enters the equation as well. A buck's D = Vout ⁄ Vin never touches a transformer; a flyback's D = n·Vout ⁄ (Vin + n·Vout) has Vout sitting in both the numerator and the denominator. Even at n = 1 the two formulas disagree — a genuine structural difference between the topologies, not an extra term bolted onto a familiar one.
What happens to duty cycle as the turns ratio increases?
It rises, and it never quite reaches 100%. Because n multiplies Vout in both the numerator and the added term in the denominator, a bigger turns ratio pushes duty cycle upward — at n = 1, 12 V to 5 V needs 29.41%; at n = 2, the same voltages need 45.45%. Designers trade turns ratio against duty cycle deliberately, since a controller's maximum-duty-cycle limit and a transformer's realistic winding count both push back on how far this knob turns.
Does this formula hold in discontinuous conduction mode?
No. This relationship comes from volt-second balance in continuous conduction mode, where the transformer's magnetizing current never reaches zero between switching cycles. In discontinuous mode — common at light load — duty cycle also depends on magnetizing inductance, switching frequency, and load current, so the clean D = n·Vout ⁄ (Vin + n·Vout) relationship stops applying on its own.
Why do different sources define transformer turns ratio in opposite directions?
Because there is no universal convention — some write turns ratio as secondary-over-primary, others as primary-over-secondary, and the two are reciprocals of each other. This calculator's Turns ratio, Ns ⁄ Np field wants secondary turns divided by primary turns, so a transformer wound with twice as many secondary turns as primary turns is entered as 2, not 0.5. Check which convention a datasheet is using before copying a number in; swapping the direction inverts the ratio's effect on duty cycle.
Does the formula include the output diode's forward voltage drop?
No, it treats the diode as ideal, dropping nothing. A real Schottky or ultrafast diode subtracts roughly 0.3 to 0.7 V from whatever the transformer delivers, so a bench duty cycle for a given output usually runs a percent or two higher than this sheet predicts, especially at low output voltages where that drop is a larger fraction of Vout.
Why do PWM controllers cap the maximum duty cycle for flyback designs?
To guarantee the transformer core fully resets before the next switching cycle begins. If the switch stays closed too long relative to the off-time, magnetizing current never returns to its starting point, and the core walks toward saturation cycle after cycle. Most flyback controller ICs limit maximum duty cycle to somewhere between 50% and 80%, specifically to leave that reset window open.