# Flyback Converter Equations and Design Steps

Flyback converters are common in systems that require multiple outputs when converting AC to DC. They can also provide isolation that protects the user working on the output side of a system, which is why they are often used in switch-mode power supplies. Because these systems require a transformer to implement switching action and voltage level conversion, they can be difficult to design with off-the-shelf components.

The main flyback converter equations needed to design these circuits are presented below. These design equations can be used with discrete components or integrated flyback controllers.

## Flyback Converter Equations

To get started designing a flyback converter, we prefer to start at the output and work back to the input. When getting started, we need to know the following:

- An input voltage source (could be DC or rectified AC)
- Target output voltage
- Target output current
- Margin of safety for overcurrent on the output

Here we can use these values to derive the specifications for the transformer and the PWM switching circuit. The basic design process for determining the required components follows the steps outlined below.

### Step 1: Determine the Flyback Voltage

First, take a look at the typical flyback converter topology shown below. The target output voltage will initially be used to determine the voltage required at the secondary winding, while also including the diode’s forward voltage drop (usually 0.7 or 0.5 V).

The flyback voltage is the voltage measured across the primary coil in the transformer. This voltage will be the pulsating voltage that is set based on the PWM duty cycle of the switching transistor Q1. The turns ratio satisfies the following relation:

### Step 2: Determine the Duty Cycle

The required duty cycle will be determined by the input voltage (Vin) versus the flyback voltage. The duty cycle is calculated as follows:

This equation requires the input be DC. If the input is AC, we first feed it through a bridge rectifier to produce a pulsating DC voltage, which is then filtered (usually a pi filter) to produce a much more stable DC voltage. If the input is a standard 115 V AC RMS input, then the pulsating DC value will be 162.6 V. After accounting for the forward voltage drop on the diodes, this will be the DC value reaching the primary coil of the transformer.

Note that this duty cycle is a required value based on the turns ratio of the transformer used in Step 1. If a different transformer turns ratio is used, then the required duty cycle will be different. The switching controller you use will have some duty cycle limit that it can generate, so make sure to check this calculated duty cycle against the controllers’ capabilities before finalizing component selection.

### Step 3: Determine Ls and Lp

Based on the target maximum output current, we can determine some values for Ls and Lp using the duty cycle and turns ratio. The basic circuit shown above uses the transformer inductances to set the turns ratio. However, we need to know the limits on the secondary side inductance (Ls), then the primary side inductance (Lp) can be calculated with the turns ratio.

First, calculate the maximum value of Ls, then calculate the corresponding value of Lp:

The values of frequency and duty cycle to use here depend on the regulation strategy. Typically, PWM is used for switching, and there will be some maximum value that the switching controller can provide, which limits the input voltage range. The corresponding frequency may also be adjusted to hit some minimum/maximum on the ON time for Q1.

### Step 4: Determine Peak Currents

The flyback converter will be operating with pulsed currents, and the pulsed current on the primary side may be large enough to overwhelm the switching element Q1. Therefore, we need to determine these peak current values.

The peak secondary current and primary current values are:

This completes the design of the flyback converter. The transformer must now be designed to withstand the peak current values listed here, and it must have the inductances determined in Step 3. Q1 will also have some current limit; above this value the FET will burn up, or the current will be clamped if you are using a controller with overcurrent protection.

### The Most Difficult Part: The Transformer

From the above steps, we should be able to see one of the most difficult parts of the design: selecting a transformer. Off-the-shelf transformers do not always provide the required turns ratio needed to ensure they are compatible with other components in the design. Conversely, integrated switching controllers used in flyback converters might have operating limits that are incompatible with off-the-shelf transformers.

In both cases, you may need to design a custom transformer. There are companies that specialize in the physical design and manufacture of custom transformers. They may select a core former and core material, and they could size the turns count and wire gauge to hit your operating current limits. In some cases where the footprint is very aggressive, they may have to design a custom core former and core geometry. As long as you can specify the inductances required, then the manufacturer can generally assist you with designing a custom transformer.

When you’re ready to design and simulate your flyback converter designs, use the complete set of simulation tools in PSpice from Cadence. PSpice users can access a powerful SPICE simulator as well as specialty design capabilities like model creation, graphing and analysis tools, and much more.

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