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The leakage inductance of the power transformer of an isolated dc-dc converter may significantly affect its efficiency and cost. Using lossless recovery circuits improves efficiency and avoids problems arising from transformer leakage-inductance spikes.

In the dual-transistor forward (full-bridge and half-bridge) converters, where the switching transistors are connected in series, energy stored in the transformer leakage inductance may be recycled through the clamping diodes that are an integral part of this architecture. However, in the “single-ended” topologies, such as forward, flyback, push-pull and current-fed, in which the switching transistors are connected to electrical ground, the energy stored in the leakage inductance may significantly affect a converter's performance.

If no measures are taken to recover the energy stored in this inductance, the energy will be dissipated either in the converter components or in the snubber circuits, absorbing voltage spikes caused by the leakage inductance. Energy stored in the leakage inductance of the power transformer during each switching cycle may be represented by this equation:

where L_{S} is the leakage inductance between primary and secondary windings, and I_{M} is the peak current in the primary transformer winding.

Power loss (P_{LS}) associated with the leakage is proportional to the switching frequency (f_{SW}):

The efficiency loss associated with P_{LS} may be determined as a ratio of the power dissipation caused by the leakage inductance to the power drawn from the primary source (V_{CC}). For a single transistor topology, the drawn power is:

where D is the switching transistor duty cycle.

Taking the ratio of Eq. 2-to-Eq. 3 and making simple transforms gives a simple equation quantifying the efficiency loss associated with the leakage inductance effect:

where K_{C} is the transformer coupling factor K_{C}=1-L_{S}/L_{µ}, L_{µ} is the magnetizing inductance, and is the magnetizing current magnitude normalized to the peak current:

Assume that the magnetizing current of a typical transformer doesn't exceed (0.1 to 0.2)I_{M}. Then according to Eq. 4, even with a power transformer having a comparatively low leakage inductance (K_{C} = 0.99), the efficiency loss associated with LS reaches 2.5% to 5%.

Conventional ways of alleviating this issue — providing better winding coupling or using active clamps — usually affect the cost and dynamic performance of a converter.

At the same time, the efficiency loss associated with leakage inductance may be recovered while maintaining low cost and high reliability in a dynamic load environment. This can be achieved if energy stored in the leakage inductance could be recovered back to the primary source. This function may be provided with the help of the lossless clamping circuits described next.

### Basic Lossless Clamping

The simplest lossless clamping circuit suitable for a single transistor forward and for flyback converters is shown in **Fig. 1**. The circuit incorporates the recovery reset winding (W2), with its number of turns equal to the primary winding (W1), a blocking capacitor C2, coupling identical leads of the two windings and a clamping diode D1. Since there is no dc voltage drop across transformer windings, C2 represents a floating dc source with a voltage equal to V_{CC}. Once the switching transistor Q1 turns off and voltage across it exceeds 2 V_{CC}, D1 starts conducting and recovers energy stored in the magnetic field of the transformer T1 and its leakage inductance back to the primary source.

Minimum capacitance required for effective clamping can be determined as:

where is a normalized ripple voltage on C2 predetermined by design:

Let us assume the converter operates from the power-factor correction (PFC) stage with output voltage V_{CC} =400 V; the transformer leakage inductance between primary and secondary windings L_{S}=20 µH; maximum switching transistor current I_{M}=10 A; and we would like to limit peak voltage across the switching transistor at V_{DSMAX}=2.01 V_{CC} (i.e. =0.01). Plugging these numbers in Eq. 5 gives C2_{MIN}=0.625 µF. This is the minimum capacitor value that allows clamping of the voltage across the switching transistor at a level V_{DSMAX}=804 V. This value is obtained on the assumption that capacitor ESR is negligible as compared to its reactance at a frequency:

If that is not the case, an additional voltage drop across the capacitor (ESR × I_{M}) should be taken into account. It is also important to note that during the transistor turn-off time period, a current in a series resonant circuit consisting of a clamping capacitor and leakage inductance between two primary windings may add copper losses on the primary side. To prevent this from happening, the resonant frequency of this circuit should be made lower than the switching frequency:

where L_{SP} is leakage inductance between primary transformer windings.

This could be provided by increasing capacitor C2's value and using an electrolytic capacitor. In several cases, using a larger-value electrolytic capacitor rated to withstand V_{CC} could also be more cost-effective than using minimum-value ceramic caps. The diode D1 should be able to withstand a reverse voltage V_{R} = 2 V_{CC}. In conventional applications, it conducts only the reset current of the primary transformer winding. In this case, it should have a peak current rating exceeding I_{M}. Average current flowing through this diode depends on magnetizing current and the primary/secondary winding leakage inductance. Normally, it is quite low and doesn't exceed a small percentage of the average current drawn from the primary source.

One of the advantages of using a large-value electrolytic capacitor is that current drawn from the primary source never drops to zero. When the switching MOSFET turns off, the snubber circuit continues to draw current flowing through the primary windings and charges the clamping capacitor C2. This results in significant (2x) reduction of the current step in the primary source and the associated EMI. Another advantage related to the lossless snubber is the opportunity to relax the transformer coupling requirements and allow converter operation with increased leakage inductance. In turn, this helps to reduce current ramp rates and peak current magnitudes as well as the generated noise level.

While the dc component of the switching transistor current flows exclusively through the main primary winding (W1) connected to the positive terminal of the primary source, the ac component of the switching transistor current is split evenly between both primary windings. Assuming, for simplicity, that transistor current waveform has a flat top, RMS current of the primary winding can be determined by this equation:

where D is duty cycle, which is the fraction of the switching cycle corresponding to the transistor's on state.

The RMS current of the recovery winding (W2) can be determined by this equation:

All other equations describing converter operation do not differ from the traditional topologies.

The maximum duty cycle (D_{MAX}) that can be achieved in this topology is 0.5. It is important that this limit not be exceeded. If the duty cycle exceeds 50%, the transformer may saturate. The circuits providing stiff lossless clamping at larger duty cycles are described next.

### Higher-Order Lossless Clamping

The circuit of **Fig. 1** may be used as a basic building block for lossless clamping of the leakage-voltage spikes in push-pull and current-fed push-pull converters operating in nonoverlapping conduction mode. These topologies are shown in **Figs. 2** and **3**, respectively. In **Fig. 3**, an additional winding with an equal number of turns on the feeding inductor L1 core is also required.

In practice, the transformer core in the push-pull converter operating in a voltage mode may drift off the center of the origin of its B-H curve. This occurs because of pulse duration differences caused by tolerances of the driver circuits and switching transistors. To prevent this from happening, a current-mode control is normally required for this topology. If for some reason a single current sensor, being an integral part of this control, has to be placed on the primary side in the lossless clamping topology, it is reasonable to position this sensor between the sources (which will be tied together) of the transistors Q1 and Q2 and the ground (negative terminal of the primary source). In this case, one sensor will monitor true currents flowing through each of the switching MOSFETs, which include current components that are provided by the clamping capacitors C1 and C2 (**Fig. 2**).

For forward and flyback converters with D_{MAX} < 0.5, where voltage spikes need to be clamped at a level below 2 V_{CC}, the clamping circuit shown in **Fig. 4** is recommended. In this circuit, the recovery winding is split into two sections: WR1 (WR1=W1) and WR2. The number of turns of WR2 depends on the maximum duty cycle required in the converter and may be determined by this equation:

Voltages across blocking capacitors C1 and C2 in steady state are equal to:

Typical timing diagrams showing voltages across the switching transistor in forward and flyback converters using lossless clamping are shown in **Fig. 5**. Using stiff voltage clamping in these topologies eliminates voltage spikes and provides classic waveform shapes that are characteristic of ideal cases.

For converter topologies with D_{MAX} > 0.5, the clamping circuit shown in **Fig. 6** may be used. This circuit clamps the transistor peak voltage to the level of 3 V_{CC} and allows operation with duty cycles up to 0.66. It is also recommended for the current-fed push-pull converter operating in overlapping conduction mode.

Splitting the recovery winding into two not-directly coupled halves allows for rearranging the topology shown in **Fig. 6** into a clamping circuit for a dual-transistor forward/flyback converter, allowing expansion of its duty cycle to 0.66 and getting stiff clamping to the level of 1.5 V_{CC} for each of its switching MOSFETs. This circuit is shown in **Fig. 7**.

Similar clamping circuits may be proposed for converters operating at duty cycles exceeding 0.66; however, because of their complexity and increased discrete part count, their usage may be considered impractical.

### Design Tips

There are a few key points to bear in mind when designing with lossless voltage-clamping components. One is that the current flowing through the recovery windings does not include the dc content of the switching transistor current. Therefore, a small gage wire can be used. Another consideration is that the clamping capacitors connect the winding taps with equal numbers of turns. To prevent capacitor-charging currents from flowing through the switching transistor, it is recommended that designers avoid errors in the numbers of turns.

Also note that stiff clamping provides an opportunity for relaxing the transformer coupling requirement. This option allows operating with increased leakage inductance, which in turn helps reduce current ramp rates and generated noise level. And finally, observe that clamping capacitors are essentially connected in parallel with the main V^{CC} decoupling capacitor. Therefore, the main V_{CC} decoupling function can usually be shared among several capacitors, including those that provide stiff voltage clamping.