Minimum Load for ZVS in Synchronous Buck Converters

The Problem: The Hard Turn-On Transition

Let's quickly revisit the problem we are trying to solve. In the previous lesson, we touched on the losses caused by the reverse recovery of the low-side MOSFET's body diode. This occurs during the turn-on of the high-side switch (let's call it M1) when the inductor current is positive.

To see a detailed analysis of why this transition is so lossy, watch the first part of this lecture from the University of Colorado Boulder.

As the video explains, this hard turn-on process, dominated by reverse recovery, is the primary source of switching loss in a synchronous buck. The key to eliminating it lies in changing the state of the inductor current at the switching instant.

Inductor Current: The Key to ZVS

The inductor current ($I_L$) in a buck converter isn't a constant value. It consists of two components:

1. The average DC current, which is equal to the output load current, $I_{out}$.
2. A triangular AC ripple current ($\Delta I_L$) superimposed on top of the average.

Therefore, the inductor current oscillates between a valley and a peak:

• $I_{valley}=I_{out}-\frac{\Delta I_L}{2}$
• $I_{peak}=I_{out}+\frac{\Delta I_L}{2}$

The crucial insight for achieving ZVS on the high-side switch (M1) is this: for the inductor's energy to drive the switch node voltage up from 0V to $V_{in}$ (discharging M1's capacitance), the inductor current must be flowing "backwards" into the switch node. This means the inductor current must be negative when the low-side switch (M2) turns off.

What happens when we ensure the inductor current is negative at that transition? The problem of reverse recovery and hard switching vanishes.

The next segment of the same lecture demonstrates this "magic." The only change made to the circuit is reducing the inductor value, which increases the current ripple ($\Delta I_L$).

This phenomenon gives the converter a special name: a Zero Voltage Switching Quasi-Square-Wave (ZVS-QSW) converter. It's fundamentally a synchronous buck converter designed or operated in a way that guarantees negative inductor current at the critical transition.

Defining the Minimum Load Condition

Now we can define the condition for ZVS. For the inductor current to be negative at the valley, we need:
$I_{valley}<0$

Substituting our formula for valley current:
$I_{out}-\frac{\Delta I_L}{2}<0$

Rearranging this gives us the fundamental condition for achieving ZVS:
$I_{out}<\frac{\Delta I_L}{2}$

This is a critical rule of thumb: ZVS is achieved when the DC load current is less than half the peak-to-peak inductor current ripple.

This is why this mode is sometimes referred to as operating in synchronous Discontinuous Conduction Mode (DCM), as the current crosses zero.

A Small Refinement: Minimum Negative Current

In practice, the inductor current doesn't just need to be negative; it needs to be negative enough to provide the energy required to charge and discharge the switch node capacitances within the available dead-time. The energy needed is $E_{cap}=\frac{1}{2}{C}_{node}{V}_{in}^2$, which must be supplied by the inductor's energy, $E_{ind}=\frac{1}{2}L{I}^2$.

This means there is a minimum negative inductor current, which we can call $I_{neg}$, required to ensure the ZVS transition completes successfully. A research paper on this topic, "A High Efficiency, Soft Switching DC–DC Converter," confirms this and provides an experimental example where $I_{neg}$ was found to be around 150 mA.

The more precise condition for ZVS, therefore, is that the valley current must be less than or equal to this minimum negative current:
$I_{valley}\le -I_{neg}$
$I_{out}-\frac{\Delta I_L}{2}\le -I_{neg}$
$I_{out}\le \frac{\Delta I_L}{2}-I_{neg}$

For your purpose of reviewing PCBs, the first approximation ($I_{out}<\Delta I_L/2$) is often sufficient for a high-level assessment.

The Efficiency Trade-Off

If achieving ZVS is as simple as increasing the current ripple (e.g., by using a smaller inductor), why don't all converters do this? The answer lies in the classic engineering trade-off.

While ZVS eliminates switching losses, the larger ripple current significantly increases the conduction losses. Conduction losses are proportional to the square of the RMS current ($P_{cond}=I_{RMS}^2\times R_{DS(on)}$). A larger triangular ripple results in a higher RMS value for the same average DC current.

This creates a fascinating dilemma:

• At heavy loads, a standard hard-switched converter (with small ripple) is often more efficient because conduction losses dominate.
• At light loads, the ZVS-QSW approach (with large ripple) can be more efficient because switching losses become more significant.

Interestingly, a standard hard-switched converter will naturally start to achieve ZVS at very light loads anyway, because the fixed ripple $\Delta I_L$ will eventually become larger than twice the small load current $I_{out}$.

This final segment from the lecture provides an excellent summary of this load-dependent efficiency trade-off.

Conclusion

Today, you've learned to pinpoint the exact condition that enables ZVS in a synchronous buck converter, moving from a qualitative understanding to a quantitative one.

Key Takeaways:

• ZVS for the high-side switch is achieved when the inductor current is negative at the switching transition.
• This occurs when the load current is less than half the inductor current ripple: $I_{out}<\frac{\Delta I_L}{2}$.
• This condition can be met intentionally by design (a QSW converter with a small inductor) or can happen naturally in a standard converter at light loads.
• There is a critical trade-off: increasing ripple to get ZVS reduces switching losses but increases conduction losses, making efficiency highly dependent on the load.

Understanding this boundary condition is fundamental to analyzing why a certain inductor value was chosen in a design and predicting how the converter's efficiency will behave as the load changes.

In our next lesson, we'll move to a new topology and see why achieving ZVS isn't always this straightforward. We will explore the operational challenges and limitations of achieving ZVS in synchronous boost converters.