# Considerations on output capacitance for soft switching converters

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By eeNews Europe

Introduction
Power conversion switching frequency is being continuously increased to maximize power density. Soft switching techniques such as zero voltage switching (ZVS) have become popular to extend the frequency further. As switching frequency increases, power MOSFET parasitic characteristics are not negligible any more. Among all parasitic elements, an output capacitance is crucial parasitic parameter to set power converter design up in ZVS topologies. It determines how much inductance is required to provide ZVS conditions.

Traditionally, many designers used rough assumptions to find out fixed value of output capacitance for the equations. [1-2] This conventional equivalent output capacitance value, however, is not too helpful in real applications because it is varied by drain-source voltage and does not provide stored energy information accurately during switching on/off transition. A new concept of output capacitance which gives equivalent stored energy at a working voltage of the power converter can enable optimization of the power converter design.

Output capacitance in ZVS converters
In the soft switching topologies, zero voltage turn-on is achieved by using the energy stored in inductor, the leakage and series inductance or magnetizing inductance of the transformer, to discharge the output capacitance of the switches through resonant action. The inductance should be precisely designed to prevent hard switching that causes additional power losses. The following equations are basic requirements for zero voltage switching.

(Equation 1)

where Ceq is equivalent output capacitance of switches and CTR is parasitic capacitance of transformer

(Equation 2)

where CS is equivalent output capacitance of switches

The equation (1) is for phase-shifted full bridge topology [2] and the equation (2) is for LLC resonant half bridge topology. [3] The output capacitance plays important role in both equations. If too big output capacitance has assumed in (1), the equation gives larger inductance. Then the big inductance will lower primary di/dt and cut effective duty of power converter down. On the contrary, too small output capacitance will result in smaller inductance and unwanted hard switching. Also, too big an output capacitance in (2) will limit magnetizing inductance and cause increase in circulating current. Therefore, obtaining exact output capacitance of the switches is very critical to optimum design of the soft switching converters.

Usually conventional assumptions for the equivalent output capacitance tends to have bigger value. So, designers should adjust their power converter after selecting inductance from (1) or (2). Several design iterations are required because everything is related to each other, for instance, turn ratio, leakage inductance, and effective duty cycle. Moreover, the output capacitance of power MOSFET is varied by drain-source voltage. An output capacitance giving equivalent stored energy at working voltage of power converter is the best alternative for these applications.

Getting stored energy in output capacitance
In the voltage-charge plane, capacitance is a slope of a straight line and stored energy in the capacitance is an area filled by the line. The output capacitance of power MOSFET is, however, non-linear and varies according to drain-source voltage. But, it is still applicable that stored energy in output capacitance is an area under the non-linear capacitance line. Consequently, if we can find a straight line which gives the same area as that filled by varying the output capacitance curve as shown in Figure 1, a slope of the line is exactly the equivalent output capacitance giving the same stored energy.

Figure 1. Concept of equivalent output capacitance

For some old planar technology MOSFETs, designers may use curve fitting to find out equivalent output capacitance based on output capacitance value in the datasheet that is usually specified at 25 V of drain-source voltage.

(Equation 3)

Then, stored energy can be obtained with simple integration.

(Equation 4)

Finally, effective output capacitance becomes

(Equation 5)

Figure 2 shows the measurement of output capacitance and fitted curve by equation (3). It looks fine with old technology MOSFET as shown in Figure 2(a). However, MOSFETs with new technology such as super-junction have more non-linear output capacitance characteristics and simple exponential curve fitting is sometimes not good enough .

Figure 2(b) shows output capacitance measurement of the latest technology MOSFET and fitted curve using equation (3). The gap at high voltage region results in huge difference for the equivalent output capacitance because the voltage is multiplied to the capacitance during integration. The estimation in Figure 2(b) will give a much bigger equivalent capacitance that may mislead initial design of the converters.

(Click on image to enlarge)

Figure 2. Output capacitance estimation, (a) old MOSFET, (b) new MOSFET

If output capacitance values according to drain-source voltage are available, the energy stored in the output capacitance can be obtained using equation (4). Although capacitance curves are shown in the datasheets, reading the capacitance precisely from the graph is not easy. Therefore, the stored energy in output capacitance according to drain-source voltage is provided by graph in the datasheet of the latest power MOSFETs. With the curve shown in Figure 3, the equivalent output capacitance at desired DC bus voltage can be obtained using equation (5).

Figure 3. The stored energy in output capacitance

Common questions about the output capacitance
In many cases, designers of switching power supplies question about temperature coefficient of MOSFET capacitance because power MOSFET is usually operated at elevated temperature. In summary, MOSFET capacitance can be considered as constant over temperature.

The MOSFET capacitance is determined by depletion length, doping concentration, channel width, and permittivity of silicon but all of these are not much changed by temperature. Also MOSFET switching characteristics such as switching losses or on/off transition speed are not changed much by temperature because MOSFET is majority carrier device and so switching characteristics are basically determined by its capacitance. The equivalent series gate resistance at gate is increased a little bit as temperature goes up. This can slow down MOSFET switching at high temperature a little.

Figure 4 shows change in capacitance according to temperature. There is less than 1% of change over 150 degrees.

Figure 4. MOSFET capacitance vs temperature

Another area designers are interested in is test conditions for MOSFET capacitances. In most cases, output capacitance is measured with 1MHz frequency and 0V of Vgs. There are actually gate-to-drain capacitance, gate-to-source capacitance, and drain-to-source capacitance. In practice, however, measuring each capacitance separately is not possible. Therefore, sum of the gate-to-drain capacitance and drain-to-source capacitance is decribed as output capacitance and it is measured by paralleling two capacitances. To make them in parallel, gate and source are shorted together that means Vgs=0V. In switching applications, output capacitance is shorted by MOSFET channel when MOSFET is turned-on with gate bias. The output capacitance value only be considered when the MOSFET is turned-off.

Regarding frequency, capacitance increases a little bit with lower frequency at low voltage as shown in Figure 5. At low frequency, capacitance at low drain-source voltage is sometimes not measurable because of the limitations of test equipment.

In Figure 5, capacitance at 100 kHz is not available when drain-source voltage is less than 4 V. Although there is little change in output capacitance, equivalent output capacitance is almost constant because a little change of output capacitance at low voltage does not affect the stored energy much which is shown in Figure 3.

Figure 5. MOSFET capacitance vs frequency

Conclusion
The output capacitance is important part of soft switching converter design. The equivalent value should be considered rather than single value at fixed drain-source voltage. Discussions on test conditions and temperature coefficient are provided.

References
[1] J.A. Sabate, et al, “Design Considerations for High-Voltage High-Power Full-Bridge Zero-Voltage-Switched PWM Converter”, IEEE APEC, 1990

[2] Bill Andreycak, “Designing a Phase Shifted Zero Voltage Transition (ZVT) Power Converter”, Unitrode Seminar Manual, 1993

[3] J. Jung and J. Kwon, “Theoretical Analysis and Optimal Design of LLC Resonant Converter”, EPE, 2007