A Graphical Approach To MOSFET Evaluation

Oct 1, 2005 12:00 PM
By Alan Elbanhawy, Director, Computing and Telecommunications Segments, Advanced Power Systems Cente

Using a new version of power MOSFET figure of merit and constant-power dissipation curves, designers can calculate the optimum combination of factors to select a device for a power supply application and minimize its dissipation.

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The demands of modern power supplies for increasingly higher efficiencies at higher frequencies have propelled MOSFET technology in the last few years to heights of performance that were hard to anticipate only a few years ago. The proliferation of these devices in almost all power applications requires a means of comparison to allow design engineers to choose the optimum device as easily and accurately as possible.

The product of a MOSFET's on-resistance, R_DS(ON), and total gate charge, Q_G, has been used as the figure of merit (FOM) for power MOSFETs for years. The lower the value, the better the MOSFET. In general, this value represents how good one fabrication process is compared to another. But, does this value indicate whether a given MOSFET will perform better than another in a particular application? The use of this FOM implies that two MOSFETs with the same value would perform the same in a given application. But, is that true regardless of the individual value of R_DS(ON) and Q_G that constitute this FOM?

To answer this question, we will show that we need a different tool to pinpoint the subtle differences. This tool is the FOM that results from multiplying the on-resistance (referred to in the equations as R_DS(ON) for the high-side MOSFET and R_DS(ON)sr for the low-side MOSFET), and the gate-to-drain charge, Q_GD. We will show that this FOM works best to predict the performance of the high-side control MOSFET, QHS (Fig. 1), in a synchronous buck converter, because its performance and losses are governed to a large degree by its dynamic losses. Meanwhile, Q_G × R_DS(ON) continues to predict the performance of the low-side synchronous rectifier, QLS, because the losses in the low-side device are mostly governed by ohmic losses. We also will demonstrate a simple method to evaluate a given MOSFET for a specific application. Furthermore, comparisons between several MOSFETs can be made to choose the most suitable device from a large selection of components.

For simplicity, consider only the common synchronous buck converter of Fig. 1 for the analysis. Assume that QLS is initially turned off and QHS is turned on. This applies the input voltage on one end of the inductor, causing the inductor current to rise. When QHS is turned off, the current will continue flowing through the inductor but now it flows through the diode D1. After a dead time on the order of a few tens of nanoseconds — dictated by the PWM controller — QLS turns on. This allows all the inductor current to flow through QLS rather than D1, since the voltage drop across its R_DS(ON) is lower than the diode voltage drop. Assuming that the current through the inductor does not reach zero (the continuous conduction mode), the voltage across QLS will simply be R_DS(ON) × I_LOAD during the full off period of QHS.

At the end of the off period of QHS, QLS will turn off, allowing the inductor current to flow in the diode D1. After the dead time, QHS will turn on and the cycle continues. The average voltage at the output will depend on the average on-time of QHS if the inductor current is continuous.

MOSFET Loss

Losses will be calculated based on the simple first-order silicon losses without any consideration of the package's parasitic effects. This is done to simplify the equations and make them easy to implement in a spreadsheet while at the same time getting reasonable results.

Let's consider the two sources of losses in any switching MOSFET. The first is from conduction losses or ohmic losses, and the second is from dynamic losses. In conduction loss, power dissipates according to I² × R × duty cycle, while the dynamic or switching losses are those that result when the MOSFET turns on or off, because there will be a finite voltage (a value between zero and the input voltage) between the MOSFET's drain and source while current is flowing through the transistor. The losses for the high-side MOSFET may be calculated as follows:

Where t_R and t_F are the rise and fall times, f_S is the switching frequency, ΔPWM is the duty cycle, Q_G is the gate charge, V_IN is the input voltage, R_DS(ON) is the high-side MOSFET on-resistance, V_DRIVE is the gate-drive voltage and I_LOAD is the load current.

To calculate t_R and t_F, we need to make the following assumptions:

1. t_R ≈ t_F

2. For switching, consider only the gate-to-drain charge component Q_GD, as the rest of the gate charge Q_G does not play any role in switching:

Empirically, the constant K_RF ≈ 4.6, and I_DRIVE is the gate-drive current, R_G is the gate-path resistance and V_DRIVE is the gate-drive voltage. Using the same treatment as above for the low-side MOSFET, we can derive the equations for the synchronous rectifier:

Where V_D is the voltage drop across the body diode or a Schottky diode in parallel. The drain-to-source capacitor loss will not be considered in this analysis because it represents a small percent of the total power loss compared to the dynamic and conduction losses.

A Device Evaluation Chart

Based on Eqs. 1 and 2, it is clear that R_DS(ON) and Q_GD, and not Q_G, play a major role in determining the power losses in the high-side MOSFET in synchronous buck converters. While both R_DS(ON) and Q_GD determine how much conduction loss and switching loss is to be expected, the balance between the two losses is different in a given MOSFET used in the high-side position compared to the synchronous rectifier position in a synchronous buck converter. With that in mind, a new tool is needed that allows us to readily evaluate whether a given MOSFET is well suited for operation in a given position (high-side or synchronous rectifier) based on the power dissipation. This tool should also help in comparing two MOSFETs head-to-head for a specific application using both Q_GD and R_DS(ON).

In order to evaluate MOSFET power dissipation, we need to create a reference circuit representative of a commonly used buck converter. The following specifications are typical for a buck converter application:

Input voltage = 12 V

Output voltage = 1.5 V

Load current = 15 A

This represents a typical phase of a multiphase power supply for the new generation of microprocessors.

Using the power dissipation equations listed previously, in an Excel spreadsheet, one can create a set of constant-power dissipation lines using a MOSFET's R_DS(ON) and Q_GD. This set of lines represents possible combinations of Q_GD and R_DS(ON) that will produce the same power dissipation if used in the reference circuit. This should be repeated several times using power dissipation values from 0.05 W to 2.2 W. These values represent a realistic MOSFET power dissipation. Separate graphs are needed for the high-side and the low-side MOSFETs.

A spreadsheet-generated graph should represent R_DS(ON) on the X-axis and Q_GD on the Y-axis. Several constant-power dissipation lines are drawn on the graph. Fig. 2 is the high-side MOSFET graphs where the thin slanted lines are the constant-power dissipation lines calculated at a 300-kHz switching frequency. The associated value of power dissipation is in black on the bottom and right-hand side of the graph. Several constant-FOM lines are also drawn on the graph; those are the thick blue hyperbolas with the associated FOM value on the top left side of the graph.

Fig. 2 is calculated at load current of 15 A and a switching frequency of 300 kHz at a duty cycle, ΔPWM, of 0.125. Fig. 3 depicts constant-power dissipation graphs for the control MOSFET at load current of 30 A and a switching frequency of 500 kHz. It is worthwhile noting that even a Q_GD × R_DS(ON) FOM of 10 is not capable of delivering power dissipation under 1 W, and in reality delivers a power dissipation of 1.4 W only at the optimum combination of Q_GD and R_DS(ON).

In Fig. 3, a power dissipation of less than 1 W at 30 A and 500 kHz is to be found only in future developments in this fast-moving semiconductor industry. The optimum mix of R_DS(ON) and Q_GD for a given FOM may be obtained by plotting the constant-power dissipation graph and a set of FOM curves of interest. It can be easily observed that any constant-power dissipation line will intersect with the FOM hyperbola in two points, each with a different mix of R_DS(ON) and Q_GD. Ultimately, there is one constant-power dissipation line with a tangent to this FOM hyperbola that clearly from the graph has the lowest power dissipation and would have a single pair of optimum values for Q_GD and R_DS(ON). Fig. 4 depicts this situation for FOMs of 10 and 15 and constant-power dissipation lines of 1.4 W and 1.7 W. It is clear that for an FOM of 15, one can never get a power dissipation of less than 1.7 W (i.e., 1.4 W is unattainable for an FOM of 15).

For synchronous rectifiers, we need a different chart because the loss equations are different from those of the high-side MOSFET. Fig. 5 depicts data from this new chart as a set of constant-power dissipation lines calculated at 15 A and 300-kHz switching frequency, as well as a set of FOM hyperbolas for the synchronous rectifier. Note that the constant-power dissipation lines are almost vertical, indicating that they are mostly dependant on R_DS(ON) and, to a much lesser degree, on Q_GD and dynamic losses.

MOSFET Evaluation

To compare two MOSFETs:

• Plot the values of R_DS(ON) and Q_GD on the graph.

• Run a line parallel to the constant-power dissipation line through each of the points plotted.

• Observe the value of the power dissipation on the topside. Obviously, the lower the power dissipation, the better the MOSFET.

To determine the best mix between the R_DS(ON) and Q_GD:

• Determine the FOM of the process.

• Plot a curve R_DS(ON) × Q_GD = FOM, which is a hyperbola.

• On the graph, draw a line parallel to the constant-power line as a tangent to this hyperbola.

• Read the associated value of R_DS(ON) and Q_GD.

As an example, the table includes three MOSFETs, M1, M2 and M3, and using the typical values in the data sheets, we get that M1 FOM is about 30% better than M3 and 42% better than M2 (Fig. 2). This might cause the user to expect at least that much improvement in performance. However, according to the graph, the differences between the devices from the power dissipation, and hence efficiency, point of view is minimal. These results are supported by efficiency tests that we performed on all of these MOSFETs. Please remember that in the graph I am using the typical values of Q_GD and R_DS(ON) and not the actual devices with their spreads in parameters, which should account for the difference. Still, remember that the difference in the power dissipation is about 0.1 W between M1, M2 and M3.

An implementation of this idea is quite possible using the complete set of switching equations together with the package- and die-parasitics to get a more accurate comparison. Such a model will be so complex that the use of an advanced mathematical sheet such as Maple becomes mandatory. This ambitious approach is probably worthwhile, but it is not likely to be easy to fully understand and use.

Based on the results derived in this article, I propose the use of the more accurate FOM, which is the gate-drain charge times MOSFET on-resistance (Q_GD × R_DS(ON)). As you can see, for a given constant “new” FOM, the power dissipation on the high-side MOSFET will vary significantly. For example, with an FOM of 100, the power dissipation can be as low as 1.3 W or as high as 2.2 W, depending on the individual MOSFET value of R_DS(ON) and Q_G = FOM/ R_DS(ON).

It is clear now that FOM is not a very precise tool to measure whether a given MOSFET with a given FOM will perform well or not in a given topology and a given position (e.g. in a synchronous buck converter, the high-side MOSFET requires a different mix of Q_GD and R_DS(ON) compared to the synchronous rectifier). We actually need the individual value of R_DS(ON) and Q_GD for such a MOSFET to know how good this MOSFET will perform by plotting the point on the graph and reading the value of the power dissipation.

Comparison between two given MOSFETs is very easily achieved by plotting both of them on the graph and calculating the power dissipation. A secondary benefit is actually finding the best combination of Q_GD and R_DS(ON) for a given FOM by finding the tangent parallel to the constant-power lines of FOM curve and directly reading the combination of Q_GD and R_DS(ON).

The use of a spreadsheet lends itself to “what-if” analysis by allowing the user to change the parameters in the reference design and generating a new graph. For example, one might examine the effects of changing the frequency on the performance of any given MOSFET. A separate spreadsheet and graph should be used for the low-side MOSFET (Fig. 5).

Table. Representative MOSFETs and their figures of merit.

Part Number	Total QG	QGD	RDS(ON)	RDS(ON) × QG
M1	13	4.7	11.2	146
M2	18	5	11.5	207
M3	19	4.5	10	190