Power Electronics Technology October 2005 www.powerelectronics.com October 2005 www.powerelectronics.com44

A Graphical Approach To MOSFET Evaluation

Using a new version of power MOSFET fi gure 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.

By Alan Elbanhawy,By Alan Elbanhawy,By Alan Elbanhawy Director, Computing and Telecommunications Segments, Advanced Power Systems Center, Fairchild Semiconductor, San Jose, Calif.Center, Fairchild Semiconductor, San Jose, Calif.Center,

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, RDS(ON)

, and total gate charge, Q

G, has been used as the fi gure 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

QG 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 RDS(ON)

for the high-side MOSFET and RDS(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) R

DS(ON) R continues to predict the performance of the low-

side synchronous rectifi er, 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 specifi c 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 fl owing through the inductor but now it fl ows 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 fl ow 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 fl ow 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 LossLosses will be calculated based on the simple fi rst-order

silicon losses without any consideration of the package’s

Fig. 1. The classical synchronous buck converter uses two switching MOSFETs: the high-side (control) device, QHS, and the low-side synchronous rectifi er, QLS.

PWPWMControlleController

andandDriverDriver

0

21

D1D1D1

QLSQLSQLS

QHSQHS

L1

Cf

++

–

O

VVcc

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MOSFET EVALUATION

Fig. 2. The constant-power dissipartion curves for a high-side MOSFET running at a 15-A load at a frequency of 300 kHz.

10

9

8

7

6

5

4

3

2

10 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

GDQ

DS (ON)R

101010102525 3535 5050

7575 100100 150

0.5 WW 0.6 WW 0.7 0.7 0.7 WWW 0.8 0.8 0.8 0.8 WWWW 0.9 0.9 0.9 WWWWWW1.0 1.0 1.0 WWW 1.1 1.1 1.1 1.1 WWW 1.2 1.2 1.2 WWWW 1.3 1.3 WWWWW

2.2 W2.0 W

1.4 1.4 WW 1.5 1.5 1.5 WW 1.6 1.6 1.6 WWW1.7 1.7 1.7 1.7 WWW1.8 1.8 WW1.9 1.9 1.9 1.9 WW

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 fi rst 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 fi nite voltage (a value between zero and the input voltage) between the MOSFET’s drain and source while current is fl owing through the transistor. The losses for the high-side MOSFET may be calculated as follows:

P t t I V f VDYP tDYP tNAMIP tNAMIP tC RP tC RP t F Lt IF Lt I OAD IV fD IV fN SV fN SV f DRIVVDRIVV EP t= +P tP t= +P tP tC RP t= +P tC RP t1

2C R2C R( )P t( )P t t I( )t IC R( )C RP tC RP t( )P tC RP t F L( )F Lt IF Lt I( )t IF Lt I= +( )= +P t= +P t( )P t= +P tC R= +C R( )C R= +C RP tC RP t= +P tC RP t( )P tC RP t= +P tC RP t V f V fD I D IV fD IV f V fD IV fV fN SV f V fN SV f + Q fG SQ G SQ fG Sf

P I R PWMCONDUCTIONP ICONDUCTIONP ILOAD DSR PDSR PP I=P I 2( )R P( )R PON( )ONR PONR P( )R PONR P∆R P∆R P

P PDIP PDIP PSSIP PSSIP PPAP PPAP PTIONP PTIONP PDYP PDYP P NAMICP P=P P + PCONDUCTIONPCONDUCTIONP (Eq. 1)Where t

R and t

R and t

R F are the rise and fall times, f

Sise and fall times, f

Sise and fall times, f is the

switching frequency, PWM is the duty cycle, QG is the gate charge, VIN is the input voltage, R

DS(ON) is the high-side

MOSFET on-resistance, VDRIVE

is the gate-drive voltage and I

LOAD is the load current.

To calculate tR and t

F, we need to make the following

assumptions:1. tR ≈ tF2. For switching, consider only the gate-to-drain charge

component QGD

, as the rest of the gate charge QG does not

play any role in switching:

Constant KRF

Constant K

IV

R

Constant Kt t Constant KR Q

Constant KR Q

Constant KV

DRIVEDRIVVDRIVV E

G

R F Constant KR F Constant K Constant Kt t Constant KR F Constant Kt t Constant KG G Constant KG G Constant KR QG GR Q

Constant KR Q

Constant KG G Constant KR Q

Constant KD Constant KD Constant KDRIVVDRIVV E

=

Constant K= = Constant K Constant Kt t Constant K= = Constant Kt t Constant KR Q×R QR QG GR Q×R QG GR Q

Empirically, the constant KRF

≈ 4.6, and IDRIVE

is the gate-drive current, R

Gdrive current, R

Gdrive current, R 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 rectifi er:

(Eq. 2)

P tP tDIP tDIP tSSIP tSSIP tPAP tPAP tTIONP tTIONP tsr RP t=P t

1

22 (Eq. 2)2 (Eq. 2)

( +P t( +P tR( +R t )I V f +

(Eq. 2)I (Eq. 2) (Eq. 2)2 (Eq. 2)I (Eq. 2)2 (Eq. 2) (Eq. 2)R ( (Eq. 2) (Eq. 2)1 (Eq. 2) (Eq. 2)- (Eq. 2) (Eq. 2)PW (Eq. 2)

F Lt )F Lt )I F LI OAI OAI D DI D DI V D DV Sf +Sf +

LOAD (Eq. 2)LOAD (Eq. 2) (Eq. 2)I (Eq. 2)LOAD (Eq. 2)I (Eq. 2)DS (Eq. 2)DS (Eq. 2) (Eq. 2)R ( (Eq. 2)DS (Eq. 2)R ( (Eq. 2)(O (Eq. 2)(O (Eq. 2) (Eq. 2)R ( (Eq. 2)(O (Eq. 2)R ( (Eq. 2)N) (Eq. 2)N) (Eq. 2) (Eq. 2)R ( (Eq. 2)N) (Eq. 2)R ( (Eq. 2) (Eq. 2)∆ (Eq. 2) (Eq. 2)M) (Eq. 2) (Eq. 2)M (Eq. 2)M) (Eq. 2)M (Eq. 2)

Where VD 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 ChartBased on Eqs. 1 and 2, it is clear that R

DS(ON) and Q

GD, and

not QG, 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 rectifi er 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 rectifi er) based on the power dissipation. This tool should also help in comparing two MOSFETs head-to-head for a specifi c 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

Power Electronics Technology October 2005 www.powerelectronics.com October 2005 www.powerelectronics.com46

MOSFET EVALUATION

Part Number Total QG QGD RDS(ON) RDS(ON) x QG

M1 13 4.7 11.2 146

M2 18 5 11.5 207

M3 19 4.5 10 190

Table. Representative MOSFETs and their fi gures of merit.

Fig. 3. The constant-power dissipation curves for a high-side (control) MOSFET at a 30-A load current and 500-kHz frequency.

0.8 W1.1 W0.9 W1.4 W1.7 WFOM= 15FOM= 25

1.0 W1.2 W1.3 W1.5 WFOM= 10FOM= 20

4

3.5

3

2.5

2

1.5

10.0015 0.0025 0.0035 0.0045 0.0055 0.0065 0.0075 0.0085 0.0095

DS (ON)

GDQ

NGD

QN

GDF

R

Fig. 4. The points where the FOM hyperbolas intersect the constant-power dissipation lines determine the minimum power dissipation for the MOSFET.

R DS (ON)

C

NFGDC

NFGDC

NF

4

3.5

3

2.5

2

1.5

10.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

1.4 WFOM= 10

1.7 WFOM= 15

used buck converter. The following specifications are typical for a buck converter application:

Input voltage = 12 VOutput voltage = 1.5 VLoad current = 15 AThis 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 QGD

and RDS(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)R

DS(ON)R on the X-axis and Q

GDon 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, ∆PWM, 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 QGD

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

QGD

. 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

RDS(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 rectifi ers, 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 QGD

and dynamic losses.

MOSFET EvaluationTo 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.

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Fig. 5. Constant-power dissipation lines plotted against FOM hyperbolas for the synchronous rectifi er at 15 A and 300-kHz switching frequency.

10

9

8

7

6

5

4

3

2

10 0.002 0.004 0.006 0.008 0.01

R DS (ON)

QGD

1010

2525

3535

5050

7575

100100100

0.5 WW

0.7 0.7 W

0.8 0.8 W

0.9 0.9 WW

1.0 W

1.1 W1.2 1.2 W

1.3 WW

1.4 W

1.5 W

1.6 WW 1.7 1.7 WW

1.9 1.9 W

2.0 WW

2.2 2.2 W

To determine the best mix between the R

DS(ON) and Q

GD:

● Determine the FOM of the process.

● Plot a curve RDS(ON)

QGD

= 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 RDS(ON)

and QGD

.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 effi ciency, point of view is minimal. These results are supported by effi ciency 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 not the not

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 t i m e s M O S F E T on-resistance (Q

GD

RDS(ON)

). As you can see, for a given co n s t a n t “n e w ”

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 QG = 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 rectifi er). 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 benefi t is actually fi nding the best combination of Q

GD and R

DS(ON)

for a given FOM by fi nding 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). PETech

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