 # Power MOSFET Design Equations

There are only few power MOSFET design equations to take note when doing design involving this electronic part. You may try deriving these equations if you want a better understanding on how these formulated. These are also given in application notes and some technical blogs but maybe in different form but will result to the same calculation results.

The important parameters to take note when dealing with Power MOSFET are current, voltage, power dissipation and thermal. Power dissipation and thermal are often related to each other. In this another topic I will going to give the power MOSFET design equations that I used in my actual design projects.

### Current:

Current is can be rms or dc or pulse or peak drain current. RMS stands for root mean square but do not dwell too much on this description. Let us put in this way, if the current in the circuit is not a straight line, then use the rms value to compute the power dissipation. However, if the current in the circuit is straight line, then use the dc value as reference. We are particularly talking here the drain current.

Peak drain current is a rating often specified in a single pulse or few pulses. This is relevant to transient conditions like short circuit.

### Voltage:

The voltage that we talked here refers to the drain to source voltage level when the MOSFET is at off state. MOSFET is sensitive to this voltage level.

### Power Dissipation:

Power Dissipation is the actual power dissipated by the device. This is the total of the conduction loss or the static loss and the switching loss or dynamic loss. The datasheet provided the maximum power dissipation limit.

## Thermal:

Thermal is very important in power electronics. The devices must not get too hot to avoid damaging it. The datasheet has specified temperature limit.

## Derivation of the Drain Current

The drain current is could be rms or dc level. The exact value is dependent to the actual circuit. For a MOSFET functioning as a switch, the drain current is can be derived as supply voltage divided by the total resistance in series to the MOSFET. For MOSFET operating as part of the switching converter, the derivation of the rms current is bit complicated. We will discuss this on another topic.

## Power MOSFET Design Equations – Derivation of the Power Dissipation

Power dissipation is the sum of the conduction loss and the switching loss. Conduction loss is also called a static loss. On the other hand, switching loss is also called as dynamic loss. The total MOSFET power loss is:

Pdiss = Pconduction +Pswitching

Note: When a MOSFET is used in a circuit that does not perform continuous switching, only the conduction loss is present.

Pconduction = Idrain2 x Rdson

Where; Pconduction – conduction loss

Idrain – is the drain current

Rdson is the drain to source on state resistance

Pswitching = Pgatecharge + PCoss + Ptrise_tfall

Pgatecharge = 0.5 X Qgtotal X Vgate X Fsw

Pcoss = 0.5 X Coss X Vdrain2 X Fsw

Ptrise_tfall = 0.5 X (trise + tfall) X Idrain X Vgate X Fsw

Where; Pswitching – switching loss

Pgatecharge is the power loss during MOSFET turn on

PCoss – is the power loss due to the output dynamic capacitance

Ptrise_tfall – is the power loss due to the rise and fall time of the MOSFET drain voltag

Qgtotal – is the total gate charge given in the datasheet

Vgate – is the applied gate to source voltage

Fsw – is the switching frequency

Coss – is the output dynamic capacitance

Vdrain – is the maximum drain voltage level

trise – rise time of the drain voltage

tfall – fall time of the drain voltage

## Power MOSFET Design Equations – Derivation of the Power Capability

Datasheet used to give power dissipation rating. However, that is a rating taken at 25’C. Actual operation usually has higher temperature that can go easily 100’C.

### Power Capability with no heatsink:

Pcapability = (Tjmax – Tamb) / Rthja

### Power Capability with heatsink:

Pcapability = (Tjmax – Tcase) / (Rthjc + Rthchs + Rthhsa)

Where; Tjmax – maximum junction temperature as specified in the datasheet

Tamb – ambient temperature of operation

Rthja – thermal resistance junction to ambient

Tcase – case temperature of the MOSFET

Rthjc – thermal resistance junction to case

Rthchs – thermal resistance case to heatsink or the thermal resistance of the compound

or paste that bonding or in between the MOSFET case and the heatsink surface

Rthhsa – thermal resistance heatsink to air or simply the thermal resistance of the

heatsink used.

## Power MOSFET Design Equations – Derivation of the Junction Temperature

### No Heatsink

Tj = (Pdiss X Rthja) + Tamb

### With Heatsink

Tj = Pdiss X (Rthjc + Rthchs + Rthhsa) + Tcase

Where; Tj – junction temperature of the MOSFET

Pdiss – total power dissipation

Rthja – thermal resistance junction to ambient

Tamb – ambient temperature of operation

Rthjc – thermal resistance junction to case

Rthchs – thermal resistance case to heatsink

Rthhsa – thermal resistance heatsink to air

Tcase – MOSFET case temperature

These power MOSFET design equations are not exact. It is still the call of the design engineer to ensure a good design. However, these equations are good enough to establish a baseline. Usually, I add a margin to the result of these equations to compensate the approximations.

## Example on How to Use the Power MOSFET Design Equations

### Conduction Loss Derivation

Known design values and assumptions:

Idrain = 20A

Tamb = 50’C

Tcase = 100’C

The datasheet provided Rrson max of 2.6mohm. However, this value is maybe taken at nominal temperature, so we will consider the operating temperature we set that is Tcase of 100’C. So, at 100’C, the normalized value is 1.4 based on the Tj versus Rdson graph below. Do not be confused if I used here the the Tj data for the Tcase. We are doing design here, so we can do this if no other data provided. As long as we can add descent design margin, then would be good. Thus, the effective Rdson will be

2.6mohm X 1.4 = 3.64mohm

Since the Idrain is known, we can compute now the conduction loss as below.

Pconduction = Idrain2 x Rdson

Pconduction = 20A2 x 3.64mohm = 1.456W

### Switching Loss Derivation

Known design values and assumptions:

Vgate = 15V

Fsw = 100kHz

Vdrain = 48V

Gate Charge Loss

From the datasheet, the maximum gate charge value is 120nC (see below table). The gate charge loss will be:

Pgatecharge = 0.5 X Qgtotal X Vgate X Fsw

Pgatecharge = 0.5 X 120nC X 15V X 100kHz = 0.09W

Coss Loss

The max Coss is 1300pF per datasheet (see below table). The Coss loss will be:

Pcoss = 0.5 X Coss X Vdrain2 X Fsw

Pcoss = 0.5 X 1300pF X (48V)2 X 100kHz = 0.15W

Rise/Fall Time Loss

The rise time and fall time specified in the datasheet are 11ns and 13ns respectively. The corresponding loss will be:

Ptrise_tfall = 0.5 X (trise + tfall) X Idrain X Vgate X Fsw

Ptrise_tfall = 0.5 X (11ns + 13ns) X 20A X 15V X 100kHz = 0.36W

The total switching loss will be:

Pswitching = Pgatecharge + PCoss + Ptrise_tfall

Pswitching = 0.09W + 0.15W + 0.36W = 0.6W

And the total power dissipation is

Pdiss = Pconduction + Pswitching

Pdiss = 1.456W + 0.6W = 2.056W

### Power Capability Derivation

Known design values and assumptions:

Tamb = 50’C

Power capability is the power dissipation limit of the MOSFET considering actual design scenarios.

Power Capability with no heatsink:

From below table, the max junction temp is 175’C. The thermal resistance junction to ambient is given as 62’C/W for a smaller PCB footprint. So, the power capability with no heatsink attached to the device is then:

Pcapability = (Tjmax – Tamb) / Rthja

Pcapability = (175’C – 50’C) / (62’C/W) = 2.016W

The computed total power dissipation of the MOSFET is 2.056W, therefore it is not possible to operate the MOSFET with no heatsink attached as the actual power capability is only 2.016W. For a MOSFET like this, a thicker and a wider pad is can be used as a heatsink to increase its power capability.

Power Capability with heatsink:

Known design values and assumptions:

Tcase = 100’C

Rthchs = this is not given. So, we will assume that this is negligible (zero)

Rthhsa = this is the heatsink thermal resistance. Assuming we will be utilizing only the PCB pad size and thickness, then we can assume a value of 10’C/W.

Then the power capability would be:

Pcapability = (Tjmax – Tcase) / (Rthjc + Rthchs + Rthhsa)

Pcapability = (175’C – 100’C) / (0.7’C/W + 0 + 10’C/W) = 7.009W

With the heatsink, the power stress on the MOSFET decreases dramatically.

### Junction Temperature Derivation

In some cases, junction temperature is required to be computed. If the power stress on the MOSFET is very low, the junction temperature is also very low and may not need to be computed.

No Heatsink

Tj = (Pdiss X Rthja) + Tamb

Tj = (2.056W X 62’C) + 50’C = 177.472’C

This value is already beyond the MOSFET junction temp limit of 175’C.

with Heatsink

Tj = Pdiss X (Rthjc + Rthchs + Rthhsa) + Tcase

Tj = 2.056W X (0.7’C/W + 0 + 10’C/W) + 100’C = 121.9992’C

This is a good junction temperature for a 175’C MOSFET.

Some articles related to MOSFETs:

How to Use MOSFET as Reverse Battery Protection

MOSFET RDSon Temperature Coefficient Usage and Interpretation

How to Use MOSFET RDSon Data from the Datasheet

MOSFET Efficiency Factors for Switching Converters