# MOSFET Gate Driver | Calculations

## Maths

Posted by Angel G. Miranda on January 15, 2018

keywords: Power MOSFET series gate resistor value, Power MOSFET series resistor power requirement, Power MOSFET Driver calculation

### The Objectives

This is a simple, but very useful calculator to estimate:

1. MOSFET gate current, iG$i_{G}$ [A].
2. Time that the MOSFET will turn on, tON$t_{ON}$ [us].
3. The resistor (RG2$R_{G2}$) value that must be added to the MOSFET gate and achieve the above two estimations [Ohm]
4. The average power (Pave$P_{ave}$) which must be endured by RG2$R_{G2}$. This value must be employed instead of the pulse power. RG2$R_{G2}$ will limit the power delivered by the MOSFET driver which can be tuned to limit tON$t_{ON}$.

### 1 Metal Oxide Semiconductor Field Effect Transistors (MOSFET)

MOSFETs need to be matched to the power requirements with a factor of safety (FoS) of at least 1.2 for both currents and voltages. You will encounter two types of channels, N and P{channel; P-channel MOSFETs are rarely used and thus, you will have to go with the N-channels. N-channel MOSFETs have the advantage of having less conduction losses owing to the fact that they employ electron-based minority carriers which are much more efficient than the hole-based minority carriers of the P-channel ones.

#### 1.1 Important MOSFET parameters

The important parameters which will be employed in later sections are:

 VGS$V_{GS}$ Normally found at the maximum ratings section, this is the gate-source voltage range; it may range from 10 to 20V. QG$Q_{G}$ A dynamic characteristic which is the total charge of the MOSFET’s gate [nC]. It can be employed to estimate the instantaneous current needed to turn on a MOSFET in a speci ed time. ton$t_{on}$ This is a design parameter to maximize or minimize the worst case input gate current [ns]. RG$R_{G}$ This is the internal gate resistance of the MOSFET. We will use this fixed resistance to calculate an additional resistor to limit the gate current, iG$i_{G}$.

#### 1.2 Gate current equations

   The gate current, iG$i_G$, is a parameter that is essential to choose a MOSFET driver (more on this on the next section). The gate current can be calculated as follows:

iGiG=C(dV/dt)=QG/ton(1)$$$\begin{split} i_G &= C (dV/dt) \\ i_G &= Q_G/t_{on} \end{split}$$ \qquad (1)$

which is a convenient way to estimate the maximum current that the MOSFET driver will have to supply during the ton$t_{on}$. The iG$i_G$ is necessary in order to calculate the wire diameters/material or PCB widths.

#### 1.3 MOSFET driver | RG2$R_{G2}$ equation

The RG2$R_{G2}$ value can be calculated with the simple formula:

RG2=VGS/iGRG(2)$$$R_{G2} = V_{GS}/i_G – R_G$$ \qquad (2)$

#### 1.4 Power determination of the RG2$R_{G2}$

    The underlying pulse and average power (Ppulse$P_{pulse}$ and Pave$P_{ave}$, respectively) relationships of the MOSFET are presented as follows:

PpulsePave=iGVGS=PpulsetonTPWM(3)$$$\begin{split} P_{pulse} &= i_G V_{GS}\\ P_{ave} &= P_{pulse}\frac{t_{on}}{T_{PWM}} \end{split}$$ \qquad(3)$

where either one of iG$i_G$ or ton$t_{on}$ is a design parameter while the other is calculated with equation (1) and TPWM$T_{PWM}$ is the PWM period. Ppulse$P_{pulse}$ is the maximum instantaneous power that the MOSFET driver will provide which is limited by RG2$R_{G2}$ (refer to equation (2)). However, Ppulse$P_{pulse}$ will only be under effect during ton$t_{on}$. Therefore, it is advisable to buy one that can endure 1 or 2 times the Pave$P_{ave}$ instead of buying a full power Ppulse$P_{pulse}$ rated resistor.

   Note: Pave$P_{ave}$ is only dependent on VGS$V_{GS}$, QG$Q_G$ and TPWM$T_{PWM}$ and is easily found after some equation rearrangements.

## 2 Putting all the equations to work! MOSFET iG$i_G$, RG2$R_{G2}$ and power calculation example

In this section,the following design parameters are employed:

VGSTPWM=12[V]=10[μs]$$$\begin{split} V_{GS} &= 12 [V]\\ T_{PWM} &= 10 [\mu s] \end{split}$$$ QGRG=55[nC]=1[Ω]$$$\begin{split} Q_G &= 55 [nC]\\ R_G &= 1 [\Omega] \end{split}$$$

where the maximum QG$Q_G$ was taken. If a ton$t_{on}$ of 500 [ns] is defined, then an iG$i_{G}$ can be calculated with equation (1) as follows:

iG=55[nC]500[ns]=0.11[A]$$$i_G = \frac{55 [nC]}{500 [ns]} = 0.11 [A]$$$

Please note that this current will only be applied to the first 500[ns] needed to turn on the MOSFET, after that, a very small current will be needed to maintain the MOSFET ON because MOSFETs are voltage-driven. Of course, smaller ton$t_{on}$ will require much higher iG$i_G$.

With the previous iG$i_G$ of 0.11 [A], using equation (2), an RG2$R_{G2}$ of 108 [latex options:inline]\Omega[/latex] is to be bought and soldered to the final PCB. Of course, you would rather choose a lower standard resistance over a higher one in order to turn on the gate a little faster than calculated.

In this example, we will use a 100 [ohm] resistor. Therefore, the new gate current is calculated by rearranging eqn. (2):

iGiG=VGS/(RG2+RG)=0.1212[A]$$$\begin{split} i_{G}& = V_{GS}/(R_{G2} + R_{G}) \\ i_{G} &= 0.1212 [A] \end{split}$$$

And the new time to turn on the MOSFET is, after rearranging eqn. (1):

tONtON=QG/iG=453.8[ns]$$$\begin{split}t_{ON} &= Q_G/i_{G}\\ t_{ON} &= 453.8 [ns] \end{split}$$$

The rated power of the RG2$R_{G2}$ is calculated using eqn. (3) and given as:

PpulsePave=1.45[W]=0.066[W]$$$\begin{split} P_{pulse} &= 1.45 [W]\\ P_{ave} &= 0.066[W] \end{split}$$$

In this case, a resistor with a rated power of 1/4 [W] will be chosen, which is well above the average power.

Edit: VBS will be employed instead of VGS if you are using a bootstrap IC. VBS is the MOSFET driver’s effective voltage to turn on the MOSFET. VBS is equal to the driving voltage of the bootstrap IC minus the voltage drop of the Bootstrap diode.