How a MOSFET Transitions from Cutoff to Conduction

As V_GS rises, the transition is not perfectly smooth. A step appears in the waveform, as shown in Figure 4.4.1. This step is commonly known as the Miller step or Miller plateau.

Figure 4.4.1 | Miller plateau

The Miller Effect in an Inverting Amplifier

Consider an ideal inverting voltage amplifier with a gain of -A_V, as shown in Figure 4.4.2. An impedance with a value of Z is connected between the amplifier's output and input. If the input current is defined as I_i, while the amplifier's own input current is assumed to be zero, and the input impedance is defined as Z_in, the corresponding relationships are shown below.

Figure 4.4.2 | Ideal inverting voltage amplifier

The inverting voltage amplifier therefore increases the effective input capacitance by a factor of 1 + A_V. This effect was first identified by John Milton Miller and published in his work in 1920, which is why it is known as the Miller effect.

Parasitic Capacitances in a MOSFET

Figure 4.4.3 | MOSFET parasitic capacitance equivalent circuit

A MOSFET operates as a common-source amplifier in its small-signal representation. The drain is the output terminal, the source is connected to ground, and the MOSFET gate is the input terminal.

The three main interterminal capacitances are the gate-to-drain capacitance C_GD, gate-to-source capacitance C_GS, and drain-to-source capacitance C_DS. They can be derived from the capacitance parameters specified in the MOSFET datasheet:

C_GD = C_RSS

C_GS = C_ISS - C_RSS

C_DS = C_OSS - C_RSS

Here, C_RSS is the reverse-transfer capacitance, C_ISS is the input capacitance, and C_OSS is the output capacitance. Their values can be found in the MOSFET datasheet, as illustrated in Figure 4.4.3.

According to the MOSFET small-signal model, the device forms an inverting voltage amplifier.

Figure 4.4.4 | Equivalent circuit of the inverting voltage amplifier formed by a MOSFET

The voltage gain of the amplifier formed by a MOSFET depends on its output and input resistances. Different MOSFETs have different characteristics, so the gain is difficult to quantify in general. Under some conditions, the voltage gain can reach several hundred.

C_GD forms a feedback path between the output terminal, the drain, and the input terminal, the gate. This feedback path produces the Miller effect in the MOSFET.

MOSFET Turn-On Sequence

Three signals are particularly important when analyzing MOSFET turn-on: V_GS, V_DS, and I_D. The turn-on process is shown in Figure 4.4.4.

Figure 4.4.5 | MOSFET turn-on process

Starting at time zero, V_GS begins to rise, while V_DS and I_D remain essentially unchanged. During this interval, the gate-drive current charges C_GS, causing V_GS to increase. At time t₁, V_GS reaches the gate-threshold voltage, V_GS(th). Before t₁, the MOSFET remains in the cutoff region.

After t₁, the MOSFET begins to conduct. The clearest indication of turn-on is that the drain current I_D starts to rise. During this interval, the gate-drive current continues to charge C_GS. Between t₁ and t₂, I_D gradually increases until it reaches the inductor current at t₂.

As the inductor current rises, V_DS decreases slightly. This occurs because the current slew rate, dI/dt, produces a voltage drop across stray inductance. Consequently, the measured drain-to-source voltage includes this additional voltage drop. From t₁ onward, the MOSFET is considered to be in the saturation region.

How the Miller Plateau Forms

When I_D reaches its maximum value at t₂, the device immediately enters the Miller plateau interval. During this interval, V_GS remains nearly constant for a period of time.

In the saturation region, the MOSFET transfer characteristic can be expressed as:

I_D = V_GS × G_m

Here, G_m is the transconductance. If I_D remains constant, V_GS also remains essentially constant. Once the drain current has risen to the inductor current, I_D is equal to I_L. Because the MOSFET is still in the saturation region, V_GS holds at approximately the Miller-plateau voltage.

I_D is the channel current, flowing between the drain and source in the direction. When the gate-drive current charges C_GS by an amount that increases V_GS by ΔV_GS, the drain current increases by ΔI_D. As a result, V_DS decreases, which also causes V_GD to decrease.

Figure 4.4.6 | MOSFET drain channel current

The changing drain-to-gate voltage drives current through the gate-drain capacitance:

I_GD = C_GD × ΔV_GD/Δt

As I_GD increases, more of the gate-drive current is diverted into the feedback capacitance, leaving less current available to increase V_GS. Therefore, V_GS can increase only very slowly and remains near the Miller plateau.

This is a negative-feedback process, which is why C_GD is also called the feedback capacitance. The sequence can be summarized as follows:

• V_GS rises → I_D rises
• Current supplied through C_DS increases → V_DS falls
• V_GD falls → I_GD rises
• The rising slope of V_GS decreases

Before time t₃, C_GS is much larger than C_GD, so the rising slope of V_GS is mainly determined by C_GS. Starting at t₃, however, the changing V_GD causes the effective capacitance seen at the gate to increase significantly. The gate is being charged, but the voltage at the other terminal of the capacitance is changing rapidly at the same time. This increases the effective charge required to change the gate voltage and slows the rise of V_GS.

When the MOSFET turns on and the drain voltage falls rapidly, the gate-drain Miller capacitance C_GD increases substantially. The resulting change in the effective capacitance associated with V_GS limits its rising slope and produces the visible step in the waveform.

Figure 4.4.7 | Sudden change in effective capacitance

MOSFET Turn-On Behavior in Soft-Start Circuits

In telecommunications equipment and microwave circuit design, MOSFETs are often used to control inrush current and provide a gradual power-up. MOSFETs combine low on-state resistance, R_DS(on), with simple gate drive requirements. A soft-start circuit can therefore be built with only a small number of additional components.

Although the circuit itself may be simple, a thorough understanding of MOSFET switching behavior is necessary to analyze how it operates. Engineers commonly use the gate-charge curve to understand the MOSFET turn-on process. This curve can be found in the MOSFET datasheet.

Under normal conditions, a PMOS device is used on the positive supply side, while an NMOS device is used on the negative supply side. The operating principle of soft-start circuits can then be analyzed through the MOSFET's gate-charge characteristics and Miller-plateau behavior.

Figure 4.4.8 | MOSFET turn-on process and V_GS