# Understanding MOSFET transconductance and cutoff region

2023-10-16Archive

Compared to transistors, MOSFETs are relatively complex and their working process is difficult to understand. Then hardest part of it might be understanding switching losses of MOS tubes. Compared to conduction losses and freewheeling losses, process of turning a MOS lamp on and off is much more complicated.

In order to better analyze process of opening MOS, we will first look at two main concepts. U = I * R, R is resistance, which can effectively reflect effect of changing current flowing through resistance on voltage across it. For example, if current flowing through this resistance is greater, voltage across it will be higher. . Conductivity is inverse of resistance. If we use Λ to represent it, then above formula can be converted to I = ΛU.

This formula can be used to express effect of a change in voltage in a circuit on current flowing through a device. This effect can be amplitude or phase. The effect of amplitude is relatively clear to everyone. For example, higher voltage applied to both ends of a resistor, greater current flowing through it. From point of view of influence on phase, most typical scenarios, such as a parallel LC resonant circuit, will not be analyzed here.

There is a concept of steepness in MOS tube device. Then slope, which is essentially conduction, represents effect of voltage changes in device on current, but describes relationship between respective parameters of two circuits. Specifically in MOSFETs, transconductance gm is effect of Vgs, i.e. gate voltage on Ids. If this is described by a formula, then Ids = gm*(Vgs-Vth).

What does above formula mean?

① Only when voltage Vgs exceeds voltage Vth, current Ids will change significantly.

②Before Vgs reaches platform voltage, difference between current Ids and (Vgs-Vth) is a proportional relationship, and proportional gain of this proportional relationship is slope. The concept of transconductance is somewhat similar to increasing current β in a transistor, but parameter β represents ratio between current and current, so this increase cannot be called transconductance. The transconductance characteristic is an inherent natural property of MOS lamps, and we will not go into it for now.

Another process that is difficult to understand is that in plateau region, voltage Vds begins to fall linearly. In fact, process of reducing Vds corresponds to process of lengthening the cutoff region.  As you can see from figure above, cutoff voltage V at cutoff point is always equal to Vgs - Vth, that is, unchanged. As cutoff region continues to rise, Vds must continue to decrease. When voltage at D (drain) pin also reaches Vgs-Vth, MOS lamp is basically fully turned on. In subsequent process, voltage Vd will gradually decrease to 0 V, and at this time, basically Vgd = Vgs (ignoring on-state resistance of MOSFET). As a general rule, in real projects we will keep increasing Vgs, expanding channel width even more, and then decreasing Rds, but at moment effect of Vgs is already very small.

The analysis clarifies two processes that are relatively difficult to understand, and below we can derive corresponding calculation of lamp switching losses in more detail. But note that these calculations are essentially only rough estimates, in a sense it is impossible to accurately calculate switching losses.

The first article ends here, and in next article we will calculate switching losses of a MOS lamp in detail.