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GM Ids V Gs Q. G M.: 1-5-1 Transconductance

This section discusses transconductance (gm) in MOS transistors, defining it as the slope of the ids versus vgs characteristic at a specific point. It highlights the relationship between gm and the input/output current and voltage, providing various equations to calculate gm based on different parameters. Additionally, it notes the relationship between transconductance and on-resistance, and introduces the small-signal model for MOS transistors in saturation.

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50 views1 page

GM Ids V Gs Q. G M.: 1-5-1 Transconductance

This section discusses transconductance (gm) in MOS transistors, defining it as the slope of the ids versus vgs characteristic at a specific point. It highlights the relationship between gm and the input/output current and voltage, providing various equations to calculate gm based on different parameters. Additionally, it notes the relationship between transconductance and on-resistance, and introduces the small-signal model for MOS transistors in saturation.

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unknown
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CHAPTER 1: MOS TRANSISTOR MODELS 25

1-5-1 Transconductance gm
The relationship between ids and vgs is given by the slope of the ¿ds versus vgs
characteristic at point Q. It is called the transconductance gm. Indeed, it has the
dimension of a conductance and it gives the ratio between the signal output current
to the signal input voltage, i.e., the signal transfer.
This slope is actually the derivative of ids to vgs in that point (Eq. (l-18c)), which
yields

gm = 2—— (VGse - Vt) (l-22a)

Alternative expressions are obtained by substitution, such as

(1-226)

2Idsq (l-22c)
or s"=

Remember that KP/2m can always be replaced by K'. All these expressions will be
used later during the design procedures, so the reader must be familiar with them all.
Two out of the three variables Idsq, ^gsq — Vt, and W/L are sufficient to determine
gm. This will later be exploited in the design procedures for amplifiers.
The transconductance is thus proportional to the square root of the current in
Eq. (l-22è). Quadrupling the current only doubles the transconductance.
It is worth noting that comparison of Eq. (l-22a) and Eq. (l-%) shows that the
on resistance Rds-, in the linear region, is approximately the inverse of the transcon­
ductance gm in the saturation region. It is difficult to find an intuitive reason for this,
and yet it is worth considering. Insight into FET operation may be gained from this
observation.
The small-signal model of the MOST in saturation is depicted in Fig. l-8a. The
input node at the gate is isolated. Its small-signal or AC voltage vgs controls the
current from drain to source idS by means of a voltage-controlled current source with
value gmvgs.

FIGURE 1-8 Small-signal or AC equivalent circuitry.

G B

vgS ^hs

S -

(fl) (b)

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