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# Haveids itest vtest gmvtest itest rlrs the terms and simplifying the expression

436 C H A P T E R

E I G H T

t h e s m a l l - s i g n a l
VS
s o u r c e f o l l o w e r
before3is the source follower shown in Figure 8.38. The source follower in the figure

+
vI
-

RS vO

RL

FIGURE 8.38 Source-follower circuit.

where vgs is the voltage between the gate and the source of the MOSFET. Using KVL, observe that vgs = vivo. Therefore, we can write

v 1
(8.55)
(8.56)
o RLRS
vo = RLRS gm (8.57)
RL + RS + RLRS gm RLRS gm
vo
(8.58)
vi = RL + RS + RLRS gm

Thus the gain is slightly less than 1. An important special case of Equation 8.59 is when RL is very large. Thus, when RL → ∞,

vo RS gm

.

(8.59)
vi = 1 + RS gm
small-signal model. gm, the
+vgs
RS RL
transconductance of the MOSFET,
is given by K(VGSVT), where VGS is the operating-point value of
gmvgs

vo

the gate-to-source voltage for the
MOSFET. (See Example 7.8 or

-

Problem 7.5 in Chapter 7 to see
+ vgs
is a il

8.2 The Small-Signal Model

C H A P T E R

437
ids = gmvgs RS RL +
FIGURE 8.40 Source-follower
-

When gm is large, irrespective of the values of RL and RS, Equation 8.58 can be rewritten as

vo

1.

vi

The input resistance ri is easily calculated. Since no current flows into the MOSFET, the input resistance is infinity.

Computing the output resistance needs more work. As depicted in Figure 8.40, let us

(8.60)
(8.61)

Rearranging the terms and simplifying the expression, we obtain

v

g

1
test m + RLRS
rvtest RLRS
out = = gmRLRS + RL + RS

When gm, RL, and RS are large, RL + RS becomes insignificant compared to gmRLRS. Therefore, we can simplify,

rout ≈1 gm

.

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