Haveids itest vtest gmvtest itest rlrs the terms and simplifying the expression
436  C H A P T E R 

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 

RS  vO 







v  �  1  (8.55)  
(8.56)  
o  RL∥RS  
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 
smallsignal model. gm, the  +vgs  RS  RL  

transconductance of the MOSFET,  
is given by K(VGS − VT), where VGS is the operatingpoint value of  
gmvgs  


the gatetosource voltage for the  
MOSFET. (See Example 7.8 or  


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


437  

ids = gmvgs  RS  RL  +  FIGURE 8.40 Sourcefollower  
 
When gm is large, irrespective of the values of RL and RS, Equation 8.58 can be rewritten as
vo 


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 

1  �  

test  m +  RL∥RS  � 
rvtest  RLRS  

out =  =  gmRLRS + RL + RS  


rout ≈1 gm 
