1044
Chapter 14 Single-Transistor Amplifiers
Exercise: Verify the results of the SPICE simulation of Design Ex. 14.12.
Exercise: Suppose the JFET chosen for the circuit in Fig. 14.45 also had λ = 0.015 V−1 .
What are the values of r o and the new voltage gain? (Use the Q-point values from the
example.) Does neglecting the output resistance seem a reasonable thing to do?
Answers: 333 k, 43.5; No, r o is important in this circuit! We will not achieve the desired
gain with this JFET.
Exercise: (a) Redesign the circuit using the 25 V/0.25 V case from Table 14.15. Use the
same JFET device parameters. (b) Verify your design with SPICE.
Answers: 5.60 k, 68 k, VD D = 25 V, 0.022 F, 8200 pF, 20 pF
Exercise: (a) Create a two-port model (Fig. 10.10) for the midband region of the commonsource amplifier in Fig. 14.45. (b) Use the model to calculate the voltage gain with the
100-k load attached to the amplifier.
Answers: (a) Rin = 75 , A = 200, Rout = 100 k; (b) 50.0
14.8 THE INFLUENCE OF BODY EFFECT
ON AMPLIFIER PERFORMANCE
Up to now we have considered only three-terminal MOSFETs in our analog circuits. However,
in many circuits, the body of the MOS transistor cannot be connected to its source. This is
particularly true in the implementation of analog and digital circuits in integrated form. In this
section we analyze the characteristics of the FET amplifiers using MOSFETs in a four-terminal
configuration, and we modify the expressions from Table 14.9 to include the influence of body
effect on the performance of the prototype amplifier circuits.
14.8.1 Common-Source Amplifier
The common-source amplifier in Figs. 14.42 and 14.43 is the first example of analysis of an analog
circuit that includes the body effect. The small-signal model in Fig. 14.43 includes the dependent
current source that models the effects of the back-gate transconductance gmb . Remember from
Chapter 13 that gmb = ηgm .
Voltage Gain
To find the terminal voltage gain of the circuit in Fig. 14.43, we must find the output current io
given by
io = gm vgs + gmb vbs
(14.122)
14.8
The Influence of Body Effect on Amplifier Performance
RL
Rout
1045
vo
RI
vi
Rin
RG
RS
Figure 14.42 Common-source amplifier employing MOSFET in the four-terminal configuration.
vg
G
RI
io
D
+
vgs
gmvgs
gmbvbs
–
vi
RG
S
RS
–
+
vs
vbs +
B R
L
vo
–
Figure 14.43 Small-signal model for the common-source amplifier of Fig. 14.42.
in which
vgs = vg − vs
and
vbs = −vs
(14.123)
The voltage at the MOSFET source can also be written in terms of io :
vs = io R S = (gm vgs + gmb vbs )R S
(14.124)
Substituting Eqs. (14.123) into (14.124) and solving for vs yields
vs =
gm R S
gm R S
vth =
vth
1 + (gm + gmb )R S
1 + gm (1 + η)R S
(14.125)
gm
vg
1 + gm (1 + η)R S
(14.126)
Dividing vs by R S yields io :
io =
The output voltage is expressed as vo = −io R L , and the terminal voltage gain is:
Avt =
vo
gm R L
=−
vg
1 + gm (1 + η)R S
(14.127)
This expression is the same as that derived earlier for the common-source amplifier, except for the
addition of the (1 + η) factor in the denominator. If η = 0, this expression reduces to Eq. (14.10),
as it should.
Input and Output Resistances
Because the gate current i g is zero in Figs. 14.42 and 14.43, the input resistance (and current
gain) will be infinite and is not changed by existence of the four-terminal connection. The output
1046
Chapter 14 Single-Transistor Amplifiers
ig = 0
ix
i
gmvgs
vgs
gmbvbs
ro
vx
RI R 4
vbs
RS
Figure 14.44 Small-signal model for finding the output resistance of the common-source amplifier.
resistance can be calculated based on the circuit model in Fig. 14.44. Here we see that vbs is
identical to vgs , so the two dependent current sources can be combined into one source:
i = gm vgs + gmb vbs = (gm + gmb )vgs = gm (1 + η)vgs
(14.128)
With this transformation, the circuit model becomes similar to that used to find the output resistance
for the three-terminal BJT and FET case (Fig. 14.10), and we can use the results from Eq. (14.29)
with gm replaced by gm (1 + η):
CS
Rout
= ro [1 + gm (1 + η)R S ]
(14.129)
14.8.2 Common-Drain Amplifier
Analysis of the common-drain amplifier in Fig. 14.45 is very similar to that for the commonsource amplifier in Fig. 14.46, except that the output is taken across the resistor in the source. The
output current has exactly the same form as Eq. (14.126):
io =
gm
vg
1 + gm (1 + η)R L
(14.130)
The output voltage is expressed as vo = +io R L , and the terminal voltage gain is
Avt =
vo
gm R L
=
vg
1 + gm (1 + η)R L
(14.131)
ig = 0
vg
RI
vi
RG
gmvgs
vgs
R th
io
Rin
gmbvbs
ix
Rout
RL
vo
vx
vbs
Figure 14.45 Common-drain amplifier including
Figure 14.46 Circuit for finding the
body effect.
common-drain output resistance.
14.8
The Influence of Body Effect on Amplifier Performance
1047
Again it can be observed in Fig. 14.45 that Rin is defined looking directly into the gate of the FET.
Because i g is zero, Rin and Aith are both infinite. The output resistance can be found with the aid
of the circuit diagram in Fig. 14.46. Because i g = 0, the circuit connection again forces vbs to be
equal to vgs . Thus, the two parallel current generators can be combined into one source, and we
can simply modify the output resistance results for the FET from Eq. (14.56):
CD
Rout
=
1
gm (1 + η)
(14.132)
14.8.3 Common-Gate Amplifier
Finally, the schematic diagram for the common-gate amplifier is given in Fig. 14.47. Here, we
observe that the circuit forces vbs = vgs to always be true, and the FET results from Sec. 14.4 can
all be used directly by replacing gm with gm (1 + η):
ACvtG = gm (1 + η)R L
RinC G =
1
gm (1 + η)
(14.133)
CG
= ro [1 + gm (1 + η)(R I R S )]
Rout
vs
RI
Rin
vi
RS
vbs
–
–
vgs
+
+
Rout
RL
vo
Figure 14.47 Common-gate amplifier with four-terminal MOSFET.
Exercise: Draw the small-signal model for the circuit in Fig. 14.44 and use it to directly
derive the results presented in Eqs. (14.133).
Table 14.16 gives the results of the preceding analyses as well as results for the signal limits.
Including the body effect through the parameter η, a positive number, improves some of the
characteristics of the amplifiers and degrades others. The gain of the common-gate amplifier more
closely approaches the R L /Rth limit, but the gain of the source follower is degraded. Body effect
tends to lower the input resistance and output resistance of the common-gate and the commondrain amplifiers, respectively, and raises the output resistance of both the common-source and
common-gate amplifiers; η also increases the input signal range. The improvements may come as
a surprise because body effect usually degrades the performance of digital circuits. However, we
will find, in later chapters, that body effect indeed causes additional problems, particularly with
Q-point design in CMOS analog circuits.
1048
∞
Terminal current gain
∞
RG
R I + RG
0.2(VG S − VT N ) ·
(1 + gm (1 + η)R L )
0.2(VG S − VT N ) ·
(1 + gm (1 + η)R S )
gm R L
1 + gm (1 + η)R L
Input signal range
+
1
gm (1 + η)
ro + µ f R S (1 + η)
RG
R I + RG
1
gm R L
∼
=
1 + gm (1 + η)R L
1+η
Output resistance
+
∞
gm R L
1 + gm (1 + η)R S
gm R L
1 + gm (1 + η)R S
∞
−
−
COMMON-DRAIN AMPLIFIER
Input resistance
Terminal voltage gain
vo
Avt =
v1
Signal-source voltage gain
vo
Av =
vi
COMMON-SOURCE AMPLIFIER
TABLE 14.16
Four-Terminal MOSFET Amplifier Summary
+
RS
R I + RS
+1
0.2(VG S − VT N )·
[1 + gm (1 + η)(R I R S )]
µ f (R I R S )(1 + η)
1
gm (1 + η)
gm (1 + η)R L
1 + gm (1 + η)(R I R S )
+gm (1 + η)R L
COMMON-GATE AMPLIFIER