Basic MOSFET Amplifier Configurations

1-Almost-linear amplification can be obtained by biasing the MOSFET at an

appropriate point in its saturation region of operation and by keeping the signal
vgs small.
2-Amplifier parameters such as voltage gain and input and output resistances are
derived from the small signal analysis.
3-Here the amplifiers are presented in their most simple, or “stripped down”
version.
4-Thus, the dc biasing arrangements are not shown in the analysis.

The Three Basic Configurations

1-There are three basic configurations for connecting the MOSFET as an
amplifier.
2-Each of these configurations is obtained by connecting one of the three
MOSFET terminals to ground, thus creating a two-port network with the
grounded terminal being common to the input and output ports.

Common-source

1-In the circuit the source terminal is connected to ground

2-The input voltage signal vi is applied between the gate and ground, and the
output voltage vo signal is taken between the drain and ground, across the
resistance RD.
3-This configuration, therefore, is called the grounded-source or common-source
(CS) amplifier.
4-It is the most popular MOS amplifier configuration.
Common-gate (CG)

1-The common-gate (CG) or grounded-gate amplifier is obtained by connecting

the gate to ground.
2-Applying the input vi between the source and ground, and taking the output vo
across the resistance RD connected between the drain and ground.

Common-drain (CD)

1-The common-drain (CD) or grounded-drain amplifier is obtained by

connecting the drain terminal to ground
2-Applying the input voltage signal between gate and ground, and taking the
output voltage signal between the source and ground, across a load resistance RL.
3-This configuration is more commonly called the source follower
Characterizing Amplifiers
1-Characterizing the performance of an amplifier as a circuit building block is
very important.

(a) An amplifier fed with a voltage signal vsig having a source resistance Rsig, and feeding
a load resistance RL

1-The above figure shows an amplifier fed with a signal source having an open-
circuit voltage and an internal resistance Rsig.
2-These can be the parameters of an actual signal source or, in a cascade
amplifier, the Thevenin equivalent of the output circuit of another amplifier
stage preceding the one under study.
3-The amplifier is shown with a load resistance RL connected to the output
terminal.
4-Here, RL can be an actual load resistance or the input resistance of a succeeding
amplifier stage in a cascade amplifier.

(b) Equivalent-circuit representation

of the circuit in (a)

1-The above figure shows the amplifier circuit with the amplifier block replaced
by its equivalent-circuit model.
2-The input resistance Rin represents the loading effect of the amplifier input on
the signal source.
3-It is found from figure that

4- Here Rin together with the resistance Rsig forms a voltage divider that reduces
vsig to vi that appears at the amplifier input.

5-All the amplifier circuits studied in this section are unilateral. That is, they
do not contain internal feedback, and thus Rin will be independent of RL.
6-The second parameter in characterizing amplifier performance is the open-
circuit voltage Gain Avo, defined as

(c) Determining the amplifier output resistance Ro.

7-The third and final parameter is the output resistance Ro.

8-Ro is the resistance seen looking back into the amplifier output terminal with
vi set to zero.
9-Thus Ro can be determined, from the above Fig with
10-The controlled source Avovi and the output resistance Ro represent the
Thevenin equivalent of the amplifier output circuit, and the output voltage vo
can be found from

Thus, the voltage gain of the amplifier Av can be found as

and the overall voltage gain Gv,

Overall gain can be determined by combining Eqs as-

The Common-Source (CS) Amplifier
1-The common source MOS amplifier configurations, is the most widely used.
2-In a cascaded amplifier the overall voltage gain is obtained by using one or
more common-source stages in the cascade

(a) Common-source amplifier fed with a signal vsig from a generator with a resistance
Rsig. The bias circuit is omitted.

3- The above Figure shows a common-source amplifier (with the biasing

arrangement omitted)
4-The amplifier is fed with a signal source vsig having a source resistance Rsig.

5- RD is considered as a part of the amplifier

6-If a load resistance RL is connected to the amplifier output, it appears in parallel

with RD.
Characteristic Parameters of the CS Amplifier

(b) The common-source amplifier with the MOSFET replaced with its hybrid- model

1-The input resistance Rin is infinite

2-The output voltage vo is found by multiplying the current (gmvgs) by the total
resistance between the output node and ground,

Since vgs = vi the open-circuit voltage gain Avo ≡ vo ⁄ vi can be obtained as

3-Here the overall gain of the FET is controlled by output resistance ro where the
voltage gain decreases with the increase in ro.

4-In discrete-circuit amplifiers, RD is usually much lower than ro and express Avo
simply as

5-The output resistance Ro is the resistance seen looking back into the output
terminal with set to zero.
6- From Fig. (b) if vi is set to zero vgs will be zero, and thus gmvgs will be zero,
resulting in

Here, ro has the beneficial effect of reducing the value of Ro

7-In discrete circuits, this effect is slight and hence the approximation can be done
as

Observations

1. The input resistance is ideally infinite.

2. The output resistance is moderate to high (in the kilohms to tens of kilohms
range).

3. Reducing RD to lower Ro is not a viable proposition, since the voltage gain

is also reduced. Alternatively, if a low output resistance (in the ohms to
tens of ohms range) is needed, a source follower stage will arise.

4. The open-circuit voltage gain Avo can be high, making the CS

configuration the workhorse in MOS amplifier design.

Overall Voltage Gain

1-To determine the overall voltage gain Gv, it is considered that the
infinite input resistance will make the entire signal vsig appear at the amplifier
input,
vi = vsig
2-To maintain a reasonably linear operation, vi and hence vsig should be kept much
smaller than 2 VOV
3-If a load resistance RL is connected to the output terminal of the amplifier, this
resistance will appear in parallel with RD It follows that the voltage gain Av can
be obtained by simply replacing RD in the expression for Avo by, RD || RL

This expression together with the fact that vi = vsig provides the overall voltage
gain
Performing the Analysis Directly on the Circuit Diagram

Performing the analysis directly on the circuit diagram with the MOSFET model used
implicitly.

1-Although small-signal, equivalent-circuit models provide a systematic process

for the analysis of any amplifier circuit, the effort involved in drawing the
equivalent circuit is sometimes not justified as in simple situations and after a lot
of practice, one can perform the small-signal analysis directly on the circuit
schematic.
2- The above Fig shows direct analysis of the CS amplifier where the resistance
ro is “pulled out” from the transistor, thus making the transistor drain conduct
gmvgs while still accounting for the effect of ro

The T Equivalent-Circuit Model

Through a simple circuit transformation it is possible to develop an alternative
equivalent-circuit model for the MOSFET. The development of such a model,
known as the T model,
The Common-Source Amplifier with a Source Resistance

1-It is beneficial to insert a resistance Rs in the source lead of the common-source

amplifier as shown in Fig. (a).

2-The corresponding small-signal equivalent circuit is shown in Fig. (b), where

the MOSFET has been replaced with its T equivalent-circuit model.

3-The T model is used in preference to π the model because it makes the analysis
simpler.
4-Whenever a resistance is connected in the source lead, the T model is preferred.
5-The source resistance then simply appears in series with the resistance 1 ⁄ gm
and can be added to it.
6-It should be noted that ro is not included in the equivalent-circuit model.

The CS amplifier with a source resistance Rs: (a) Circuit without bias details

7-In this case the effect of ro on the operation of the discrete-circuit amplifier is
not important.
 (b) Equivalent circuit
with the MOSFET represented by its T model.

8-From Fig.(b) the input resistance Rin is infinite and thus vi = vsig.

9-Here only a fraction of vi appears between gate and source as vgs.

10-It can be determined from the voltage divider composed of 1 ⁄ gm and Rs that
appears across the amplifier input, as follows:

(Benefits of Rs)

11-Thus the value of Rs can be used to control the magnitude of the signal vgs and
ensures that vgs does not become too large and cause unacceptably high nonlinear
distortion which is the benefit of including resistor Rs.
12- Rs causes the useful bandwidth of the amplifier to be extended. The
mechanism by which Rs causes such improvements in amplifier performance is
negative feedback. If while keeping vi constant, for some reason the drain current
increases, the source current also will increase, resulting in an increased voltage
drop across Rs. Thus, the source voltage rises, and the gate-to-source voltage
decreases. The latter effect causes the drain current to decrease, counteracting the
initially assumed change, an indication of the presence of negative feedback.
13-The output voltage vo is obtained by multiplying the controlled-source current
i by RD,

vo = –i RD-------------------(1)

The current i in the source lead can be found by dividing vi by the total resistance
in the source,

-------------------(2)

Thus, combining equ 1 and 2 the voltage gain Avo can be found as

---------------------(3)

which can also be expressed as

----------------------(4)

Equation (4) indicates that including the resistance Rs reduces the voltage gain
by the factor (1 + gmRs).

14-This is the price paid for the improvements that accrue as a result of Rs. The
factor (1 + gmRs) is the “amount of negative feedback” introduced by Rs. It is also
the same factor by which bandwidth and other performance parameters improve.
Because of the negative-feedback action of Rs it is known as a source-
degeneration resistance.

15-For the drain current in Eq.(2): The quantity between brackets on the right-
hand side can be thought of as the “effective transconductance with Rs included.”
Thus, including Rs reduces the transconductance by the factor (1 + gmRs).

16-This is the result of the fact that only a fraction (1 + gmRs) of vi appears as vgs
17-The voltage gain between gate and drain is equal to the ratio of the total
resistance in the drain (RD) to the total resistance in the source (1 ⁄ gm + Rs),

18-If Rs = 0 in Eq. (3) the gain changes to Avo of the CS amplifier.

19-A load resistance RL is considered to be connected at the output.

20- The gain Av can be obtained using the open-circuit voltage gain Avo together
with the output resistance Ro,
which can be found by
Ro = RD
Thus Av, can be obtained by simply replacing RD in Eq. (3) or (4) by (RD || RL)
; thus,

Or

As Rin is infinite, vi = vsig and the overall voltage gain Gv is equal to Av.

The Common-Drain Amplifier or Source Follower

1-The last basic MOSFET amplifier configuration is the common-drain amplifier.

2- It has applications in the design of both small-signal amplifiers as well as
amplifiers that are required to handle large signals and deliver substantial
amounts of signal power to a load.
3- The common drain amplifier is more commonly known as the source follower.
The Need for Voltage Buffers

Illustrating the need for a unity-gain buffer amplifier

1-As shown in Fig-(a) a signal source is connected to a circuit which delivers a

signal of strength (1 V).

2- If the internal resistance of 1 M of the source is connected to a 1-K load

resistance.
The output appearing across load is=
Vsig
( ) RL
Rsig+RL

Thus, the signal appearing across the load is attenuated and will be only
1 ⁄ (1000 + 1) of the input signal or about 1 mV.

3- To avoid this drop an alternative circuit is shown in Fig. (c).

4-Here an amplifier is introduced between the source and the load.

5- But this amplifier has a voltage gain of only unity.

6-This is because the signal is already of sufficient strength and it is not required
to increase its amplitude.
7-This amplifier has a very large input resistance, thus almost all of vsig (i.e., 1 V)
will appear at the input of the amplifier properly.

8-Since the amplifier has a low output resistance (100 Ω), 90% of this signal (0.9
V) will appear at the output.

9-The source follower can easily implement the unity-gain buffer amplifier.

Characteristic Parameters of the Source Follower

(a) Common-drain amplifier or source follower

1-Above Figure shows a source follower with the bias circuit omitted.

2-The source follower is fed with a signal generator (vsig, Rsig) and has a load
resistance RL connected between the source terminal and ground.

3- RL includes both the actual load and any other resistance that may be present
between the source terminal and ground (e.g., for biasing purposes).

4-Since the MOSFET has a resistance RL connected in its source terminal, it is

most convenient to use the T model, as shown in Fig. (b).
 (b) Equivalent circuit of the source follower obtained by replacing the MOSFET
with its T model.
ro appears in parallel with RL and in discrete circuits, ro » RL .

5- ro, is connected simply because it is very easy to do so. However, since ro in

effect appears in parallel with RL, and since in discrete circuits ro » RL hence ro
can be neglected and the simplified equivalent circuit can be obtained as shown
in Fig. (c).

© Neglecting ro, the simplified equivalent circuit

6-From Fig (a) Rin = ∞

7-From Fig (b) Av is obtained from the voltage divider formed by 1 ⁄ gm and RL
as

Setting RL = ∞
Avo = 1

8-The output resistance Ro is found by setting vi = 0 (i.e., by grounding the gate).

9- Now looking back into the output terminal, excluding RL, simply 1 ⁄ gm is seen
thus
Ro = 1 ⁄ gm

10-Finally, because of the infinite Rin, vi = vsig, and the overall voltage gain is

11-Thus Gv will be lower than unity.

12-As 1 ⁄ gm is usually low, the voltage gain can be close to unity.

13-The unity open-circuit voltage gain Avo = 1 indicates that the voltage at the
source terminal will follow that at the input, hence the name source follower.

Conclusion,
1-The source follower features a very high input resistance (ideally, infinite)
2-A relatively low output resistance
3-An open-circuit voltage gain that is near unity (ideally, unity).
4-Thus, the source follower is ideally suited for implementing the unity-gain
voltage buffer.
5-The source follower is also used as the output (i.e., last) stage in a multistage
amplifier, where its function is to equip the overall amplifier with a low output
resistance, thus enabling it to supply relatively large load currents without loss of
gain (i.e., with little reduction of output signal level).