SOURCE FOLLOWER
(COMMON-DRAIN AMPLIFIER)
Main use: Voltage Buffer
In a CS amplifier, if output voltage signal
goes to a load RL (directly, or via a large
coupling capacitor), RL will significantly
alter the gain (as it appears in parallel to
RD or to the ro resistors of the CS
amplifier).
We always want RL “seen” by the CS
amplifier to be very large.
Buffering Action
Input resistance of source follower is large.
CS amplifier, connected to a Source
Follower, will see as a load Rin of the
Source Follower.
Rin of the Source Follower is unaffected by
RL of the Source Follower. Variations in RL
has no effect on Rin of the MOSFET.
Source Follower with RS resistance
Source Follower: Input signal comes into the
Gate; Output signal comes out of the Source.
Load connected between Source and ground.
Source Follower with RS resistance: Large Signal
Behavior
If Vin<VTH M1 is off.
As Vin exceed VTH M1 is in Saturation.
M1 goes into Triode Mode only when Vin
exceeds VDD.
Intuitive explanation: Why Vout follows Vin?
Source followers exhibit a Body Effect: As ID
increases, VS=IDRS increases. As VSB increases,
VTH increases.
For a given VG need to solve a quadratic
equation for ID.
Intuitive explanation: Why Vout follows Vin? (Cont’d)
If Vin slightly increases, ID slightly increases and therefore
Vout slightly increases.
As ID increases VTH increases due to Body Effect.
FACT: VGS increases but not at the same rate that Vin
increases.
Large Signal Relationships
DC conditions: 0.5kn’(W/L)(Vin-VTH-Vout)2RS≈Vout
A very crude but useful approximation: If RS is
sufficiently large then ID≈(VG-VTH)/RS
Large Signal Relationships
DC conditions: 0.5kn’(W/L)(Vin-VTH-Vout)2RS=Vout
Can study ∂VTH/∂Vin and ∂Vout/∂Vin
gm= µnCOX(W/L)(Vin-VTH-Vout) : Is gm increasing
as Vin increases?
Source Follower Main Formulas
g m RS RS RS
Av
1 ( g m g mb ) RS 1 / g ( g m g mb ) R 1 / g m RS
m S
gm
1 1 1
Rout ||
g m g mb g m g mb
Source Follower Gain Formula
Vin V1 Vout
Vbs Vout
g mV1 g mbVout Vout / RS
Then: (neglecting ro)
Vout g m RS
Av
Vin 1 ( g m g mb ) RS
Source Follower Gain
g m RS RS RS
Av
1 ( g m g mb ) RS 1 / g ( g m g mb ) R 1 / g m RS
m S
gm
How does AV vary as Vin increases?
Gain Dependence on VG
When VG is slightly above VTH, gm is very small,
and therefore AV is small.
When gm becomes large enough (i.e. gmRS>>1),
then AV approaches 1/(1+η).
Gain Dependence on VG (cont’d)
Recall η=gmb/gm
As VG increases, and Vout increases, η
decreases, and the gain may approach 1.
In most practical circuits η remains >0.2.
In summary for this Source Follower configuration:
Can it still serve as a good buffer even if the voltage gain
is <1?
Rin is independent of RL, which means that the driving CS
amplifier’s gain is independent of RL.
Total amplifier gain is the CS gain times the Source
Follower’s gain. How constant is the Source Follower’s
gain?
In summary for this Source Follower configuration:
Source Follower’s gain may suffer from
nonlinearities: Dependence on output signal
current, dependence on input signal amplitude
(all through variations of gm and other
parameters).
Problem with RS configuration:
Large ID variations, as Vin varies.
This causes a nonlinear performance.
Solution: Replace RS with a Current
Source.
Source Follower with Current Source
Load
Left: Conceptual diagram
Right: Actual implementation, using a NMOS
operating in Saturation Mode.
Example
Let (W/L)1=20/0.5, I1=200µA, VTHO=0.6V,
2ΦF=0.7V, µnCOX=50µA/V2, = 0.4V1/2
Let Vin=1.2V, what is Vout?
Example (cont’d)
Current: (Vin-VTH-Vout)2 = 2ID/µnCOX(W/L)1
However – VTH depends on Vout.
Iterative solution: First take VTH≈0.6V. Solve for
Vout. We get Vout≈0.153V.
Example (cont’d)
Substitute Vout≈0.153V, into VTH ≈ VTHO +
((2ΦF+Vout)1/2-(2ΦF)1/2)≈ 0.635V
Substitute back into current equation:
Vout≈0.119V, and so on. Solution converges.
Example (cont’d)
Let’s take Vout=0.119V. This should be Vout for
the right circuit too, as long as M2 is in
saturation.
What should be (W/L)2?
Example (cont’d)
Vout=VDS2=0.119V≥Vb-VTH2 = [2ID/µnCOX(W/L)2]1/2
We see that (W/L)2 ≥ 283/0.5 (using ID=200µA
and µnCOX=50µA/V2).
We see that M2 contributes significantly to the
output node’s capacitance.
Output Resistance of the Ideal Source Follower with
Current Source Load
I X g mVX g mbVX 0
V1 VX 1
Rout
g m g mb
Output Resistance of the Ideal Source Follower with
Current Source Load
1 1 1
Rout ||
g m g mb g m g mb
Output Resistance of the Ideal Source Follower with Current Source
Load becomes smaller with the help of the Body Effect!
Only in a Source Follower the current source
gmbVbs is equivalent to a resistor 1/gmb in parallel
to the output.
Gain of Source Follower with Ideal
Current Source Load
With no body effect the output resistance of a
Source Follower with a current source load
would be 1/gm.
Overall voltage gain is obtained through voltage
division between 1/gm and 1/gmb!
Gain of Source Follower with Ideal
Current Source Load
gm
AV
g m g mb
Gain Formula: NMOS Source Follower with NMOS Current Source
and RL Loads
1
|| ro1 || ro 2 || RL
g mb1
Av
1 1
( || ro1 || ro 2 || RL )
g mb1 g m1
Gain Formula: NMOS Source Follower with PMOS Current Source
Load
1 1
|| ro1 || ro 2 ||
g mb1 g m 2 g mb 2
Av
1 1 1
( || ro1 || ro 2 || )
g mb1 g m 2 g mb 2 g m1
Sources of Nonlinearities in NMOS
Source Followers
Body Effect in the driving NMOS transistor
causes VTH to vary with Vin
Are we allowed to connect substrate to source in
the driving NMOS? (to eliminate the body effect).
Answer: No! All NMOS transistors in the entire
circuit share the same substrate, so it has to be
grounded!
ro resistors vary with VDS. Problem becomes
more and more aggravated as L becomes
smaller and smaller
PMOS Source Follower
Key idea: PMOS transistors have each a
separate substrate. Each can be powered
differently
CMOS fabrication process: All NMOS share the same
substrate, each PMOS has a separate substrate
PMOS Source Follower Advantage
Body Effects eliminated – device is more
linear than NMOS Source Follower
PMOS Source Follower Drawbacks
PMOS carriers mobility is smaller than that of
NMOS.
As a result of mobility differences: PMOS source
followers have larger output resistance, than NMOS
followers.
CS Amplifier directly driving a Source Follower: DC
levels considerations
CS Amplifier alone: VX≥VGS1-VTH1 to assure that
M1 is in Saturation.
With Source Follower: VX≥VGS2+(VGS3-VTH3) to
assure that M3 is in Saturation.
CS Amplifier directly driving a Source Follower: DC
levels considerations
If VGS1-VTH1 ≈ VGS3-VTH3 then VX,with Source Follower
must be bigger than VX, without Source Follower by
about VGS2.
Swing of CS reduces by VGS2.
Source Followers as Level Shifters
Example (a): DC level of Vin cannot exceed VDD-
|VGS2|+VTH1
Example (b): If Vin has a DC level of around VDD,
we put first a Source Follower.
Source Followers as Level Shifters
If Vin≈VDD, then for M1 to be in Saturation, we
need: VDD-VGS3-VTH1≤VDD-|VGS2
Source Followers as Level Shifters
Source Followers can be used as DC level
shifters.
Source Followers produce substantial noise
