Transcript Source Follower

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
Rout
1
1
1

||

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
V1  VX 
I X  g mVX  g mbVX  0
Rout
1

g m  g mb
Output Resistance of the Ideal Source Follower with
Current Source Load
Rout
1
1
1


||
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
g mb1
Av 
(
1
g mb1
|| ro1 || ro 2 || RL
1
|| ro1 || ro 2 || RL ) 
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