### Differential Pair

```Differential Amplifiers
Outline
Single-Ended Versus Differential
Operation
The transitions disturb
the differential by
equal amounts, leaving
the difference in tact.
Immunity to Supply Noise
If VDD changes by
∆V, Vout changes by
the same amount.
Noise in VDD affects VX and VY,
but not Vx-Vy
Reduction of Coupled Noise
Noise coupled from L3 to L1 and L2 to L1 cancel each other.
Sensitivity to the Common mode
level
Excessive low
Vin,CM turns off
Devices.
Basic Differential Pair
Schematic of Differential
Amplifier
Input/Output Characteristics
Minimum Slope
Independent of Vin,cm
Maximum Slope
Thus maximum Gain
Range of Vin,cm
Lower bound of Vin,cm:
VP should be sufficiently high in order for M3 to act
as a current source.
Upper bound of Vin, cm
M1 and M2 need to remain in saturation.
Sensitivity to Vin, cm
M3 in the linear
region is modeled
as a resistor
M1=M2
=On
M1=M2
=Off
M3=Linear
M1=M2
=Off
M1=M2
=On
M3=Linear
M1=M2
=Off
M1=M2
=On
M3=Linear
Small signal Gain as a function
of Vin, CM
Maximum Allowable Output
Swing
The higher the input CM level, the smaller
the allowable output swings.
Transconductance
∆Vin1Represents the maximum differential signal a differential
pair can handle.
Linearity
W/L increases
ISS Constant
Constant W/L
ISS increases
Determinations of Small Signal
Gain
1.
2.
3.
4.
CS with resistive source degeneration
Thevenin Resistance
Cascode
Superposition Principle
CS with resistive source
degeneration
Interpretation: The resistance at the drain
Divided by the resistance in the source path
Treat M1 as a CS stage with
resistive source degeneration to
find VX/Vin
Replace M1 by its Thevenin
Equivalent Circuit
If RS is sufficiently large, then the small signal gain of the amplifier
can be obtained using thevenin’s equivalent circuit (see hand out)
Gain of CG
Replace M1 by its Thevenin
Equivalent Circuit
Small Signal Gain
Half-Circuit Concept
Conversion of Arbitrary inputs to
Differential and Common-Mode
Components
Superposition Principle
Schematic of Differential
Amplifier
Simulation
Vin,m=1 mV
Vout,m=8.735 mV
Av=-8.735
Calculations:
Gm=1mS
ro=30.53 KOhm
RL=12 Kohm
Av=-Gm(ro||RL)=-8.615
Common-Mode Response
•
•
•
•
Sensitivity of Vout,CM due to Vin,CM
In the presence of resistor mismatch
In the presence of transistor mismatch
Common Mood Rejection Ratio
(CMRR)
Sensitivity of Vout,CM due to Vin,CM
Vin,CM ↑, VP ↑, I(RSS) ↑,VX,V↓
Output CM Sensitivity due to Vin, CM
Vout,m
=0.285 mV
Vin,cm
=1 mV
RL=12 K
Gm=1.043 mS
Gds3=58.29 uS
Av, CM(Analytical)=0.343
Av, CM(Simulation)=0.285
(Excluding gmb, ro)
Common-Mode to Differential
Conversion at High Frequencies
Even if the output resistance of the current source is high,
the common-mode to differential conversion becomes significant
at high frequencies.
Resistor Mismatch
(from CS with resistive source degeneration)
Common Mode to Differential
Mode Conversion
Voutp-Voutn
Differential Mode signal at the output: 1.176 uV
Effect of CM Noise in the
Presence of Resistor Mismatch
Common Mode to Differential Conversion
Transistor Mismatch
Supply Noise Sensitivity
CMRR