Differential Amplifiers
Jan 07, 2016
Differential Amplifiers
Outline
Single-Ended Versus Differential Operation
The transitions disturbthe differential by equal amounts, leavingthe difference in tact.
Immunity to Supply Noise
If VDD changes by ∆V, Vout changes bythe 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 lowVin,CM turns offDevices.
Basic Differential Pair
Schematic of Differential Amplifier
Input/Output Characteristics
Independent of Vin,cm
Maximum SlopeThus maximum Gain
Minimum Slope
Range of Vin,cm
Lower bound of Vin,cm:VP should be sufficiently high in order for M3 to actas a current source.Upper bound of Vin, cm
M1 and M2 need to remain in saturation.
Sensitivity to Vin, cm
M3=Linear M3=Linear M3=Linear
M1=M2=Off
M1=M2=Off
M1=M2=Off
M1=M2=On
M1=M2=On
M1=M2=On
M3 in the linear region is modeled as a resistor
Small signal Gain as a function of Vin,
CM
Maximum Allowable Output Swing
The higher the input CM level, the smallerthe allowable output swings.
Transconductance
∆Vin1Represents the maximum differential signal a differentialpair can handle.
Linearity
W/L increasesISS Constant
Constant W/L ISS increases
Determinations of Small Signal Gain
1. CS with resistive source degeneration
2. Thevenin Resistance3. Cascode 4. Superposition Principle
CS with resistive source degeneration
Interpretation: The resistance at the drainDivided 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 amplifiercan 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
SimulationVin,m=1 mVVout,m=8.735 mVAv=-8.735
Calculations:Gm=1mSro=30.53 KOhmRL=12 KohmAv=-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 KGm=1.043 mSGds3=58.29 uS
Av, CM(Analytical)=0.343Av, 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 significantat 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
Diode Connected Load
Problem: Difficult to decrease (W/L)P without dropping the common mode voltage of Vout.
Addition of Current Source to Increase Voltage Gain
Reduce gm by reducing current rather than the aspect ratio.Reduce I(M3) and I(M4).
Variable Gain Amplifier