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