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 V in,CM turns off Devices.

Basic Differential Pair

Schematic of Differential Amplifier

Input/Output Characteristics Independent of V in,cm Minimum Slope Maximum Slope Thus maximum Gain

Range of V in,cm Lower bound of V Upper bound of V in,cm as a current source.

in, cm : VP should be sufficiently high in order for M3 to act M1 and M2 need to remain in saturation.

Sensitivity to V in, cm M3 in the linear region is modeled as a resistor M1=M2 =Off M1=M2 =On 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 V in, CM

Maximum Allowable Output Swing The higher the input CM level, the smaller the allowable output swings.

Transconductance ∆V in1 Represents 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. CS with resistive source degeneration 2. Thevenin Resistance 3. Cascode 4. 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 V out,CM due to V in,CM In the presence of resistor mismatch In the presence of transistor mismatch Common Mood Rejection Ratio (CMRR)

Sensitivity of V out,CM due to V in,CM V in,CM ↑, V P ↑, I(RSS) ↑,V X ,V↓

Output CM Sensitivity due to V in, 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

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