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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,

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## Differential Amplifiers

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**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.**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 M1=M2 =On M1=M2 =On M1=M2 =Off M1=M2 =Off M3=Linear M3=Linear M3=Linear**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**• 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)**Conversion of Arbitrary inputs to Differential and**Common-Mode Components**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)**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**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).

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