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**Differential Amplifiers**

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Outline

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**Single-Ended Versus Differential Operation**

The transitions disturb the differential by equal amounts, leaving the difference in tact.

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**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

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**Reduction of Coupled Noise**

Noise coupled from L3 to L1 and L2 to L1 cancel each other.

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**Sensitivity to the Common mode level**

Excessive low Vin,CM turns off Devices.

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**Basic Differential Pair**

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**Schematic of Differential Amplifier**

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**Input/Output Characteristics**

Minimum Slope Independent of Vin,cm Maximum Slope Thus maximum Gain

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**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.

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**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 =Off M1=M2 =On M1=M2 =Off M3=Linear M3=Linear M3=Linear

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**Small signal Gain as a function of Vin, CM**

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**Maximum Allowable Output Swing**

The higher the input CM level, the smaller the allowable output swings.

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Transconductance ∆Vin1Represents the maximum differential signal a differential pair can handle.

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Linearity W/L increases ISS Constant Constant W/L ISS increases

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**Determinations of Small Signal Gain**

CS with resistive source degeneration Thevenin Resistance Cascode Superposition Principle

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**CS with resistive source degeneration**

Interpretation: The resistance at the drain Divided by the resistance in the source path

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**Treat M1 as a CS stage with resistive source degeneration to find VX/Vin**

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**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)

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Gain of CG

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**Replace M1 by its Thevenin Equivalent Circuit**

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Small Signal Gain

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Half-Circuit Concept

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**Conversion of Arbitrary inputs to Differential and Common-Mode Components**

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**Superposition Principle**

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**Schematic of Differential Amplifier**

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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

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**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)

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**Sensitivity of Vout,CM due to Vin,CM**

Vin,CM ↑, VP ↑, I(RSS) ↑,VX,V↓

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**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)

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**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.

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Resistor Mismatch (from CS with resistive source degeneration)

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**Common Mode to Differential Mode Conversion**

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Voutp-Voutn Differential Mode signal at the output: uV

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**Effect of CM Noise in the Presence of Resistor Mismatch**

Common Mode to Differential Conversion

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Transistor Mismatch

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**Supply Noise Sensitivity**

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CMRR

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Diode Connected Load Problem: Difficult to decrease (W/L)P without dropping the common mode voltage of Vout.

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**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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**Variable Gain Amplifier**

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