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Unit 2 - Differential Amplifiers - Coggle Diagram

- - - - Vout
        
        Vou1 - Vin
        
        Peak Vout1 = Vout2 = V0 => Vout = 2V0
        
        Common mode level of Vout = 0
        
        Pure AC signal
      - Advantages
        
        Coupling corruption prevented
        
        Supply Noise corruption prevented
        
        Increased max achievable voltage
        
        Max O/P swing: 2(VDD - VOD)
        
        Amps need transistors in saturation
        
        Simpler Biasing
        
        O/P DC voltage already zero
        
        Capacitor needed in single-ended
        
        Higher Linearity
        
        O/P linear to I/P
        
        Constant gain
        
        O/P varies only for large Vin
  - - - Keeps signal swing > 0
- - - - Vout,cm = Vdd - IdRd
      - Vin, cm controls Id
      - Vin,cm decrease causes Vout,cm to increase
      - M1, M2 turn off at low Vin,cm
      - Workaround
        
        Basic Differential Amplifier
        
        Diagram
        
        Tail current source Iss
        
        Vout,cm = Vdd - RdIss/2
        
        Vout,cm independent of Vin,cm
        
        Current in M1, M2 constant at Iss/2
        
        Qualitative Analysis
        
        3 cases
        
        Vin1 = Vin2
        
        Vin1 << Vin2
        
        Vin1 >> Vin2
        
        I/O characteristics
        
        Max/Min of Vout
        
        independent of Vin,cm
        
        Well-defined
        
        Small signal gain
        
        slope of Vout vsVin
        
        Max at Vin1 = Vin2
        
        Zero for large |Vin|
        
        Non-linear for large Vin swings
        
        Equilibrium at Vin1 = Vin2
        
        Common-mode behaviour
        
        Range of Vin,cm
        
        VGS1,2 + VGS3 – VTH3 ≤ Vin,CM ≤ min[VDD – RDISS /2 + VTH1,2 , VDD ]
        
        Range for Vout independent Vin,cm
        
        All transistors in Saturation
        
        No clipping
        
        4 cases
        
        Vin,cm = 0
        
        M1, M2 Off
        
        M3 deep triode region
        
        Vout1 = Vout 2 = Vdd
        
        Vin,cm > Vth
        
        M1, M2 turn on
        
        Id3 = Id1 + Id3 != constant
        
        M3 in triode
        
        Vout,1,2= Vdd - Id1,2*R1,2
        
        VoutNOT independent of Vin,cm
        
        Vin,cm large
        
        Vin,cm = Vp = Vd3 > Vgs3-Vth3
        
        M3 in Saturation
        
        Id3 constant = Iss
        
        M3 is current source
        
        Vout independent of Vin,cm
        
        Vout1,2 = Vdd - RdIss/2
        
        Vin,cm v large
        
        Vin1 exceeding Vout1 + Vth1
        
        M1,M2 in triode region
        
        Diff gain lowers
        
        Vin,cm <= Vout1,2 + Vth1,2 = Vdd-RdIss/2 + Vth1,2
        
        Vout constant until this point
        
        Quantitative Analysis
        
        Differential Voltage Gain
        
        Derivation
        
        find Vin
        
        Use
        
        find Id1 - Id2
        
        find Gm max
        
        2 more items...
        
        Max differential gain
        
        The Expression
        
        2 more items...
        
        find Vout
        
        At 0 gain
        
        Gm = 0 for DeltaV = sqrt(Iss*delta)
        
        DeltaVin donated as DeltaVin1
        
        Only one transistor is ON
        
        Id1 or Id2 = Iss
        
        Observations
        
        Max Gm at DeltaVin = 0
        
        Gm follows Av
        
        DeltaVin1 is linearity/max input range
        
        Gm decreases as DeltaVin1 increases
        
        Gain and linearity tradeoff
        
        Solve assignment on page 190
        
        Small Signal Analysis
        
        Half-circuit Method/Lemma
        
        About
        
        6 more items...
        
        Proof of lemma
        
        8 more items...
        
        Without fully differential I/P
        
        5 more items...
        
        Common-Mode Response
        
        Common-mode suppression
        
        Needs symmetrical circuit
        
        Needs ideal tail current source
        
        Fraction CM variation affects O/P
        
        Types/Cases for non-ideality
        
        Mismatched Rd
        
        No expressions discussed
        
        Vout1,2 = Vdd - Id1,2*Rd1,2
        
        Vout1 != Vout2
        
        Vout != 0
        
        More severe than Rss != infinite case
        
        Mismatched transistors
        
        gm1 != gm2
        
        Unequal dimensions & Vth
        
        Assume non-ideal current source
        
        Expression, small-signal gain
        
        10 more items...
        
        Assume channel length modulation = body effect = 0
        
        Non-ideal tail current source
        
        Finding Av,cm expression
        
        6 more items...
        
        Lowers Vx & Vy
        
        Increases drain current
        
        Vp increases with Vin
        
        O/P resistance = Rss != 0
        
        If Rss = infinite, Av = 0
        
        Try exercise on pg 207
- - - - consume voltage headroom
        
        After connecting current source
        
        Vx,ymax = Vdd - |Vgs - Vth| => HIGH => Good
        
        For saturation, min V = Vgs - Vth
        
        load replaced with resistor
        
        Vx,y = Vdd - Vth3,4 => LOW
        
        Vdsmin = Vgsmin = Vth
        
        load be in saturated mode
      - O/P volt swing vs gain tradeoff
        
        Overcome with OMOS current sources || diode loads
        
        Av increase 5x with gm 1/5x
        
        W/L stays same => Vout,cm same
        
        gmp decreased 1/5x
        
        gmp controlled by current, not W/L
        
        for high Vgsp, O/P CM level low = Vdd - |Vgsp|
        
        But this also Vgs increases
        
        high gain needed means (W/L)p low
    - - Av = -gmn/gmp
      - ron and rop >> 1/gmp, ignored
      - Av = -gmn(1/gmp || ron || rop)