Amplifiers by HC1112140287

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									Amplifiers
       BASIC AMPLIFIER
         CONCEPTS
Ideally, an amplifier produces an output
signal with identical waveshape as the
input signal, but with a larger amplitude.

            vo t   Av vi t 
       Inverting Amplifiers
Inverting amplifiers have negative voltage
gain, and the output waveform is an
inverted version of the input waveform.
    Non-inverting Amplifiers
Non-inverting amplifiers have positive
voltage gain amplify the input signals.
    Voltage-Amplifier Model




Ri: input resistance Ro: output resistance
Avo: Open loop voltage gain ( vo / vi )
        Voltage-Amplifier Model
                         Ri: input resistance Ro: output resistance
                         Avo: Open loop voltage gain ( vo / vi )

                                    Ri
                         vi  vs
                                 Ri  RS
                         if Ri  , vi  vS and ii  0,
                         then power delivered by vS  0.
1. It will ensure vs is not degraded.
2. It enhances the power efficiency as limited power is
   drawn from the signal source.
 Voltage-Amplifier Model
                   Ri: input resistance Ro: output resistance
                   Avo: Open loop voltage gain ( vo / vi )

                                RL
                   vo  Avovi
                              RL  Ro
                   if Ro  0, vo  Avovi
                   it will not reduce the amplified signal.

A zero output resistance will maintain the gain.
   Current Gain




    io vo RL      Ri
Ai          Av
    ii vi Ri      RL
           Power Gain




              Av Ai   Av 
   Po Vo I o                 2 Ri
G   
   Pi Vi I i                   RL
CASCADED AMPLIFIERS




     Av  Av1 Av 2
                 1500
vi 2  200vi1              150vi1
               1500  500
                  100
vo 2  100vi 2            50vi 2  50  150vi1
               100  100
      7500vi1          Avo=Avo1*Avo2=200*100=20000
                     Not agree with the calculation
                     Why? As Ro1≠0, Ro2 ≠0
If Ro1=Ro2=0

               1500
vi 2  200vi1        200vi1
               1500
               100
vo 2  100vi 2      100vi2  100  200vi1
               100
      20000vi1       Desirable output resistance as small
                       as possible.
  Operational Amplifier
1. Ideal Op-Amp and its analysis
2. Practical Op-Amp and its limitations
3. Application of Op-Amp
IDEAL OPERATIONAL AMPLIFIERS
Power Supply Connection of Op-amp
    Characteristics of Ideal Op Amp


 Infinite gain for the differential input signal
 Infinite input impedance
 Zero output impedance
 Zero gain for the common-mode input signal
 Infinite bandwidth
OP-Amp Model
Ideal OP-Amp
    •Rin = ∞,
    so that it will not draw any power from
    the input signals
    •Rout = 0
    so that it will not degrade the signal
    due to the output resistance
    •Avd = ∞
    it is to amplify the differential signals
    •Avcommon = 0
    it is to reject any common mode input
    signals
    Bandwidth = ∞
    so that it can be used for any signal
    spectrum
   i1




                                    V-   _
                               i1
        i2

                               i2
                                         +
                                    V+


Ideal op-amp rule
1. No current ever flows into either input terminal.
   i1, i2 = 0

2. There is no voltage difference between the two
   input terminals
   v- = v+

We call this Summing Point Constraint
               Ideal Op-Amp
                            vs  v         vout  v 
                       is           , iF             , iin  0
                               Rs              RF
                       is  i F , is  i F  0
                       vs  v  vout  v 
                                          0
                          Rs       RF
                       Since, v   0, vout  Av o ( v   v  )   Av o v 
                                vout
                       v  
                                Av o
   vs  v  vout  v       vs v  vout v                  v
As                     0,               0, and v    out
      Rs       RF           Rs Rs RF RF                     Av o
vs   v     v     v
    out  out  out  0
Rs Av o Rs RF Av o RF
vs      v      v    v                  v     v              R
    ( out  out  out ), If Av o  , s   out , vout   F vs
Rs     Av o Rs RF Av o RF              Rs     RF            Rs
          RF               v
Avc        , Also v    out  0          Avc is the closed loop gain
          Rs               Av o
      Negative Feedback Effect
• The effect of the feedback connection from the
  output to the inverting input is to force the
  voltage at the inverting input to be equal to
  that at the non-inverting input.

                      v- = v+
                      It is called ;
                      • summing point constraint, or
                      • virtual ground concept
Illustration of the principle of summing point constraint




As i- and i+ are both zero, then, i1 = i2

     vin        0  vo  vo
i1       i2        
     R1           R2    R2
      vo     R2
Avc      
      vin    R1
INVERTING AMPLIFIERS




         vo     R2
     Av     
         vin    R1
   Practical Design Difficulty




Design an inverting amplifier with gain -100,
R1 = 50K, then R2 = 5M , too much for real practical resistor
                                                     v x  vo
                                                i4 
                             Vx                         R4
     0 v x    vx
i2         
       R2      R2
                                       0  vx
                                  i3 
                                         R3
                                       vx
                    ii  0          
                                       R3


            vin
       i1 
            R1
                               vx         vx       v v
                       i2         , i3       , i4  x o
                               R2          R3          R4

                       i2 i 3  i4
                           v x v x v x  vo
                                
     vin          vx       R2 R 3     R4
i1       i2  
     R1           R2         R2    1  1   1  vo
                        vin      
                                  R  R  R  R
                                              
                             R1    2       4 
v x  0  i2 R2                         3        4

                            vo     R2       R4 R4 
           R2          Av            1 
                                               
     vin                  vin    R1       R3 R2 
                                                   
           R1
Av = -100, R1 = 50K


     vo     R2    R4 R4 
Av            1 
                          
     vin    R1       R3 R2 
                            
     vo       R4  R4
            R2
Av        1 
                    
     vin     
            R1    R3  R1
                     
R2 R4          R4
      8, and     10.5
R1 R1          R3
R1  50 K , R2  R4  400 K
R3  38.1K
      NON-INVERTING AMPLIFIER

                                    v1 v1  vo
                          At node A,          0
               i-                   R1   R2
     Node A
                                        vin vin  vo
                          As vin  v1 ,             0
                                        R1     R2
                          vin R2  R1vin  R1vo  0
vi  0, ii  0, i   0   vin ( R2  R1 )  R1vo
and vin  v1              vo ( R2  R1 )      R2
                                         1     Avc
                          vin    R1           R1
NON-INVERTING AMPLIFIER
         iF  iS  iin
         Since ideal op  amp, Rin    iin  0
         v   vS  v 
              v        vout  v 
         iS     , iF             , i F  iS
              RS           RF
         v  vout  v   v   v  vS
                        S  out
         RS     RF       RS     RF
         RF vS  RS ( vout  vS )
         RF vS  RS vS  RS vout
                  vS ( RF  RS )          R
         vout                    vS (1  F )
                        RS                RS
         vout              RF
               Avc  (1     )
         vS                RS
                   Summer
                  iF  i1  i2  i3  ..iN  0
                       vS 1        vS 2            vSj               vout
                  i1       , i2       ,... i j      .., and i F 
                       RS1         RS 2            RSj               RF
                   vS 1 vS 2      vSj      vSN    vout
                             ..      ..     
                   RS1 RS 2       RSj      RSN    RF

          RF          RF          RF             RF           RF
vout         vS 1       vS 2       vS 3  ... vSj  ...      vSN
          RS 1        RS 2        RS 3           RSj          RSN
            N
               RF
                 vSi
          i 1 RS i
Voltage Follower

          vout  vS
             Differential Amplifier
                                    v1  v  vout  v 
                      i1  i2  0          
                                       R1        R2
                      v1  v  v   vout
                              
                         R1        R2
                      R2 v1  R2 v   R1v   R1vout
                      R1vout   R2 v1  R1v   R2 v 
                                    R2       R2
                      vout     v1    v v
                                    R1         R1
        R2
v  v2          v                 R2        R2         R2 R2
       R1  R2                 v1     v2          v2
                                    R1      R1  R2      R1 R1  R2
                                                                 2
                                    R2        R2               R2
                               v1     v2          v2
                                    R1      R1  R2      R1 ( R1  R2 )
        Common Mode Rejection
                       _
                                    +          Vo
                                    Vo    Acm 
Vcm     +                                     Vcm
                       +             -
        _                                 Common Mode Voltage Gain



An op-amp is a differential amplifier. It is desirable to reject
any signal in common to V_ and V+ terminal.
In other words, Acm should be as small as possible.
The quality of rejecting the common mode signal is defined by
CMMR (Common mode rejection ratio)  Avo                         Avo
                                                     or 20 log10
                                               Acm                 Acm
Common Mode Rejection CMMR
                     f
                             v1= 2 + 3 sin10tV
                             v2= 2V

                             The common component of
                             the two input signal is 2V.

It is desirable for the amplifier to amplify the difference
of v1 and v2, that is 3 sin10t, and not to amplify the
common component 2V.

How good the amplifier does to reject the common
component is defined by the CMMR.
   OP-AMP IMPERFECTIONS IN THE LINEAR
                RANGE
             OF OPERATION
Real op amps have several categories of
imperfections compared to ideal op amps.
Real op amps have finite input impedance, nonzero
output impedance and finite open loop gain

                             Ri ≠ ∞, Avo ≠ ∞, Ro ≠ 0
                             iin ≠ 0
                     Bandwidth




Bandwidth = fH-fL
Idea op-amp, the bandwidth is infinity, so that signal at any
frequency can be amplified by the amplifier.

Practical op-amp, the bandwidth is limited. That is, the gain
is not uniform.
The gain at frequency higher than the fBOL is diminished gradually
at a -20dB rate of decline.
The unit bandwidth product is to define how good is the
frequency response of the amplifier, i. e, how wide is it bandwidth.
Unity bandwidth product = Avo*fBOL
   LINEAR WAVEFORM DISTORTION



If the gain of an amplifier has a different
magnitude for the various frequency
components of the input signal, a form of
distortion known as amplitude distortion
occurs. Due to bandwidth limitation.
         Phase Distortion

If the phase shift of an amplifier is not
proportional to frequency, phase
distortion occurs.
  NONLINEAR LIMITATIONS

The output voltage of a real op amp is
limited to the range between certain limits
that depend on the internal design of the op
amp. When the output voltage tries to
exceed these limits, clipping occurs.
   Slew-Rate Limitation

Another nonlinear limitation of actual op-
amp is that the magnitude of the rate of
change of the output voltage is limited.


               dvo
                    SR
                dt
DC IMPERFECTIONS

								
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