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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 am plified signal.
A zero output resistance will maintain the gain.
Current Gain
io vo RL
Ri
Ai  
 Av
ii
vi Ri
RL
Power Gain
Po Vo I o
2 Ri
G

 Av Ai   Av 
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
Desirable output resistance as small
 20000vi1
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, i 2 = 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  iF , is  iF  0
vs  v  vout  v 

0
Rs
RF
Since, v   0, vout  Av o ( v   v  )   Av o v 
v  
vout
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
Avc  
RF
v
, Also v    out  0
Rs
Av o
Avc is the closed loop gain
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 
R4
Vx
0 v x
vx
i2 

R2
R2
0  vx
i3 
R3
ii  0
vin
i1 
R1
 vx

R3
 vx
 vx
v x  vo
i2 
, i3 
, i4 
R2
R3
R4
i2 i 3 i4
vin
vx
i1 
 i2  
R1
R2
v x  0  i2 R2
R2
  vin
R1

vx vx vx  vo


R2 R 3
R4
R2  1
1
1  vo

 vin

  

R1  R2 R3 R4  R4
v
R
Av  o   2
vin
R1

R4 R4 
1 
 
R3 R2 

Av = -100, R1 = 50K
vo
R2
Av 

vin
R1
 R4 R4 
1 


R3 R 2 

 R4  R4
1 
 
R3  R1

R2 R4
R

 8, and 4  10.5
R1 R1
R3
vo
R2
Av 

vin
R1
R1  50K , R2  R4  400K
R3  38.1K
NON-INVERTING AMPLIFIER
iNode A
v1 v1  vo
At node A, 
0
R1
R2
vin vin  vo
As vin  v1 ,

0
R1
R2
vin R2  R1vin  R1vo  0
vi  0, ii  0, i   0
and vin  v1
vin ( R2  R1 )  R1vo
vo ( R2  R1 )
R2

 1
 Avc
vin
R1
R1
NON-INVERTING AMPLIFIER
iF  iS  iin
Since ideal op  am p, 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
vout 
vS ( RF  RS )
R
 vS (1  F )
RS
RS
vout
R
 Avc  (1  F )
vS
RS
Summer
iF  i1  i2  i3  ..iN  0
vSj
vS 1
vS 2
vout
i1 
, i2 
,... i j 
.., and i F 
RS1
RS 2
RSj
RF
vSj
vS 1 vS 2
vSN
vout

 ..
 ..

RS1 RS 2
RSj
RSN
RF
vout
RF
RF
RF
RF
RF

vS 1 
vS 2 
vS 3  ... vSj  ... 
vSN
RS1
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 
vout
R2
v  v2
 v
R1  R2

R2

 R2
  v1
v v
R1
R1
R2
R2
R2 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
_
Vcm
+
_
+
+
Vo
-
Vo
Vcm
Common Mode Voltage Gain
Acm 
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
Acm
or 20log10
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 opamp is that the magnitude of the rate of
change of the output voltage is limited.
dvo
 SR
dt
DC IMPERFECTIONS