Transcript A v

Operational Amplifier
OpAmp
Overview
•
•
•
•
•
Amplifier impedance
The operational amplifier
Ideal op-amp
Negative feedback
Applications
– Amplifiers
– Summing/ subtracting circuits
Impedances
• Why do we care about the input and output impedance?
• Simplest "black box" amplifier model:
ROUT
VIN
RIN
AVIN
VOUT
• The amplifier measures voltage across RIN, then generates a voltage
which is larger by a factor A
• This voltage generator, in series with the output resistance ROUT, is
connected to the output port.
• A should be a constant (i.e., gain is linear)
Impedances
• Attach an input - a source voltage VS plus source impedance RS
RS
VS
ROUT
VIN
RIN
AVIN
VOUT
• Note the voltage divider RS + RIN.
• VIN=VS(RIN/(RIN+RS)
• We want VIN = VS regardless of source impedance
• So want RIN to be large.
Q: What would be the input impedance of an ‘ideal amplifier’?
 The ideal amplifier has an infinite input impedance
Impedances
Attach a load - an output circuit with a resistance RL
RS
VS
ROUT
VIN
RIN
AVIN
VOUT
RL
• Note the voltage divider ROUT + RL.
• VOUT=AVIN(RL/(RL+ROUT))
• Want VOUT=AVIN regardless of load
• We want ROUT to be small.
Q: What would be the output impedance of an ‘ideal amplifier’?
 The ideal amplifier has zero output impedance
Operational Amplifier
• Integrated circuit containing ~20 transistors, multiple amplifier stages
Ideal Operational Amplifier
Operational amplifier (Op-amp) is made of many transistors,
diodes, resistors and capacitors in integrated circuit technology.
Ideal op-amp is characterized by:
Infinite input impedance
Infinite gain for differential input
Zero output impedance
Infinite frequency bandwidth
Operational Amplifier
• An op amp is a high voltage gain, DC amplifier with high input
impedance, low output impedance, and differential inputs.
• Positive input at the non-inverting input produces positive output
• Positive input at the inverting input produces negative output.
741 Op Amp IC
A component-level diagram of the common 741 op-amp.
Dotted lines outline: current mirrors (red); differential
amplifier (blue); class A gain stage (magenta); voltage level
shifter (green); output stage (cyan).
IC Product
OFFSET
NULL
-IN
1
8
N.C.
2
7
V+
6
OUTPUT
5
OFFSET
NULL
+IN
3
V
4

+
DIP-741
OUTPUT A
1
-IN A
2
+IN A
3
V
4
8 V+

+
7 OUTPUT B

6
+
5 +IN B
-IN B
Dual op-amp 1458 device
Operational Amplifier
11
A small-scale integrated circuit, the 741 opamp shares with most op-amps an internal
structure consisting of three gain stages:
1. Differential amplifier (outlined blue) —
provides high differential amplification
(gain), with rejection of common-mode
signal, low noise, high input impedance
2. Voltage amplifier (outlined magenta) — provides
high voltage gain, a single-pole frequency rolloff, and in turn drives the
3. Output amplifier (outlined cyan and green) —
provides high current gain (low output
impedance), along with output current limiting,
and output short-circuit protection.
Additionally, it contains current mirror (outlined
red) bias circuitry and a gain-stabilization
capacitor (30 pF).
Op Amp Equivalent Circuit
vd = v2 – v1
v2
A is the open-loop voltage gain
v1
Voltage controlled
voltage source
Operational Amplifier
• Can model any amplifier as a "black-box" with a parallel input
impedance Rin, and a voltage source with gain Av in series with an
output impedance Rout.
Ideal op-amp
• Place a source and a load on the model
RS
+
vout
RL
-
• Infinite internal resistance Rin (so vin=vs).
• Zero output resistance Rout (so vout=Avvin).
• "A" very large
• iin=0; no current flow into op-amp
So the equivalent circuit of an
ideal op-amp looks like this:
Ideal vs. Real op-amps!
Symbols for Ideal and Real Op Amps
OpAmp
uA741
LM111
LM324
Ideal Vs Practical Op-Amp
Ideal
Practical
Open Loop gain A

105
Bandwidth BW

10-100Hz
Input Impedance Zin

>1M
0
10-100 
Depends only
on Vd = (V+V)
Differential
mode signal
Depends slightly
on average input
Vc = (V++V)/2
Common-Mode
signal

10-100dB
Output Impedance Zout
Output Voltage Vout
CMRR
Ref:080114HKN
Operational Amplifier
Ideal op-amp
+ AVin
Vin
Vout
~

Zout=0
Practical op-amp
+
Vin
Zout
Zin
~
Vout
 AVin
19
Typical Op Amp Parameters
Parameter
Variable
Ideal Values
A
Typical
Ranges
105 to 108
Open-Loop
Voltage Gain
Input
Resistance
Ri
105 to 1013 
∞
Output
Resistance
Ro
10 to 100 
0
Supply
Voltage
Vcc/V+
-Vcc/V-
5 to 30 V
-30V to 0V
N/A
N/A
∞
Almost Ideal Op Amp
• Ri = ∞ 
– Therefore, i1 = i2 = 0A
• Ro = 0 
• Usually, vd = 0V so v1 = v2
– The op amp forces the voltage at the inverting input terminal to
be equal to the voltage at the noninverting input terminal if there
is some component connecting the output terminal to the
inverting input terminal.
• Rarely is the op amp limited to V- < vo < V+.
– The output voltage is allowed to be as positive or as negative as
needed to force vd = 0V.
Many Applications, e.g.,
•
•
•
•
•
•
Amplifiers
Adders and subtractors
Integrators and differentiators
Clock generators
Active Filters
Digital-to-analog converters
Applications
• Audio amplifiers
– Speakers and microphone circuits in cell phones,
computers, mpg players, boom boxes, etc.
• Instrumentation amplifiers
– Biomedical systems including heart monitors and
oxygen sensors.
• Power amplifiers
• Analog computers
– Combination of integrators, differentiators, summing
amplifiers, and multipliers
Applications
Originally developed for use in analog computers:
Using op-amps
• Power the op-amp and apply a voltage
• Works as an amplifier, but:
• No flexibility (A~105-6)
• Exact gain is unreliable (depends on chip, frequency and temp)
• Saturates at very low input voltages (Max vout=power supply voltage)
• To operate as an amp, v+-v-<VS/A=12/105 so v+≈v• In the ideal case, when an op-amp is functioning properly in the
active region, the voltage difference between the inverting and noninverting inputs≈0
Voltage Transfer Characteristic
Range where
we operate
the op amp as
an amplifier.
vd
Inverting Apmlifier
Non-inverting amplifier
Noninverting Amplifier
vO  A(v   v  )

R2 

vO  A vIN  vO
R1  R2 


AR2 
  AvIN
vO 1 
 R1  R2 
AvIN
vO 
AR2
1
R1  R2
When A is very large:
Take A=106, R1=9R, R2=R
AvIN
vO 
AR2
1
R1  R2
AvIN
vO 
R2
A
R1  R2
vO  vIN
R1  R2
R2
>>1
10 6 vIN
vO 
6
10
R
1
9R  R
10 6 vIN
vO 
6 1
1  10 
10
vO  vIN 10
• Gain now determined only by resistance ratio
• Doesn’t depend on A, (or temperature,
frequency, variations in fabrication)
Negative feedback:
• How did we get to stable operation in the linear
amplification region???
• Feed a portion of the output signal back into the input
(feeding it back into the inverting input = negative feedback)
• This cancels most of the input
• Maintains (very) small differential signal at input
• Reduces the gain, but if the open loop gain is ~, who
cares?
• Good discussion of negative feedback here:
http://www.allaboutcircuits.com/vol_3/chpt_8/4.html
Why use Negative feedback?:
• Helps to overcome distortion and non-linearity
• Improves the frequency response
• Makes properties predictable - independent of
temperature, manufacturing differences or other
properties of the opAmp
• Circuit properties only depend upon the
external feedback network and so can be easily
controlled
Positive Feedback
When we flip the polarization of the op-amp as shown on the
figure we will get a positive feedback that saturates the
amplifier output.
This is not a good idea.
Negative vs. Positive Feedback
Familiar examples of negative feedback:
• Thermostat controlling room temperature
• Driver controlling direction of automobile
• Pupil diameter adjustment to light intensity
Familiar examples of positive feedback:
• Microphone “squawk” in sound system
• Mechanical bi-stability in light switches
EE 42/100 Fall 2005
Week 8, Prof. White
Fundamentally
pushes toward
stability
Fundamentally
pushes toward
instability or
bi-stability
48
v+
vi
v-
+
vo
R
1
Rf
v+
v-
Rf
Ra
)vi

Rf
Voltage follower
Ref:080114HKN
2
v-
o
R
f
Noninverting input with voltage divider
Rf
R2
vo  (1  )(
)vi
Ra R1  R2
v
v+
i
vo
v

a
+
vo  vi
R
R
Noninverting amplifier
vo  (1 
+
i

Ra
vi
v+
v
R
1
R
2
v-
+
v
o

R
f
Less than unity gain
R2
vo 
vi
R1  R2
Operational Amplifier
49
Inverting Amplifier
Rf
(1) Kirchhoff node equation at V+
yields, V  0
Ra

(2) Kirchhoff node equation at V
yields, Vin  V_ V  V
 o  0
Ra
Rf
(3) Setting V+ = V– yields
Vo  R f

Vin
Ra
Ref:080114HKN
V ~
in

V
o
+
Notice: The closed-loop gain Vo/Vin is
dependent upon the ratio of two
resistors, and is independent of the
open-loop gain. This is caused by the
use of feedback output voltage to
subtract from the input voltage.
Operational Amplifier
50
Op amp circuit 1: Voltage follower
• So vO=vIN
•or, using equations
vO  vIN
R1  0
R2  
• What's the gain of this circuit?
R1  R2
R2
Op amp circuit 1: Voltage follower
(unity buffer amplifier)
• So vO=vIN
•or, using equations
vO  vIN
R1  R2
R2
R1  0
R2  
• What's the application of this circuit?
•Buffer
Useful interface between different circuits:
voltage gain = 1
Has minimum effect on previous and next
input impedance=∞
circuit in signal chain
output impedance=0
RS
VS
ROUT
VIN
RIN
AVIN
VOUT
RL
Voltage Follower
Special case of noninverting amplifier is a voltage follower
Since in the noninverting amplifier
vo = v1(1+ R2 /R1)
so when R2=0
vo = v1
=>
Op amp circuit 2: Inverting Amplifier
• Signal and feedback resistor,
connected to inverting (-) input.
• v+=v- connected to ground
iS  iF  iin  0
i S  i F
vout  v 
vS  v 

v+ grounded, so:
RF
RS
v  v  0
v 0
vS  0
  out
RF
RS
vout
RF
vS

RS
vout
RF
Gain 

vS
RS
Op amp circuit 3: Summing Amplifier
• Same as previous, but add more
voltage sources
i1  i2  .....  iN  iF
vS 1 vS 2
vSN
vout

 ..... 

RS1 RS 2
RSN
RF
vout
 RF

RF
RF
 
vS 1 
vS 2  ..... 
vSN 
RS 2
RSN
 RS1

If RS1  RS 2  ...  RSN  RS
vout
RF

(vS 1  vS 2  ...  vSN )
RS
Multiple Inputs
(1) Kirchhoff node equation at V+
yields, V  0

Va
Vb
(2) Kirchhoff node equation at V Vc
yields,
V_  Vo
Rf

Rf
Ra
Rb
Rc

V
o
+
V  Va V  Vb V  Vc


0
Ra
Rb
Rc
(3) Setting V+ = V– yields
c V
 Va Vb Vc 
j
Vo   R f       R f 
j a R j
 Ra Rb Rc 
Ref:080114HKN
Operational Amplifier
58
Summing Amplifier Circuit
Ra
ia
in
–
+
ic
vc
–
+
vb
+
Rc
vn +
vp
– –
in = 0  ia + ib + ic = -if
+
–
+
ib
if
–
va
Rb
Rf
+
vo
–
superposition !
Rf
Rf 
 Rf
vo  
va 
vb 
vc 
Rb
Rc 
 Ra
vp = 0  vn = 0
EE 42/100 Fall 2005
Week 8, Prof. White
59
Summing Amplifier Applications
• Applications - audio mixer
• Adds signals from a number of waveforms
• http://wiredworld.tripod.com/tronics/mixer.html
• Can use unequal resistors to get a weighted sum
• For example - could make a 4 bit binary - decimal converter
• 4 inputs, each of which is +1V or zero
• Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)
Another non-inverting amplifier
• Feedback resistor still to inverting input,
but no voltage source on inverting input
(note change of current flow)
• Input voltage to non-inverting input
iS  iF
v  v
since iin  0
and v   v   vS
vout
v   0 vout  v 

RS
RF
 RF  
v
 1 
 RS 
 RF 
vS
vout  1 
 RS 
vout
RF
Gain 
 1
vS
RS
Differential Amplifier (subtractor)
i1  i2  0
vout  v 
v1  v 

R1
R2
v  v
R2
v 
v2  v 
R1  R2

vout 
R2
(v2  v1 )
R1
Useful terms:
• if both inputs change together, this is a common-mode input change
• if they change independently, this is a normal-mode change
• A good differential amp has a high common-mode rejection ratio (CMMR)
Amplifies the difference in voltage between its inputs.
The name "differential amplifier" must not be confused with
the "differentiator”