Lecture 2 Operational Amplifiers 1. Goals Understand behavior and characteristics of ideal op amps....
-
Upload
kimberly-hayes -
Category
Documents
-
view
222 -
download
1
Transcript of Lecture 2 Operational Amplifiers 1. Goals Understand behavior and characteristics of ideal op amps....
Lecture 2Operational Amplifiers
1
Goals
• Understand behavior and characteristics of ideal op amps.
• Demonstrate circuit analysis techniques for ideal op amps.
• Characterize inverting, non-inverting, summing and difference amplifiers, voltage follower and integrator.
• Learns factors involved in circuit design using op amps.
2
Ideal Operation Amplifier (Op Amp)
Ideal op amps are assumed to have infinite voltage gain, andinfinite input resistance.
These conditions lead to two assumptions useful in analyzing ideal op amp circuits:
1. The voltage difference across the input terminals is zero.2. The input currents are zero.
Ideal Op Amp Example
vs isR1 i2R2 vo 0
is i2 vs v
R1
is vs
R1
Av vo
vs
R2
R1
Writing a loop equation:
From assumption 2, we know that i- = 0.
Assumption 1 requires v- = v+ = 0.
Combining these equations yields:
Assumption 1 requiring v- = v+ = 0
creates what is known as a virtual ground.
Ideal Op Amp Example (Alternative Approach)
is vs
R1
i2 v vo
R2
vo
R2
Av vo
vs
R2
R1
Writing a loop equation:
From assumption 2, we know that i- = 0.
Assumption 1 requires v- = v+ = 0.
Combining these equations yields:
Design Note: The virtual ground is not an actual ground. Do not short the inverting input to ground to simplify analysis.
vs
R1
vo
R2
Operational Amplifier Complete Model
Represented by:
A= open-circuit voltage gain
vid = (v+-v-) = differential input signal voltage
Rid = amplifier input resistance
Ro = amplifier output resistance
Signal developed at amplifier output is in phase with the voltage applied at + input (non-inverting) terminal and 1800 out of phase with that applied at - input (inverting) terminal.
3
Operational Amplifier Mathematical Model: With Source and Load
RL = load resistanceRS = Thevenin equivalent resistance
of signal sourcevs = Thevenin equivalent voltage of
signal source
LRoRLR
A id
v*ov
•Op amp circuits are mostly dc-coupled amplifiers. Signals vo and vs may have a dc component representing a dc shift of the input away from Q-point. •Op-amp amplifies both dc and ac components.
LRoRLR
SR
idR
idR
vA svov
SR
idR
idR
svid
vand
4
Ideal Operational Amplifier
• Ideal op amp is a special case of ideal differential amplifier with infinite gain, infinite Rid and zero Ro .
and
– If A is infinite, vid is zero for any finite output voltage.– Vid = 0, v+=v- (Virtual Short Model)– Infinite input resistance Rid forces input currents i+ and i- to be zero.
• Summary, Ideal op amp has following assumptions:• A=∞ , Where A is Open-loop gain• i- = i+ = 0, Input resistance is infinite• Zero output resistance• Infinite bandwidth
Aov
idv 0
idvlim
A
8
Vo
V+
+VS
-VS
V-
Vid = V+ - V-
+
-
A
i-
i+
Inverting Amplifier: Configuration
• Positive input is grounded.
• Feedback network, resistors R1 and R2 connected between inverting input and signal source and amplifier output node respectively.
9
Inverting Amplifier:Voltage Gain
• Negative voltage gain implies 1800 phase shift between dc/sinusoidal input and output signals.
• Gain greater than 1 if R2 > R1
• Gain less than 1 if R1 > R2
• Inverting input of op amp is at ground potential (not connected directly to ground) and is said to
be at virtual ground.
0ov22
i1
isv RRs
1
svsi R
But is=i2 and v-=0 (since vid=v+-v-=0)
and
1
2
svov
R
RvA
10
Inverting Amplifier: Example
11
• Problem:Design an inverting amplifier
• Given Data: Av=40 dB, Rin =20k,
• Assumptions: Ideal op amp• Analysis: Input resistance is controlled by R1 and voltage gain is set
by R2 / R1. and Av=-100 A minus sign is added since the amplifier is inverting.
100dB20/dB4010 vA
k201 inRR
MRRR
RvA 2
1100
21
2
Non-inverting Amplifier: Configuration
• Input signal is applied to the non-inverting input terminal.
• Portion of the output signal is fed back to the negative input terminal.
• Analysis is done by relating voltage at v1 to input voltage vs and output voltage vo .
12
outRinR
Non-inverting Amplifier:Voltage Gain, Input Resistance and Output Resistance
Since i-=0 and
But vid =0
Since i+=0
211
ov1
vRR
R 1
vid
vsv
1vsv
1
211
21
svov
121
svov
R
R
RRR
vA
RRR
i
svinR
Rout is found by applying a test current source to amplifier output and setting vs = 0 and is identical to the output resistance of inverting amplifier i.e. Rout =0
13
Unity-gain Buffer
• A special case of non-inverting amplifier, also called voltage follower with infinite R1 and zero R2. Hence Av =1.
• Provides excellent impedance-level transformation while maintaining signal voltage level.
• Ideal voltage buffer does not require any input current and can drive any desired load resistance without loss of signal voltage.
• Unity-gain buffer is used in may sensor and data acquisition systems.
14
Summing Amplifier
• Scale factors for the 2 inputs can be independently adjusted by proper choice of R2 and R1.
• Any number of inputs can be connected to summing junction through extra resistors.
• This is an example of a simple digital-to-analog converter.1
1v
1i
R
22
v2
iR
3ov
3i
R
Since negative amplifier input is at virtual ground,
Since i-=0, i3= i1 + i2,
2v
2
31
v
1
3ov
R
R
R
R
15
vi2 = 0
v+ = 0 = v-, vo(1) = -R2.vi1 (inverting amplifier) R1
Vi1 = 0
V+ = R4. vi2, vo(2) = (1+ R2/R1) . R4.vi2 R3 + R4 R3+R4
non-inverting amplifier
vo = vo(1) + vo(2)
= (1+ R2). R4 vi2 - R2.Vi1
R1 R3 + R4 R1
Difference Amplifier
Assume an ideal op-ampUse the superposition theory
Difference Amplifiers
In order to provide equal gain for both inputs vo = -R2/R1 (v1 – v2)
(1 + R2 ) . R4 = R2
R1 R3 + R4 R1
R4/R3 = R2/R1 Balance Condition
Difference Amplifier
• Also called a differential subtractor, amplifies difference between input signals.
• Rin2 is series combination of R1 and R2 because i+ is zero.
• For v2=0, Rin1= R1, as the circuit reduces to an inverting amplifier.
• For general case, i1 is a function of both v1 and v2.
)2
v1
(v
1
2v R
Ro
For R2= R1)
2v
1(vv o
18
Operational Amplifier Complete Model
Represented by:
A= open-circuit voltage gain
vid = (v+-v-) = differential input signal voltage
Rid = amplifier input resistance
Ro = amplifier output resistance
3
Non-ideal Operational Amplifier
• Various error terms arise in practical operational amplifiers due to non-ideal behavior.
• Some of the non-ideal characteristics include:
– √ Finite open-loop gain that causes gain error
– Nonzero output resistance
– Finite input resistance
– Finite CMRR
– Common-mode input resistance
– √ DC error sources
– √ Output voltage and current limits
20
Vo
+VS
-VS
-+
+
-
A VinV+
V-
Vin = V+ - V-
vo = A (v+ - v-) = A.vin
|v+ - v- | > 0
Finite Open-loop Gain
Example 1, Inverting Amplifier
S
SV-
V+
i
i
21
in
f
in
out
in
in
f
in
out
in
in
inffout
in
in
in
out
f
out
f
out
outout
in
in
in
-
f
-
f
out
f
out-
in
in
-
R
R
v
vA
ARA
R
R
v
v p gain Closed loo
R
v
ARARRv
R
v
AR
v
AR
v
R
v
Avv)-vA(v,vv
R
v
R
v
R
v
R
v
R
- vv
R
vv i
, V
inite pedance ise input imtill assum, We can s i i
,
111
111
,0
0
inf0
22