V+
Operational Amplifiers
inv input
non-inv
input
-
output
+
gnd
V-
Aims:
To know:
• Basic Op Amp properties – Real & Ideal
• Basic ideas of feedback.
To be able to do basic circuit analysis of op amps:
• using KCL, KVL with dependent sources.
• Inverting and Non-inverting Amplifiers.
• Voltage follower and summing amplifier.
Lecture12
7
Lecture
1
Voltage Amplifiers
Probably the most common building block in electronics is the
voltage amplifier.
Often shown
schematically as
V
IN
A
VOUT
Vout = AVin
⎛V ⎞
AdB = 20 log10 ⎜ out ⎟
⎝ Vin ⎠
The key requirement is the ability to generate an exact copy of an
input waveform without modifying its shape or time dependence.
Key parameters are:
•Linearity
•Well controlled frequency response
•High input impedance
•Low output impedance
Lecture12
7
Lecture
2
1
Linearity
Ideal linear characteristic
(slope = gain)
saturation
Vout
Real characteristic
(exaggerated)
distortion
zero offset
Vin
Lecture12
7
Lecture
3
Frequency Response
Peaking
Gain (dB)
R eal characteristic
(exaggerated)
Ideal characteristic
H igh frequency
roll-off
Low frequency
roll-off
ω
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Lecture
4
2
Input and Output Impedance (Resistance)
Thevenin equivalent
of source
Amplifier
VIN
ZT
ZIN
AVIN
+
Load
ZOUT
VL
ZL
VT
(Two port equivalent circuit)
Input impedance: Must be high to ensure that VIN is a good approximation to VT
VIN = VT
Z IN
ZT + Z IN
Output impedance:
For voltage amplifier ZOUT must be low to ensure that VL is a good approximation
to VOUT=AVIN
For power amplifier ROUT=RL , or more generally for impedances ZOUT=ZL*
(maximum power transfer)
Lecture12
7
Lecture
5
The Operational Amplifier
This is an important building block that allows us to construct amplifiers with a
wide range of characteristics.
Rout
inv input
-
non-inv +
input
Rin
+
-
Controlled
voltage source
output
V = A(V+ - V-)
The key features are
• TWO inputs: Inverting and Non-inverting (+ and - )
• Output is a controlled voltage source with a value A(V+ - V-).
A is very large
• Very high input resistance (Rin)
• Very low output resistance (Rout)
Lecture12
7
Lecture
6
3
Op Amps
Package outline
V+
inv input
non-inv
input
Detailed schematic
-
output
+
gnd
V-
All components fabricated on a small chip of
silicon (< 1 mm square)
Circuit symbol
Lecture12
7
Lecture
7
V+
Op Amp Parameters
inv input
Parameter
Ideal op amp
Real op amp
Open loop gain, A
∞
105 - 107
Input resistance Rin
∞
10 MΩ – 1 GΩ
Output resistance
0
10 – 100 Ω
non-inv
input
-
output
+
gnd
V-
Three important consequences:
1) Very small (or zero) currents flow into the input terminals
2) Output is like an ideal voltage source (Vout independent of current)
3) Voltage difference between input terminals is very small (or zero) because
of large gain
Vout = A(V+ − V− )
(V+ − V− ) = Vout / A, which → 0 as A → ∞
Lecture12
7
Lecture
8
4
Feedback Amplifier (inverting amplifier)
R2
I2
R2
I1
VIN
VIN
R1
-
R1
V-
VOUT
X
+
VOUT
rout
rin
V+
schematic
equivalent circuit
• Generally two ways of analysing these circuits:
• (i) Assume Op-Amp is ideal
• (ii) Assume Open loop gain, A, is finite initially.
Lecture12
7
Lecture
9
Feedback Amplifier (inverting amplifier)
R2
I2
R2
I1
VIN
VIN
R1
X
R1
V-
VOUT
+
rin
VOUT
rout
V+
schematic
equivalent circuit
• For an ideal op-amp, no current flows into V_, so I1= - I2 (KCL)
• For an ideal op-amp, open loop gain is infinite, so V_ = V+ = 0
Point X is a virtual earth. ‘Earth’
because V= 0, ‘virtual’ because there is a
high impedance to true earth
Lecture12
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Lecture
I1 =
VIN
V
= − I 2 = − OUT
R1
R2
VOUT
R
=− 2
VIN
R1
10
5
Feedback Amplifier (inverting amplifier)
R2
I2
R2
I1
VIN
VIN
R1
-
R1
V-
VOUT
X
+
rin
VOUT
rout
V+
schematic
equivalent circuit
• For an ideal op-amp, no current flows into V_, so I1= - I2 (KCL)
• For an ideal op-amp, open loop gain is infinite, so V_ = V+ = 0
Point X is a virtual earth. ‘Earth’
because V= 0, ‘virtual’ because there is a
high impedance to true earth
I1 =
VIN
V
= − I 2 = − OUT
R1
R2
VOUT
R
=− 2
VIN
R1
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Lecture
11
Feedback Amplifier (inverting)
R2
VIN
R1
X
+
VOUT
VOUT
R
=− 2
VIN
R1
Closed loop gain
This is a remarkable result – this tells us that for an ideal amplifier, the gain is
determined ONLY by the feedback components and not by the properties of the
amplifier.
This is negative feedback. Very important in the design of many kinds of
amplifier.
You can think of this as a kind of ‘thermostat’ trying to keep V- equal to V+.
If V_ rises, then VOUT falls and corrects V_ by exactly the right amount.
Lecture12
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Lecture
14
6
Feedback Amplifier (non-inverting)
R
VIN
+
VOUT
R1
R2
Now V+ is equal to the input voltage
(no current into the + terminal so
V+ = VIN independently of R)
Open loop gain is ∞, so V- = V+ = VIN, so
Lecture12
7
Lecture
15
Feedback Amplifier (non-inverting)
R
VIN
+
VOUT
R1
R2
Now V+ is equal to the input voltage
(no current into the + terminal so
V+ = VIN independently of R)
Open loop gain is ∞, so V- = V+ = VIN, so
VIN = VOUT
R1
R1 + R2
(potential divider)
so
VOUT
R
= 1+ 2
VIN
R1
Lecture12
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Lecture
16
7
Voltage Follower
VIN
+
VOUT
-
A special case of the non-inverting amplifier with R1=∞ and R2=0
so VOUT= VIN
The output voltage is an exact copy of the input.
Because the input impedance is very high, this circuit is very useful for
separating (buffering) two parts of a circuit (e.g. sections of a filter)
Lecture12
7
Lecture
18
Summing Amplifier
V3
R3
V2
R2
V1
R1
The current balance at the virtual earth now
gives us
RF
-
V1 V2 V3 VOUT
+
+ +
=0
R1 R2 R3
RF
VOUT
⎛V V V
⎞
VOUT = − RF ⎜ 1 + 2 + 3 K ⎟
R
R
R
2
3
⎝ 1
⎠
+
If all resistors are equal, the output voltage is the sum of the input voltages (negative)
Lecture12
7
Lecture
19
8
Active Filters
Op-amps can simplify filter design by giving a high impedance separation
between different RC or RL sections of a circuit and by offering gain to
compensate for the loss in the passive filter:
E.g. bandpass filter:
This circuit has a transfer function like
C2
A (dB)
Note the gain is > 1
R2
20
R1
VIN
-
0
VOUT
C1
+
-20
log10ω
Using an op amp allows complex
filters to be constructed.
Lecture12
7
Lecture
21
9