Operational Amplifiers
(Op-Amps)
1
Basic Op-Amp
Operational amplifier or op-amp, is a very high gain differential
amplifier with a high input impedance (typically a few mega ohms)
and low output impedance (less than 100 ohms).
Note the op-amp has two inputs and one output.
2
Vd = Vi 2 − Vi1
3
Ideal Op-Amp Properties
1.
2.
3.
4.
5.
6.
7.
Infinite Input Resistance:
Ri = ∞
Zero Output Resistance:
Ro= 0
Infinite Voltage Gain:
Ad = ∞
Infinite Bandwith:
BW = ∞
Infinite output current
Perfect Balance i.e.
Vo= 0 when Vi1 = Vi2
Above characteristics do not drift with
temperature
4
MC1530 Operational Amplifier
5
I 0 = I1 =
VB1
VEE + VB1 − 0.7
DC Analysis (MC1530 )
R1
R5
= (− VEE + 2 × 0.7 )
= −3.14V
R4 + R5
h fe = h FE = 100,
α = 1,
VBE = VD = 0.7 V
I 0 = 0.99 mA
IC2 = IC3 =
I6 =
VE 4
R6
=
I0
= 0.495 mA
2
VB 4 − 0.7
R6
VB 4 = VCC − R 3I C 3 = 2.18V
I 6 = 0.986 mA
IC5 =
I6
= 0.493 mA
2
V3 = VCC − R 7 I C 5 = 4.52V
V4 = V3 − 0.7 = 3.82V
I 8 ≅ IC7 =
VEE − VD 3
R8
= 1.56mA
6
Output stage
v o = VB 8 + I10 R 10
VB 8 = 0.7 + 0.7 − VEE = −4.6V
I10 = I C 7 − I B 8 − I 9
I9 =
V 4 − VB 8
R9
= 1.4 mA
I10 = 0.16 mA
v o = 200mV ≅ 0V
7
AC Analysis (MC1530 )
h fe = h FE = 100,
A v1 =
α = 1,
VBE = VD = 0.7 V
h fe R L 2
V2
= −2 A d =
V1
h ie 2
R L 2 = R 2 || h ie 4 = R 3 || h ie 3 = 3.12 kΩ
h ie 2 ≅ h ie 3 = h ie 4 = 5.2 kΩ
A v 1 = 60
Av2 =
V3
h R
= A d = − fe 7 = −28.9
V2
2h ie 4
Av3 =
V4
≅1
V3
A v4 =
Vo
R
≅ − 10 = −5
V4
R9
8
Improvements
9
Op-Amp Gain
Op-Amps have a very high gain. They can be connected open- or closed
loop.
Open-loop refers to a configuration where there is no feedback from
output back to the input. In the open-loop configuration the gain can
exceed 10,000.
Closed-loop configuration reduces the gain. In order to control the gain
of an op-amp it must have feedback. This feedback is a negative
feedback. A negative feedback will reduce the gain and improve many
characteristics of the op-amp.
10
Inverting Op-Amp
The input is applied to the inverting (-) input; the non-inverting input (+) is grounded. The
resistor Rf is the feedback resistor; it is connected from the output to the negative
(inverting) input. This is negative feedback.
11
Virtual Ground
An understanding of the concept of virtual ground provides a better understanding of how an opamp operates.
The non-inverting input pin is at ground. The inverting input pin is also at 0V for an AC signal.
This is because the op-amp has such high input impedance that even with a high gain there is no
current from inverting input pin, therefore there is no voltage from inverting pin to ground.
All of the current is through Rf.
The AC equivalent circuit.
12
Inverting Op-Amp Gain
Gain can be determined from external resistors: Rf and R1.
Av =
Unity Gain:
Vo
R
=− f
Vi
R1
Voltage gain is 1.
Av =
Rf = R1
− Rf
= −1
R1
The negative sign denotes a 180 degree phase shift between input and output.
Constant Voltage Gain:
Rf is a multiple of R1.
13
Practical Op-Amp Circuits
These Op-amp circuits are commonly used:
1.
2.
3.
4.
5.
6.
Inverting Amplifier
Noninverting Amplifier
Unity Follower
Summing Amplifier
Integrator
Differentiator
14
Inverting Op-Amp
Vo =
− Rf
V1
R1
15
Noninverting Amplifier
⎛
R ⎞
Vo = ⎜⎜ 1 + f ⎟⎟ V1
R1 ⎠
⎝
Notice the output formula is similar to Inverting Amplifier, but they are not the same.
16
Unity Follower
Vo = V1
17
Summing Amplifier
Because the op-amp has a high input impedance the multiple inputs are treated as
separate inputs.
⎛R
⎞
R
R
Vo = − ⎜⎜ f V1 + f V2 + f V3 ⎟⎟
R2
R3
⎝ R1
⎠
18
Integrator
The output is the integral of the input. Integration is the operation of summing the area
under a waveform or curve over a period of time. This circuit is useful in low-pass filter
circuits and sensor conditioning circuits.
v o (t) = −
1
∫ v 1 (t)dt
RC
19
Differentiator
The differentiator takes the derivative of the input. This circuit is useful in highpass filter circuits.
v o (t ) = − RC
dv 1 (t )
dt
20
Logarithmic Amplifier (Exercise)
HINT: Use diode characteristic equation
21
Op-Amp Specifications – DC Bias and Offset Parameters
Even though the input voltage is 0, there will be an output. This is called offset.
The following can cause this offset:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Input Bias Current
Input Offset Current
Input Offset Voltage
Input Offset Voltage and Current
Drifts
Power Supply Rejection Ratio
Open-loop voltage gain
Slew rate
Common-Mode Rejection Ratio
Input Resistance
Output Resistance
Open-Loop Bandwidth
Power Consumption (no input, no
load)
Power Dissipation (with input, with
load)
22
Input Bias Current (IIB)
I IB =
I B1 + I B 2
2
Input Offset Current (IIO)
I IO = I B1 − I B 2
23
Input Offset Voltage (VIO)
VIO = V1 − V2
Input Offset Voltage and Current Drifts
ΔVIO
ΔT
and
ΔI IO
ΔT
T : Temperature
24
Power Supply Rejection Ratio
S+ =
S− =
ΔVIO
ΔVS+
VS− = 0
ΔVIO
ΔVS−
VS+ = 0
Open-loop voltage gain (AV)
Very high e.g. for 741 Av ≅ 2 x 105
25
Slew Rate (SR)
Slew rate is the time rate of change of the closed-loop amplifier output voltage under
large-signal conditions, that is, the maximum rate at which an op-amp can change output
without distortion.
SR =
ΔVo
Δt
V/μs
The SR rating is given in the specification sheets as V/μs rating.
Maximum Signal Frequency
The slew rate determines the highest frequency of the op-amp without distortion.
f≤
SR
2 πVp
where Vp is the peak voltage
26
Common-Mode Rejection Ratio (CMRR)
One rating worth mentioning that is unique to op-amps is CMRR or Common-Mode
Rejection Ratio.
Because the op-amp has two inputs that are opposite in phase (inverting input and the noninverting input) any signal that is common to both inputs will be cancelled.
A measure of the ability to cancel out common signals is called CMRR.
CMRR =
Ad
Ac
27
Open-loop Bandwidth
The op-amp’s high frequency response is limited by internal circuitry. The plot shown is
for an open loop gain (AOL or AVD).
This means that the op-amp is operating at the highest possible gain with no feedback
resistor.
In the open loop, the op-amp has a narrow bandwidth.
The bandwidth will widen in closed loop operation, but then the gain will be lower.
28
Op-Amp Performance
The specification sheets will also include graphs that indicate the performance of the opamp over a wide range of conditions.
29
Effects of VIO and IIO
( I B1 − I f )R 1 − I f R f + Vo = 0
(I B1 − I f )R 1 + VIO − I B 2 R 2 = 0
If
⎛
R ⎞
R f = R 2 ⎜⎜ 1 + f ⎟⎟
R1 ⎠
⎝
⇒
⎛
⎛
R ⎞
R ⎞
Vo = VIO ⎜⎜ 1 + f ⎟⎟ + R f I B1 − R 2 ⎜⎜ 1 + f ⎟⎟I B 2
R1 ⎠
R1 ⎠
⎝
⎝
or in other words
R 2 = R 1 || R f
⎛
R ⎞
Vo = ⎜⎜ 1 + f ⎟⎟ VIO + R f I IO
R1 ⎠
⎝
30
⎛
⎛
R ⎞
R ⎞
Vo = VIO ⎜⎜ 1 + f ⎟⎟ + R f I B1 − R 2 ⎜⎜ 1 + f ⎟⎟I B 2
R1 ⎠
R1 ⎠
⎝
⎝
Value of R2 in order to cancel the bias currents and offset voltages in the above
equation is found to be:
R2 =
(
)
V IO
I
+ R f || R1 B1
I B2
I B2
31
Examples
1. Change the circuit shown below so that vo = 0V
where VIO = 0V, IIO = 0A, IB1 = IB2 = 100nA
⎛
⎛
R ⎞
R ⎞
v o = VIO ⎜⎜ 1 + f ⎟⎟ + R f I B1 − R 2 ⎜⎜ 1 + f ⎟⎟I B 2
R1 ⎠
R1 ⎠
⎝
⎝
v o = R f I B1 = 30mV
Solution:
32
2. Change the circuit shown below so that vo = 0V
where VIO = 0V, IB1 = 100nA, IB2 = 80nA
I IO = I B1 − I B 2 = 20 nA
⎛
⎛
R ⎞
R ⎞
v o = VIO ⎜⎜ 1 + f ⎟⎟ + R f I B1 − R 2 ⎜⎜ 1 + f ⎟⎟I B 2
R1 ⎠
R1 ⎠
⎝
⎝
v o = 6mV
Solution:
33
3. Change the circuit shown below so that vo = 0V
where VIO = 2mV, IB1 = 100nA, IB2 = 80nA
I IO = I B1 − I B 2 = 20 nA
⎛
⎛
R ⎞
R ⎞
v o = VIO ⎜⎜ 1 + f ⎟⎟ + R f I B1 − R 2 ⎜⎜ 1 + f ⎟⎟I B 2
R1 ⎠
R1 ⎠
⎝
⎝
v o = 14mV
Solution:
34
Op-Amp Applications
35
Op-Amp Applications
A.
B.
C.
D.
E.
F.
Constant-Gain Multiplier
Voltage Summing
Voltage Buffer
Controlled Sources
Instrumentation Circuits
Active Filters
36
A. Constant–Gain Amplifier
A=−
Rf
R1
A =1+
Rf
R1
37
Multiple-Stage Gains
The Total Gain:
More specifically:
A = A1 x A2 x A3
⎡ R ⎤⎡ R ⎤⎡ R ⎤
A = ⎢1 + f ⎥ ⎢ − f ⎥ ⎢ − f ⎥
⎣ R1 ⎦ ⎣ R 2 ⎦ ⎣ R 3 ⎦
38
B. Voltage Summing
The output is the sum of individual signals times the gain:
⎞
⎛R
R
R
Vo = − ⎜⎜ f V1 + f V2 + f V3 ⎟⎟
R3
R2
⎠
⎝ R1
39
C. Voltage Buffer
Any amplifier with no gain (or loss) is called a unity gain amplifier.
The advantages of using a unity gain amplifier:
• very high input impedance
• very low output impedance
Realistically these circuits will be designed using resistors that are equal (R1 = Rf) to void
out problems with offset voltages.
40
F. Active Filters
Adding capacitors to op-amp circuits provides an external control for the cutoff
frequencies. The op-amp active filter provides controllable cutoff frequencies and
controllable gain.
• Low-Pass Filter
• High-Pass Filter
• Bandpass Filter
41
Low-Pass Filter
First-order low-pass filter.
The upper cutoff frequency:
Low freq. gain:
Av = 1 +
fOH =
1
2 πR 1C1
RF
RG
42
Low-Pass Filter (Cont’d)
Second-order low-pass filter:
By adding more RC networks the roll-off can be made steeper.
43
High-Pass Filter
The lower cutoff frequency: f OL =
1
2πR1C1
44
Bandpass Filter
There are two cutoff frequencies: upper and lower. They can be calculated using the same
low-pass cutoff and high-pass cutoff frequency formulas in the appropriate sections.
The frequency response plot:
45