STUDENT LECTURE 1
OPERATIONAL AMPLIFIERS
ME 6405 Introduction to Mechatronics
Andrew GibsonKonstantin FroelichBenjamin HaefnerRoshan Kalghatgi
September 24, 2009
+-
2ME 6405 | Student Lecture 1 | Operational Amplifiers
Outline
What is an Operational Amplifier? Characteristics of Ideal and Real Op-Amps Common Op-Amp Circuits Applications of Op-Amps References
3ME 6405 | Student Lecture 1 | Operational Amplifiers
What is an Op-Amp?
An Operational Amplifier is an electronic device used to perform mathematical operations in a circuit – they are generally abbreviated as “Op-Amps”
Op-Amps are high gain devices that amplify a signal using an external power supply
They are composed of multiple transistors, resistors, and capacitors
Common types of op-amps: Inverting Non-Inverting Integrating Differential Summing
4ME 6405 | Student Lecture 1 | Operational Amplifiers
What is an Op-Amp? All op-amps use a voltage supply (Vcc) to amplify the signal
The supply voltages can either have equal value but opposite signs, or the low side is grounded and the high side has a value of twice the voltage input
Some common applications of op-amps: Low Pass Filters
Strain Gauges
PID Controllers
V-
Inverting Input
V+
Non-Inverting Input
V-
V+
VoutV+
V-
Vout
Vout
+Vcc
-Vcc
5ME 6405 | Student Lecture 1 | Operational Amplifiers
The History of Op-Amps
First invented in 1941 using vacuum tubes
In 1947, the term “Operation Amplifier” is first used and defined
First IC op-amps invented in 1961
Replacing vacuum tubes with transistors greatly reduces size
The μA741 Op-Amp is released in 1968, this becomes the standard for op-amps
Vacuum Tube Op-Amp (1941)
Discrete IC Op-Amp (1961)
6ME 6405 | Student Lecture 1 | Operational Amplifiers
Features of Modern Op-Amps
Integrated Circuit Multiple op-amps on a single chip Easy to manufacture Very inexpensive
7ME 6405 | Student Lecture 1 | Operational Amplifiers
Typical 8 Pin Op-Amp
8ME 6405 | Student Lecture 1 | Operational Amplifiers
The Internal Circuit (ex. 741 Op-Amp)
It is important to note that it is not
necessary to model the internal
behavior of the op-amp in order to
calculate its effect on the circuit
It is important to note that it is not
necessary to model the internal
behavior of the op-amp in order to
calculate its effect on the circuit
9ME 6405 | Student Lecture 1 | Operational Amplifiers
Amplifier Gain All op-amps can be represented by the
formula:
Where K is the gain, and is a property of the individual op-amp
This gain should be distinguished from the gain of the op-amp circuit which is generally denoted by Av
A potential source of confusion comes from failing to properly distinguish between the op-amp and the op-amp circuit
Vout = K (V+ - V-)
Av = Vout / Vin
V-
V+
Vout
Op-Amp
Op-Amp Circuit
10ME 6405 | Student Lecture 1 | Operational Amplifiers
Outline
What is an Operational Amplifier? Characteristics of Ideal and Real Op-Amps Common Op-Amp Circuits Applications of Op-Amps References
11ME 6405 | Student Lecture 1 | Operational Amplifiers
Characteristics of an Ideal Op-Amp
Amplification (gain) K = Vout / (V+-V-) = ∞
Input impedance Zin = ∞
Input currents I+ = I- = 0
Output impedance Zout = 0
Unlimited bandwidth Temperature-independent
Vout+
-Zout
V-
V+
Zin
i- = 0
i+ = 0
K
12ME 6405 | Student Lecture 1 | Operational Amplifiers
Ideal v. Real Op-Amps
Ideal Op-Amp Typical Op-Amp
Operational Gain infinity 105 - 109
Input Resistance infinity 106 (BJT)
109 - 1012 (FET)
Input Current 0 10-12 – 10-8 A
Output Resistance 0 0 – 1000
Bandwidth unlimited Attenuates and phases at high frequencies (depends on slew
rate) => 1-20 MHz
Temperature independent Influence on Bandwidth and gain
http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opampcon.html#c1
13ME 6405 | Student Lecture 1 | Operational Amplifiers
Saturation
+ Saturation:Vout = Vsat+ ≈ Vvcc+
Linear Mode:
Vout = K (V+- V-) Vin
Vout
Vsat+
Vsat- - Saturation:Vout = Vsat- ≈ Vvcc-
14ME 6405 | Student Lecture 1 | Operational Amplifiers
Outline
What is an Operational Amplifier? Characteristics of Ideal and Real Op-Amps Common Op-Amp Circuits Applications of Op-Amps References
15ME 6405 | Student Lecture 1 | Operational Amplifiers
Open-Loop vs. Closed-Loop
Vout
Vin
+
-R1
R2
Vin
+
-V-
V+
Vout
Vin
+
-R1
+
-V-
V+
In contrast to open-loops, closed-loop op-amps have feedback
16ME 6405 | Student Lecture 1 | Operational Amplifiers
Negative vs. Positive Feedback
Vout+
-
R1
R2
Vin
V-
V+
Vout
Vin
+
-R1
R2
Vin
+
-V-
V+
Closed loops either have negative or positive feedback Negative feedback leads to the inverting input, positive to
the non-inverting input
17ME 6405 | Student Lecture 1 | Operational Amplifiers
Basic Circuits Review
Kirchhoff’s Current Law (KCL)
The sum of all currents flowing into a node
equals the sum of all currents flowing out.
∑ iin = ∑ iout
Kirchhoff’s Voltage Law (KVL)
The sum of all the voltage drops around a loop equals the sum of the
input voltages.
∑ Vk = 0-Vin + V1 + V2+ V3 = 0
i1
i4
i2
i3
i1 + i2 = i3 + i4
V1 + V2+ V3 = Vin
Vin
V1
V3
V2
18ME 6405 | Student Lecture 1 | Operational Amplifiers
Basic Circuits Review
Resistance (R)
Series addition
Parallel addition
Capacitance (C)
Inductance (L)
R = V / I
R1 R2 Rn
R1 R2 Rn
n21eqR...RRR
n21eqR1
...R1
R1
R1
VQ
C dtdV
CdtdQ
I
dt
tdiLtV
19ME 6405 | Student Lecture 1 | Operational Amplifiers
Comparator A comparator is an example of an open-loop op-amp
If V+ > V- Vout = Vsat ≈ Vcc
If V+ < V- Vout = -Vsat ≈ - Vcc
i- = 0A
i+ = 0A
+Vcc
-Vcc
Vout+
-V-
V+Vin-
Vin+
Vout
Vin+ - Vin-
+ Vsat
- Vsat
20ME 6405 | Student Lecture 1 | Operational Amplifiers
Comparator
21ME 6405 | Student Lecture 1 | Operational Amplifiers
Calculation Rules for Op-Amps
Assumptions: Calculation based on the models of an ideal op-amp
(Zin = ∞, Zout = 0, K = ∞)
Op-Amp operates in its linear amplifying mode (Vout between saturation borders)
Calculation Rules
(1) i+ = i- = 0
(2) V+ = V- Vout+
-Zout
V-
V+
Zin
i- = 0
i+ = 0
K
22ME 6405 | Student Lecture 1 | Operational Amplifiers
Inverting Op-Amp
Circuit Characteristics
Output connected to inverting input (V-)
Non-inverting input leading to ground
Input voltage connected to inverting input (V-)
Input voltage is amplified with a negative gain
Vout
Vin
Vout+
-R1
R2
+
-R1
R2
V-
V+
23ME 6405 | Student Lecture 1 | Operational Amplifiers
Inverting Op-Amp
(1) Vin + (V+ - V-) = R1 i1
→ i1 = Vin / R1
(2) Vout + (V+ - V-) = R2 i2
→ Vout = R2 i2
(3) i2 + i1 + i-= 0
→ i2 = - i1
Vout = - R2 /R1 x Vin
Vout
Vin
Vout+
-R1
R2
+
-R1
R2
V-
V+
(1)
(2)
i1
i2
i-
(3)
24ME 6405 | Student Lecture 1 | Operational Amplifiers
Inverting Op-Amp - Example
Let‘s assume we need to create an output signal of 10 V.
Vcc+ = 30 V, R1 = 10 kΩ, Vin = - 5 V.
How do we have to choose R2?
Vout = - (R2 /R1) x Vin = (-20 kΩ / 5 kΩ) x (-10V) = 40 V ???
No! Since Vout > Vcc+ → Vout = Vcc+
What would be Vout , if Vcc+ = 30 V, R1 = 5 kΩ, R2 = 20 kΩ and Vin = -10 V?
Vout = - (R2 /R1) x Vin
→ R2= -Vout x R1/Vin = (-10 V x 10 kΩ) / (-5 V) = 20 kΩ
25ME 6405 | Student Lecture 1 | Operational Amplifiers
Non-inverting Op-Amp
Circuit Characteristics
Input voltage is amplified with a positive gain
Output connected to inverting input (V-)
Inverting input leading to ground
Input voltage connected to non-inverting input (V+)
Vin
Vout+
-R1
R2
Vout+
-V-
V+
R2
26ME 6405 | Student Lecture 1 | Operational Amplifiers
Non-inverting Op-Amp
Vin
Vout+
-R1
R2
Vout+
-V-
V+
R2
(3)
(3) Vin = i1 R1 + (V+ - V-) KVL
V+ - V- = 0 op-amp rule (2)
→ Vin = i1 R1
i1
i2
i-
(1)
(1) i2 + i- = i1 KCL
i- = 0 op-amp rule (1)
→ i2 = i1
Vout/Vin = (i1R1 + i2R2) / (i1R1)
= (i1R1 + i1R2) / (i1R1)
= (R1 + R2) / R1
= 1 + (R2 / R1)
(2) Vout = i1 R1 + i2 R2 KVL
(2)
in1
2out V
RR
1V
27ME 6405 | Student Lecture 1 | Operational Amplifiers
Non-inverting Op-Amp - Example
A non-inverting op-amp has an input voltage of 2 V.R1 = 6 kΩ, R2 = 30 kΩ. What is the output voltage?
in1
2out V
RR
1V
V5.6
k10k10
1
V13
RR
1
VV
1
2
outin
The saturation output voltage of an non-inverting op-amp is Vsat=13 V. R1 = 10 kΩ, R2 = 10 kΩ. Determine the maximum input voltage so that the output voltage does not saturate.
V12V2k6k30
1
28ME 6405 | Student Lecture 1 | Operational Amplifiers
Op-Amps for Math
Closed-loop operational amplifiers with negative feedback can be used to fulfil various mathematic operations:
Integrating
Vin Vout dtRC
1
Subtracting
Vin1 Vout1K
Vin2 2K
+-
Vin1 Vout1K
Vin2 2K
+
+
Summing
dt
d)RC(Vin Vout
Derivative
29ME 6405 | Student Lecture 1 | Operational Amplifiers
Summing Op-Amp Application of a non-inverting op-amp and
Millman‘s theorem
Vout = VinA + VinB + VinC
VinAVout+
-
RA
R2
V-
V+
VinB
VinC
RB
RC
R1
(1) Millman’s theorem:
CBA
C
inC
B
inB
A
inA
R1
R1
R1
RV
RV
RV
'V
if RA = RB = RC = R
)VVV(3/1'V inCinBinA
(1)
(2) Non-inverting Op-Amp:
'VRR
1V1
2out
3RR
1if1
2
)VVV(3/1x3V inCinBinAout
(2)
V’
30ME 6405 | Student Lecture 1 | Operational Amplifiers
Substraction (Differential) Op-Amp
Vout = VinA - VinB
Applying Kirchhoff’s Rules and Op-Amp Calculation Rules yields:
inB3
4inA
3
43
21
2out V
RR
VR
RRRR
RV
VinB
Vout+
-
R4
V-
V+VinA R1
R2
R3
if R1 = R2 = R3 = R4
inBinAout VVV
Note:
if R1 = R3 = R and R2 = R4 = a R
inBinAout VVaV
31ME 6405 | Student Lecture 1 | Operational Amplifiers
Derivative Op-Amp
Applying Kirchhoff’s Rules and Op-Amp Calculation Rules yields:
dt)t(dV
)RC(V inout
Vin
Vout+
-
R
V-
V+R
CVin
Vout
dt
d)RC(
32ME 6405 | Student Lecture 1 | Operational Amplifiers
Integrating Op-Amp
Vin
Vout+
-R V-
V+R
C
Vin
Vout
dtRC1
Applying Kirchhoff’s Rules and Op-Amp Calculation Rules yields:
dVRC1
Vt
0inout
33ME 6405 | Student Lecture 1 | Operational Amplifiers
Op-Amps for Math - Examples
We want to design a summing op-amp circuit to add 4 input voltages. Tsun-Yen insists that R2 = 12 kΩ.
What should be the resistance of R1?
Consider an op-amp circuit to obtain the following input-output voltage relationship: Vout = VA - 2 VB
Calculate a possible combination of the resistor values.
(example + solution on page 196 in Cetinkunt, Mechatronics)
nRR
1if,1
2
Vout = V1 + V2 + V3+ V4
4Rk12
11
k4R1
34ME 6405 | Student Lecture 1 | Operational Amplifiers
Outline
What is an Operational Amplifier? Characteristics of Ideal and Real Op-Amps Common Op-Amp Circuits Applications of Op-Amps References
35ME 6405 | Student Lecture 1 | Operational Amplifiers
Filters
R2
+
-
+
V0
__
+ Vcc
- Vcc
-
+
Types:•Low pass filter•High pass filter•Band pass filter•Cascading (2 or more filters connected together)
R1
C
Low pass filter
Low pass filter Cutoff frequency
Low pass filter transfer function
36ME 6405 | Student Lecture 1 | Operational Amplifiers
Strain Gauge
Use a Wheatstone bridge to determine the strain of an element by measuring the change in resistance of a
strain gauge
(No strain) Balanced Bridge R #1 = R #2
(Strain) Unbalanced Bridge R #1 ≠ R #2
37ME 6405 | Student Lecture 1 | Operational Amplifiers
R + ΔR
Strain Gauge
Rf
+
- +
V0
__
+ Vcc
- Vcc
-
+
Rf
Vref
Half-Bridge Arrangement
R
R - ΔR
R
Using KCL at the inverting and non-inverting terminals of the op amp we find that ε ~ Vo = 2ΔR(Rf /R2)
Op amp used to amplify output from strain gauge
38ME 6405 | Student Lecture 1 | Operational Amplifiers
•Goal is to have VSET = VOUT
•Remember that VERROR = VSET – VSENSOR
•Output Process uses VERROR from the PID controller to adjust Vout such that it is ~VSET
P
I
D
Output Process
Sensor
VERRORVSET VOUT
VSENSOR
PID Controller – System Block Diagram
39ME 6405 | Student Lecture 1 | Operational Amplifiers
ApplicationsPID Controller – System Circuit Diagram
Calculates VERROR = -(VSET + VSENSOR)
Signal conditioning allows you to introduce a time delay which could
account for things like inertia
System to control
Source: http://www.ecircuitcenter.com/Circuits/op_pid/op_pid.htm
-VSENSOR
40ME 6405 | Student Lecture 1 | Operational Amplifiers
ApplicationsPID Controller – PID Controller Circuit Diagram
VERROR
Adjust Change
Kp RP1, RP2
Ki RI, CI
Kd RD, CD
VERROR PID
41ME 6405 | Student Lecture 1 | Operational Amplifiers
Buying Operational Amplifiers
No money? Click on “Samples”.
Go to www.national.com, click on “Order”, then click on “Samples”.
42ME 6405 | Student Lecture 1 | Operational Amplifiers
Outline
What is an Operational Amplifier? Characteristics of Ideal and Real Op-Amps Common Op-Amp Circuits Applications of Op-Amps References
43ME 6405 | Student Lecture 1 | Operational Amplifiers
References
Centinkunt, Sabri. MechatronicsHoboken, NJ: John Wiley & Sons Inc., 2007.
Hambley, Allen. Electrical Engineering.Upper Saddle River, NJ: Pearson Education Inc., 2008.
Nilsson, James W., Riedel Susan A. Electric Circuits
Upper Saddle River, NJ Pearson Prentice Hall, 2005. www.allaboutcircuits.com www.ecircuitcenter.com www.ti.com hyperphysics.phy-astr.gsu.edu en.wikipedia.org