ME 6405
Operational Amplifiers
10/2/12
Alex Ribner  Eric Sanford  Christina Biggs
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Outline
by: Alex Ribner
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What is an Op Amp?
Ideal versus Real Characteristics
Types of Op Amps
Applications
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Background
• Operational amplifiers (op-amps), use an external power
source to apply a gain to an input signal.
• Made of resistors, transistors, diodes and capacitors.
• Variety of functions such as: mathematical operations,
perform buffering or amplify AC and DC signals.
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741 Op-Amp Schematic
current mirror
current mirror
voltage
level
shifter
output
stage
differential amplifier
current mirror
high-gain amplifier
Timeline
• 1946 –patent for an opamp using vacuum tubes.
• 1953 –op-amps for sale
• 1961 – discrete IC op-amp
• 1965 – successful
monolithic op-amps
• 1968 – uA741
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General Schematic
Active device! Requires power.
Some Op Amps have more than these 5 terminals
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Feedback
• Closed loop configurations reduce the
gain of the amplifier, but adds stability.
• Part of the output signal is applied
back to the inverting input of the
amplifier.
• Op amps use negative feedback.
• Negative feedback helps to: overcome
distortion and non-linearity, tailor
frequency response, and stabilize
circuit properties from outside
influences such as temperature.
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Behavior of an Op Amp
Achieves:
• Very high input impedance
• Very high open loop gain
• Very low output impedance.
In Three Steps:
1. Differential input stage, draws
negligible amounts of input
current enables assumption for
ideal Op Amp properties.
2. Voltage gain stage, responsible
for gaining up input signal and
sending it to output stage.
3. Output stage, delivers current to
op amp’s load.
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‘Golden Rules’ of Ideal Op-Amps
by: Eric Sanford
• These characteristics can be summarized with
two ‘golden rules’:
1 - The output attempts to do whatever is necessary
to make the voltage difference between the inputs
equal to zero (when used in a closed-loop design).
2 - The inputs draw no current.
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Ideal Op-Amp
• Characteristics:
 Gain, K = Vout / (V+-V-) = ∞
 Input impedance, Zin = ∞


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Input currents, i+ = i- = 0
Output impedance, Zout = 0
Unlimited bandwidth
Temperature-independent
i- = 0
-
V-
K
+
i+ = 0
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Zout
Zin
V+
Vout
Real Op-Amp
• Characteristics (typical values):




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Gain, K = Vout / (V+-V-) = 105 < K < 109
Input impedance, Zin = 106  (BJT), 109  - 1012  (FET)
Input currents, i+ = i- = 10-12 – 10-8 A
Output impedance, Zout = up to 1000 
Finite bandwidth, 1-20 MHz
All parameters change with temperature
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Ideal versus Real Op-Amps
Parameter
Ideal Op-Amp Real Op-Amp
Differential Voltage Gain
105 - 109
∞
Gain Bandwidth Product (Hz)
1-20 MHz
∞
Input Resistance (R)
106 - 1012 Ω
∞
Output Resistance (R)
0
100 - 1000 Ω
Ideal
Real
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Saturation Voltages
• + saturation:
Vout = Vsat+ ≈ Vcc+
• Linear Mode:
Vout = K (V+- V-)
• - saturation:
Vout = Vsat- ≈ VccNote: vd = vin, v0 = vout, vcc = source voltage
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Basic Op-Amp Types
by: Christina Biggs
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Inverting
Non-Inverting
Integrating
Differential
Summing
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Three Op Amp Setups
1) Differential Input
2) Inverting Mode
3) Non-inverting Mode
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Non-Inverting Amplifier Analysis
• Amplifies the input
voltage by a constant
• Determined by voltage
output
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Derivation of Non-inverting Amplifier
Vout=K(V+-V-)
R1/(R1+R2)  Voltage Divider Rule
V-=Vout (R1/(R1+R2) )
Vout=[Vin-Vout (R1/(R1+R2))] K
Vout=Vin/[(1/K)+ (R1/(R1+R2))]
As discussed previously assuming, K is very large, we have:
Vout=Vin/(R1/(R1+R2))
Vout=Vin (1+(R2/R1))
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Inverting Amplifier
• Amplifies and inverts
the input voltage
• Polarity of the output
voltage is opposite to
the input voltage
virtual ground
• Determined by both
voltage input and
output
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Derivation of Inverting Amplifier
Vout=K(V+-V-)
V-=Vout(Rin/(Rin+Rf))+Vin(Rf/(Rin+Rf))
V-=(VoutRin+VinRf)/(Rin+Rf)
Vout=K(0-V-)
Vout=-VinRf/[(Rin+Rf)/K+(Rin)]
Vout=-VinRf/Rin
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Op-Amp Integrator
• Integrates the inverted
input signal over time
• Magnitude of the
output is determined
by length of time
voltage is present at
input
• The longer the input
voltage is present, the
greater the output
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Op-Amp Differentiator
• Magnitude of output
determined by the
rate at which the
applied voltage
changes.
• Faster change, greater
output voltage
• The resistor and
capacitor create an RC
network
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Op-Amp Summing Amplifier
• Scales the sum of the
input voltages by the
feedback resistance
and input to produce
an output voltage.
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Op-Amp Differential Amplifier
• Produces an output
proportional to the
difference of the input
voltages
If R1 = R2 and Rf = Rg:
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Applications
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Filters,
Strain Gages,
PID Controllers,
Converters,
Etc…
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PID Controllers
•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
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Strain Gages
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
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2nd Order Op-Amp Filters
Three 2nd order filters: low pass, high pass, and bandpass.
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Conclusion
Questions?
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References
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[1] "What Is an Op Amp?" What Is an Op Amp? National, n.d. Web. 25 Sept. 2012.
<http://www.national.com/AU/design/courses/268/the02/01the02.htm>.
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[2] Student Lecture Fall 2010. Op-Amps… and why they are useful to us.
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[3] Student Lecture Fall 2011. What is an Op-Amp?
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[4] "Operational Amplifier." Wikipedia. Wikimedia Foundation, n.d. Web. 25 Sept. 2012.
<http://en.wikipedia.org/wiki/Operational_amplifier>.
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[5] "Op-Amp Basics." Op-Amp Basics. N.p., n.d. Web. 27 Sept. 2012.
<http://www.bowdenshobbycircuits.info/opamp.htm>.
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[6] Jung, Walter G. Op Amp Applications Handbook. Burlington, MA: Newnes, 2006.
Web. 26 Sept. 2012. <http://www.analog.com/library/analogDialogue/archives/3905/op_amp_applications_handbook.html>.
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[7] "Operational Amplifiers." Operational Amplifiers. N.p., n.d. Web. 25 Sept. 2012.
<http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opamp.html>.
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