me 6405 operational amplifiers 10/2/12 alex ribner eric sanford christina biggs 1
TRANSCRIPT
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ME 6405
Operational Amplifiers10/2/12
Alex Ribner Eric Sanford Christina Biggs
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Outlineby: Alex Ribner
• 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
differential amplifier high-gain amplifier
voltage level
shifteroutput stage
current mirror
current mirror current mirror
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Timeline
• 1946 –patent for an op-amp 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
Some Op Amps have more than these 5 terminals
Active device! Requires power.
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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 AmpAchieves:• 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-Ampsby: 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 = ∞ Input currents, i+ = i- = 0 Output impedance, Zout = 0 Unlimited bandwidth Temperature-independent
Vout+
-Zout
V-
V+
Zin
i- = 0
i+ = 0
K
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Real Op-Amp
• Characteristics (typical values): 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-AmpDifferential Voltage Gain ∞ 105 - 109
Gain Bandwidth Product (Hz) ∞ 1-20 MHzInput Resistance (R) ∞ 106 - 1012 ΩOutput 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- ≈ Vcc-
Note: vd = vin, v0 = vout, vcc = source voltage
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Basic Op-Amp Typesby: Christina Biggs
• 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
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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))
Vout=K(V+-V-)
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Inverting Amplifier
virtual ground
• Amplifies and inverts the input voltage
• Polarity of the output voltage is opposite to the input voltage
• 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
If R1 = R2 and Rf = Rg:
• Produces an output proportional to the difference of the input voltages
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Applications
• 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 FiltersThree 2nd order filters: low pass, high pass, and bandpass.
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Conclusion
Questions?
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References• [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>.
• [2] Student Lecture Fall 2010. Op-Amps… and why they are useful to us.
• [3] Student Lecture Fall 2011. What is an Op-Amp?
• [4] "Operational Amplifier." Wikipedia. Wikimedia Foundation, n.d. Web. 25 Sept. 2012. <http://en.wikipedia.org/wiki/Operational_amplifier>.
• [5] "Op-Amp Basics." Op-Amp Basics. N.p., n.d. Web. 27 Sept. 2012. <http://www.bowdenshobbycircuits.info/opamp.htm>.
• [6] Jung, Walter G. Op Amp Applications Handbook. Burlington, MA: Newnes, 2006. Web. 26 Sept. 2012. <http://www.analog.com/library/analogDialogue/archives/39-05/op_amp_applications_handbook.html>.
• [7] "Operational Amplifiers." Operational Amplifiers. N.p., n.d. Web. 25 Sept. 2012. <http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opamp.html>.