ME 6405 Operational Amplifiers 10/2/12

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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.

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-AmpsParameter 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

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>.