1. ME 6405 Operational Amplifiers 10/2/12
Alex Ribner  Eric Sanford  Christina Biggs

2. Outline by: Alex Ribner
What is an Op Amp?
Ideal versus Real Characteristics
Types of Op Amps
Applications

3. 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.

4. 741 Op-Amp Schematic current mirror current mirror
voltage level shifter
output stage
differential amplifier
current mirror
high-gain amplifier

5. 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

6. General Schematic Active device! Requires power.
V+ - non-inverting input
V- - inverting input
Vout – output
Vs+ - positive power supply
Vs- - negative power supply
Vout=K(V+ - V-)
Some Op Amps have more than these 5 terminals

7. 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.
Although a closed loop configuration reduces the gain of the amplifier, it adds stability. In closed loop configuration, part of the output signal is applied back into the inverting input of the amplifier. This creates negative feedback, which is generally the type of feedback used with op amps. Positive feedback is mainly used in oscillators.
t helps to overcome distortion and non-linearity.
It allows the user to "tailor" frequency response to the desired values.
It makes circuit properties predictable and less dependent on elements such as temperature or the internal properties of the device.
Circuit properties are dependent upon the external feedback network and are thus easily controlled by external circuit elements.
The System designer can concentrate on function and not the details of operating point selection, biasing, and the internal characteristics of discrete transistor amplifier design.

8. Behavior of an Op Amp Achieves: In Three Steps:
Very high input impedance
Very high open loop gain
Very low output impedance.
In Three Steps:
Differential input stage, draws negligible amounts of input current enables assumption for ideal Op Amp properties.
Voltage gain stage, responsible for gaining up input signal and sending it to output stage.
Output stage, delivers current to op amp’s load.
The first stage is the differential input stage. It must have very high input impedance. This causes the op amp to draw very negligible amounts of input current. The very small input current enables the user to utilize the ideal op amp equations for circuit analysis purposes. In some designs this stage also provides the DC gain of the amplifier.
The next stage is the voltage gain stage. This stage is mainly responsible for gaining up the input signal and sending it to the output stage.
The output stage of the op amp delivers current to the op amp's load. It must have very low output impedance so that the loading of the output is minimized. This final stage may or may not have short circuit protection.

9. ‘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.

10. 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

11. Real Op-Amp Characteristics (typical values):
Gain, K = Vout / (V+-V-) = 105 < K < 109
Input impedance, Zin = 106  (BJT), 109   (FET)
Input currents, i+ = i- = – 10-8 A
Output impedance, Zout = up to 1000 
Finite bandwidth, 1-20 MHz
All parameters change with temperature

12. Ideal versus Real Op-Amps
Parameter
Ideal Op-Amp
Real Op-Amp
Differential Voltage Gain ∞
Gain Bandwidth Product (Hz)
1-20 MHz
Input Resistance (R) Ω
Output Resistance (R) Ω
Ideal
Real

13. Saturation Voltages + saturation: Vout = Vsat+ ≈ Vcc+ Linear Mode:
Vout = K (V+- V-)
- saturation: Vout = Vsat- ≈ Vcc-
Note: vd = vin, v0 = vout, vcc = source voltage

14. Basic Op-Amp Types by: Christina Biggs
Inverting
Non-Inverting
Integrating
Differential
Summing

15. Three Op Amp Setups Differential Input 2) Inverting Mode
3) Non-inverting Mode
Where should this go?

16. Non-Inverting Amplifier Analysis
Amplifies the input voltage by a constant
Determined by voltage output

17. 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))]
Use Voltage Divider Rule!!
As discussed previously assuming, K is very large, we have:
Vout=Vin/(R1/(R1+R2))
Vout=Vin (1+(R2/R1))

18. Inverting Amplifier Amplifies and inverts the input voltage
Polarity of the output voltage is opposite to the input voltage
Determined by both voltage input and output
virtual ground

19. 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)]
Use Voltage Divider Rule!!
K = gain
Vout=-VinRf/Rin

20. 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

21. 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

22. Op-Amp Summing Amplifier
Scales the sum of the input voltages by the feedback resistance and input to produce an output voltage.

23. Op-Amp Differential Amplifier
Produces an output proportional to the difference of the input voltages
If R1 = R2 and Rf = Rg:

24. Applications
Filters,
Strain Gages,
PID Controllers,
Converters,
Etc…

25. PID Controllers Goal is to have VSET = VOUT
Set point = Input; P = Non-inverting, (dependent on gain); I =integrator; D=differentiator
3 different Op-Amps in one setup!!!
Inverter after each one negative gain.
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

26. 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

27. 2nd Order Op-Amp Filters
Three 2nd order filters: low pass, high pass, and bandpass.

28. Conclusion
Questions?

29. References
[1] "What Is an Op Amp?" What Is an Op Amp? National, n.d. Web. 25 Sept <
[2] Student Lecture Fall Op-Amps… and why they are useful to us.
[3] Student Lecture Fall What is an Op-Amp?
[4] "Operational Amplifier." Wikipedia. Wikimedia Foundation, n.d. Web. 25 Sept <
[5] "Op-Amp Basics." Op-Amp Basics. N.p., n.d. Web. 27 Sept <
[6] Jung, Walter G. Op Amp Applications Handbook. Burlington, MA: Newnes, Web. 26 Sept < 05/op_amp_applications_handbook.html>.
[7] "Operational Amplifiers." Operational Amplifiers. N.p., n.d. Web. 25 Sept <