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

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

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 current mirror current mirror voltage level shifter output stage differential amplifier current mirror high-gain amplifier

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

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

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.

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.

‘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.

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

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

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) 100 - 1000 Ω Ideal Real

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

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

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

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

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!! http://en.wikipedia.org/wiki/Voltage_divider As discussed previously assuming, K is very large, we have: Vout=Vin/(R1/(R1+R2)) Vout=Vin (1+(R2/R1))

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

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!! http://en.wikipedia.org/wiki/Voltage_divider K = gain Vout=-VinRf/Rin

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

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

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

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

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

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

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

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

Conclusion Questions?

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>.