# Operational Amplifiers ME 6405 Operational Amplifiers 10/2/12 Alex Ribner Eric Sanford Christina Biggs 1 Outline by: Alex Ribner

What is an Op Amp? Ideal versus Real Characteristics Types of Op Amps Applications 2 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. 3 741 Op-Amp Schematic current mirror current mirror voltage level shifter differential amplifier

current mirror high-gain amplifier output stage 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 5 General Schematic Active device! Requires power. Some Op Amps have more than these 5 terminals 6 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. 7 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 amps load.

8 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. 9

Ideal Op-Amp Characteristics: Gain, K = Vout / (V+-V-) = Input impedance, Z = in Input currents, i+ = i- = 0 Output impedance, Zout = 0 Unlimited bandwidth Temperature-independent i- = 0 -

V- K + i+ = 0 10 Zout Zin V+

Vout 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 11

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 Output Resistance (R) 0

100 - 1000 Ideal Real 12 Saturation Voltages + saturation: Vout = Vsat+ Vcc+ Linear Mode: Vout = K (V+- V-) - saturation: Vout = Vsat- VccNote: vd = vin, v0 = vout, vcc = source voltage

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

Differential Summing 14 Three Op Amp Setups 1) Differential Input 2) Inverting Mode 3) Non-inverting Mode 15 Non-Inverting Amplifier Analysis

Amplifies the input voltage by a constant Determined by voltage output 16 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)) 17 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 18 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 19

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 20

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 21 Op-Amp Summing Amplifier Scales the sum of the

input voltages by the feedback resistance and input to produce an output voltage. 22 Op-Amp Differential Amplifier Produces an output proportional to the difference of the input voltages If R1 = R2 and Rf = Rg:

23 Applications Filters, Strain Gages, PID Controllers, Converters,

Etc 24 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 25 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 26 2 Order Op-Amp Filters nd

Three 2nd order filters: low pass, high pass, and bandpass. 27 Conclusion Questions? 28 References  "What Is an Op Amp?" What Is an Op Amp? National, n.d. Web. 25 Sept. 2012.

.  Student Lecture Fall 2010. Op-Amps and why they are useful to us.  Student Lecture Fall 2011. What is an Op-Amp?  "Operational Amplifier." Wikipedia. Wikimedia Foundation, n.d. Web. 25 Sept. 2012. .

 "Op-Amp Basics." Op-Amp Basics. N.p., n.d. Web. 27 Sept. 2012. .  Jung, Walter G. Op Amp Applications Handbook. Burlington, MA: Newnes, 2006. Web. 26 Sept. 2012. .

 "Operational Amplifiers." Operational Amplifiers. N.p., n.d. Web. 25 Sept. 2012. . 29