Operational Amplifiers Brandon Borm Shelley Nation Chloe Milion

Outline Introduction n Background n Fundamentals of Op-Amps n Real vs. Ideal n Applications n

What is an Op-Amp n Low cost integrating circuit consisting of ¨ transistors ¨ resistors ¨ capacitors n Op-amps amplify an input signal using an external power supply

Uses for Op-Amps n n Op-Amps are commonly used for both linear and nonlinear applications Linear ¨ Amplifiers ¨ Summers ¨ Integrators ¨ Differentiators ¨ Filters n (High, Low, and Band Pass) Non-linear ¨ Comparators ¨ A/D converters

Vacuum Tube Op-Amps n First op amps built in 1930’s 1940’s ¨ Technically feedback amplifiers due to only having one useable input n Used in WWII to help how to strike military targets ¨ Buffers, summers, differentiators, inverters n Took ± 300 V to ± 100 V to power http: //en. wikipedia. org/wiki/Image: K 2 -w_vaccuum_tube_op-amp. jpg 1

Solid State Discrete Op-Amps n Solid state op amps invented in 1960’s ¨ Possible due to invention of silicon transistors and the IC ¨ Chip and discrete parts Reduced power input to ± 15 V to ± 10 V n Packaging in small black boxes allowed for integration with a circuit n

Monolithic Integrated Circuit Op-Amp n First created in 1963 ¨ μA 702 n by Fairchild Semiconductor μA 741 created in 1968 ¨ Became widely used due to its ease of use ¨ 8 pin, dual in-line package (DIP) n Further advancements include use of field effects transistors (FET), greater precision, faster response, and smaller packaging

Features of Op-Amps n n n n +Vin: non-inverting input -Vin: inverting input +Vs: positive source -Vs: negative source Vout: output voltage ON: Offset Null NC: Not Connected +Vs +Vin + -Vin - Vout -Vs ON -Vin NC +Vs +Vin Vout -Vs ON

Characteristics of Op-Amps Ideal Op-Amp n Infinite open loop gain (GOL): n Infinite bandwidth: n ¨ Zero n Real Op-Amp ¨ Decreases with increase in frequency ¨ Non-zero common mode gain ¨ Range of frequencies with non-zero gain Limited open loop gain: Limited Bandwidth: ¨ Gain becomes zero at high frequencies

Characteristics of Op-Amps Ideal Op-Amp Real Op-Amp n Infinite slew rate n Finite slew rate n Infinite input impedance n Large input impedance ¨ No n input current Zero output impedance ¨ Infinite output current ¨ Small n input current Non-zero output impedance ¨ Limited output current

Summary of Characteristics Parameter Ideal Op-Amp Typical Op-Amp GOL ∞ 105 - 109 Common Mode Gain 0 10 -5 Bandwidth ∞ 1 -20 MHz Input Impedance ∞ Output Impedance 0 106 Ω (bipolar) 109 -1012 Ω (FET) 100 -1000 Ω

Ideal Op-Amp n n Active device Infinite open loop gain Infinite input impedance Zero output impedance +Vs iin = 0 A + Vdiff Vout = Vdiff x Gopenloop -Vs

Negative Feedback n Vout is a linear function of the input voltage n Zin = infinity n Modelisation of basic mathematical operation Iin=0 A Vdiff=0 V

Non Inverting Circuit iin = 0 A Vin +Vs + (1) V- - Vout = R 2 x i Vout Vdiff = 0 V 0 A R 1 V- = V+ = Vin -Vs i (2) i = -Vin/R 1 R 2 (1) V- (2) V- = - R 1 x i Vin – Vout = -Vin x R 1/R 2 V- - Vout = (1 + R 1/R 2) x Vin

Inverting Circuit +Vs iin = 0 A (1) V- - Vout = R 2 x i + Vout Vdiff = 0 V (2) Vin - V- = R 1 x i -Vs Vin R 1 Vin – V- i R 2 V- - Vout V- = V + = 0 (1) i = Vin / R 1 Vout = - R 2/R 1 x Vin

Follower Circuit + Vs Vin Vout - Vs

Summing Op-Amp • Adds analog signals Ohm’s Law: Solving for Vout:

Summing Op-Amp

Difference Op-Amps • Subtracts analog signals • Output voltage is proportional to difference between input voltages:

Difference Op-Amp

Integrator Op-Amps • Similar layout to inverting op-amp, but replace feedback resistor with a capacitor • A constant input signal generates a certain rate of change in output voltage • Smoothes signals over time • Output voltage is proportional to the integral of the input voltage:

Integrator Op-Amp

Differentiating Op-Amp • Similar to inverting op-amp, but input resistor is replaced with a capacitor • Accentuates noise over time • Output signal is scaled derivative of input signal:

Differentiating Op-Amp

Active Filters n Different types of active filters: ¨ Low n Filters out frequencies above a cutoff frequency ¨ High n Pass Filters out frequencies below a cutoff frequency ¨ Band n Passes a range of frequencies between two cutoff frequencies

Active Low-Pass Filter n Cutoff frequency:

Active High-Pass Filter n Switch positioning of capacitors and resistors from lowpass filter locations to create high-pass filter.

Active Band-Pass Filter n n Created by connecting output of a high-pass filter to the input of a low-pass filter or vice versa. Also can create using only 1 op-amp with feedback and input capacitors

No negative feedback n Vout is a non-linear function of the differential input voltage V+ - V- n V+ - V- = Vdiff n Vout = sign(Vdiff) x Vs n Binary logic and oscillator

Comparator Vout ( volts ) +Vs iin = 0 A + Vout Vdiff + Vs - V+ Vdiff 0 V V- -Vs - Vs

Comparator

Questions?

References n n “Operational Amplifiers. ” http: //en. wikipedia. org/wiki/Op_amp “Real vs. Ideal Op Amp. ” http: //hyperphysics. phy -astr. gsu. edu/hbase/electronic/opamp. html#c 4 “ 741 Op Amp Tutorial. ” http: //www. uoguelph. ca/~antoon/gadgets/741/74 1. html “Op Amp History. ” Analog Devices. http: //www. analog. com/library/analog. Dialogue/ar chives/39 -05/Web_Ch. H_final. pdf