Operational Amplifiers Hunter Greene Wendy Siemens 20 February 2006

Operational Amplifier Outline Introduction Characteristics Idealizations Cautions Applications References

Introduction Performs operations on input voltages Active component V+ and V- power Can amplify inputs V+V+ V-V-

Characteristics Symbol Positive-going input Negative-going input Open loop operation: a very small difference between +V in and -V in swings the output voltage to the corresponding V ref (V + or V - ) V+V+ V-V-

Characteristics Open Loop Operation If V 1 >V 2, V out =+15V If V 1 <V 2, V out =-15V If V 1 =V 2, V out =0V Typical op-amps swing from V + to V - with mV input voltage differences +15V -15V V out V1V1 V2V2

Characteristics Closed Loop Operation Golden Rule 1: The output attempts to make the input voltage difference zero. Golden Rule 2: The inputs draw no current.

Characteristics V + =V in and V - =V + R 1 /V in =R 2 /(V out -V in ) V in /V out =(R 1 +R 2 )/R 1 => Non-inverting Amplifier

Idealizations Infinite open loop gain Infinite bandwidth Infinite input impedances (zero input current) Zero output impedance Zero noise Zero input offset voltage Zero temperature dependence V+V+ V-V- V out V1V1 V2V2

Idealizations Ideal Op-AmpTypical Op-Amp Input Resistanceinfinity 10 6  (bipolar) 10 9   (FET) Input Current – A Output Resistance0 100 – 1000  Operational Gaininfinity Common Mode Gain BandwidthinfinityAttenuates and phases at high frequencies (depends on slew rate) TemperatureindependentBandwidth and gain

Cautions Cautions: Active regions: clipping occurs when the output saturates Inputs: feedback must be negative for proper operation Input difference limits: ignoring limits on input differences cause harmful current levels.

Applications Cheaper than buying a commercial PID controller. Saves microcontroller processing time

R 1 = R 2 = R F V out = -(V 1 +V 2 ) Applications

Integrator Circuit Applications

Positions/velocity measurement The output signal from an accelerometer can be integrated once to give a voltage output proportional to velocity. This signal can then be integrated again to give a voltage proportional to position. This can be much cheaper than other position measuring devices such as LVDT’s which can range from $70-$300.

Applications Microphone/Speaker Amplification A non-inverting amplifier is typically used to amplify the small signals from microphones before the sound can be processed. Computer sound systems must amplify the signals from Digital-to-Analog converters before sending the sound signal to the speakers.

References For further information: Wikipedia: The Art of Electronics, Horowitz and Hill Introduction to Mechatronics and Measurement Systems, Alciatore and Histand Electrical Engineering, Hambley ME 3056 and 4053 lab manual appendices show details of op- amp circuits used in data acquisition