Amplifiers: From Ideal to Real Why amplify? Gain = Vout / Vin = sensitivity Ideal Op Amp Negative gain summation amplifier Positive gain for increased Rin Differential amplifier circuit Gain-bandwidth product; CMRR Nonlinear gain: The ideal diode Instrumentation Amp Isolation Amplifier

Horowitz & Hill, The Art of Electronics, Cambridge Univ Press James K. Roberge, Operational Amplifiers: Theory & Practice can download at: Burr-Brown HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS can download at: References:

If Rf = 1000*Rs and G is 10 6, then Vin is in the range of 1mV, a so-called virtual ground.

Summation

Input impedance of NGSA mechatronics.mech.northwestern.edu/design_ref/electrical_design Input resistance = Vin/Iin = R1= Rs ≈ 1KΩ Way less than the Ω of the op amp itself NG: R1 may become voltage divider with sensor output resistance Impedance includes frequency-dependent current-voltage relationship e.g. V(jω)=jωC*I(jω); impedance is a complex number

Unity Gain Voltage Follower A good circuit for isolation

Positive gain single input op amp ckt If Rs = 0 then Vout = Vin, UGVF The positive gain amplifier cannot have a gain less than 1. It can have only one input.

Differential amplifier with external resistors

Current-voltage relationship of a diode Where kT/q is about 25mV at room temp

Ideal diode / half wave rectifer When VIN > 0 volts output current can flow through the diode and does so until Vin = Vout. (low Rf, like UGVF) When Vin < 0 the the diode looks like a high resistance, the op amp output saturates at the negative supply voltage, and the left resistor "pulls down" VOUT until it's zero.

Log amplifier ATP8b/exponentialFunction.htm

Absolute value / Full wave rectifier

A compression function of input: suppresses large spikes on input

Exponential (anti-log) amplifier A non-linear amplifier used to emphasis positive spikes in waveform; makes sense only when Vs > 0. … getting the signs of Vin and Vout figured out…

Op Amp as integrator Where we know a capacitor’s current-voltage relationship is (from Laplace transforms)

GBWP and CMRR (LF353) dB = 20*log 10 (out/in) (Implies first order LP filter in op amp)

Instrumentation Amplifier AD524 No external components needed pins to select gains of 10, 100, GBWP 25MHz Common mode rejection ratio of 120 dB Data sheet: p. 4: differential resistance 10 9 Ω p. 8: Absolute Maximum Ratings dimensions in mm p. 10: CMRR (freq) Gain (freq) Settling time: 10μsec p. 18: Ground, analog and digital; ground mecca

Isolation Amplifier AD203 UGVF optical isolation; (wireless isolation) transformer isolation amplifiers/ad203/products/product.html Data sheet: Modulator is a Volt→Freq converter on input, and “tach” on output single +15v supply input impedance Ω low GBWP about 1MHz CMRR about 120 dB

Iso Amp block diagram

Op amp as example of negative feedback When we come later to the topic of automatic control by negative feedback, we will see the op amp as a good example