1. 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

2. Horowitz & Hill, The Art of Electronics, Cambridge Univ Press James K. Roberge, Operational Amplifiers: Theory & Practice can download at: http://web.mit.edu/klund/www/books/opamps181.pdf Burr-Brown HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS can download at: http://focus.ti.com/lit/an/sboa092a/sboa092a.pdf References:

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

5. Summation

6. Input impedance of NGSA mechatronics.mech.northwestern.edu/design_ref/electrical_design Input resistance = Vin/Iin = R1= Rs ≈ 1KΩ Way less than the 10 12 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

7. Unity Gain Voltage Follower http://ytdp.ee.wits.ac.za/cctpng/Follower.png A good circuit for isolation

8. 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.

9. Differential amplifier with external resistors

10. Current-voltage relationship of a diode Where kT/q is about 25mV at room temp http://keywon.com/wiki/images/ http://electricalandelectronics.org

11. 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.

12. Log amplifier http://www.regentsprep.org/Regents/math/algtrig/ ATP8b/exponentialFunction.htm

13. Absolute value / Full wave rectifier www.eleinmec.com/ www.physics.udel.edu/~nowak/phys645/More_opamp_circuits.htm

14. A compression function of input: suppresses large spikes on input

15. www.corollarytheorems.com/Design/opamp.htm 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…

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

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

18. Instrumentation Amplifier AD524 No external components needed pins to select gains of 10, 100, 1000. GBWP 25MHz Common mode rejection ratio of 120 dB Data sheet: www.analog.com/static/imported-files/data_sheets/AD524.pdf 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 www.analog.com/en/other-products/militaryaerospace/ad524/products/product.html#ppa_print_table

19. Isolation Amplifier AD203 UGVF optical isolation; (wireless isolation) transformer isolation www.analog.com/en/amplifiers-and-comparators/isolation- amplifiers/ad203/products/product.html Data sheet: www.analog.com/static/imported-files/data_sheets/AD203SN.pdf Modulator is a Volt→Freq converter on input, and “tach” on output single +15v supply input impedance 10 12 Ω low GBWP about 1MHz CMRR about 120 dB

20. Iso Amp block diagram

21. 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