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lecture 2&3: Amplifiers

lecture 2&3: Amplifiers. The heart of EE. Lecture outline. Reading: 1)Hambley Ch 1,2, section 8.1 2) Lab 2 handout. Ideal Op-Amp Negative Feedback Application to Filters Linear systems Bode plots Op-amp nonidealities Positive feedback. Amplifiers.

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lecture 2&3: Amplifiers

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  1. lecture 2&3:Amplifiers • The heart of EE

  2. Lecture outline Reading: 1)Hambley Ch 1,2, section 8.1 2) Lab 2 handout • Ideal Op-Amp • Negative Feedback • Application to Filters • Linear systems • Bode plots • Op-amp nonidealities • Positive feedback

  3. Amplifiers • They are everywhere: Music, Computers, Sensors • Used to turn a small voltage into a bigger voltage that can be manipulated easily. • Some filtering is used as well.

  4. amplifiers give gain • Simple amp-1 input and 1 output • Gain, A=Vout/Vin

  5. Example • If the amplifier above gives an output voltage of 1000V with an input voltage of 50V, what is the gain?

  6. ideal operational-amplifier(op-amp) http://www.youtube.com/watch?v=TQB1VlLBgJE • Inputs draw no current-infinite input impedace • Vout=A(Vplus-Vminus) A-open loop gain. • A is ideally infinity-How is this useful? • Output can provide as much voltage/current as needed-zero output impedance

  7. negative feedback • Negative feedback (NF) tries to reduce the difference • with NF, Vplus=Vminus ALWAYS • summing point constraints • virtual ground.

  8. Inverting amplifier • Input goes into Vminus input-INVERTING input • Gain, Ainv=-R2/R1, gain is negative because inverting

  9. inverting amplifier • Vplus=Vminus • Inputs draw no current

  10. Non-inverting amplifier • Input goes into Vplus input-NON-INVERTING input • Gain, Ainv=1+R2/R1, gain is positive

  11. unity gain buffer • Gain is 1 i.e. Vin=Vout • Used to isolate one side from the other

  12. Real op-amps http://www.national.com/mpf/LM/LM324.html#Overview • Output voltage determined by rails (power supply) • Open loop gain not infinity • Inputs draw small amount of current-nA’s or less Quad LM324 Single LM741

  13. bandpass Filter amplifier • f1=0.3Hz, f2=10Hz • High freq., cap is short, low freq., cap is open

  14. frequency<f1 • all caps are open. • What is the gain?

  15. F1<Frequency<F2 • C1 is short. C2 is open. • What is the gain?-midband gain.

  16. frequency>f2 • All caps are shorts • What is the gain?

  17. linear systems • T(s) has zeros when T(s)=0 • T(s) has poles when T(s)=infinity

  18. linear systems • Any voltage signal can be represented by a sum of sinusoidal voltage signals-Fourier/Laplace theorems • If s=jω, the input voltage is represented by: • V0exp(jωt)= V0exp(st) • Allows us to use algebra instead of differential eqns. • RLC circuit, for example. t t t t

  19. filter op-amp • What is T(s)?

  20. filter op-amp • zero at s=0 • poles at 1/R1C1 and 1/R2C2 • What happens at the zero? At the poles?

  21. bode plots • Frequency response on log/log axes • x-axis frequency on log scale • y-axis gain in decibels (dB) • gain in dB=20log|Vo/Vi| • 20dB/decade will appear often. • Can sketch quickly without doing too much math

  22. bode plot rules See Hambley section 8.1 • Zeros of transfer function • +20dB/decade increase in gain starting at zero • phase contribution at zero frequency is +45° • Total phase change is 90° attained at 10 times zero freq. • Poles of transfer function • -20dB/decade decrease in gain starting at zero • phase contribution at pole frequency -45° • Total phase change is -90° attained at 10 times pole freq.

  23. bode plot errors • Bode magnitude plot only has straight lines • not true near break frequencies ~3dB error • Bode phase plot only has straight lines • not true for phase near break frequencies ~5° error

  24. Bode plot of filter • Zero at s=0, poles at s=1/R1C1 and 1/R2C2 • Gain at midband =R2/R1or 20log(R2/R1) dB • midband, inverted output so phase=180°

  25. bode plot of filter 180 135 90

  26. op-amp non-idealities • Slew rate -maximum rate of change of voltage at output-arises from compensating capacitor • i.e. dv/dt|max • If input voltage changes too quickly, op-amp can’t keep up-leads to distortion of output. • Gain-bandwith product-high frequency, lower gain. • AOLfOL=ACLfCL HINT for prelab! Eqn 2.39 • Unity gain frequency

  27. Positive feedback http://en.wikipedia.org/wiki/Schmitt_trigger • Amplifies differences, so output is always +/-Vcc

  28. Schmitt trigger • Switches between 2 output rails +/-M. • Switch when inputs equal each other • Use resistors to control this • Inverting and non-inverting Schmitt triggers Inverting Schmitt Standard Schmitt

  29. inverting schmitt trigger • Vtrigger=+/-VR2/(R1+R2) • Input into inverting input

  30. Schmitt application • To minimize switching too often in noisy environment • e.g. Thermostat-switch only when T=+/-1degree Does this represent inverting or non-inverting Schmitt?

  31. EE SHORT: Tubes vs. Op-Amps http://www.youtube.com/watch?v=PbJ1GZMi_ho • Old amplifiers used tubes-BIG! • New amplifiers use op-amps. Compact, high performance

  32. more transfer functions & Timer circuits • frequency response cont.

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