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00_Op Amp intergrator, diff and other applications

00_Op Amp intergrator, diff and other applications. Case Study : How to do integration and differentiation before digital electronic computers Choice #1: analytically BUT: for calculation of e.g. the times of high tide and low tides this was not feasible

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00_Op Amp intergrator, diff and other applications

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  1. 00_Op Amp intergrator, diff and other applications Case Study : How to do integration and differentiation before digital electronic computers • Choice #1: analytically • BUT: for calculation of e.g. the times of high tide and low tides this was not feasible • Solution: mechanical Integrators and Differentiators  large machines • High cost, not always too accurate (http://www.usscod.org/tdc-restore.html) • From the 1950s … 1960s: analogue electronic integrators with the help of OP AMPs W. Bergholz GEE2 Spring 2012

  2. 21_Op Amp intergrator, diff and other applications Op Amp as an integrator: • Why does it integrate the input voltage? W. Bergholz GEE2 Spring 2012

  3. 21_Op Amp intergrator, diff and other applications Op Amp as an integrator: W. Bergholz GEE2 Spring 2012

  4. 21_Op Amp intergrator, diff and other applications Op Amp as an integrator: W. Bergholz GEE2 Spring 2012

  5. 21_Op Amp intergrator, diff and other applications • Improvement of plot? W. Bergholz GEE2 Spring 2012

  6. 21_Op Amp intergrator, diff and other applications • Improvement of plot? • Log log plot •  straight line •  slope -1 W. Bergholz GEE2 Spring 2012

  7. 21_Op Amp intergrator, diff and other applications Op Amp as differentiator: W. Bergholz GEE2 Spring 2012

  8. 21_Op Amp intergrator, diff and other applications Op Amp as differentiator: W. Bergholz GEE2 Spring 2012

  9. 21_Op Amp intergrator, diff and other applications Op Amp as integrator / differentiator: • Up to now, we have done our calculations in the timedomain • The magnitude and the phase shift of the output signal can –of course - also be worked out using • the frequency representation, i.e. the complex reactance of the capacitor • including the negative sign of the gain Xc = -j/C Gain = - Xc/RI for the integrator (i.e. Inverting amp and an additional phase shift of -90 degrees) W. Bergholz GEE2 Spring 2012

  10. 21_Op Amp intergrator, diff and other applications 2 feedback paths Op amp as a square wave oscillator: W. Bergholz GEE2 Spring 2012

  11. 21_Op Amp intergrator, diff and other applications Op amp as a square wave oscillator: • How does this work out in detail? • NI = non inverting input, II= inverting input 1 2 2 1 W. Bergholz GEE2 Spring 2012

  12. 21_Op Amp intergrator, diff and other applications Op amp as a square wave oscillator: • How does this work out in detail? 3 2 3 1 W. Bergholz GEE2 Spring 2012

  13. 21_Op Amp intergrator, diff and other applications Op amp as a square wave oscillator: • Result 2 3 1 W. Bergholz GEE2 Spring 2012

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