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Dr. Un-ki Yang Particle Physics Group

Amplifiers and Feedback 1. Dr. Un-ki Yang Particle Physics Group. ukyang@hep.manchester.ac.uk or Shuster 5.15. Real Experiment. How can we catch cosmic particles & measure their energies?. Real Experiment. Trigger. cosmic ray. scintillator. coincidence. integration.

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Dr. Un-ki Yang Particle Physics Group

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  1. Amplifiers and Feedback 1 Dr. Un-ki Yang Particle Physics Group ukyang@hep.manchester.ac.uk or Shuster 5.15

  2. Real Experiment • How can we catch cosmic particles & measure their energies?

  3. Real Experiment Trigger cosmic ray scintillator coincidence integration Signal ADC X10 Amp.

  4. Outline • Aims: to understand how analogue signals are amplified, manipulated, and how they can be interfaced to digital systems • Prerequisites: 1st-year electronics, and vibration & waves • Lectures: 4 hours lectures (2 hours per day) • Oct. 5 & Oct. 12 (1st) , Oct 19 & Oct 26 (2nd) • Learning outcomes • To understand the behavior of an ideal amplifier • under negative (positive) feedback • To be able to apply this to simple amplifier, summer, integrator, phase shifter, and oscillator • To understand the limitations of a real amplifier • To understand basic methods of analogue-to-digital conversion (ADC)

  5. Lecture notes and references

  6. Basic Circuit Theory • Kirchoff’s Laws • Conservation of energy: for a closed loop • Conservation of charge: net charge into a point (node) • Ohm’s Law: V = IR • V is the potential difference across the resister • R is the resister (): typically k   • I is the current (A): typically mA

  7. Dividers • Voltage Divider • Current Divider

  8. AC Circuit • Z is a complex number  is a phase • Alternating current (AC) circuits: v(t), i(t) Consider v(t), i(t) with sinusoidal sources • Extension of Ohm’s law to AC circuits

  9. AC Circuit with Capacitor & Inductance • In AC circuit, capacitance (C) and inductance (L) are used to store energy in electric and magnetic fields • Capacitance : v = q/C • Source of i and v • To smooth a sudden change in voltage • Typically F or pF (farad) • Inductance : v = L di/dt • To smooth sudden change in current • Typically H or mH (henry)

  10. RC Circuit with Sinusoidal Source • Resistive impedance: ZR=R, • same phase • Capacitive impedance: Zc = 1/jC, • -/2 phase • Inductive impedance: ZL = jL, • /2 phase

  11. Capacitor i(t) V C -/2 phase Z() • Circuit with capacitor • In a DC circuit, inf it acts like an open circuit • The current leads the voltage by 90o

  12. RC Low-Pass Filter R Vin Vout C

  13. RC Low-pass filter R Vin Vout C • Low pas filter acts as an integrator at high frequency

  14. RC High-pass filter • High pass filter acts as a differentiator at low frequency Vin Vout

  15. RC circuits

  16. Amplifiers • The amplification (gain) of a circuit • Ideal amplifier • Large but stable gain • Gain is independent of frequency • Large input impedance (not to draw too much current) • Small output impedance • Obtained by “negative feedback”

  17. Negative Feedback • An overall gain G is independent of G0, but only depends on  • Stable gain

  18. Operational Amplifier • Vout =G0 (V+ - V-) (called as differential amp.) • Vout = - G0 V- , if V+ =0 : inverting amplifier • Vout = G0 V+ , if V- =0 : non-inverting amplifier • Amplifier with a large voltage gain (~105) • High Zin (~106 ) • Low Zout(<100 )

  19. OP Amplifier 741 +15V V+ Vout V- -15V Many interesting features about OP amplifier http://www.allaboutcircuits.com/vol_3/chpt_8/3.html

  20. Non-inverting Amplifier Golden rules Infinite Gain Approx. (IGA) • Small v(=V+- V-): V+=V- • Small input currents: I+=I-=0 (large Zin)

  21. Inverting Amplifier • Inverting Amplifier Golden rule: V+= V- (v- is at virtual ground) Calculate gain!

  22. Differentiator Not necessary to assume Vin>>V-

  23. Realistic OP Amplifier • Gain is NOT infinite • Gain is NOT constant against frequency • Output response is NOT instantaneous • Gain drops at high frequency • Bandwidth: a stable range, -3dB • Slew rate: response rate

  24. Gain • Closed gain, G(R,C): const. for a wide range G -3dB Bandwidth • Bandwidth: the range of frequencies for gain to be within 3dB • Open gain, Go ~ 105: const. for a small range Go

  25. Slew Rate t • Output response is not instantaneous • Slew rate: the rate at which the output voltage can change: V/t

  26. Output Impedance • Vout will drop by r/(r+R), thus output impedance can be measured using an external register, r

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