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

2. 2 Real Experiment  How can we catch cosmic particle and measure it’s energy?

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

4. 4Outline  Prerequisites: 1st-year electronics, and vibration & waves  Aims: to understand how analogue signals are amplified, manipulated, and how they can be interfaced to digital systems  Learning outcomes To understand the behavior of an ideal amplifier under negative (positive) feedback To be able to apply this to simple amplifier, summer, integrators, phase shifter, and oscillator To understand the limitations of a real amplifier ( gain, bandwidth, and impedance) To understand basic methods of analogue-to-digital conversion (ADC)  Lectures: 3 lectures (2 hours per each) Nov 10, Nov 17, and Nov 24

5. 5 Lecture notes and references

6. 6 Basic Circuit Theory  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  Kirchoff’s Laws Conservation of energy: for a closed loop Conservation of charge: net charge into a point (node)

7. 7 Dividers  Voltage Divider  Current Divider

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

9. 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, dv/dt = 1/C dq/dt = i/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. 10 RC Circuit with Sinusoidal Source  Resistive impedance: Z R =R, same phase  Capacitive impedance: Zc = 1/j  C, -  /2 phase  Inductive impedance: Z L = j  L,  /2 phase

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

12. 12 RC Low-Pass Filter R C VinVout

13. 13 RC Low-pass filter  Low pas filter acts as an integrator at high frequency R C VinVout

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

15. 15 RC circuits Low-pass filter high  High-pass filter low 

16. 16 Combined Impedance Vin Vout

17. 17 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”

18. 18 Operational Amplifier  Vout =G 0 (V + - V - ) (called as differential amp.) Vout = - G 0 V -, if V + =0 : inverting amplifier Vout = G 0 V +, if V - =0 : non-inverting amplifier  Amplifier with a large voltage gain (~10 5 )  High Zin (~10 6  )  Low Zout(<100  )

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

20. 20 Negative Feedback  An overall gain G is independent of G 0, but only depends on   Stable gain

21. 21 Non-inverting Amplifier  Golden rules: Infinite Gain Approximation (IGA) Small  v(=v + - v - ): v + =v - Small input currents: I + =I - =0 (large Zin)

22. 22 Inverting Amplifier  Inverting Amplifier Golden rule: v + = v - ( v - is at virtual ground) Calculate gain!

23. 23 Differentiation  Differentiation circuit Golden rule: v + = v - ( v - is at virtual ground)  Prove this is a differentiation circuit!  How would you configure to make an integration circuit?

24. 24 Summer circuit  Summer Circuit v - is a virtual ground Prove that

25. 25 Phase shifter Golden rule: v + = v -  Calculate a phase shift