1 Dr. Un-ki Yang Particle Physics Group or Shuster 5.15 Amplifiers and Feedback 1

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

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

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, integrator, phase shifter, and oscillator To understand the limitations of a real amplifier To understand basic methods of analogue-to-digital conversion (ADC)  Lectures: 4 hours lectures (2 hours per day) Oct. 5 & Oct. 12 (1 st ), Oct 19 & Oct 26 (2 nd )

5 Lecture notes and references

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 Dividers  Voltage Divider  Current Divider

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 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: Z R =R, same phase  Capacitive impedance: Zc = 1/j  C, -  /2 phase  Inductive impedance: Z L = j  L,  /2 phase

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 RC Low-Pass Filter R C VinVout

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

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

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

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 G 0, but only depends on   Stable gain

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 OP Amplifier 741 Many interesting features about OP amplifier +15V -15V Vout V- V+V+

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 V in >>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  Open gain, G o ~ 10 5 : const. for a small range GoGo G  Closed gain, G(R,C): const. for a wide range -3dB Bandwidth  Bandwidth: the range of frequencies for gain to be within 3dB

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

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