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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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slide1

Amplifiers and Feedback 1

Dr. Un-ki Yang

Particle Physics Group

ukyang@hep.manchester.ac.uk or Shuster 5.15

real experiment
Real Experiment
  • How can we catch cosmic particles & measure their energies?
real experiment1
Real Experiment

Trigger

cosmic ray

scintillator

coincidence

integration

Signal

ADC

X10

Amp.

outline
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)
basic circuit theory
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
dividers
Dividers
  • Voltage Divider
  • Current Divider
ac circuit
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
ac circuit with capacitor inductance
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)
rc circuit with sinusoidal source
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
capacitor
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

rc low pass filter1
RC Low-pass filter

R

Vin

Vout

C

  • Low pas filter acts as an integrator at high frequency
rc high pass filter
RC High-pass filter
  • High pass filter acts as a differentiator at low frequency

Vin

Vout

amplifiers
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”
negative feedback
Negative Feedback
  • An overall gain G is independent of G0, but only depends on 
  • Stable gain
operational amplifier
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 )
op amplifier 741
OP Amplifier 741

+15V

V+

Vout

V-

-15V

Many interesting features about OP amplifier

http://www.allaboutcircuits.com/vol_3/chpt_8/3.html

non inverting amplifier
Non-inverting Amplifier

Golden rules

Infinite Gain Approx. (IGA)

  • Small v(=V+- V-): V+=V-
  • Small input currents:

I+=I-=0 (large Zin)

inverting amplifier
Inverting Amplifier
  • Inverting Amplifier

Golden rule: V+= V-

(v- is at virtual ground)

Calculate gain!

differentiator
Differentiator

Not necessary

to assume

Vin>>V-

realistic op amplifier
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
slide24
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

slew rate
Slew Rate

t

  • Output response is not instantaneous
  • Slew rate: the rate at which the output voltage can change: V/t
output impedance
Output Impedance
  • Vout will drop by r/(r+R), thus output impedance can be measured using an external register, r