dr. un-ki yang particle physics group
DESCRIPTION
Amplifiers and Feedback 1. Dr. Un-ki Yang Particle Physics Group. [email protected] or Shuster 5.15. Real Experiment. How can we catch cosmic particles & measure their energies?. Real Experiment. Trigger. cosmic ray. scintillator. coincidence. integration. - PowerPoint PPT PresentationTRANSCRIPT
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Dr. Un-ki Yang
Particle Physics Group
[email protected] or Shuster 5.15
Amplifiers and Feedback 1Amplifiers and Feedback 1
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Real Experiment
How can we catch cosmic particles & measure their energies?
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Real Experiment
Trigger
coincidence
cosmic ray
scintillator
Signal
X10Amp.
integration
ADC
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OutlineOutline
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 (1st) , Oct 19 & Oct 26 (2nd)
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Lecture notes and references
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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)
ΣiVi = 0
Σi Ii = 0
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Dividers
Voltage Divider
Current Divider
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AC Circuit
Alternating current (AC) circuits: v(t), i(t)
Consider v(t), i(t) with sinusoidal sources
v(t) =V0 cos(ωt+φv), i(t) =I 0 cos(ωt+φI )
v(t) =V0ej (ωt+φv ), i(t) =I 0e
j (ωt+φI )
Extension of Ohm’s law to AC circuits
v(ω,t) =Z(ω)i(ω,t),Zisageneralizedresistance:"impedance"
Z is a complex number
is a phase
Z = Z eiφ
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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)
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RC Circuit with Sinusoidal Source
Resistive impedance: ZR=R,
• same phase
Capacitive impedance: Zc = 1/jωC, • -/2 phase
Inductive impedance: ZL = jωL,
• /2 phase
v(t)−Ri(t) =0
v(t)−q(t) /C =0
v(t)−Ldi(t) / dt=0
v(t) =V0ejωt, i(t) =I 0e
jωt
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Capacitor
Circuit with capacitor
v =V0 cosωt⇔ V0ejωt
v=q /C V C
i(t)
Z(ω) -/2 phase
In a DC circuit, ω0inf
it acts like an open circuit The current leads the voltage
by 90o
v(t) =i(t) / jωCZ=−j /ωC
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RC Low-Pass Filter
G ≡Vout
Vin
=1
1+ jωRC
R
CVin Vout
ω → 0 ⇒ G(ω) →Glow = 1
ω → ∞ ⇒ G(ω) →Ghigh =1
jωRC
Ghigh =1
RCω −1
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RC Low-pass filter
Low pas filter acts as an integrator at high frequency
IR =IC
IR =Vin −Vout
R, IC =C
dVout
dtVin −Vout
R=C
dVout
dtifVin ? Vout(lowgain:highω)Vin
R≈C
dVout
dt
Vout =1
RCVindt∫
R
CVin Vout
VIN (t) Vejωt
Ghigh 1
jwRC
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RC High-pass filter
High pass filter acts as a differentiator at low frequency
Vin Vout
Vout =R
R+1 / jωCVin
Vout =jωRC
1+ jωRCVin
G≡Vout
Vin
=jωRC
1+ jωRC
ω → 0 ⇒ G(ω ) →Glow = jωRC
ω → ∞ ⇒ G(ω ) →Ghigh = 1
Vout = RCd
dtVIN at low frequency
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RC circuits
Low-pass
filter
high ω
High-pass
filter
low ω
1
jwRC
ω → 0 ω → ∞
jwRC
1
1
Vout =1
RCVindt∫
Vout =RCddt
VIN
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Amplifiers
The amplification (gain) of a circuit
G = VOUT / VIN
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”
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Negative Feedback
An overall gain G is independent of G0, but only depends on
Stable gain
VOUT =G0v, VOUT =VIN + VOUT
VOUT =G0
1−GO
VIN
G ≈−
1,ifG0 ? 1
Vout =G0V, V=VIN + Vout
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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 )
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OP Amplifier 741
Many interesting features about OP amplifier http://www.allaboutcircuits.com/vol_3/chpt_8/3.html
+15V
-15V
VoutV-
V+
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Non-inverting Amplifier
Golden rules Infinite Gain Approx. (IGA)Small v(=V+- V-): V+=V-
Small input currents:
I+=I-=0 (large Zin)
G =VOUT
VIN
≈1=
R1 + R2
R1
,
ifG0 ? 1
V−=VOUT
R1
R1 + R2
VOUT =G0 (V+ −V−), VIN =V+
G =VOUT
VIN
=G0
1+R1
R1 + R2
G0
⎛
⎝⎜⎞
⎠⎟
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Inverting Amplifier
Inverting Amplifier
Golden rule: V+= V- (v- is at virtual ground)
Calculate gain!
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Differentiator
Vin −V−
ZC
=V−−Vout
R
−jwCVin =Vout
RwhereV+ =0&V+ =V−, thusV−=0
G =VOUT
VIN
=−RZC
=−jwCR
Vout =−RCddt
VIN
Not necessaryto assume
Vin>>V-
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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
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Gain
Open gain, Go ~ 105: const. for a small range
Go
G
Closed gain, G(R,C): const. for a wide range
-3dB dB =20 logVOUT
VIN
=10 logPOUT
PIN
20 log(G / 2 ) =20 logG−3Bandwidth
Bandwidth: the range of frequencies for gain to be within 3dB
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Slew Rate
Output response is not instantaneous
Slew rate: the rate at which the output voltage can change: V/t
t
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Output Impedance
Vout will drop by r/(r+R), thus output impedance can be measured using an external register, r
VOUT ⇒r
r + RVOUT