Noise Cancellation Methods
1.
2.
3.
4.
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Filtering, down-conversion
Sideband cancellation
Balanced mixers
Reducing calibration noise
T1
Noise Cancellation Methods
Example 1: canceling unwanted sidebands by filtering
Want Q >> f f for filter where Q ∆ f ∆f
o i.f .
o
Φ(f)
L.O.
∆ω
LSB
i.f. passband
fi.f.
f
fo
L.O. noise
sidebands
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T2
Noise Cancellation Methods
Example 2: dual-down conversion with lower Q
HA ( f ) 2
fo − f1
fo
A
fo
×
B
f1 ≅ fo
f2
∆fA
f2 − f1 − fo
×
image
C
f2 << f1
0
Q ≅ f1 ∆fA ≅ f2 ∆fB
f1
fo
f
HB ( f ) 2
Multiple conversion required when:
f1 fi.f . ~
> QMAX 3
⎛
⎜ e.g. triple conversion if
⎜
⎝
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∆fB
2⎞
f1 ~ ⎛ Q ⎞ ⎟
>⎜ ⎟
fi.f . ⎝ 3 ⎠ ⎟
⎠
0
f
fo − f1
f2
T3
900-GHz Wireless Phone
> QMAX 3
f1 fi.f . ~
⎛
⎜ e.g. triple conversion if
⎜
⎝
HC ( f ) 2
f1 ~ ⎛ Q ⎞ 2 ⎞⎟
>⎜ ⎟
fi.f . ⎝ 3 ⎠ ⎟
⎠
Let f1 ≅ 108 , fi.f. ≅ 10 4
If Q = 100 (for RLC filter)
0
f
fi.f . = f2 − fo − f1
2
f1
100
= 10 4 >
, Therefore we need triple conversion
fi.f .
9
Surface Acoustic Wave (SAW) filters have Q ≅ 104, and
Q~
> 105 for crystal filters, so double conversion works here
(
)
with SAW filters 10 4 > 10 4 3 , and single conversion with
(
crystal filters (for one 10-kHz channel) 10 4 < 105 3
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)
T4
Example 3: Sideband Cancellation
×
B
S(t)
D
LAG
90°
F
+
C
×
E
+
+
cos ωot
LAG 90°
upper
sideband
USB
LPF
+
-
LPF
Recall:
cos ωo t =
j
e
jωo t
+e
2
− jωo t
1/2
− fo
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LSB
lower
sideband
L.O. “A”
1/2
fo
0
j
e jωo t − e − jωo t
sin ωo t =
2j
+
f
L.O. “B”
1/2
fo
− fo
0
f
-1/2
T5
Example 3: Sideband Cancellation
E = s(t) cos ωo t
U
S(f)
UL
LU
L
L.O.
U
L L
U L
0
-2fo
U
f
2fo
D = s(t)sin ωo t
L L
-2fo
U
U
L L
2fo
E +
diff
F -
⎧× ( − j) for f > 0
F( f ) ⇐ ⎨
⎩× ( j) for f < 0 (as result of 90° delay)
U
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L L
U
L L
2U
2U
f
0
U
⇓
U
f
0
E +
sum
F+
j
U
f
U
90° ± δ ⇒
B ~
< 0 .1
fo
2L
2L
0
f
Note: Analog signals can
be converted to digital at
any point in these circuits
T6
Example 4: Calibration
ideal
actual
gain
baseline
volts
Calibrate:
•gain
•baseline
•linearity
Example: cosmic background measurement
Optical depth τ ≅ 0.01 on 12,000-ft mountain
3°K
θ
ATM
~250°K
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T7
Example 4: Calibration
Ferrite circulator
(isolator)
(~0.4 dB; 20 dB)
main
antenna
Zo
out
×
Dicke
switch
L.O.
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Frequency meter
T8
Example 4: Calibration
Issues:
1) switch assymetry
sky
measure on sky
2) TB of He load (~4°K)
(Note hf << kTT)
vs
3) Liquid helium load VSWR
4) Isolator? (effects of LO and 2fLO leakage and
reflection from Dicke and calibration switches)
temperature
dependence
5) Atmospheric contribution
In general
1) Design for calibration; seek symmetry and redundancy
2) Use lab calibration, internal calibration, sky calibration sources
3) Use antenna pattern ranges
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T9
Example 5: Local Oscillator Noise Cancellation
USB
I.F.
0
f
LSB
f L.O.
1)
2)
3)
4)
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use quiet L.O.’s
filter the L.O’s
use high fi.f.
cancellation (balanced mixers)
V1
Example 6: Balanced Mixers
i, v out
i
vd
v in +
-
v out
i.f. signal
RL
v in = v LO + v sig
v → LPF
i.f. at beat freq. = fi.f .
⇓
i.f. signal
local osc. alone
LO and r.f. signal add, so vin produces i.f. component in vout
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V2
Example 6: Balanced Mixers
signal
output
Cancels L.O. noise, which is identical at both diodes
Signals are 180° out of phase, add
Note field symmetries: at i.f. [even] × [odd] = [odd]
L.O. (original)
output
reversed diodes cancel L.O. noise upon addition
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V3
Example 6: Balanced Mixers
Also:
3-dB hybrid
90° phase difference
signal
signal
waveguide
3dB
L.O.
L.O.
3-dB sidewall coupling
Another balanced mixer
waveguide
Time domain:
i(t)
rectified
t
signal or L.O.
-λ/4
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double balanced
mixer
or
V4
Optical detection
Classification of detectors:
Before:
Now:
Next:
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hf << kT
hf >> kT
hf ≅ kT
Rayleigh-Jeans radio limit
Optical limit (photon counting)
Infrared
A1
Photoelectric effect
E
~ 0.1 v @ 105 V cm ; ~ 1.2 V @ 107 V cm
work function
eφm
EF (Fermi level)
metal
z
e2
, z > zmin
image charge energy =
16 πεo z
eEz
~10 – 60 Å
vacuum
zmin is ~1 angstrom when electron “sea” vanishes; yields eφm
φm = 1.95 (cesium), 2.1 (rubidium), 2.3 (lithium) volts
≅ 4 – 5 volts, most common metals
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A2
Photoelectric effect
φm = 1.95 (cesium), 2.1 (rubidium), 2.3 (lithium) volts
≅ 4 – 5 volts, most common metals
φm sensitive to surface contamination and microstructure: local E
hf ~
> φme ⇒ emission [1 e.v. = e Joules]
hc
λ c.o. = c fc.o. =
≅ 0.6 − 0.7 µm for cesium
eφm
Tunneling is important for short leaps and high Ez
~ 1 µm cutoff wavelength)
(Microstructure, etc ⇒
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A3
Phototubes
-
+V
i(t)
hf
cathode
e
L
vacuum
+
RL
vo(t) = RL i(t)
-
anode
quantum efficiency η~< 30% for Ge, Si
i(t)
i( t ) = e v eI L = e at L ≅ e2 Vt meL2
a = dv dt = f me = eV me L
Problem:
e
0
t
single electron voltage spikes are lost in RL Johnson noise.
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A4
Photomultiplier Tubes (PMT’s)
dynode
cathode
anode
hf
+
+V
RL
PMT
-
+V
vo(t)
-
7 – 13 dynodes typical, G ≅ 104 – 107
With 104 – 107 electrons per detected photon,
Johnson noise from RL becomes negligible.
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A5
Photomultiplier Tubes (PMT’s)
7 – 13 dynodes typical, G ≅ 104 – 107
With 104 – 107 electrons per detected photon,
Johnson noise from RL becomes negligible.
Number of electrons emitted per dynode hit
≅ (V1/φm) • Q ≈ 4, say [impact efficiency Q < 1]
(V1 = electron kinetic energy)
Dark current from cosmic rays, thermal, etc.
(note: smaller pulses from dynodes permit rejection)
(Thermal: 1 e.v. ≈ 104K; so modest cooling helps)
> 1000 sec-1 typically
Dark count nD ~
Counting rate ~10 MHz – 1 GHz + or more
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A6