Noise - A stench to the ear,
Undomesticated music,
The chief product and
authenticating sign of
civilization
Ambrose Bierce - “The Devils Dictionary” 1907
Craig Nelson
National Institute of Standards and Technology
325 Broadway
Boulder, CO 80303
Email : craig.nelson@boulder.nist.gov
Newport
San Francisco
Beach201
2010
1
1
Topics
•
•
•
•
•
•
San Francisco 2011
Introduction and Review
Noise Types
Measurement Methods
Measurement Calibration
Common Measurement Problems
�
Conclusions
2
Weather Monitoring
RADAR
Satellite Communication
INDUSTRY and MILITARY
NEEDS for
SPECTRAL PURITY
Imaging RADAR
•Navigation
•Defense & Homeland Security
•Secure Communication
•Astronomy & Geodesy
San Francisco 2011
Noise Metrology
Atomic Frequency
Standards &
Spectroscopy
3
NOISE
PM Noise
AM Noise
2. 5
2
2
1. 5
1. 5
1
1
0. 5
0. 5
0
0
0
90
180
270
360
450
540
-0. 5
0
90
180
270
360
450
540
-0. 5
-1
-1
-1. 5
-1. 5
-2
-2
-2. 5
60
60
50
50
40
40
30
30
20
20
10
10
0
0
1
San Francisco 2011
10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235 244 253
1
10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235 244 253
4
Difficulty of using a Spectrum Analyzer
• IF bandwidth too wide
• SA internal reference too noisy
• Not enough dynamic range
• Phase noise is often below -170 dBc
• Cannot distinguish between AM and PM noise
San Francisco 2011
5
Power
Single Sideband Modulation
Frequency
San Francisco 2011
6
Power
Amplitude Modulation
Frequency
San Francisco 2011
7
Power
Phase Modulation
Frequency
San Francisco 2011
8
San Francisco 2011
9
Theory Review
Basic Model for Noisy Signal
V (t ) = A (1 + α (t )) cos(2π υ 0 t + φ (t ))
where:
A
= average amplitude
α (t ) = fractional amplitude fluctuations
υ0 = average frequency
φ (t ) = phase flucuations
San Francisco 2011
10
Basic Definitions
V (t ) = A(1 + α (t )) cos(2πυ0t + φ (t ))
phase = 2πυ0t + φ (t)
d
ω (t ) =
[ phase]
dt
1 d
1 d
υ (t) =
[2πυ 0t + φ ((t)]
t)] = υ0 +
φ ((tt)
)
2π dt
2π dt
Fractional frequency deviation
υ (t ) − υ 0
1 d
y (t ) =
=
φ (t )
υ0
2πυ 0 dt
2
1
YT ( f ) 2
S y ( f ) = P S D [ y ( t )] =
T
San Francisco 2011
0< f < ∞
1
[
]
Hz
11
Definition of Phase Noise
2
2
1
Sφ ( f ) = PSD (φ (t)) = Φ T ( f )
T
0< f <∞
rad 2
[
]
Hz
Single sideband phase noise
2
L( f ) ≡
1
2
Sφ ( f ) [dBc / Hz]
⎛ υ0 ⎞
Sφ ( f ) = ⎜ ⎟ S y ( f )
⎝ f ⎠
Definition of Amplitude Noise
2
2
Sα ( f ) = PSD (α (t )) = ΑT ( f )
T
1
San Francisco 2011
0< f <∞
1
[ ]
Hz
12
Noise Types
• Additive Noise
f
0
• Thermal
• Shot noise
• Multiplicative Noise
• Flicker
f −1
• Higher order colored noise types
San Francisco 2011
f −2 , f −3 , f −4 ...
13
Pow
er
Power
Additive Noise
Frequency
San Francisco 2011
14
Pow
er
Power
Additive Noise
Frequency
San Francisco 2011
15
P
ower
Power
Pha
se Noise
Phase
Additive Noise
Frequency
Fourier Frequency
Since it is uncorrelated to the carrier, additive noise always
appears as equal amount of AM and PM Noise.
For Amplifiers:
San Francisco 2011
kTB
Sϕ ( f ) = S a ( f ) =
NF = −174 + NF − PI @ 300 K
PI
16
Pow
er
Power
Multiplicative Noise
Frequency
San Francisco 2011
17
Pow
er
Power
Multiplicative Noise
Frequency
San Francisco 2011
18
P
ower
Power
Pha
se Noise
Phase
Additive and Multiplicative Noise
Frequency
San Francisco 2011
Fourier Frequency
19
Additive and Multiplicative Noise
10 GHz, Gain=32.5dB, NF=1
-100
Pin=-43.3dBm
Pin=-33.2dBm
Pin=-29.2dBm
Pin=-24.28
Pin=-21.22dBm, 1dB compression
L(f) [dBc/
z]
[dBc/H
Hz]
-110
-120
-130
-140
-150
-160
1E+2
1E+3
1E+4
1E+5
1E+6
Offset Frequency [Hz]
San Francisco 2011
20
Noise Figure
•Noise figure is only a figure of merit of thermal additive noise.
•It has ZERO correlation to flicker or any other type of
multiplicative noise
•In the linear region of operation. The phase noise floor for a
device can be determined from input power and noise figure
as follows:
Sϕ ( floor ) = Sα ( floor ) =
L ( floor )
San Francisco 2011
kT0 BNF
Pin
= −174 + NF − Pin
[dBrad 2 / Hz ] or [dB / Hz ]
= −177 + NF − Pin
[dBc / Hz ]
21
Multiplicative AM Noise
Ic
g m ≅ VITc
Unlike additive noise, multiplicative AM and PM are not
fundamentally correlated because they up convert
by different mechanisms.
San Francisco 2011
22
Multiplicative PM Noise
Ic
High Linearity => Low Multiplicative PM Noise (Flicker)
Separation between P1dB and IP3 is a simple indicator
> 15 dB has potential for low flicker
San Francisco 2011
23
Typical PM Flicker Noise for Different
Semiconductor Types
�
-110
X-Band GaAs AMP
SSB Phase Noise [d
[dBc/Hz]
Bc/Hz]
-120
-130
-140
X-Band HBT
X-Band Schottky Mixer
L-Band BJT
HBT Amp
-150
-160
-170
1E+0
HF-VHF BJT
HF-UHF Schottky Mixer
1E+1
1E+2
1E+3
1E+4
1E+5
1E+6
Offset Frequency [Hz]
San Francisco 2011
Courtesy of M. Driscoll
24
Noise Summary
Additive Noise Summary
•
•
•
Noise power is uncorrelated to signal power
AM = PM
AM and PM noise levels var
varyy inversel
inverselyy with carrier p
power
ower
Multiplicative Noise Summary
•
•
•
Noise power is correlated to signal power
AM ≠ PM
AM and PM noise levels are independent of carrier power
�
San Francisco 2011
25
Typical Noise Types
• Passive Devices
• Thermal f 0
• Some have flicker (magnetics, carbon resistors)
f -1
• Higher order noise may come from temperature effects f -4
• Active Devices
• Almost all have thermal and flicker
• Possible temperature effects f -4
�
-1
f 0 and f -1
�
• Sources ( May some or all of the higher order types )
•
•
•
•
•
White PM or Thermal
Flicker PM
White FM
Flicker FM
Random Walk
San Francisco 2011
f 0
�
f -1
�
f -2
f -3
f -4
26
Noise Types
f
−4
−3
White frequency
Flicker Frequency
f
−2
f
0
log[(σy)(f)]
f
log[(Sφ)(f)]
Random Walk
τ −1
τ
τ
−1
1
2
2
τ0
White phase
f −1
Flicker phase
log (Fourier Frequency)
log (τ)
White phase
Flicker phase
White frequency
Thermal Noise, Shot Noise
Electronics, recombination-generation, traps
Resonator, integrated white phase
Flicker Frequency
Resonator, integrated flicker phase
Random Walk
Temperature, Shock, Vibration, Resonator
San Francisco 2011
27
Leeson’s Effect
Resonator
Barkhausen
Gain = 1
Phase Shift = 2 π n
Phase Shifter
San Francisco 2011
Amplifier
28
Noise
Phase Noise
Leeson’s Effect - Low Q
2
fc ⎛ f0 ⎞ ⎛
fc ⎞⎤
FkT ⎡
⎢1 + + ⎜
Sϕ ( f ) =
⎟ ⎜1 + ⎟ ⎥
Pa ⎢
f ⎝ 2 fQL ⎠ ⎝
f ⎠⎥
⎣
⎦
f −3
Oscillator Noise
f
−1
Half
f0
Resonator 2Q
L
Bandwidth
f −2
f0
fc
Amplifier Noise
Fourier Frequency
San Francisco 2011
29
Leeson’s Effect - High Q
Half Resonator Bandwidth
Phase Noise
Noise
f0
2QL
2
⎡
fc ⎛ f0 ⎞ ⎛
fc ⎞⎤
FkT
⎢1 + + ⎜
Sϕ ( f ) =
⎟ ⎜1 + ⎟ ⎥
Pa ⎢
f ⎝ 2 fQL ⎠ ⎝
f ⎠⎥
⎣
⎦
f −3
f −1
Oscillator Noise
fc
f0
Amplifier Noise
Fourier Frequency
San Francisco 2011
30
Four Sources at Different Frequencies and
Similar Power
�
0
SSB Phase Noise [[d
Bc/Hz]
dBc/Hz]
-20
10 GHz
DRO
-40
-60
-80
-100
-120
-140
-160
-180
1E+0
500 MHz
SAW
100 MHz
OCXO
5 MHz
OCXO
1E+1
1E+2
1E+3
1E+4
1E+5
1E+6
1E+7
Offset Frequency [Hz]
San Francisco 2011
31
All Sources Normalized to 10 GHz
0
10 GHz
DRO
SSB Phase Noise [[d
dBc/Hz]
Bc/Hz]
-20
500 MHz
SAW
-40
-60
100 MHz
OCXO
-80
-100
-120
5 MHz
OCXO
-140
-160
-180
1E+0
1E+1
1E+2
1E+3
1E+4
1E+5
1E+6
1E+7
Offset Frequency [Hz]
San Francisco 2011
32
Composite Phase Noise Synthesis
0
10 GHz
DRO
SSB Phase Noise [[d
dBc/Hz]
Bc/Hz]
-20
500 MHz
SAW
-40
-60
100 MHz
OCXO
-80
-100
-120
5 MHz
OCXO
-140
-160
-180
1E+0
1E+1
1E+2
1E+3
1E+4
1E+5
1E+6
1E+7
Offset Frequency [Hz]
San Francisco 2011
33
Effects of Frequency
Manipulation on Phase Noise
Translation or Mixing
S Aφ ( f )
S
B
San Francisco 2011
φ
(f)
S
SMφ( f )
A
φ
(f)+S
•
•
•
B
φ
(f )+ S
M
φ
(f)
Residual Noise
AM to PM Conversion
Noise Folding
34
Frequency Multiplication
v2 (t ) = cos[ N(ωt + ϕ (t )]
ω2 = Nω
Phase Noi
se
Noise
2
2
Sφ 2 ( f ) = N Φ1,T ( f ) = N 2 Sφ ( f )
T
20 LogN dB
Ideal Response
Typical Response
Multiplier Noise Floor
Oscillator Noise
San Francisco 2011
Fourier Frequency
35
Frequency Division
1
v2 (t ) = cos[ (ωt + ϕ (t )]
N
ω2 =
ω
N
2
Phase Nois
e
Noise
Sϕ ( f )
2 ΦT ( f )
Sφ 2 ( f ) =
=
T
N
N2
Oscillator Noise
20 LogN dB
Typical Response
Divider Noise Floor
Ideal Response
San Francisco 2011
Fourier Frequency
36
Extracting Noise
Two noisy signals
V1(t) = A1(1+α1(t))cos(ω1t +ϕ1(t))
V2 (t) = A2 (1+α2 (t))cos(ω2t +ϕ2 (t))
Multiply them together
⎡ A1 A2 (1 + α1 ( t ) + α 2 ( t ) + α1α 2 ( t )) ⎤
V1 ( t ) i V2 ( t ) = ⎢
⎥ i
2
⎣
⎦
{cos ⎡⎣(ω + ω ) t + ϕ ( t ) + ϕ
1
San Francisco 2011
2
1
2
( t )⎤⎦ + cos ⎡⎣(ω1 − ω2 ) t + ϕ1 ( t ) − ϕ2 ( t )⎤⎦}
37
Phase Noise
Set ω = ω1 = ω2 and lowpass filter
⎡ A1 A2 (1+ α1 ( t ) + α 2 ( t ) + α1α 2 ( t )) ⎤
V1 ( t ) i V2⎡(At )A= (1+
⎢ α1 ( t ) + α 2 ( t ) + α1α 2 ( t )) ⎤
⎥ i
1 2
2
⎣
⎢
⎥ cos ⎡⎣ϕ1⎦( t ) − ϕ2 ( t ) + φ3 ⎤⎦
2
⎣
{cos ⎣⎡(ω (2+ωω)t ) t + ϕ ( t ) + ϕ
1
When φ3 = 90°
2
1
⎦
2
sin x ≅ x,
( t )⎦⎤ + cos ⎣⎡(ω1 − ω2 ) t + ϕ1 ( t ) − ϕ2 ( t )⎦⎤}
cos(x +90) ≅ x
⎡ A1 A2 (1+ α1 ( t ) +⎡ α
A12A(2t ⎤) + α1α 2 ( t )) ⎤
cos ⎡φ t − φ t + 90⎤⎦
⎢
⎢ 2 2 ⎥ ⎡⎣φ1 ( t ) − φ2⎥ ( t ) ⎤⎦ ⎣ 1 ( ) 2 ( )
⎣
⎦
⎦
⎣
hLPF ∗ ⎡⎣V1 ( t ) iV2 ( t ) ⎤⎦ ≅ kd ⎣⎡ϕ1 ( t ) − ϕ2 ( t ) ⎤⎦ when ω1 = ω2 ∧ φ3 = 90°
San Francisco 2011
38
Amplitude Noise
ω1 = ω2
V1(t) =V2 (t) = A1[1+α1(t)]cos[ω1t +ϕ1(t)]= A2[1+α2 (t)]cos[ω2t +ϕ2 (t
)]
⎡1 A
⎡ A1 A2A
(12+(1α+
(2tα)(+1( tα+)22+(αtα)(2+t ()αt+1)α)α2 ( t()t))⎤) ⎤ co⎡s φ φ
⎢
⎢
⎥ ⎥ cos ⎣φ[1 (3t ]) − 23 ( t ) + φ3 ⎤⎦
2
22
⎦⎦
⎣
⎣
2
When φ3 = 0° and
2
os(0) = 1
c
Remove DC term and neglect higher order term
2 2
⎡ A2
⎤
A
α
2
α
t
+
t
+
A
()
( )
⎥ cos [0]
⎢
2
⎣ 2
⎦
A2
hLPF ∗ ⎣⎡V ( t ) ⎤⎦ ≅
+ kaα ( t ) when φ3 = 0°
2
2
San Francisco 2011
39
Phase Noise Measurement
Types
• Homedyne or Residual – Single source
�
• Noise Floor
• Any two port device
measurement
• Heterodyne - Two source measurement
�
• Frequency Discriminator
• Delay Line
• Cavity Resonator
• Digital Measurement Systems
San Francisco 2011
40
Two Oscillator Measurement
PLL
φ
Reference
LPF
IF AMP
V(f) = Kd (f)δφ(f
)
Source
S φ m easu red ( f ) = S φT ( f ) + S φ R ( f ) +
San Francisco 2011
P SD [V rm s syste m ( f )]
Kd2( f )
41
Noise Floor Measurement
PLL
φ
LPF
Reference
Source
�Phase
noise
IF AMP
of source cancels
[ Δ φ R ]2 ( f ) − [ Δ φ R ]2 ( f ) PSD[Vrmssystem ( f )]
Sφ NoiseFloor ( f ) =
+
2
Kd 2 ( f )
K d ( f ) BW
0
San Francisco 2011
42
Two Port Device Measurements
DUT
φ
LPF
IF AMP
Reference
DUT
�Phase
noise of source cancels
�Two devices are needed if they have a long delay
�Two devices are needed if they change the frequency
San Francisco 2011
43
System Calibration
• Static Phase shift (PM)
• Kd or Beat Frequency Method (PM)
�
• Modulation
• Single Sideband (AM/PM)
• Phase Modulation (PM)
• Frequency Modulation (PM)
• Amplitude Modulation (AM)
• Noise Standards (AM/PM)
San Francisco 2011
44
Static Phase Shift
•A known phase shift is introduced, and the corresponding
voltage change measured
•Adjustable phase shifter (mechanical or electrical)
•Switched delay lines
•Programmable phase shift in a synthesizer
Kd
V oltage C hang e
=
P hase S hift
⎡ V ⎤
⎢⎣ rad ⎦⎥
P S D [V rm s ( f )]
Sφ ( f ) =
Kd2
Remember:
L( f ) = 12 Sφ ( f ) [dBc / Hz ]
San Francisco 2011
45
Two Oscillator Beat Frequency Calibration
PLL
φ
Reference
LPF
Source
San Francisco 2011
46
Calculating Mixer Sensitivity Kd
1.5
1.0
0.5
K d (v / rad ) =
0.0
Slope
Slope
-0.5
Slope(v / s ) ⋅ T ( s )
2π ( rad )
-1.0
-1.5
0
1.57
3.14
Period T
�
4.71
6.28
Typically 0.3 to 0.4 V/rad for a
saturated double balanced
Schottky diode mixer
Make sure both positive and negative
slopes are equal in magnitude and
symmetric
San Francisco 2011
47
Single Source Kd Calibration
φ
LPF
Power Meter
50Ω
Substitution Source
San Francisco 2011
48
Mixer Sensitivity
• Frequency
• RF and LO power
• Mixer termination at all three p
ports
orts
• Cable lengths
Calibration conditions must replicate the
measurement conditions as closely as possible
San Francisco 2011
49
Possible Errors Using Kd Calibration
�
Determines gain only at a single frequency
Noise is suppressed inside PLL bandwidth
Requires open loop PLL or substitution source
�
Beat
Beat configuration
configuration does
does NOT match
match actual
�
actual
measurement configuration
�
• Injection Locking
•
•
•
•
San Francisco 2011
50
SSB Calibration Method
φ
Δ
Source
Baseband
f
SA
f
f +Δ
f +Δ
San Francisco 2011
51
Single Sideband Modulation
AM
PM
SSB
n dB
n-6
n-6dB
dB
=
Generates equal amounts of AM and PM Noise
Phase and amplitude modulation is
detected at ½ the SSB ratio
Sϕ ( f c ) ≅ Sα ( f c ) ≅
San Francisco 2011
Pν 0 + fc
2 Pν 0
≅
+
A SSB tone at n dB below the carrier
creates phase and amplitude noise with
Pν 0 − fc
Sϕ ( f cal ) = n − 3dB
2 Pν 0
Sα ( f cal ) = n − 3dB
or L ( f cal ) = n − 6dB
52
Additive Noise Calibration Method
φ
Baseband
Reference
f
bw
2
Source
f
BPF
San Francisco 2011
fc,bw
53
AM/PM Modulator
• Can be adjusted for pure PM or AM modulation
• Extremely flat frequency response
• Calibrates
Calibrates Kd(f) with
with system locked
locked
• Can be used to find true quadrature for minimizing
AM leakage
San Francisco 2011
54
AM Modulator
Calibration Port
Diode Detector
and Power Meter
or Spectrum Analyzer
Output
-20dB
-20dB
MAXIMIZE detected AM signal
By adjusting phase shifter
Sα ( f c ) ≅
Pν 0 − fc + Pν 0 + fc
Pν 0
φ
RF
IF
Modulation
Frequency
LO
-20dB
Input
San Francisco 2011
55
PM Modulator
Output
Monitor Port
Diode Detector
and Power Meter
-20dB
-20dB
MINIMIZE detected AM signal
By adjusting phase shifter
Sϕ ( f c ) ≅
Pν 0 − fc + Pν 0 + fc
Pν 0
φ
RF
IF
Modulation
Frequency
LO
-20dB
Input
San Francisco 2011
56
Tips for Measuring Gain vs. Fourier
Frequency using Swept Modulation
�
• Measure power spectrum not PSD
• Use flattop windows for FFT
• Only small number of averages required
• 3-5 points per decade
• Create gain curve with cubic spline or linear curve
• Make sure tone does not saturate IF amplifiers
San Francisco 2011
57
Calibration Curve at X-band
Relative Ga
in (dB)
Gain
30
20
10
0
-10
-20
1
Gain : 23.1
San Francisco 2011
10
100
1K
10K
100K
1M
10M
100M
Fourier Frequency(Hz)
58
Phase Noise of X-band Synthesizer
-50
Phase Noise (dBc
(dBc/Hz)
/Hz)
-70
-90
-110
-130
-150
-170
-190
1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 1E+9
Fourier Frequency (Hz)
San Francisco 2011
59
Tips for Measuring Noise
• Measure Power Spectral Density in Vrms/√Hz
• Use Hanning window
• Confidence interval depends on number of averages
�
• Confidence interval de
depends
p
�
ends also on resolution and
and
�
video bandwidth for swept analyzers
�
• Measure system noise floor.
San Francisco 2011
60
Noise Floor Reduction Techniques
• Cross-Correlation
• Carrier Suppression
San Francisco 2011
61
Cross-correlation PM Noise System for Two
Port Measurements
�
φ
LNA
DUT
Channel 1
φ
REF
LNA
on
NoiseCrosscorrelated = NoiseCorrelated1,2 +
San Francisco 2011
Channel 2
off
NoiseUncorrelated1 + NoiseUncorrelated2
N Averages
62
Correlated Noise Measurements
-140
Channel 1
Channel 2
Cross Spectrum
Voltage N
Noise
oise (dBV/rtHz)
-150
-160
-170
-180
-190
-200
1E+6
1E+7
Frequency (Hz)
100,000 Ave :
San Francisco 2011
35 min
63
Cross-correlation Oscillator PM Measurements
φ
LNA
Channel 1
Reference 1
DUT
φ
Reference 2
Sφ ( f )Cross1,2 = Sφ ( f )DUT +
San Francisco 2011
LNA
Channel 2
Sφ ( f )Ref1 + Sφ ( f )Ref2 + Sφ ( f )System1 + Sφ ( f )System2
NAverages
64
Cross-correlation Oscillator PM
Measurements
Three oscillator cross-spectrum measurement
-100
CH1
CH2
Cross
-110
-120
L(f), [dBc/H
[dBc/Hz]
z]
-130
-140
-150
-160
-170
-180
-190
1E+0
San Francisco 2011
1E+1
1E+2
1E+3
Frequency [Hz]
1E+4
1E+5
65
AM Measurements*
v(t ) = kα P(t )
α
ϕ
or
DUT
α
Diode Power
Detector
CAL
Δv
kα P0 =
ΔP P0
In-phase non­
saturated Mixer
v(t ) = kα P0 (1 + α (t ))2 ≅ kα P0 (1 + 2α (t ) + α 2 (t) )
SVrms ( f )
Sα ( f ) =
4kα2 P02
Sα ( f ) =
San Francisco 2011
*
SVrms ( f )
Ka
,
Ka = 4kα2 P02
*The Measurement of AM noise of Oscillators – Rubiola2005
66
Cross-correlation Source AM Measurements
ChannelA
*
DUT
ChannelB
CAL
*
Sα ( f )CrossAB = Sα ( f )DUT
+
Sα ( f )CrossAB =
Sα ( f )CrossAB =
San Francisco 2011
SSystem1 ( f ) + SSystem2 ( f )
2N Ave
SvAB ( f )
4kα2A PA2 kα2B PB2
SvAB ( f )
Ka
, K a = 4kα2A PA2 kα2B PB2
*The Measurement of AM noise of Oscillators – Rubiola2005
67
Two-port AM Measurements
ChannelA
DUT
REF
ChannelB
CAL
Sa ( f )Cross1,2 = Sα ( f )DUT +Sα ( f )REF +
Sα ( f )SystemA +Sα ( f )SystemB
2NAverages
Reference AM noise must be less then DUT noise
Saturation can help in reducing AM Source noise
San Francisco 2011
68
Digital Measurement Systems
• Carrier frequencies are sampled directly with
A/D converters and phase information is
extracted
extracted mathematically.
mathematically.
• No phase lock required
• Signals can be of different frequencies.
• Limited frequency range 1 - 400 MHz.
• Fourier Range of 1 mHz to 1 MHz.
• Limited sensitivity
San Francisco 2011
69
Integral PM and AM Noise Standards
• Low noise signal source
• Two outputs with extremely low differential AM
and PM noise
• Calibrated noise source
• Greatly simplifies AM and PM measurements
• Generates a calibrated level of equal AM and PM
noise
San Francisco 2011
70
Block Diagram of NIST PM/AM Noise
Standard
�
φ
on
Si
Signal
gnal
off
Phase Shifter
Splitter
Reference
Summer
Modulated
on
White
Noise
San Francisco 2011
off
Bandpass
71
Added Noise Appears as Equal
Amounts of AM and PM
AM
PM
υ0 − f
υ0
υ0 + f
V0
S a ( f ) = Sφ ( f ) =
PSDVn (υ 0 − f ) + PSDVn (υ 0 + f )
2V02
While
∞
San Francisco 2011
∫S
0 φ
( f ) << 0.1
72
Basic Carrier Suppression
Technique (Interferometric)
�
φ
LNA
Analyzer
DUT
San Francisco 2011
73
Basic Carrier Suppression
Technique (Interferometric)
�
φ
LNA
φ
Analyzer
DUT
DUT
San Francisco 2011
74
Delay Line Measurement Systems
Residual
Delay line
PMMeasurement
MeasurementSystem
System
ϕ
Source
f
τd
Sv ( f )
Sϕ ( f ) = 2
2
k
H
(
jf
)
v(t ) ∝d Δϕ t )
2
H ( jf ) = 4sin 2 (π f τ d )
San Francisco 2011
75
Delay Line Transfer Function
�
Transfer function of delay line
10
10 us
1 us
0
IH f ( jf )I 2
-10
-20
2
⎤
10Log
⎡
10Log
H
H
j
jf
f
(
)
⎢⎣
⎥⎦ -30
2
H ( jf ) = 4sin 2 (π f τ )
-40
-50
-60
1E+3
1E+4
1E+5
1E+6
Offset Frequency [Hz]
System sensitivity is proportional to τd
Long delays reduce sensitivity due to insertion loss
Transfer Function has nulls at n/τd
San Francisco 2011
76
Delay Line Transfer Function
�
L(f), [dBc/Hz]
L(f),
[dBc/Hz]
PM noise of a DRO at 10 GHz
3 km Delayline
30
20
10
0
-10
-20
-30
-40
-50
-60
-60
-70
-80
-90
-100
-110
-120
-130
1E+0
Raw Data
Processed Data
1E+1
1E+2
1E+3
1E+4
1E+5
1E+6
Frequency [Hz]
System sensitivity is proportional to τd
Long delays reduce sensitivity due to insertion loss
Transfer Function has nulls at n/ τd
San Francisco 2011
77
Single and Dual Source Measurements
Direct Frequency Comparison
Direct Phase Comparison
(Delay Line)
Advantages:
Doesn’t require reference source
No PLL effects
Simple basic calibration
Lowest noise floor
Noise scales as f-1 near carrier
Noise floor easy to determine
Very wide band performance
Can be used for residual measurement
Disadvantages:
Noise floor scales as f-3 near carrier
Noise floor harder to determine
Multiple delay lines required to cover
different measurement conditions
Not wideband – Frequency response
has nulls
Not useful for residual measurements
Long delays have higher insertion loss
San Francisco 2011
Requires reference of comparable
quality
Requires PLL to maintain phase lock
between sources
Calibration needed for measuring inside
PLL loop bandwidth
78
Optical Encoded Delay Line Measurement
�
~0.2 dB/km insertion loss vs 1 dB/m
0
4 m Microwave Delay line
-2 0
L(f), [dBc/Hz]
-4 0
Ebay
3 km Optical
-6 0
-8 0
-1 00
-1 20
-1 40
-1 60
1 E +0
8 km state-of-the-art
correlated system
1E +1
1 E +2
1E +3
1 E +4
1E +5
1 E +6
F re q u en c y [Hz]
San Francisco 2011
79
Comparison of Noise Floors
Noise
e [dBC/Hz]
SSB Phase Nois
Typical Noise Floors @ 10 GHz
-100
-110
-120
-130
-140
-150
-160
-170
-180
-190
-200
1E+0
San Francisco 2011
Single Mixer
Correlated Mixer
Correlated Photonic Delayline
Correlated Interferometer (Rubiola)
1E+1
1E+2 1E+3 1E+4
Offset Frequency [Hz]
1E+5
1E+6
80
Measurement Problems
• Mechanical Instabilities
�
• Phase locked loop effects
�
• IF Gain Flatness
• Delay effects
• RBW effects
• AM Leakage
• FM Port noise
• Ground Loops
San Francisco 2011
81
Phase Locked Loop Effects
�
-20
Phase Noise [dBc/H
[dBc/Hz]
z]
�
-40
-60
-80
-100
-120
-140
1
San Francisco 2011
10
Offset Frequency [Hz]
100
1000
82
IF Gain Reduction in Presence
of Noise Floor
�
Measured Noise
-70
-90
-110
Frequency
-130
-150
Corrected Noise
Phase Noise (dBc
(dBc/Hz)
/Hz)
Gain
-50
-170
Frequency
-190
1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 1E+9
Fourier Frequency (Hz)
Frequency
San Francisco 2011
83
Delay Mismatch in Residual
Measurements
�
Frequency Multiplier Phase Noise
-90
Phase Noise [dB
[dBc/Hz]
c/Hz]
-100
10
50 ns
1 ns
0
-10
IH f ( jf )I 2
-20
-30
-40
-50
#1
#1 vs #2
#2
Transfer function of delay line
-110
-120
-130
-60
-70
-80
-140
1E+5
1E+6
1E+7
1E+8
Offset Frequency [Hz]
-150
-160
10
100
1000
10000
100000
1000000 10000000
Offset Frequency [Hz]
San Francisco 2011
84
Insufficient Resolution Bandwidth
Phase Noise
-80
-90
-110.0
10 Hz RBW
-100
-110
-120
-120.0
L(f), [dBc/
[dBc/Hz]
Hz]
L(f) [dBc/
[dBc/Hz]
Hz]
Phase Noise
-100.0
100 Hz RBW
-130
-140
-150
-160
-170
-180
1E+1
-140.0
-140.0
-150.0
-160.0
-170.0
-180.0
-190.0
1E+2
1E+3
1E+4
Frequency [Hz]
San Francisco 2011
-130.0
1E+5
1E+6
-200.0
1E+1
1E+2
1E+3
1E+4
1E+5
Frequency [Hz]
85
80
60
Sensitivity (dB)
PM Sens
AM Sens
DC Level
DC Offset
0.4
0.2
40
0
20
-0.2
0
-0.4
-20
-0.6
-40
-0.8
-60
-1
Mixer IF (Volts)
AM to PM Leakage in Mixer
AM Null Offset
-80
0
45
90
135
-1.2
180
Phase Angle (degrees)
San Francisco 2011
86
AM to PM Leakage in Mixer
Residual Measurement
80
α
60
SATURATED
AMPLFIER
or LIMITER
Absolute Measurement
(dB
Sensitivity (d
B))
Modulator
PM Sens
AM Sens
DC Level
DC Offset
0.4
0.2
40
0
20
-0.2
0
-0.4
20
--20
-0.6
0 .6
-40
-0.8
-60
Mixer IF (Volts)
ϕ
-1
AM Null Offset
-80
0
45
90
135
-1.2
180
Phase Angle (degrees)
∑
Move Operating Point
To Here
α
Modulator
San Francisco 2011
87
FM Port (PLL) Noise
Phase Noise
-70
-80
f −2 slope
-90
L(f) [dBC/Hz]
[dBC/Hz]
-100
-110
-120
-130
-140
-150
-160
-170
1E+1
1E+2
1E+3
1E+4
1E+5
Offset Frequency [Hz]
2
2
⎛υ ⎞
⎛ K ⎞
Sφ ( f ) = ⎜ 0 ⎟ S y ( f ) = ⎜ υ ⎟ PSD (V
rms )
⎝ f ⎠
⎝ f
⎠
San Francisco 2011
Kv is VCO sensitivity in Hz/V
88
Ground Loops and EMI
Noise f loor at X-Band
-80
-90
L(f)
L
(f) [[dBc/
dBc/Hz
z]]
-100
-110
-120
-130
-140
-150
-160
-170
-180
-190
-200
1E+1
San Francisco 2011
1E+2
1E+3
1E+4
1E+5
Frequenc y [Hz]
1E+6
1E+7
89
Ground Loops and EMI
San Francisco 2011
90
Ground Loops and EMI
•
•
•
•
•
•
•
•
•
San Francisco 2011
Power devices from batteries
Shielding – Faraday and magnetic
DC Blocks
Replace IF Gain with RF gain (Interferometric)
Isolate or remove computer connections
Plug in AC power all at same place
EMI filtered power strips/ Ferrite Cores
Ground lifting plugs (dangerous)
Isolation transformers (dangerous)
91
Conclusions
• Great care must be taken when calibrating the
mixer sensitivity.
• Calibrating Kd versus Fourier can be achieved by
utilizing a modulation technique.
• For ultra-low noise floors cross-correlation or
carrier-suppression techniques can be used.
San Francisco 2011
92
References
1. Algie L. Lance, Wendell D. Seal, and Frederik Labaar, Phase noise and
AM noise measurements in the frequency domain, Infrared and
Millimeter Waves, vol. 11, 1984, pp. 239–284.
2. D.B. Sullivan, D.W. Allan, D.A. Howe, and F.L. Walls, Characterization
of Clocks and Oscillators, NIST Tech. Note
1337, 1-342, 1990
3. E. Rubiola, The measurement of AM noise of oscillators
4. E. Rubiola, V. Giordano, Advanced interferometric phase and amplitude
noise measurements , Rev. Sci. Instrum. vol.73 no.6 p.2445-2457,
June 2002.
2002.
5. Enrico Rubiola, Phase noise and frequency stability in oscillators,
Cambridge University Press, Cambridge, UK, November 2008.
6. F. L. Walls, Secondary standard for PM and AM noise at 5, 10 and 100
MHz, IEEE Trans. Instrum. Meas. 42 (1993) no. 2, 136–143.
7. J. R. Vig, IEEE Standard Definitions of Physical Quantities for
Fundamental Frequency and Time Metrology--Random Instabilities,
IEEE Standard 1139-1999
8. W. F. Walls, Cross-correlation phase noise measurements, Proc.Freq.
Control Symp., IEEE, New York, 1992, May 27-29 1992, pp. 257-261.
San Francisco 2011
93