Phase Noise in RF and Microwave Amplifiers

Transcription

Phase Noise in RF and Microwave Amplifiers
Enrico Rubiola and Rodolphe Boudot
IFCS, Newport, CA, 1–4 June 2010
Outline
•
•
•
•
Noise types (white and flicker)
Amplifier networks
Experiments
Conclusions
home page http://rubiola.org
DB
2
file: amp-noise-tree
AM-PM noise types
AM-PM noise
parametric
environmental
noise originates
near DC
internal
temperature
50 Hz B fields
flicker (1/f)
power supply
rnd walk (1/f2)
acoustic
drift
radiation
additive
noise
originates
around !0
environmental
internal
RF leakage
white
DB
3
The difference between additive and parametric noise
additive noise
u(t)
input
parametric noise
v(t)
noise-free
amplifier
Σ
u(t)
v(t)
AM
output
input
RF noise,
close to !0
z(t)
PM
x(t)
noise-free
amplifier
output
y(t)
file: amp-add-vs-param
(output)
(noise)
Su(f)
PSD
Sv(f)
Sz(f)
sum
PSD
near-dc
noise
Sv(f)
Sy(f)
(output)
(noise)
ion
s
r
ve
n
o
-c
p
u
Su(f)
(input)
(input)
!
stopband
passband
!0
stopband
the noise sidebands are
independent of the carrier
!
stopband
passband
!0
stopband
the noise sidebands are
proportional to the carrier
DB
White noise in cascaded amplifiers
White noise is chiefly the noise of the first stage
kT0
(F1–1)kT0
input
file: amp-cascaded-Friis
F1
A1
(F2–1)kT0
F2
A2
(F3–1)kT0
F3
A3
(F3 − 1)kT0
(F2 − 1)kT0
+
+ ...
Ne = F1 kT0 +
2
2
2
A1
A2 A1
(F2 − 1) (F3 − 1)
F = F1 +
+
+ ...
2
2
2
A1
A2 A1
F kT0
b0 =
P0
output
Friis formulae
H. T. Friis, Proc. IRE 32
p.419-422, jul 1944
Noise is chiefly that of
the 1st stage
white
phase noise
F1 kT0
(F2 − 1)kT0
(F3 − 1)kT0
b0 =
+
+
+ ...
2
2
2
P0
A 1 P0
A 2 A 1 P0
Friis formula
for phase noise
4
DB
Parametric noise in cascaded amplifiers
5
There is a nonlinear model that gives exactly the same results, see Chap. 2 of
E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge 2008, ISBN 978-0521-88677-2
u(t)
input
file: cascaded-ampli
!1
"1
AM
PM
x1(t)
noise-free
amplifier
y1(t)
!2
"2
AM
PM
x2(t)
ampli 1
v(t)
noise-free
amplifier
output
y2(t)
! = !1 + !2
" = " 1 + "2
ampli 2
Flicker: the two amplifiers are independent
E{α2 } = E{α12 } + E{α22 }
Sα = Sα 1 + Sα 2
E{ϕ2 } = E{ϕ21 } + E{ϕ22 }
Sα = Sϕ 1 + Sϕ 2
Environment: a single process drives the two amplifiers
α = α1 + α2
ϕ = ϕ1 + ϕ2
E{α } = E{(α1 + α2 ) }
2
2
E{ϕ2 } = E{(ϕ1 + ϕ2 )2 }
Yet there can be a time constant, not necessarily the same for the two devices
DB
Flicker noise in parallel amplifiers
6
vi (t)
uk (t)
um(t)
A1
v1 (t)
ψ1
Ak
vk (t)
ψk
Am
vm(t)
ψm
m−way power combiner
input
m−way power divider
u1 (t)
output
vo(t)
ϕ
• The phase flicker coefficient b–1 is about independent of power
• The flicker of a branch is not increased by splitting the input
power
• At the output,
�
1 �
• the carrier adds up coherently
b
=
b
−1
−1 cell
• the phase noise adds up statistically
m
• Hence, the 1/f phase noise is reduced by a factor m
• Only the flicker noise can be reduced in this way
DB
Volume law
The analysis of the parallel amplifier suggests that:
For a given technology, the flicker
coefficient b–1 should be proportional to the
inverse of the volume of the active region
Gedankenexperiment
- Flicker is of microscopic origin because it has Gaussian PDF
(central limit theorem)
- Join the m branches of a parallel device forming a compound
- Phase flicker is proportional to the inverse size of the
amplifier active region
7
DB
8
Parametric noise in regenerative amplifiers
R. Boudot, E. Rubiola, arXiv:1001.2047v1, Jan 2010. Submitt. IEEE Transact. MTT
RF filter
Vin
Vout
A0
A0
A=
1 − A0 β
feedback ß
short delay
file: amp-regen-sch
10–10
10–15
S!(f)
A = Am
0
phase adj.
[rad2/Hz]
10 –1
1
/f
(b
–1 /f
)
ampl. adj.
A0 ejψ
A→
1 − A0 β ejψ
�
�
1
A0
1+j
ψ .
A=
1 − A0 β
1 − A0 β
roundtrip
carrier
≈10–19 rad2/Hz
(few roundtrips)
10–16
(b0)
10–20
f
file: amp-regen-mecha
1kHz
1MHz
1GHz
• Short roundtrip time, vs. flicker
time frame
• Quasi-static analysis holds
−1
Am−1
0
⇒ β=
Am
0
1
ψ(t)
ϕ(t) =
1 − A0 β
�2
�
1
(b−1 )ampli
(b−1 )RA =
1 − A0 β
(b−1 )RA = m2 (b−1 )ampli
9
Measurement methods
3 dB
atten
atten
RF
DUT
IF
atten
LNA
LO
FFT analyzer
Saturated mixer (common laboratory practice)
90º adj
Bridge (interferometer)
V0 cos(!0t)
pump
0º
–90º
dark
bridge
DUT
hybrid
junction
–90º
0º
0º
0º
0º
x(t)
AM noise
"(t)
coherent
detector
#(t)
y(t)
FFT
hybrid
junction
(microwave)
error amplifier
–90º
PM noise
–90º
–90º
phase & ampl.
adjustment
null
x(t) cos(!0t) – y(t) sin(!0t)
File: bridge
E. Rubiola, V. Giordano, Rev. Sci. Instrum. 73(6) pp.2445-2457, June 2002
DB
Flicker noise of some amplifiers
Amplifier
AML812PNB1901
AML412L2001
AML612L2201
AML812PNB2401
AFS6
JS2
SiGe LPNT32
Avantek UTC573
Avantek UTO512
Frequency
(GHz)
8 – 12
4 – 12
6 – 12
8 – 12
8 – 12
8 – 12
3.5
0.01 – 0.5
0.005–0.5
Gain
(dB)
22
20
22
24
44
17.5
13
14.5
21
P1 dB
(dBm)
17
10
10
26
16
13.5
11
13
8
F
(dB)
7
2.5
2
7
1.2
1.3
1
3.5
2.5
DC
bias
15 V, 425 mA
15 V, 100 mA
15 V, 100 mA
15 V, 1.1A
15 V, 171 mA
15 V, 92 mA
2 V, 10 mA
15 V, 100 mA
15 V, 23 mA
b−1 (meas.)
(dBrad2 /Hz)
−122
−112.5
−115.5
−119
−105
−106
−130
−141.5
−137
10
Phase noise vs. power
• The 1/f phase noise b–1 is about independent of power
• The white noise b0 scales as the inverse of the power
• The corner frequency is misleading because it depends
on power
11
−100
Phase noise, dBrad 2 /Hz
DB
P=−50dBm
Amplifier X−9.0−20H at 4.2 K
P=−60dBm
P=−70dBm
Data from IEEE UFFC 47(6):1273 (2000)
.
P=−80dBm
−110
P=−80dBm
−120
P=−70dBm
P=−60dBm
P=−50dBm
E. Rubiola, Phase Noise and Frequency Stability in
Oscillators, Cambridge 2008, ISBN 978-0521-88677-2
−130
1
101
R. Boudot, PhD thesis
Measured at LAAS
102
104
103
Fourier frequency, Hz
105
DB
Phase noise in cascaded amplifiers
The expected flicker of
a cascade increases by:
3 dB, with 2 amplifiers
4.8 dB, with 3 amplifiers
White noise is limited by
the (small) input power
12
DB
Phase noise in parallel amplifiers
Connecting two amplifier in parallel, a
3 dB reduction of flicker is expected
13
DB
Flicker noise in parallel amplifiers
14
−140
AML812PNA0901 (100mA)
Phase noise, dBrad 2 /Hz
AML812PNB0801 (200mA)
AML812PNC0801 (400mA)
−150
−160
AML812PND0801 (800mA)
−170
101
102
103
104
105
Fourier frequency, Hz
106
Specification of low phase-noise amplifiers (AML web page)
amplifier
AML812PNA0901
AML812PNB0801
AML812PNC0801
AML812PND0801
unit
gain
10
9
8
8
dB
parameters
F
bias power
6.0
100
9
6.5
200
11
6.5
400
13
6.5
800
15
dB
mA
dBm
102
−145.0
−147.5
−150.0
−152.5
phase noise vs. f , Hz
103
104
−150.0
−158.0
−152.5
−160.5
−155.0
−163.0
−157.5
−165.5
dBrad2 /Hz
105
−159.0
−161.5
−164.0
−166.5
DB
Phase noise of a regenerative amplifier
Thanks to K.Volyianskiy for
the OEO noise spectrum
Indirect measurement: The RA replaces the two-stage sustaining amplifier in a Opto-Electronic oscillator
• A RA is set for the gain of two cascaded amplifiers
• As expected, the RA flicker is 3 dB higher than the two amplifiers
• Indirect measurement through the frequency flicker
15
DB
Environmental effects in RF amplifiers
16
Amplifier phase noise
–5
f
courtesy of J. Ackermann N8UR, http://www.febo.com
comments on noise are of E. Rubiola
–5
f
–5
f
Spectracom 8140T
b–1 = –113.5 dB
1
D-
D
TA
HP 5087A and
TADD-1 10 MHz
b–1 = –133 dB
in dBrad2/Hz (dBc/Hz + 3 dB)
814
D
TA
0T
1
508
D-
HP
b–1 is the 1/f noise coefficient
7A
background
b–1 = –142 dB
TADD-1 5 MHz
b–1 = –138.5 dB
It is experimentally observed that the temperature
fluctuations cause a spectrum Sα(f) or Sφ(f) of the 1/f5 type
Yet, at low frequencies the spectrum folds back to 1/f
DB
Correlation between AM and PM noise
17
u(t)
AM
input
a
noise-free
amplifier
PM
c
x(t)
b
d
y(t)
v(t)
output
correlated
z(t) noise
file: AM-PM-correl
a=0.4
b=0.4
c=0.2
d=0.8
a=b=0.7
c=d=0
a=0.4
b=0.92
c=d=0
a=b=0
c=d=0.7
a2 + b2 + c2 + d2 = 1
The need for this model comes from
the physics of popular amplifiers
• Bipolar transistor. The fluctuation of the
carriers in the base region acts on the base
thickness, thus on the gain, and on the
capacitance of the reverse-biased basecollector junction.
• Field-effect transistor. The fluctuation of
the carriers in the channel acts on the
drain-source current, and also on the gatechannel capacitance because the distance
between the èlectrodes' is affected by the
channel thickness.
• Laser amplifier. The fluctuation of the
pump power acts on the density of the
excited atoms, and in turn on gain, on
maximum power, and on refraction index.
AM and PM fluctuations are
correlated because originate from
the same near-dc random process
Conclusions
• The model predicts the noise of the amplifier
and of networks
• First noise model of the regenerative (positive-feedback) amplifier
• Experimental data validate the model
• Correlation between AM noise and PM noise
(needs further work)
Thanks to K.Volyanskiy for the measurement of the OEO noise, to Y. Gruson for help with phase
noise measurements, to P. Salzenstein and to V. Giordano for support and discussions.
This work results from a long-term transverse program on oscillators and frequency synthesis,
supported by the following contracts: ANR-05-BLAN-0135-02, CNES 60265/00, CNES 60281/00,
ESA 20135/06/D/MRP, LNE/DRST 08 7 002.
home page http://rubiola.org
18

Phase Noise in RF and Microwave Amplifiers

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Phase Noise in RF and Microwave Amplifiers