The effect of AM noise on correlation PM noise measurements 1/f - - PowerPoint PPT Presentation
The effect of AM noise on correlation PM noise measurements 1/f noise in RF and microwave amplifiers Enrico Rubiola, Rodolphe Boudot, Yannick Gruson FEMTO-ST Institute, Besanon, France CNRS and Universit de Franche Comt TimeNav 07
FEMTO-ST Institute, Besançon, France CNRS and Université de Franche Comté
home page http:/ /rubiola.org
TimeNav’07 – May 31, 2007
Enrico Rubiola, Rodolphe Boudot, Yannick Gruson Part 1 – The effect of AM noise ... Part 2 – Amplifier noise ...
D3 D4 D1 D2
input LO input RF IF load IF
v
v = kϕϕ + VOS for |ϕ| ≪ 1
Vr cos[ω0t + ϕ] Vl cos[ω0t] LO power → VOS RF power → VOS
phase detection
static: P → VOS (offset) noise: AM noise → DC noise mistaken for phase noise
diode and balun asymmetry RF mixer: balun asymmetry ≈ const. vs. frequency microwave: balun asymmetry depends on frequency
3
FFT analyzer device 2−port
phase dc
A
DUT (ref)
LO RF
x FFT analyzer µw
Σ
device 2−port
dc
DUT bridge
D
(noise only) meter output Δ
(ref)
phase and ampl.
phase detector
RF LO
x FFT analyzer phase lock
dc RF LO
x DUT REF
B
FFT analyzer phase lock
phase dc
DUT REF
RF LO
x
C
delay
A null of AM sensitivity (sweet point) can be found in some mixers A delay de-correlates the two inputs, thus it destroys the sweet point
tip: use a phase offset, or a DC bias at the mixer IF
With two separated inputs, the effect of AM noise adds up In a bridge, the AM noise propagates to the output only through the LO. The effect is strongly reduced by the RF amplification before detecting
4
vo(t) = kϕ ϕ(t) + klr α(t) vo(t) = kϕ ϕ(t) + kl αl(t) + kr αr(t) vo(t) = kϕ ϕ(t) + kl αl(t) + kr αr(t) vo(t) = kϕ ϕ(t) + ksd α(t)
−
Σ
Δ
Σ
Δ
FFT analyzer x=c−a c(t) y=c−b + − a(t) + b(t)
phase noise measurements DUT noise, normal use a, b c instrument noise DUT noise background, ideal case a, b c = 0 instrument noise no DUT background, with AM noise a, b c ≠ 0 instrument noise AM-to-DC noise Syx = E {Y X∗}
Syx = Y X∗m measured, m samples
a, b and c are incorrelated expand X = C − A and Y = C − B
Syx = Scc a, b, c independent Syx = Scc + O(
measured, m samples
5
Averaging on a sufficiently large number m of spectra is necessary to reject the single-channel noise
dc DUT (ref) (ref)
RF RF LO LO
x y arm a arm b
A
FFT analyzer dc dc DUT REF REF
RF RF LO LO
y x arm b arm a
C
FFT analyzer dc dc phase lock phase lock REF DUT REF
RF RF LO LO
y x arm a arm b
B
device 2−port
Σ Σ
FFT analyzer dc dc µw
D
FFT analyzer device 2−port
phase phase
dc
(noise only)
µw
phase and ampl.
(ref)
Δ Δ
DUT
phase and ampl.
bridge b bridge a y x
LO LO RF RF meter output
AM AM
delay common delay common
6
AM VOS AM VOS AM VOS
pink: noise rejected by correlation and averaging
Should set both channels at the sweet point, if exists The delay de-correlates the two inputs, so there is no sweet point The effect of the AM noise is strongly reduced by the RF amplification AM VOS VOS Should set both channels at the sweet point of the RF input, if exists, by
7
LO & RF → IF: coefficient klr LO or RF → IF: coefficients kl and kr LO → IF in a sync.-detection scheme: coefficient ksd
least in the scheme B-C)
dc bias lock−in amplifier
in
amplit. modulat. dc lock−in amplifier
in
amplit. modulat. lock−in amplifier
in
dc dc
RF LO RF (LO) LO (RF) phase
amplit. modulat. attenuat.
phase LO RF
Σ Σ Σ
A D B−C
dc bias dc bias
vo(t) = kϕ ϕ(t) + klr α(t) vo(t) = kϕ ϕ(t) + kl αl(t) + kr αr(t) vo(t) = kϕ ϕ(t) + ksd α(t)
Narda 4805 SN0973 r
l or kr (mV) kl kl
k
kr kr k k phase offset, degrees
7 mar 2006
r
200 −200 100 11GHz 8dBm 10GHz 8dBm 11GHz 8dBm 8.5GHz 8dBm 8GHz 8dBm 9GHz 7dBm −50 −25 25 50 −100 phase offset, degrees
r
kr
(mV) kl kr
kl kl kl
Pulsar MM−02−SC
mar 2006
k 200 −200 7GHz 8dBm 6GHz 6dBm 6GHz 8dBm 7GHz 6dBm 7GHz 8dBm −50 −25 25 50 100 −100
8
The AM sensitivity depends on frequency. This is ascribed to the microstrip baluns, and to the diode capacitances The AM sensitivity can have opposite sign at the two inputs
11 mar 2006
Narda 4805 SN 0973 6dBm 7dBm 8dBm 9dBm
11 40 60 80 100
(GHz)
kl (mV)
ν
8 9 10 20
Narda 4805 SN 0973
11 mar 2006
9dBm 8dBm 7dBm 6dBm
(mV) 8 9 10 11 20 40 60 80 100
(GHz)
kr
ν
mar 2006
Pulsar MM−02−SC 6dBm 7dBm 8dBm 9dBm
8 5 7 20 40 60 80 100
(GHz)
kl (mV) 6
ν
Pulsar MM−02−SC
mar 2006
6dBm 7dBm 8dBm 9dBm
8
ν
5 7 20 40 60 80 100
(GHz)
kr 6 (mV) 9
The effect of power is somewhat weaker than that of frequency
10
Mixer kϕ klr kr kl ksd Narda 4805 s.no. 0972 272 16 7.9 37 6.5 Narda 4805 s.no. 0973 274 18.3 17.1 44 9.8 NEL 20814 279 51.5 12.1 37.9 2.7 NEL 20814 305 41 1.9 30.2 3.73 unit mV/rad mV mV mV mV Test parameters: ν0 = 10 GHz, P = 6.3 mW (8 dBm)
Some relevant facts
ZFM2 r
(mV) kl kr
kl
kl kl kl kr kr kr phase offset, degrees k 60 −30 −60
200MHz 5dBm 200MHz 9dBm 6MHz 5dBm 6MHz 9dBm 200MHz dBm 200MHz 9dBm 6MHz 5dBm 6MHz 9dBm
30 −50 −25 25 50
l
kl kr kr kr kr
(mV)
kl
HP10514
kl kr
kl k phase offset, degrees −50 −30 −60
6MHz 9dBm 6MHz 5dBm 6MHz 9dBm 200MHz 9dBm 200MHz 5dBm 200MHz 5dBm
30 60
200MHz 9dBm 6MHz 5dBm
−25 25 50
TFM10514M2
kl kl kl k
l
kr kr kr kr r
k
l
k
phase offset, degrees
(mV)
60 −30 −60
200MHz 5dBm 200MHz 9dBm 6MHz 5dBm 6MHz 9dBm 200MHz 5dBm 200MHz 9dBm 6MHz 5dBm 6MHz 9dBm
30 −50 −25 25 50
TFM10514M3
kr
kl kl kl
kl kr kr kr kr
(mV) k
phase offset, degrees
l
60 −30 −60
200MHz 5dBm 200MHz 9dBm 6MHz 5dBm 6MHz 9dBm 200MHz 5dBm 200MHz 9dBm 6MHz 5dBm 6MHz 9dBm
30 −50 −25 25 50
11
(klr, and ksd are not reported)
12
15 dB
101 102 103 104
5
10 −180 −170 −160 −150 −140 −120 −110 −130 −100
Fourier frequency, Hz
p
l u t i
f r
A M n
s e /Hz floor −173 dBrad2/Hz frequency flicker −30dB/dec −67 @ 1Hz specifications
Wenzel 501−04623 AM noise, dBV/V/Hz PM noise, dBrad 2/Hz
dBrad2 m e a s u r e d A M n
s e ( b e s t c a s e )
13
The AM noise is taken in via the DC-offset sensitivity to the power The AM noise rejection is of 15–40 dB For a given mixer, there is no predictable relation between the AM noise sensitivity in different configurations The sweet point exists only in some configurations The sweet point is generally not observed in VHF mixers In correlation systems, rejecting the AM noise is possible
The AM noise can even limit the single-channel measurements
home page http:/ /rubiola.org
Free downloads (texts and slides)
AM/PM noise
additive parametric local (flicker) environmental white
b0 = FkT0 P0
white phase noise
Sϕ =
bif i
power law f Sφ(f) low P0 high P0 P0
∑
V0 cos ω0t nrf(t) Noise figure F, Input power P0 g Cascaded amplifiers (Friis formula) N = F1kT0 + (F2 − 1)kT0 g2
1
+ . . .
The (phase) noise is chiefly that of the 1st stage
15
B B S(ν ) P0 Ne=FkT0 ν0−f ν0 ν0+f LSB USB ν P=FkT0B
RF spectrum g3 g1 g2 F2 F1 F3
The Friis formula applied to phase noise
b0 = F1kT0 P0 + (F2 − 1)kT0 P0g2
1
+ . . .
stopband
stopband
16
near-dc flicker
no carrier
S(f) f
t
S(f) f
noise up-conversion
t a
near-dc noise
expand and select the ω0 terms carrier
vi(t) = Vi ejω0t + n′(t) + jn′′(t)
non-linear (parametric)amplifier
vo(t) = Vi
get AM and PM noise
α(t) = 2 a2 a1 n′(t) ϕ(t) = 2 a2 a1 n′′(t)
The AM and the PM noise are independent of Vi , thus of power
vo(t) = a1vi(t) + a2v2
i (t) + . . . substitute
(careful, this hides the down-conversion)
the parametric nature of 1/f noise is hidden in n’ and n”
ω0 = ?
no flicker
ω0
The noise sidebands are proportional to the input carrier
near-dc noise
17
b0 , higher P0 b0 , lower P0
fc = ( b–1 / FkT0 ) P0 depends on P0
f
f"c f'c b–1 const. vs. P0
b–1 f–1
b0 = FkT0 / P0 S(f) , log-log scale
typical amplifier phase noise RATE GaSs HBT SiGe HBT Si bipolar microwave microwave HF/UHF fair −100 −120 good −110 −120 −130 best −120 −130 −150 unit dBrad2/Hz
The phase flicker coefficient b–1 is about independent of power. Hence, describing the 1 /f noise in terms of fc is misleading because fc depends on the input power
18
=−10dBm Pin=−5dBm Pin=0dBm −165 −160 −155 −150 −145 −140 −135 −130 −125 −120 f, Hz Phase noise, dBrad 2/Hz SiGe LPNT32
bias 2V, 20 mA
=−15dBm
100 1 10 1000 10000 100000 −175 P −170
in
Pin
The 1/f phase noise b–1 is about independent of power The white noise b0 scales up/down as 1/P0, i.e., the inverse of the carrier power
2
10 103 Fourier frequency, Hz −110 1 −130 −120 −100 Phase noise, dBrad /Hz
2 1 5
104 10 10
P=−50dBm P=−80dBm P=−80dBm P=−70dBm P=−60dBm P=−50dBm P=−70dBm
Amplifier X−9.0−20H at 4.2 K
Data from IEEE UFFC 47(6):1273 (2000) P=−60dBm
in a cascade, (b–1)tot does not depend of the amplifier order in practice, in a cascade each stage contributes about equally b–1 is roughly proportional to the gain through the number of stages
19
m cascaded amplifiers
b0 , higher P0 b0 , lower P0
fc = ( b–1 / FkT0 ) P0 depends on P0
f
f"c f'c b–1 const. vs. P0
b–1 f–1
b0 = FkT0 / P0 S(f) , log-log scale
The phase flicker coefficient b–1 is about independent of power. Hence: (b−1)tot =
m
(b−1)i AB and BA have the same 1/f noise A B B A
20
2
23 Jan 07 Avantek UTC573, 10 MHz 56 dB
NMS floor
f, Hz
120 130 140 150 160 170 180 1 10 100 1000 10000 100000
1Amp Pin=5dBm 3Amps Pin= 24dBm 2Amps Pin= 5dBm
2
S (f), dB.rad /Hz
AML812PNB1901 (SiGe HBT) 15 Feb 2007 2 cascaded Amplifiers, Pin=−27.5dBm
f, Hz
50 70 90 110 130 150 170 1 10 100 1000 10000 100000
The expected flicker of a cascade increases by: 3 dB, with 2 amplifiers 5 dB, with 3 amplifiers
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, the carrier adds up coherently the phase noise adds up statistically Hence, the 1/f phase noise is reduced by a factor m Only the flicker noise can be reduced in this way
21
ϕ m−way power divider m−way power combiner (t) vi input vo(t)
ψ1 (t) u1 A1 (t) v1 (t) vk (t) uk Ak (t) um Am (t) vm ψk ψm
b−1 = 1 m
Gedankenexperiment: join the m branches of a parallel amplifier forming a single large active device: the phase flickering is proportional to the inverse physical size of the amplifier active region
22
ϕ m−way power divider m−way power combiner (t) vi input vo(t)
ψ1 (t) u1 A1 (t) v1 (t) vk (t) uk Ak (t) um Am (t) vm ψk ψm
uk(t) = 1 √mvi(t) branch-amplifier input vo(t) = 1 √m
m
vk(t) main output vk(t) = 1 √mVi
k(t) + jn′′ k(t)
branch → output ψk(t) = 2a2 a1 n′′
k(t)
branch ϕk(t) =
1 mVi 2a2n′′ k(t) ej2πν0t
a1Vi ej2πν0t branch → output = 1 m 2a2 a1 n′′
k(t)
Sϕ(f) =
m
1 m2 4a2
2
a2
1
Sn′′
k (f)
Sϕ(f) = 1 m 4a2
2
a2
1
Sn′′(f) Sϕ(f) = 1 m Sψ(f) m equal branches → output b−1 = 1 m
23
2
S (f), dB.rad /Hz
AFS6, 10 GHz 27 Feb 2007
f, Hz
Single AFS6 Amplifier Pin= −45 dBm 2 Parallel AFS6 Amplifiers Pin= −33 dBm 50 70 90 110 130 150 170 1 10 100 1000 10000 100000
S (f), dB.rad /Hz
2
Pin= −5 dBm Single amplifier Pin= −6 dBm JS2, 10 GHz 15 Feb 2007
f, Hz
50 70 90 110 130 150 170 1 10 100 1000 10000 100000
Connecting two amplifiers in parallel, the expected flicker is reduced by 3 dB
24
Fourier frequency, Hz Phase noise, dBrad /Hz
5
104 103 10
6 2
101
2
10 −170 −160 −150 −140 10
AML812PNB0801 (200mA) AML812PNA0901 (100mA) AML812PND0801 (800mA) AML812PNC0801 (400mA)
Specification of low phase-noise amplifiers (AML web page) amplifier parameters phase noise vs. f, Hz gain F bias power 102 103 104 105 AML812PNA0901 10 6.0 100 9 −145.0 −150.0 −158.0 −159.0 AML812PNB0801 9 6.5 200 11 −147.5 −152.5 −160.5 −161.5 AML812PNC0801 8 6.5 400 13 −150.0 −155.0 −163.0 −164.0 AML812PND0801 8 6.5 800 15 −152.5 −157.5 −165.5 −166.5 unit dB dB mA dBm dBrad2/Hz
25
temperature vibrations input carrier phase amplitude
g
etc.
φ = φA + φB and α = αA + αB regardless of the amplifier order A B B A Sz(f) = ZZ∗ = (X + Y ) (X + Y )∗ = XX∗ + Y Y ∗ + XY ∗ + Y X∗ = Sx + Sy + Sxy
+ Syx
let z(t) = x(t) + y(t)
Cascaded amplifiers
Phase noise Cascading m equal amplifiers, Sα(f) and Sφ(f) increase by a factor m2. If the amplifier were independent, Sα (f) and Sφ(f) would increase only by a factor m. A time constant can be present
26
Spectracom 8140T b–1 = –113.5 dB HP 5087A and TADD-1 10 MHz b–1 = –133 dB TADD-1 5 MHz b–1 = –138.5 dB background b–1 = –142 dB
Amplifier phase noise
courtesy of J. Ackermann N8UR, http://www.febo.com comments on noise are of E. Rubiola
HP 5087A T A D D
T A D D
b–1 is the 1/f noise coefficient in dBrad2/Hz (dBc/Hz + 3 dB)
8140T
f – 5 f – 5 f – 5
It is experimentally observed that the temperature fluctuations cause a spectrum Sα(f) or Sφ(f) of the 1/f5 type Yet, at lower frequencies the spectrum folds back to 1/f
27
Flicker AM/PM noise results from parametric modulation from the near-dc 1/f noise The 1/f noise coefficient b–1 is about independent of the carrier power Describing the 1/f noise in terms of fc is misleading Cascading m amplifiers, the 1/f noise increases by a factor m Connecting m amplifiers in parallel, the 1/f noise drops by a factor m Thermal fluctuations induce 1/f5 PM noise, which folds back to 1/f at lower frequencies
home page http:/ /rubiola.org
Free downloads (texts and slides)