California Eastern Laboratories

California Eastern Laboratories
APPLICATION NOTE
AN1026
1/f Noise Characteristics Influencing Phase Noise
Abstract
In applications such as VCO’s where 1/f noise is one of the
major contributors to phase noise, the device with the best
1/f noise will yield the best phase noise. To better understand
how 1/f noise changes with bias and from device to device, the
1/f noise of two different bipolar devices were measured and
compared. Nonlinear models were developed and the predicted
and measured 1/f noise spectrums compared. In addition,
how manufacturers quantify 1/f for simulation purposes is
evaluated to provide the designer who is new to noise
simulation with better insight into what the 1/f coefficient and
exponent mean, and how the values effect the 1/f noise
simulations.
I. Introduction
The phase noise of an oscillator, quantified by its short term
frequency stability, determines a system’s ability to separate
adjacent channels. With the significant increase in portable,
wireless traffic, better frequency stability is required. Phase
noise becomes an important consideration. Choosing the
appropriate topology for a low phase noise source is important,
as is the choice of resonator and coupling network [1]. Many
articles exist on how to design an oscillator for low phase noise
by selecting the appropriate topology, resonator and coupling
network[2]. This article focuses on the important characteristics
for device evaluation and selection.
1 Hz
Fosc
Figure 1. Single sideband phase noise
Oscillator phase noise has two components: phase noise
resulting from direct upconversion of white noise and 1/f
noise, and phase noise resulting from the changing phase of
the noise sources modulating the oscillation frequency, ∆ freq.
The composite oscillator phase noise spectrum consists of the
white noise and 1/f noise directly upconverted around the
carrier, and the phase modulated noise spectrum. The frequency
noise in the frequency domain is converted to phase noise in
the frequency domain by multiplying by 1/f2. The white noise
spectra, f0, then contributes 1/f2 and the 1/f noise spectra
contributes 1/f3, see Table 1.
Noise Source
Phase Noise Spectrum
Upconverted
II. Oscillator Phase Noise
Phase perturbations due to random noise in the oscillator
result in a random shift of the oscillator frequency. These
random frequency variations are caused by thermal noise,
shot noise, and flicker noise. Thermal noise is a function of the
temperature, bandwidth and resistance, shot noise is a function
of the DC bias current, and flicker noise is a function of the
active device characteristics. Single sideband phase noise is
defined as the noise power in a 1-Hz bandwidth at some offset
frequency from the carrier, Fosc, and has the units of dBc/Hz,
Figure 1.
∆ freq
white noise
white noise
1/f2
1/f noise
1/f noise
1/f3
Table 1. Noise sources and their phase noise spectrum
AN1026
SSB Phase Noise (dBc/Hz)
For a low Q oscillator where the half-bandwidth frequency,
fo/2Q, is greater than the flicker corner frequency, fc, the
oscillator phase noise characteristics will be determined by
the white noise, 1/f2, and the flicker noise, 1/f3, Figure 2.
-60
-80
f -3flicker FM
S(f)df = (KF)IBAFdf / Fc
-100
where:
KF
AF
IB
Fc
f -2
-120
white FM
-140
-160
-10
fc 1k
100
10k fo/2Q 100k
Baseband offset Frequency (Hz)
Figure 2. Baseband noise spectrum for fc<fo/2Q, Low Q.
SSB Phase Noise (dBc/Hz)
For a high Q oscillator where the halfbandwith frequency,
fo/2Q, is less than the flicker corner frequency, fc, the oscillator
phase noise characteristics will be determined by the frequency
modulated flicker noise, 1/f-3, and the upconverted 1/f noise,
Figure 3.
-60
(1)
= flicker noise constant
= flicker noise exponent
= DC base current
= flicker noise corner frequency
A. Noise Test Setup
The test setup to measure 1/f noise is shown in Figure 4. The
50 ohm terminations insure amplifier stability at higher
frequencies. The entire test setup is contained in an EMI
shielded box. The supply voltages, VBB and VCC are
provided by batteries to eliminate 60 Hz noise.
Vcc
LPF
VBB
-80
-100
Flicker noise in BJTs is also known as 1/f noise because of the
1/f slope characteristics of the noise spectra. This noise is
caused mainly by traps associated with contamination and
crystal defects in the emitter-base depletion layer. These traps
capture and release carriers in a random fashion. The time
constants associated with the process produce a noise signal at
low frequencies. The flicker noise spectral density is given
by:
FET Test Setup
CPU/ Printer
LPF
f -3flicker FM
50
f -1
-120
50
-140
-160
fo/2Q
-10
100
1k
10k
Baseband offset Frequency (Hz)
100k
Figure 3. Baseband noise spectrum for fc>fo/2Q, High Q.
III. 1/f Measurements
1/f measurements are performed to obtain the flicker noise
frequency spectra and determine the flicker corner frequency.
From this spectra, the simulation coefficient KF and the
simulation exponent AF necessary for modeling the 1/f noise
spectra can be determined.
Figure 4. 1/f Noise Test Setup
The measured 1/f noise spectrum for the NE68819 at Vce =
3V, Ic=12mA is shown in Figure 5. The measured flicker
corner frequency, Fmeas = 5.6kHz, is determined by noting
the intersection of the 1/f noise spectrum and the white noise
spectrum. This intersection is where the measured flicker
noise power and the white noise power are equal.
AN1026
Calculated AF and KF values resulting from 1/f measurements
for the NE68519 and the NE68819 are provided in Table 2.
-110
NE68519
-120
Ic
(mA)
-130
-140
-150
-160
-170
110
1K
5.6 KHz 10K
100K
Bv(f) [dBv/Hz] vs. f[Hz]
NE68819
VCE=1V
AF
KF
VCE=3V
AF
KF
VCE=1V
AF KF
VCE=3V
AF KF
5
1.56
454
1.35
80
1.9
5
1.18
10
10
1.48
231
1.19
18
1.39
72
1.22
15
20
1.89
7.6K
1.12
13
1.19
14
1.23
16
30
1.6
774
1.25
30
1.16
10
1.26
26
Table 2. AF and KF for the NE68519 and the NE68819
(KF values are times 10-15)
C. Bias Dependency
Figure 5. 1/f measurement for the NE68819 at Vce=3V,
Ic=12 mA
To determine the intrinsic base flicker noise corner, Fbn,
requires solving the following equation [3]:
Fbn = Fmeas [1 + 1/β + 2VthGin/IB]
(2)
where:
Fbn
= intrinsic base flicker noise corner
Fmeas = measured flicker corner
β
= collector-base current gain
Vth
= thermal voltage = kT/q
Gin
= external input conductance
IB
= DC base biasing current
Next we examine the bias dependency of the flicker corner
frequency for the same two NEC devices. The base voltage
was varied to obtain the collector currents shown in Table 3.
The flicker corner frequency, Fbn, was determined at VCE=1V
and VCE=3V as shown in Table 3 and Figure 6.
Fbn (KHz)
Ic
(mA)
5
The equation for the intrinsic base flicker corner modifies the
measured flicker corner to account for the input conductance,
base current, and DC current gain of the device. The formula
for Fbn is valid providing the measured output noise
characteristics are dominated by the base flicker and base shot
noise sources. The design of the test setup and selection of
biasing circuitry is chosen to insure these conditions.
NE68519
Vce=1V
Vce=3V
5.8
7.3
NE68819
Vce=1V
Vce=3V
5.6
5.1
10
8.8
9.9
5.9
5.8
20
12.4
11.2
7.7
6.7
30
18.6
11.9
8.3
7.3
Table 3. Fbn versus bias - NE68519, NE68819
20
Measuring the flicker corner frequency at two different base
currents provides two different flicker corner values. Using
equation (3) twice, once for each IB and Fbn value provides two
equations and two unknowns, resulting in a solution for AF
and KF.
Fbn = (KF)IB(AF-1) / 2q
(3)
Fbn (KHz)
15
B. Calculating AF and KF
10
5
0
0
5
10
15
20
Ic (mA)
25
30
NE68519
NE68819
The resulting expressions for AF and KF are:
AF = log(F1) - log(F2) + Z
Z
Z = log (IB1) - log (IB2)
(4)
KF = 10 (log (Fbn) + log (IB) -18.49 - (AF)log (IB)) (5)
Figure 6a. Fbn at VCE=1V for the NE68519 and the
NE68819
35
Fbn (KHz)
AN1026
20
-110
15
-120
10
-130
5
0
-140
0
5
10
15
20
Ic (mA)
25
30
35
-150
-160
NE68519
NE68819
-170
Figure 6b. Fbn at VCE=3V for the NE68519 and the
NE68819
100
5 9.5K
1K
10K
5V (f) [dBv/Hz] vs. f (Hz)
100K
The flicker corner frequencies for the two devices are within
3% at the lower bias of Vce=1V and Ic=5mA; Fbn = 5.8kHz for
the NE68519 and Fbn=5.6kHz for the NE68819. At higher
biases, the NE68819 has lower 1/f noise.
Figure 7b. 1/f measurement with Vce constant, Vce=3V,
and Ic=5mA aand 10mA for the NE68519
As the bias voltage increases from 1V to 3V with a constant
collector current Ic=20mA, the amplitude of the 1/f slope is
unchanged but the amplitude of the white noise floor increases
due to the increase in thermal noise voltage as shown in Figure
7a. The higher noise floor results in a lower 1/f corner
frequency of 11.8kHz at Vce=3V. At Vce=1V the 1/f corner
frequency is 16kHz.
A nonlinear model was developed for the NE68519 and the
NE68819. The simulation schematic and the variable values
for the NE68819 are shown in Figures 8a and 8b. The
simulator used is the LIBRATM harmonic balance simulator by
HP/EESOF [4]. The test bench is shown in Figure 8c. Note
that AF=1.26 and KF=2.6e-14 to provide flicker noise
simulation. Simulated 1/f noise for the NE68819 at Vce=3V,
Ic=10mA is shown in Figure 9.
IV. 1/f Noise Simulation
A. NE68819 simulated versus measured
-110
-120
-130
-140
3V
1V
-150
Measured 1/f noise spectra at Vce=3V, Ic=12mA, Figure 5,
was compared to simulated 1/f noise at Vce=3V, Ic=10mA,
Figure 9. Although the collector currents were 20% different,
the 1/f corner frequencies - measured vs model - were within
10% of each other. The white noise floor was -149dB
(measured) compared to -151dB (model) resulting in a 1.32%
difference. The 1MHz noise amplitude was -131dB (measured
compared to -132dB (modeled), a difference of only 0.76%.
-160
B. Modeling 1/f noise with AF and KF
-170
100
1K
10K
9V(f) [dBv/Hz] vs. f[Hz]
100K
Figure 7a. 1/f measurement with IC constant, Ic=20mA
and Vce=1V and 3V for the NE68519
As the bias current increases from 5mA to 10mA and the bias
voltage stays constant at Vce=3V, the 1/f spectrum amplitude
increases proportionally with increases in base current, and
the shot noise component of the white noise floor increases
proportionally with increasing base current, Figure 7b.
Most commercial simulators set AF and KF to default values
of 1.0 and 0 respectively. Inspection of equation (1) shows
that if KF = 0, the flicker noise spectral density will also be 0,
resulting in the presence of white noise only. Examining
figure 10c with KF=1e-13 shows the 1/f spectra approaching
the white noise spectra. Figures 10a and 10b model the 1/f
spectra changes as KF and AF are varied. Note that the Yintercept of the 1/f spectra increases proportionally to KF, as
expected from equation (1). The Y-intercept of the 1/f spectra
decreases more rapidly with increases in AF. Equation (2)
verifies this to be the case with the 1/f spectral density
decreasing exponentially with increases in AF, since IB is less
than unity.
AN1026
CAP
Co
C = 1000000000
AMMETER
AMM1
RES
RL
R = 2000
TEMP = TEMP2
IND
Lc
L = Lc
CAP
Ccb
C = Ccb
PORT
P1
port = 1
CAP
Ci_g
C= 1000000000
RES
AMMETER
Rbb
AMM2
R = rbb
TEMP = TEMP2
CAP
Ccc
C = Ccc
IND
Lb
L = Lb
BJT
BJT1
AREA = 1
MODEL = NE688 chip model
MODE = nonlinear
+ DCVS
SRC1
_ DC = 5.48
PORT
P2
port = 2
CAP
Cc1
C = 1000000000
IND
La
L = 1000000000
+ DCVS
SRCc
- DC = 23
IND
Le
L = Le
BJTM
NE688 chip model
IS = is
BR = br
BF = bf
NR = nr
NF = nf
VAR = var
VAF = vaf IKR = ikr
IKF = ikf
ISC = isc
ISE = ise
NC = nc
NE = ne
RB = rb
IRB = irb
RBM = rbm
RE = re
RC = rc
CJE = cje
VJE = vje
MJE = mje
TF = tf
XTF = xtf
VTF = vtf
ITF = itf
PTF = 0
CJC = cjc
VJC = vjc
MJC = mjc
XCJC = xcjc
TR = tr
CJS = 0
VJS = 0.75
MJ5 = 0
XTB = 0
EG = 1.11
XT = 3
KF = kf
AF = af
FC = fc
TYPE = type
NK = 0.50
TNOM = 27
FFE = 1
KB = 0
AB = 1
FB = 1
ISS = 0
NS = 1
Figure 8a. NE68819 Simulation Schematic
DATA
UNITS
UNITS_DEFAULT
FREQ=GHz
RES=0hm
COND=S
IND=nH
CAP=pF
LNG=mil
TIME=psec
ANG=deg
POWER=dBm
VOLT=V
CUR=mA
DIST=mi
TEMP
TEMP_DEFAULT
TEMP=27
DATA
DATA
DATA
RREF
RREF_DEFAULT
R=50
TAND
TAND_DEFAULT
TAND=0
SIGMA
SIGMA_DEFAULT
SIGMA=0
tf=1.10e-11
xtf=0.36
vtf=0.65
itf=0.61
ptf=50
cjc=5.49e-13
vjc=0.65
mjc=0.48
xcjc=0.56
tr=3.20e-11
fc=0.75
kf=2.60e-14
cf=1.26
Ccb=0.24
Cce=0.27
Lb=0.72
Lc=0.51
Le=0.19
rbb=50000
DATA
TEMP
TEMP2
TEMP=0
Var
Eqn
VAR
_VAR
is=3.80e-16
bf=135.70
nf=1.00
vaf=28
ikf=0.60
ise=3.80e–15
ne=1.49
br=12.28
nr=1.10
var=3.50
ikr=0.06
isc=3.50e-16
nc=1.62
rb=6.14
irb=1.00e-03
rbm=3.50
re=0.40
rc=4.20
cje=7.96e-13
vje=0.71
mje=0.38
NE688_chip_model PARAMETERS AND BONDING PARASITICS
DATE:
10/2/96
PROJECT NAME:
68800
LIBRA DEFAULT FILE:
68800_def
Figure 8b. NE68819 nonlinear model parameter values
68800_noise_sch
X1
FREQUENCY
FPLAN
value = ESWEEP 1.00e-07 1.00e-04 50
VNOISEQ
VNOISEQ1
PORT = 2
OUTPUT
EQUATION
OUT EQN
OUTEQN
v_noise_out = 20* log(VNOISEQ1)
Figure 8c. NE68819 test bench
DATA
PERM
PERM_DEFAULT
MUR=1
TANM=0
AN1026
68800_mod_noise10_tb
v_noise_out
68800_noise
OUT EQN
Re
-100.0
-105.0
-110.0
-115.0
-120.0
-125.0
-132 dB -130.0
-131 dB -135.0
-140.0
-145.0
-150.0
-155.0
-160.0
-165.0
-170.0
0.1
-100.0
-110.0
Measured
KF = 20e-13
-120.0
Model
KF = 10e-13
-130.0
KF = 5e-13
-151 dB
-149 dB
KF = 2e-13 KF = 1e-13
-140.0
-150.0
5.8 KHz 6.3 KHz
Frequency KHz
NE68800 noise voltage - effect of varying AF & KF
VCE = 3 V
IC = 10 mA
-160.0
100.0
Model
Measured
-170.0
0.1
Figure 9. 1/F noise simulation for the NE68819 at Vce=
3V, Ic=10 mA
Frequency KHz
100.0
NE68800 noise voltage - effect of varying AF & KF
AF = 1.6, Vce = 3V, KF = 1e-13 to 2e-12
Ic = 10mA
Figure 10c. Effect of varying KF from 1e-13 to 20-e-13
with AF=1.6
CONCLUSIONS
1.
-100.0
AF = 1
-110.0
2.
-120.0
-130.0
3.
-140.0
-150.0
4.
AF = 2
-160.0
-170.0
0.1
100
Frequency KHz
NE68800 noise voltage - effect of varying AF & KF
AF = 1 to 2, KF = 5e-13
Vce = 3V
Ic = 10ma
Figure 10a. Effect of varying AF from 1 to 2 with
KF=5e-13
-100.0
-110.0
REFERENCES
[1] Roger Muat, “Choosing devices for quiet oscillators”,
Microwave & RF, August 1984, pp. 166-170.
[2] Grant Moulton, “Dig for the roots of oscillator noise”,
Microwave & RF, pp. 65-69, April 1986.
[3] Julio Costa et al, “Extracting 1/f Noise Coefficients for
BJT’s,” IEEE Transactions on Electron Devices, Vol. 41,
No.11, pp. 1992-1999, Nov. 1994
[4] “Simulating Noise in Nonlinear Circuits Using the HP
Microwave and RF Design Systems,” HP Product note 851804, c 1993.
KF = 20e-13
KF = 10e-13
KF = 5e-13
-120.0
KF = 2e-13
-130.0
-140.0
KF = 1e-13
-150.0
California Eastern Laboratories
-160.0
-170.0
0.1
5.
Using the test setup and measurement techniques
described, 1/f noise can be measured.
Using an accurate nonlinear model, 1/f noise simulations
agree closely to measured data.
As Vce increases, the flicker corner increases as the white
noise increases, but the magnitude of the 1/f noise is
constant.
As base current increases, the flicker corner frequency
increases with the magnitude of the 1/f noise and the
increased shot noise current.
1/f noise increases linearly as KF increases and decreases
with increases in AF for IB less than 1.0 amp, as is
expected from equation (1).
Frequency KHz
100.0
NE68800 noise voltage - effect of varying AF & KF
AF = 1, KF = 1e-13 to 2e-12
Ic = 10mA
Figure 10b. Effect of varying KF from 1e-13 to 20-e-13
with AF=1
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© California Eastern Laboratories 02/04/2003