input noise: current, voltage (i n , e n )
DESCRIPTION
Input Noise: Current, Voltage (i n , e n ). Op Amp Noise Model. V N. I N +. I N -. Noise Model (I N + and I N - are not correlated). OPA277 Data. Tina Simplified Model. V N. I N. Understanding The Spectrum: Total Noise Equation (Current or Voltage). - PowerPoint PPT PresentationTRANSCRIPT
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Input Noise: Current, Voltage (in, en)
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Op Amp Noise Model
OPA277 Data
VVNN
IINN--IINN
++
Noise Model
(IN+ and IN- are not correlated)
Tina Simplified Model
*n
VU
1
*fA
U2
-
+
IOP1
INVN
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Understanding The Spectrum:Total Noise Equation (Current or Voltage)
0.1 1 10 100 1k 10k1
10
100
1k
10k
100k
)V
olt
age
No
ise
(nV
/H
z
1/f Noise Region(Pink Noise Region)
White Noise Region(Broadband Noise Region)
en1/f calculation
fHfL
Frequency (Hz)
enBB calculation
enT = √[(en1/f)2 + (enBB)2]
where:enT = Total rms Voltage Noise in volts rms en1/f = 1/f voltage noise in volts rmsenBB = Broadband voltage noise in volts rms
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fP fBF
Small Signal BW
Noise BW
Skirt of1-Pole FilterResponse
Brickwall
Frequency (f)
0
0.1fP 10fP
-20
-40
-80
Fil
ter
Att
en
ua
tio
n (
dB
)
Skirt of2-Pole FilterResponse
Skirt of3-Pole FilterResponse
Real Filter Correction vs Brickwall Filter
where: fP = roll-off frequency of pole or polesfBF = equivalent brickwall filter frequency
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Number of Poles in Filter
KnAC Noise Bandwidth Ratio
1 1.57
2 1.22
3 1.16
4 1.13
5 1.12
AC Noise Bandwidth Ratios for nth Order Low-Pass Filters
Real Filter Correction vs Brickwall Filter
BWn = (fH)(Kn) Effective Noise Bandwidth
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Broadband Noise Equation
enBB = (eBB)(√[BWn])
where:enBB = Broadband voltage noise in volts rmseBB = Broadband voltage noise density ; usually in nV/√HzBWn = Noise bandwidth for a given system
BWn = (fH)(Kn)
where:BWn = noise bandwidth for a given systemfH = upper frequency of frequency range of operationKn = “Brickwall” filter multiplier to include the “skirt” effects of a low pass filter
eBB
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1/f Noise Equation
en1/f = (e1/f@1Hz)(√[ln(fH/fL)])
where:en1/f = 1/f voltage noise in volts rms over frequency range of operatione1/f@1Hz = voltage noise density at 1Hz; (usually in nV)fH = upper frequency of frequency range of operation (Use BWn as an approximation for fH)fL = lower frequency of frequency range of operation
e1/f@1Hz = (e1/f@f)(√[f])
where: e1/f@1Hz = normalized noise at 1Hz (usually in nV)e1/f@f = voltage noise density at f ; (usually in nV/√Hz)f = a frequency in the 1/f region where noise voltage density is known
e1/f@1Hz
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Example Noise Calculation
Given:OPA627 Noise Gain of 101
Find (RTI, RTO): Voltage NoiseCurrent NoiseResistor Noise
V1 15
V2 15
-
+ +U1 OPA627/BB
R1 100kR2 1k+
VG1
VF1
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Unity Gain Bandwidth = 16MHz
Closed Loop Bandwidth = 16MHz / 101 = 158kHz
Voltage Noise Spectrum and Noise Bandwidth
50nV/rt-Hz
5nV/rt-Hz
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Example Voltage Noise Calculation
Voltage Noise Calculation:
Broadband Voltage Noise Component:BWn ≈ (fH)(Kn) (note Kn = 1.57 for single pole)BWn ≈ (158kHz)(1.57) =248kHz
enBB = (eBB)(√BWn)enBB = (5nV/√Hz)(√248kHz) = 2490nV rms
1/f Voltage Noise Component:e1/f@1Hz = (e1/f@f)(√f)e1/f@1Hz = (50nV/√Hz)(√1Hz) = 50nV
en1/f = (e1/f@1Hz)(√[ln(fH/fL)]) Use fH = BWn
en1/f = (50nV)(√[ln(248kHz/1Hz)]) = 176nV rms
Total Voltage Noise (referred to the input of the amplifier):enT = √[(en1/f)2 + (enBB)2]enT = √[(176nV rms)2 + (2490nV rms)2] = 2496nV rms
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Example Current Noise Calculation
Note: This example amp doesn’t have 1/f component for current noise.
Gain
Req = R1 || Rf
*
Rf 3k
-
+
IOP1
VF1
*fA
U2
R1 1k Rf 3k
-
+
IOP1
VF1
*fA
U2
R1 1k
en-out= Gain x (in)x(Req)en-in= (in)x(Req)
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Example Current Noise Calculation
Broadband Current Noise Component:BWn ≈ (fH)(Kn)BWn ≈ (158kHz)(1.57) =248kHz
inBB = (iBB)(√BWn)inBB = (2.5fA/√Hz)(√248kHz) = 1.244pA rms
Req = Rf || R1 = 100k || 1k = 0.99k
eni = (In)( Req) = (1.244pA)(0.99k) = 1.23nV rms
Since the Total Voltage noise is envt = 2496nV rms the current noise can be neglected.
neglect
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Resistor Noise – Thermal Noise
The mean- square open- circuit voltage (e) across a resistor (R) is:
en = √√ (4kTKRΔf) where: TK is Temperature (ºK) R is Resistance (Ω) f is frequency (Hz) k is Boltzmann’s constant
(1.381E-23 joule/ºK) en is volts (VRMS)
To convert Temperature Kelvin to
TK = 273.15oC + TC
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Noise Spectral Density vs. Resistance
Resistance (Ohms)
Noi
se S
pect
ral D
ensi
ty v
s. R
esis
tanc
e
nV/r
t-H
z
10 100 1 103
1 104
1 105
1 106
1 107
0.1
1
10
100
1 103
468.916
0.347
4 1.38065 1023 25 273.15( ) X 10
9
4 1.38065 1023 125 273.15( ) X 10
9
4 1.38065 1023 55 273.15( ) X 10
9
10710 X
1000
10 100 1 103
1 104
1 105
1 106
1 107
0.1
1
10
100
1 103
468.916
0.347
4 1.380651023 25 273.15( ) X 10
9
4 1.380651023 125 273.15( ) X 10
9
4 1.380651023 55 273.15( ) X 10
9
10710 X
25C
125C
-55C
en density = √√ (4kTKR)
Resistor Noise – Thermal Noise
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eenr = √(4kT = √(4kTKKRRΔΔf) f)
where:where:
R = Req = R1||RfR = Req = R1||Rf
ΔΔf = BWf = BWnn
eenr = √(4 ( = √(4 (1.38E-23) (273 + 25) (0.99k)((273 + 25) (0.99k)(248kHz)) = 2010nV rms
Example Resistor Noise Calculation
Gain
Req = R1 || Rf
*
R1 2kR2 1k
-
+
IOP1
VF1
*nV
U1
*nV
U1
RfR1
en-out= Gain x (√(4kTR√(4kTRΔΔf)f))en-in= √(4kTR√(4kTRΔΔf)f)
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Total Noise Calculation
Voltage Noise From Op-Amp RTI:env = 2510nV rms
Current Noise From Op-Amp RTI (as a voltage):eni = 1.24nV rms
Resistor Noise RTI:enr = 2020nV rms
Total Noise RTI:en in = √((2510nV)2 + ((1.2nV)2 + ((2010nV)2) = 3216nV rms
Total Noise RTO:en out = en in x gain = (3216nV)(101) = 325uV rms
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Calculating Noise Vpp from Noise Vrms
Peak-to-PeakAmplitude
Probability of Havinga Larger Amplitude
2 X rms 32%
3 X rms 13%
4 X rms 4.6%
5 X rms 1.2%
6 X rms * 0.3%
6.6 X rms 0.1%
Relation of Peak-to-Peak Value of AC Noise Voltage to rms Value
*Common Practice is to use: Peak-to-Peak Amplitude = 6 X rms
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Voltage Noise (f = 0.1Hz to 10Hz) Low Frequency
Low frequency noise spec and curve:Over specific frequency range: 0.1Hz < f < 10HzGiven as Noise Voltage in pp units
Measured After Bandpass Filter:
0.1Hz Second−Order High−Pass
10Hz Fourth−Order Low−Pass