1 noise in photodiode applications by art kay and bryan zhao ( ) june 1, 2011
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1
Noise In Photodiode Applications
By Art Kay and Bryan Zhao ( 赵 伟 ) June 1, 2011
2
Contents
• Noise Review• Photodiode Review• Photodiode Noise Theory• Bandwidth and Stability• OPA827 Hand Calculation• OPA827 Tina Spice Analysis• OPA827 Measurement Example
3
4
-
+
Vout
+
VinOp-Amp
Noise Model
Resistor Noise Model
Resistor Noise Model
Vout with Noise vs Time
-4
-3
-2
-1
0
1
2
3
4
5
0 2 4 6 8 10 12
Time (mS)V
ou
t (m
V)
Vout Ideal vs Time
-4
-3
-2
-1
0
1
2
3
4
0 2 4 6 8 10 12
Time (mS)
Vo
ut
(mV
)
Vin vs Time
-1.5
-1
-0.5
0
0.5
1
1.5
0 2 4 6 8 10 12
Time (mS)
Vin
(m
V)
Intrinsic Noise
• Error Source• Generated by circuit itself (not pickup)• Calculate, Simulate, and Measure
5
0.04
-0.04
0.02
-0.02
0.00
Distribution of NoiseThermal Noise Measured In Time Domain
Vo
ltag
e (V
olt
s)
Counts Recorded During Measurement Period.
-0.04
-0.02
0
0.02
0.04
0.00E+00 5.00E-04 1.00E-03
Time (Sec)
Vo
ltag
e (V
olt
s)V
olt
age
(Vo
lts
)
Time (sec.)
Time Domain – White noise
normal distribution
6
What is Spectral Density? (Noise per unit frequency)
T
1 1k 1M 1G
Out
put n
oise
(V
/Hz½
)
0
76n
150n
T
Time (s)
0.00 200.00m 400.00m
VG1
-999.39m
999.39m
VG2
-999.39m
999.39m
VG3
-1.00
1.00
VG4
-1.00
1.00
VG5
-999.39m
999.39m
VG6
-1.00
1.00
VG7
-999.85m
999.85m
VG8
-999.85m
999.85m
tot3
-5.49
7.46
Sum of all frequenciesRandom Noise
time
frequency
7
Convert Spectral Density to RMS Convert RMS to Peak-to-Peak
fL
fH
fen2
d Erms
0.04
-0.04
0.02
-0.02
0.00
Distribution of NoiseThermal Noise Measured In Time Domain
Vo
ltag
e (V
olt
s)
Counts Recorded During Measurement Period.
-0.04
-0.02
0
0.02
0.04
0.00E+00 5.00E-04 1.00E-03V
olt
age
(Vo
lts)
Time (sec.)
0.04
-0.04
0.02
-0.02
0.00
Distribution of Noise Thermal Noise Measured In Time Domain
Vo
ltage (V
olts)
Counts Recorded During Measurement Period.
Vo
ltage (V
olts)
Time (sec.)
8
Why Photodiode Noise?
• Noise is a key parameter in photodiode design– Wide bandwidth (integrate more noise)– Low signal levels (noise more critical)
• Photodiode amplifier noise is more complex– Parasitic capacitance and sensor capacitance– Poles and zeros– Gain peaking
9
What can we do with the photodiode knowledge?
TI
Our new friends from National.
The competition is in trouble!
10
11
Photodiode Basics
Introduction • Photodiodes convert light into current or voltage.
Photodiode type• PN photodiode – more wavelength selective • PIN photodiode – wide spectral range (less selective) • APD (Avalanche photodiode) – sensitive to low light, fast
12
+-
E-fieldMagnitude
E-field
NP
Photon
+-
Photon+
+
--
+
++
+-
--
-
Depletion Region
Basic Photodiode Physics
13
Photodiode Basics
Figure1.3 Photodiode Equivalent Circuit
Figure1.4 Current VS. Voltage Characteristics
14
Photodiode Basic
a
Io
IL
ID
I' IL
ISe
eVD
kT1
I'
o
IS : Photodiode reverse saturation current e: electron charge k: Boltzmann's constant T: Absolute temperature of the photodiode
Voc
kT
cln
IL
I'
IS
1
I
Use left equivalent circuit, the output current is given as :
The open circuit voltage Voc is the output voltage when Io equals 0. Thus Voc becomes:
Figure1.4 Photodiode Equivalent Circuit
Figure1.5 Current VS. Voltage Characteristics
Io
IL
ID
I' IL
ISe
eVD
kT1
I'
IS : Photodiode reverse saturation current
e: electron charge k: Boltzmann's constant T: Absolute temperature of the photodiode
15
Photodiode and Control Source TINA model
Light exciting source: 1) Use VG1 and VG2 voltage sources to simulate light power wave. 2) Use R1 and C1 shape light signal 3) The Voltage Control Current Source (VCCS1) simulates photodiode sensitivity.Photodiode Equivalent Circuit: 1), Current Source Id simulates Dark current 2), Diode is a ideal diode 3), Cd and Rd simulate photodiode's junction capacitor and dark Resistance. 4), Rs is series resistor, which is far smaller than Rd.
Id
RdCd
Rs
Diode-
+
VCCS1 1u
+
VG1
+
VG2
C1
R1
Rf 1M
VG
Vi
Vo
-
+
Ideal OP
Simulate light source Photodiode equivalent circuit
VCCS transconductance simulate flux responsivity
16
17
-
+
VOUT
vn
Cf 4p
incopaRsincj
Photodiode Model
Op-Amp Model
Rf 100kvn
Resistor Model
Photo-Diode Amp Noise Model
18
Photodiode noise
Thermal (Johnson Noise)
ij
4kb Tn
Rsh
Shot noise (dark)
isD 2q ID
Shot noise (w. Light)
isL 2q IL
Total Diode Current Noise
in ij2
isD2 isL
2 -
+
VOUT
vn
C1 4p
incinRsincj
Photodiode Model
Op-Amp Model
R1 100kvn
Resistor Model
kb Boltzmann constant 1.38*10-23J/K
q Electron Charge 1.6*10-19 C
Tn Temperature in Kelvin (25C)
fp Transconductance bandwidth
Rsh Shunt Resistance in photodiode
ID Dark Current in photodiode
IL Photo current in photodiode
19
Noise Gain
Gain seen by the noise voltage source.
Noise_GainVout
Vn
Simplify the model to compute Noise Gain
-
+
VOUT
vn
Cf 4p
incopaRsincj
Photodiode Model
Op-Amp Model
Rf 100kvn
Resistor Model
-
+
VOUT
vn
Cf 4p
Cin = Cj + Copa
Rf 100k
20
-
+
VOUT
vn
sCf
sCin
sRf
Node
Noise Gain
T
Frequency (Hz)
1.00 1.00k 1.00M 1.00G
Vol
tage
(V
)
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Aol
Noise Gain
fz
fp
Nodal Analysis on transimpedance amp
Vn
1
s Cin
Vn Vout Rf
Vn Vout
1
s Cf
0
Solve for noise gain Vout / Vn
Vout
Vn
Rf Cf Cin s 1
Cf Rf s 1
The numerator contains a Zero
fz1
2 Rf Cf Cin
The denominator contains a Pole
fp1
2 Rf Cf
21
Noise Gain fi
Cf
Ci Cffc Intersection of the noise gain curve
with the Aol Curve
fcUnity Gain Bandwidth from Op-Amp Data Sheet
GPM 1Cin
Cf Gain Peak Magnitude
22
Aol
Noise Gain
fz
fp fi
fc
T
Frequency (Hz)
1.00 1.00k 1.00M 1.00G
Outp
ut
nois
e (
V/H
z½
)
10.00n
0.10u
200.00n 1/f region
Noise Peak
Aol
Roll Off
NoiseGainOp-Amp
Voltage Noise (Data Sheet)
Output Noise
Noise Gain
23
Simulating Noise gain and noise bandwidth
AolVF3
VF1
Noise_Gain1
VF2
VF1
I_to_V_GainVF3
AM1
• Break the loop to measure Aol, 1/B, and I to V Gain
24
Voltage Noise eni , eno and Eno
Region 1 Region 2 Region 3 Region 4 Region 5
ff zf pf if cfEno1 Eno2
Eno3
Eno4Eno5
eno An eni
1s
z
1fs
1s
p
1
s
i
25
Voltage Noise eni , eno and Eno
22 21
2 2 22
22 2 3 323 2
22
24
2
25
ln
3
f
L
z
f
p
z
i
p
i
f
nif f fnoe f nif f
Lf
f
noe nif f nif z f
f
f
nif nif p znoe f
z zf
fnif i f
noe f nif i pff
nifnif cnoe f
f
e f fE d e f
f f
E e d e f f
e f e f fE d
f f
e C CE d e f f
C
e fe fE d
f
2c
if
2 2 2 2 2 21 2 3 4 5noe noe noe noe noe noeE E E E E E
Region 1 noise:
Region 2 noise:
Region 3 noise:
Region 4 noise:
Region 5 noise:
Total voltage noise:
26
Voltage Noise eni , eno and Eno
eno
Log scale
eno
Linear scale
Eno^2
Linear scale
R.1
R.2 R.3R.4
R.5
27
Resistor Noise and Current Noise
Poles Kn
1 1.57
2 1.22
3 1.16
Current noise and resistor noise are limited by the transimpedance (I-V gain) bandwidth
T
Aol
IVgain
Voltage Noise gain
Frequency (Hz)
1.00 5.48k 30.00M
Gai
n (d
B)
0.00
40.00
80.00
120.00
BWt=fp
Voltage Noise gain
IVgain
Aol
fP fBF
Small Signal BW
Noise BW
Skirt of1-Pole FilterResponse
Brickwall
Frequency (f)
0
0.1fP 10fP
-20
-40
-80
Filte
r A
tten
uati
on
(d
B)
Skirt of2-Pole FilterResponse
Skirt of3-Pole FilterResponse
BWn Kn fp
EnoR 4K T Rf BWn
Eno1 ini Rf BWn
28
29
Parasitic Capacitance Limits the Bandwidth
T
117dB, 317kHz
Gain
70.06
86.70
103.35
120.00
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M 100M
Phase
-90.00
-45.00
0.00
117dB, 317kHz
117dB, 317kHz
-
+OP AMP
Vo
Vp
Rf 1M
Cs 500f
Rd 50GCd 200pIG1
• Max bandwidth with Min Cf
• Low Cf may be unstable
• Wide BW increases noise
• As shown Cf=Cs (stray cap)
fp1
2 Rf Cf318kHz
30
Feedback Capacitance Required for Stability
• Noise Gain is key to stability• Also called 1/Beta (in stability analysis)• ROC = Rate of Closure• ROC = (Aol slope) – (1/Beta slope)• Unstable when ROC > 20dB/decade
-
+
Rf 1M
Cin 70p
T
Frequency (Hz)1 1k 1M 1G
Gai
n (
dB
)
-20
0
20
40
60
80
100
120
Aol1/Beta
(Noise Gain)
40dB/decRate of Closure
+20dB/dec-20dB/dec
fc = 150MHzUnity Gain BW
31
Feedback Capacitance Required for Stability
T
Time (s)
0.00 50.00u 100.00u 150.00u 200.00u
IG1
0.00
2.00u
Vo
-1.48
2.88
Applying a Step Input shows instability at output-
+
Rf 1M
Cin 70p
32
Choosing a Minimum Cf for Stability
Frequency (Hz)1 1k 1M 1G
Gai
n (
dB
)
-20
0
20
40
60
80
100
120
fp
fc = 150MHzUnity Gain BW
fc 150MHz Op-amp Unity Gain Bandwidth
Cin 70pF Total input capacitance
Rf 1M Feedback resistance
Simplified equation forminimum feedback capAssumes Cin >> Cf
Cf
Cin
2 Rf fc272.5fF
Cc1
2 Rf fcIntermediate calculation usedin more exact formula
More exactformula forfeedbackcapacitance
Cfe
Cc
21 1
4Cin
Cc
273.1fF
-
+
Rf 1M
Cf 273f
Cin 70p
33
34
Noise Model for Simple Transimpedance Amp
-
+
VOUT
vn
C1 4p
incopaRsincj
Photodiode Model
Op-Amp Model
R1 100kvn
Resistor Model
35
Example Photodiode: PDB-C158
Unfortunately Cj is not specified at Vr=0V.
We called the manufacturer for this info Cj=70pF for Vr=0V
36
Calculate Diode Current Noise
-
+
VOUT
vn
C1 4p
incinRsincj
Photodiode Model
Op-Amp Model
R1 100kvn
Resistor Model
Thermal (Johnson Noise)
4kb Tn
Rsh10.472 10
15A
Hz
Shot noise (dark)
2q ID 25.314 1015
A
Hz
Shot noise (w. Light)
isL 2q IL 0
Total Diode Current Noise
ij2
isD2 isL
2 27.395 1015
A
Hz
kb 1.381023J
K Boltzmann constant
q 1.6021019C One electron Charge
Tn 298K Temperature in Kelvin (25C)
fp 397.887 103 Hz Transconductance bandwidth
Rsh 150106 Shunt Resistance in photodiode
ID 2 109 A Dark Current in photodiode
IL 0A Photo current in photodiode (our measurements are dark)
37
OPA827 Noise Hand Calculation (key numbers)
-
+
VOUT
vn
C1 4p
incinRsincj
Photodiode Model
Op-Amp Model
R1 100kvn
Resistor Model
38
OPA827 Noise Hand Calculation
-
+
vn
100k
4p
70pF
Photodiode Model
Op-Amp Model
18pF
0.1 1 10 100 1k 10k
100
10
1
enif
eat_f
fL
39
Poles and Zeros in Noise Gain Curve
fz1
2 Rf Ci Cf 17.299 10
3 Hz
fp1
2 Rf Cf397.887 10
3 Hz
fi
Cf
Ci Cffc 956.522 10
3 Hz
fp
fz
fi
40
efnorm eat_f fL 18.974 109 V
ff
efnorm2
enif2
24.931Hz
1/f (flicker) Noise Corner
fL
ff enif
eat_f
41
Output Noise from OPA Noise Voltage
Enoe1 enif2ff ln
ff
fL
44.573 109 V
Enoe2 enif2fz ff 499.444 10
9 V
Enoe3
enif
fz
2fp3
fz3
3 31.828 10
6 V
Enoe4 enif
Ci Cf
Cf
2
fi fp 65.324 106 V
Enoe5
enif fc 2fi
85.479 106 V
Enoe Enoe12
Enoe22 Enoe3
2 Enoe42 Enoe5
2 112.193 106 V
42
Thermal (Resistor) Noise at Output
-
+
VOUT
vn
C1 4p
incinRsincj
Photodiode Model
Op-Amp Model
R1 100kvn
Resistor Model
43
Current Noise to Voltage Noise at Output
-
+
VOUT
vn
C1 4p
incinRsincj
Photodiode Model
Op-Amp Model
R1 100kvn
Resistor Model
44
The Final Total Noise
Enoe 112.193 106 V Op-Amp Voltage Noise
EnoR 32.056 106 V Resistor Noise
EnoI 2.172106V Op-Amp Current Noise
Eno EnoR2
EnoI2 Enoe
2 116.703 106 V Total Output Noise for
OPA827 Transimpedance Amp
45
Reducing Noise (Higher Cf = Lower BW & Noise)
T
Frequency (Hz)10k 100k 1M 10M 100M
I to
V G
ain
(dB
)
20
40
60
80
100
120
Cf=2pF
Cf=4pF
T
Frequency (Hz)1 4k 20M
Out
put n
oise
(V
/Hz½
)
0
76n
150n Cf=2pF
Cf=4pF
T
Frequency (Hz)1 271 74k 20M
Tot
al n
oise
(V
)
0
90u
180u
Cf=2pF
Cf=4pF
46
Flux Capacitor
• Advantage– Reduces noise to zero– Available on E-Bay
• Disadvantage – Requires 1.21 gigawatts– Size
ADS1118
Quarter
47
48
OPA827 – test the model
V+V-
V-
V+J1
-
+ +3
2
7
4
6
U1 OPA827V1 18 V2 18
-
+CCVS1 1+ VG1
voltage noise
Current noise
T
Current noise density
voltage noise density
Frequency (Hz)
100.00m 1.00 10.00 100.00 1.00k 10.00k
Current noise
1.00E-15
2.00E-15
3.00E-15
voltage noise
1.00n
10.00n
100.00n
Current noise density
voltage noise density
The noise performance is the same as datasheet.
Low Noise : 4nV/√Hz at 1kHz Low Offset Voltage: 150µV max JFET Input: IB= 15pA typ
Wide Bandwidth: 22MHz
49
Simulated Spectral Density and Total Noise
V-
V+
-
+ +3
2
7
4
6
U1 OPA827
Cd 70p
R2 100k
C1 4p
Vo
T
Frequency (Hz)
200.00m 2.00k 20.00M
Out
put
nois
e (V
/Hz?
)
6.64n
42.42n
78.19n
T
Frequency (Hz)
200.00m 2.00k 20.00M
Tota
l nois
e (
V)
0.00
54.54u
109.09u
Output Noise Density
Total Output NoiseCalculated
(rms)
Simulated
(rms)
116.7uV 109.1uV
50
51
Validating Test Equipment Capability
Spectrum AnalyzerOr Scope
OPA827 Transimpedance
Amp
Noise Spectral Density = 3.8nV/rtHzTotal Noise = 109.1uVrms = 654.6uVp-p
Photodiode (No light)
What is the noise floor?
52
Tektronix DPO 4034 Oscilloscope
STDEV: 48uV (same as RMS)P-P: 6.6*STDEV=319uV40s P-P: 320uV
1) Set DC couple, 20MHz bandwidth limit2) Short input channel to measure noise floor
53
Agilent 4395A Spectrum Analyzer1. Frequency Range: 10Hz~500MHz2. Noise floor: 10nV/rtHz3. Input Impedance: 50Ω
Reference voltage Noise Floor:
10nV/rtHz
54
The Noise Floors are Not Good Enough
Spectrum AnalyzerOr Scope
OPA827 Transimpedance
Amp
Noise Spectral Density = 3.8nV/rtHzTotal noise = 109.1uVrms = 654.6uVp-p
Photodiode (No light)
Noise Floors:Scope (1mV range)= 48uV rms =320uVpp
4395A Spect. Analyzer = 10nV/rtHz
55
Solution: Use A Post AmpWhat amp do we Choose?
Spectrum AnalyzerOr Scope
OPA827 Transimpedance
Amp
Noise Spectral Density = 3.8nV/rtHzTotal noise = 109.1uVrms = 654.6uVp-p
Photodiode (No light)
Noise Floors:Scope (1mV range)= 48uVrms = 320uVp-p
4395A Spect. Analyzer = 10nV/rtHz
Post Amp
Gain BW = 22MHz
Need Gain > 10
BW> 22MHz (in gain)Noise < 3.8nV/rtHz
Amplified Signal from OPA827With Negligible additional noise
Use OPA847 as post amplifierWideband, Ultra-Low Noise, Voltage Feedback, Operational Amplifier
• At the gain of 150, the bandwidth is 26MHz
• 0.85nV/Hz Input Voltage Noise
• 2.5pA/Hz Input Current Noise
• ±100uV Input Offset Voltage (Typical))
575uVrms post amplifier noise in 20MHz bandwidth.
T
Frequency (Hz)
200.00m 2.00k 20.00M
Tot
al n
oise
(V
)
0.00
287.74u
575.48u
Post Amplifier Output Noise
V-
V+
R5 1.49k
R4 10
+
-
+DIS
U2 OPA847
R1 50 C1 33u Vo
Vin
57
T
Frequency (Hz)
1 100 10k 1M 20M
Vn827
0.00
109.54u
Vn_post
0.00
16.03m
Post AmplifierRelatively small error!
Vn827 = 109.4uV rms
Vnpost = 16.03mV rms
Vnpost/Gain = 16.03mV/150 = 106.8uV rms
Gain=150
58
Test the Noise Floor
Spectrum AnalyzerOr Scope
Post Amp
Disconnect The DUT
(Transimpedance amp)
GND input Measure Noise
59
Test The Noise Floor – Post Amp Noise Scope
Simulated
(rms)
Measured
(rms)
575uV 518uV
STDEV: 518uVP-P: 6.6*STDEV=3.4mV40s P-P: 3.88mV
60
Hardware Connections
V-V+
V-
V+
-
+ +3
2
7
4
6
U1 OPA827
Cd 70p
R2 100k
C1 4p
Vo
R5 1.5k
R4 10
+
-
+DIS
U2 OPA847
VF1
1. PDB-C158-ND photodiode2. 70pF junction capacitance at Vr=0 V3. 100dB I-V gain4. 4pF compensation capacitor5. ±5V power supply.
61
Shield the Circuit if Possible
Power SupplyVcc,Vss,GND
Input & Output BNC connectors
Shield
62
Divide by Gain for OPA827 Output Noise
63
Measured Total Output Noise (DPO 4034 Scope)
21.7
1500.145 mV =145uV
OPA847 Measured at Scope:STDEV: 21.7mVP-P: 6.6*STDEV=143mV40s P-P: 170mV
At OPA827 (DUT) Output:Divide by gainVn827 = 21.7mV/150 = 144.6uV
Calculated
(rms)
Simulated
(rms)
Measured
(rms)
116.7uV 109.1uV 144.6uV
64
Measured Spectral Density 4395A Spectrum Analyzer
Linear Scale
1. Agilent 4395A Spectrum Analyzer test 1Hz~20MHz span, 3uV/div, REF=24uV.
2. The tested noise density curve shape is the same as simulation.
Measurement 4395A
Linear Scale
T
Frequency (Hz)
0.00 2.00M 4.00M 6.00M 8.00M 10.00M12.00M14.00M16.00M18.00M20.00M
Outp
ut
nois
e (
V/H
z?)
-6.00u
-3.00u
0.00
3.00u
6.00u
9.00u
12.00u
15.00u
18.00u
21.00u
24.00u
Tina Spice
Linear Scale
T
Frequency (Hz)
200.00m 2.00 20.00 200.00 2.00k 20.00k 200.00k 2.00M 20.00M
Out
put
nois
e (V
/Hz?
)
0.00
3.00u
6.00u
9.00u
12.00u
Tina Spice
Log Scale
65
OPA827-Noise Density 4395A Spectrum Analyzer
T
Frequency (Hz)
10k 309k 608k 907k 1.2M 1.5M 1.8M 2.1M 2.4M 2.7M 3.0M
Ou
tpu
t n
ois
e (V
/rtH
z)
(29KHz, 22.7nV/rtHz)
(552KHz, 46.7nV/rtHz)
(2MHz, 24.7nV/rtHz)
(3MHz, 16.7nV/rtHz)
(29KHz, 20.7nV/rtHz)
(2MHz, 22.3nV/rtHz)
(3MHz, 14.3nV/rtHz)
(552KHz, 40nV/rtHz)
Simulated
MeasuredO
utp
ut
no
ise
(V/r
tHz)
66
Thanks• Bryan Zhao ( 赵 伟 )• Matt Hann• Collin Wells, Peter Semig, Curtis Mayberry
References• Jerald Graeme <Photodiode Amplifiers>• Art Kay < Op-Amp Noise Calculation and Measurement >• HAMAMATSU <Photodiode Technical Information>• Tim Green <Operational amp stability>
Before Questions, I must ask….
67
You will move to a new topic my young apprentice
More noise presentations have we must
Do I move over to the dark side?
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