Choosing the APC Loop Capacitors Used with MAX3735

Design Note:
HFDN-23.0
Rev.2; 04/08
Choosing the APC Loop Capacitors Used with
MAX3735/MAX3735A SFP Module Designs
Functional Diagrams
Pin Configurations appear at end of data sheet.
Functional Diagrams continued at end of data sheet.
UCSP is a trademark of Maxim Integrated Products, Inc.
LE
AVAILAB
Choosing the APC Loop Capacitors Used with MAX3735
and MAX3735A SFP Module Designs
1 Introduction
The MAX3735 and MAX3735A are DC-coupled
SFP laser drivers designed for data rates up to
2.7Gbps (Reference 1). The DC-coupled output, SFP
safety/timing specifications and monitor outputs of
the MAX3735/MAX3735A make these devices
suitable for a large variety of optical module
applications operating over a wide range of data
rates.
APC LOOP
VCC
VCC
BIAS
IBIAS
VCC
VBG
APCSET
x38
This application note is intended to aid module
designers in choosing proper values for the APC
loop capacitors. Tables for MAX3735A CAPC
selection are provided along with equations and a
Microsoft® Excel spreadsheet for the calculations of
the MA3735 loop capacitors.
2 Background Information
2.1
APC Loops
The APC loop integrated with many of Maxim’s
laser drivers is used to compensate for changes in
threshold current due to variations in temperature
and laser life. An APC loop (Figure 1) monitors the
laser back-facet photodiode current and adjusts the
bias current in order to keep the photodiode current
constant. Given that the relationship between the
photodiode current and average power is ideally
linear, the average power is held constant by keeping
the photodiode current at a constant level.
Application Note HFDN-23.0 (Rev.2; 04/08)
RAPCSET
IAPCSET
The proper choice of the APC (Automatic Power
Control) loop capacitors is critical for SFP and
multi-rate designs using the MAX3735/MAX3735A
laser drivers. If the capacitor is not chosen correctly,
instability, increased jitter, or increased turn-on time
(TON) may result.
MD
IMD
CMD
x1
APCFILT1
APCFILT2
CAPC
Figure 1. Typical APC loop
The bandwidth of the back-facet photodiode is
generally smaller than the bandwidth of the laser that
is being modulated due to capacitance of the
photodiode. Therefore, the back-facet photodiode
will not track all the high frequency changes in the
optical output. The APC loop capacitors (CAPC and
CMD) filter the incoming signal further to suppress
high-speed variations in the monitor diode current
that are caused by variations in the bit pattern.
The CMD capacitor sets the higher order pole that
filters incoming transients on the monitor diode
input pin. The CAPC capacitor sets the dominant pole
of the APC loop and also determines the APC loop
bandwidth (f3dB, Figure 2). As CAPC increases, the
APC loop bandwidth decreases.
Maxim Integrated
Page 2 of 8
Attenuation
APC Loop Bandwidth
f
3dB
(APC Loop)
Pole Set
by CAPC
Pole Set
by CMD
Frequency
Figure 2. APC loop bandwidth
Monitor diode current variations at frequencies
higher than f3dB are attenuated by the loop
capacitors. When the monitor diode current changes
at a frequency less than f3dB, the APC loop will track
and adjust the bias current to force the monitor diode
current to a constant level.
Low frequency variations of the monitor diode
current can be due to factors such as temperature and
age of the laser. As the temperature and age
increase, more bias current is required to maintain
the same monitor diode current (i.e. average power).
The APC loop is designed and intended to
compensate for these types of low frequency
variations. For more information see references 2
and 3.
2.2
Frequency Content of Data Patterns
The frequency content of the input data pattern
should be considered when choosing the APC loop
capacitors. Ethernet application for example use
coded patterns, such as 8b10b, that have very little
low frequency content. SONET PRBS test patterns
(223-1) and random NRZ data streams have a much
fuller and wider frequency spectrum that can extend
to very low frequencies (References 4, 5, 6 and 7).
If the frequency content of the data pattern is lower
than or close to the f3dB point of the APC loop, an
undesirable effect known as baseline wander can
occur. The effect on the output is similar to the
baseline wander effect caused by the low frequency
cutoff point of AC-coupling capacitors (References
5 and 6). In both cases, there is increased jitter and
Application Note HFDN-23.0 (Rev.2; 04/08)
decreased vertical eye opening when the low
frequency point is not chosen correctly.
To demonstrate how the APC loop is able to track
only low frequency changes in the data pattern, the
following tests were performed. First, a laser was
modulated at a high data rate using a repeating 1010
pattern (Figure 3). The filtered monitor diode current
and bias current were observed as well as the optical
output signal using a real-time scope. The frequency
content of the data pattern is much greater than the
APC loop bandwidth. As seen in Figure 3, the bias
and monitor diode current do not track the one and
zero bits of the data pattern and the optical output
waveform is not affected.
INPUT DATA
MONITOR
DIODE
CURRENT
BIAS
CURRENT
Optical Output
Figure 3. Input data with frequency
content >> f3dB
As the data rate is decreased to a very low frequency
(Figure 4), the filtered monitor diode current begins
to track the data pattern transitions. The APC loop
responds by increasing or decreasing the bias current
to maintain the average power. The optical output is
now affected due to the bias current variation created
when the APC loop tracks the low frequency bit
transitions of the low speed data pattern.
INPUT DATA
MONITOR
DIODE
CURRENT
BIAS
CURRENT
Optical Output
Figure 4. Input data with frequency
content near f3dB
Maxim Integrated
Page 3 of 9
Using a pseudo-random bit pattern, the baseline
wander effect, due to the APC loop, can be seen with
the optical eye diagram when infinite persistence is
enabled. Figure 5 is a filtered OC3 optical eye
diagram using the MAX3735 laser driver with a 2231 PRBS input data pattern. For this case, the APC
loop bandwidth was purposely set at a high value.
The low frequency content of the 223-1 PRBS pattern
at OC3 and the f3dB point of the APC loop is not low
enough which causes increased jitter and eye closure
as seen in Figure 5.
The output of the MAX3735/MAX3735A is DC
coupled which accommodates a wide modulation
frequency range, but the effect of the APC loop must
still be considered to obtain good performance for
the entire range of data rates. Multi-rate applications
that are intended to work from 100Mbps to 2.7Gbps
have a wide frequency spectrum range that requires
consideration of the input AC coupling (if used, see
reference 6) and the APC loop capacitors. Both of
which will have an effect on the overall baseline
wander and jitter of the optical output. In particular,
the lower data rates with long patterns may have
increased jitter and eye closure when the APC loop’s
f3dB point is not set properly with the loop capacitors.
To minimize the jitter and eye closure that can be
associated with the low-frequency content of the
data pattern, the f3dB point of the APC loop should
ideally be as low in frequency as possible by using a
very large CAPC. This is not possible for all
applications due to turn-on time requirements.
2.3
Figure 5. Optical eye – OC3, 223-1 PRBS,
CAPC = 0.01µF
By using a pattern with less low-frequency content
or by using a larger APC loop capacitor, the optical
results can be improved. As seen in figure 6, the eye
opening and the jitter have both improved by using a
larger CAPC capacitor.
Turn-on Time (TON)
The turn-on time (TON, See: SFP MSA) of the
MAX3735 and MAX3735A is a function of the CAPC
capacitor. In order to meet the SFP TON requirement
of 1ms, CAPC must be chosen correctly. Once the
CAPC value is chosen to meet the TON requirement,
the CMD and the APC loop bandwidth can be
determined. The APC loop bandwidth will help to
establish the acceptable data rates and patterns that
can be used and still maintain good optical
performance.
If the intended application does not have a
specification for TON, there is much more freedom in
choosing the CAPC values that would minimize jitter
due to baseline wander.
3 Choosing CAPC and CMD
The TON requirement (if applicable to the
application) should be the first variable to consider
when choosing the APC loop capacitors. Guides to
selecting CAPC based on TON requirements are listed
below for the MAX3735A and MAX3735. The
MAX3735A offers improved turn-on times under
the same conditions and is the preferred device for
multi-rate applications.
Figure 6. Optical eye – OC3, 223-1 PRBS,
CAPC = 0.1µF
Application Note HFDN-23.0 (Rev.2; 04/08)
MAX3735A:
Table 1 can be used to choose CAPC when using the
MAX3735A and a DC coupled laser, where laser
gain is defined as:
Maxim Integrated
Page 4 of 9
Gain DC −Coupled =
( I BIAS
I MD
(A/A)
− I TH + ( I MOD / 2))
CAPC should be chosen according to the highest gain
of the lasers (generally at cold temperature). CMD
should then be 4x to 20x smaller than CAPC. The
ratio between CAPC and CMD should be maintained to
separate the poles created by CAPC and CMD
capacitors and provide sufficient phase margin for
loop stability.
Table 1. DC-Coupled CAPC Selection
Laser Gain (A/A)
CAPC (µ
µF)
CMD (µ
µF)
0.005
0.007
0.010
0.020
0.030
0.040
0.039
0.047
0.068
0.100
0.120
0.120
0.0018 to 0.01
0.0022 to 0.012
0.0033 to 0.015
0.0047 to 0.022
0.0056 to 0.027
0.0056 to 0.027
The CAPC selection table assumes a 34% reduction in
the gain of the lasers at 85oC from the cold values
and that the Bias and MD current are within data
sheet specifications.
If CAPC is selected as shown in the table, the loop
bandwidth will be less than 17kHz and have turn on
times less than 600uS. These features allow the
device to be multi-rate and SFP compatible down to
155Mbps data rates using long patterns. See section
4 for more detail.
For AC-coupled laser, CAPC should be selected as
shown in table 2. Where Gain is now defined as:
Gain AC −Coupled =
I MD
(A/A)
( I BIAS − I TH )
Gain is a property of the laser, so it does not change
if the laser is DC coupled or AC coupled to the
driver. The affect it has on the loop is a result of the
amount of bias current generated by the laser driver.
For AC-coupled lasers the bias current will be larger
because the modulation current does not contribute
to the average current through the laser.
Table 2. AC-Coupled CAPC Selection
Laser Gain (A/A)
CAPC (µ
µF)
CMD (µ
µF)
0.005
0.007
0.010
0.020
0.030
0.040
0.100
0.120
0.150
0.150
0.168
0.180
0.0047 to 0.01
0.0056 to 0.012
0.0068 to 0.015
0.0068 to 0.015
0.0082 to 0.017
0.0082 to 0.018
MAX3735:
To estimate the TON of the MAX3735, the equations
in section 7 can be used. A Microsoft® Excel
spreadsheet is also provided to help with the
calculations (see section 8). The input parameters
required by the user are indicated in BLUE and the
output parameters from the equations are in RED.
Note that the equations assume that the laser is DCcoupled to the laser driver. The equations will give a
worst-case estimation of the TON time given the
provided information. An example in section 5
illustrates the procedure. Once CAPC is calculated to
meet the TON time, CMD can be easily calculated as
approximately 20x smaller than CAPC.
4 Determining Acceptable Data
Rates
From the data used to calculate the turn-on time, the
bandwidth of the APC loop can also be
approximated using the equations in section 7. The
loop bandwidth equation is valid for both the
MAX3735 and the MAX3735A. The loop
bandwidth is a function of the CAPC capacitor and the
gain (Figure 7), (defined in section 3). See section 7
for more details on calculating gain.
Since the MAX3735A minimum modulation current
is 10mA, the minimum bias current is assumed to be
at least 5mA for an AC-coupled laser. Given that the
minimum BIAS current is 5mA, larger CAPC values
can be used while still meeting turn-on times of less
than 600us. For AC coupled lasers, CMD should be
10x to 20x smaller than CAPC.
Application Note HFDN-23.0 (Rev.2; 04/08)
Maxim Integrated
Page 5 of 9
the entire system and determine what is acceptable
performance in their application.
APC Loop Bandwidth vs. Gain
1000
5 Example
CAPC = 2.7nF
f3dB (kHz)
100
CAPC = 10nF
10
CAPC = 100nF
1
CAPC = 470nF
An example of how to calculate the turn-on time and
loop bandwidth of the MAX3735 and MAX3735A
will be given. For these examples, the laser and
module parameters are assumed to be as shown in
Table 4.
0
0
0.01
0.02
0.03
0.04
0.05
GAIN
Figure 7. APC loop bandwidth vs. gain for
various CAPC values.
Table 3 is provided to aid in determining acceptable
data rates in multi-rate applications. This table was
generated using baseline-wander calculations
(Reference 5) with various loop bandwidths with a
long (223-1) and a short (27-1) test pattern. The
multi-rate range of operation can then be estimated
as a maximum of approximately 2.7Gbps down to
the minimum value listed in the table. Note that
Table 3 assumes that the baseline wander effect due
to AC-coupled data inputs (if used) is negligible.
Data rates below 10Mbps were not considered.
Table 3. Loop Bandwidth vs. Data Rate
Minimum Data Rate (Mbps)
APC Loop
7
Bandwidth f3dB (kHz) PRBS 223-1
PRBS 2 -1
795.8
320
502.4
200
316.7
125
199.9
2300
85
126.1
1500
55
79.6
925
35
50.2
600
21
31.7
375
14
20.0
240
10
12.6
145
10
8.0
100
10
5.0
60
10
3.2
40
10
2.0
25
10
1.3
15
10
0.8
10
10
Table 4. Module Parameters
Parameter
Slope
Efficiency
Threshold
Current
Laser to
Monitor
Transfer
Modulation
Current
Extinction
Ratio
5.1
@
o
-40 C
@
o
25 C
@
o
85 C
Units
0.024
0.022
0.016
mW/mA
1.5
6
20
mA
0.75
0.74
0.72
mA/mW
30
40
50
mA
10.4
10.4
10.4
dB
Example Calculation of TON
(MAX3735A)
From the parameters listed in table 4, the gain was
calculated to be largest at –40oC (0.018). Given the
calculated gain of 0.018, CAPC was selected to be
0.100µF and CMD was selected as 0.022µF. This will
allow for worst-case TON of approximately 600µs
and will set the loop bandwidth to approximately
8.2kHz (From equations in section 7).
Comparing the loop bandwidth with table 3,
acceptable performance can be obtained for data
rates as low as 100Mbps using long PRBS patterns
and less than 10Mbps when using shorter patterns
(See Figure 6 and Table 3).
5.2
Example Calculation of TON
(MAX3735)
The values from Table 4 were entered into the
spreadsheet (see section 8) and result in the
following turn-on times for various CAPC values
(Table 5):
Table 3 should be used as a starting point in
choosing the acceptable data rates. The module
designer should carefully consider the properties of
Application Note HFDN-23.0 (Rev.2; 04/08)
Maxim Integrated
Page 6 of 9
Table5. TON Results with Various CAPC Values
(MAX3735)
TON with:
@
o
-40 C
@
o
25 C
@
o
85 C
Units
CAPC = 0.01µF
161.6
58.6
28.3
µs
CAPC = 0.033µ
µF
533.1
193.4
93.5
µs
CAPC = 0.047µ
µF
759.3
275.5
133.1
µs
CAPC = 0.1µ
µF
1615.6
586.2
283.3
µs
From the results shown in Table 5, it is apparent that
the worst case is at cold temperature and that a
0.1µF capacitor should not be used if there is a TON
requirement of 1ms. Note also that if the extinction
ratio increases (by decreasing the bias current), the
turn-on times would increase.
Calculations for the APC loop bandwidth (f3dB) are
also made by the spreadsheet with the following
results (Table 6):
As with the TON calculation, the worst-case
condition (largest loop bandwidth) is at cold
temperature. From Table 3 it is seen that using CAPC
= 0.1µF, the device should be able to perform well at
low data rates ( 100Mbps) with long or short
patterns, while using a 0.01µF CAPC capacitor would
limit the acceptable operation of the device to data
rates greater than 1Gbps when using a long pattern.
Under the given conditions, a 0.047µF CAPC
capacitor should meet the TON requirement and also
provide good performance at lower data rates (
200Mbps) with long or short patterns.
6 Conclusion
Using the provided equations, the APC loop
capacitors can be chosen to meet the SFP TON
requirement and maintain loop stability. Given the
capacitor values, the loop bandwidth and the
corresponding usable data rates can then be
determined.
Table 6. Loop Bandwidth Results with
Various CAPC Values (MAX3735)
f3dB with:
@
o
-40 C
@
o
25 C
@
o
85 C
Units
CAPC = 0.01µ
µF
82.09
73.5
50.24
kHz
CAPC = 0.033µ
µF
24.87
22.27
15.22
kHz
CAPC = 0.047µ
µF
17.46
15.64
10.69
kHz
CAPC = 0.1µ
µF
8.09
7.35
5.02
kHz
Application Note HFDN-23.0 (Rev.2; 04/08)
Maxim Integrated
Page 7 of 9
7 Equations.
7.1
Turn-on Time (TON) and Loop Bandwidth (f3dB):
MAX3735 Turn on Time Equation (DC Coupled Laser):
TON ( µs ) ≈
(247.8 ⋅ C APC ( µF ))
Gain ⋅ (−0.0022 ⋅ I TH + 0.2060 ⋅ I TH + 0.2928) ⋅ (0.0018 ⋅ X 3 − 0.0244 ⋅ X 2 + 0.4667 ⋅ X + 0.1947)
2
MAX3735 and MAX3735A Loop Bandwidth Equation:
f 3db(kHz ) ≈
68.15 ⋅ Gain1.1
C APC ( µF )
Where ITH, IMD, IBIAS and IMOD are in units of mA and:
I MD
Gain =
I BIAS − I TH
X =
I
+ MOD
2
or
or
X = ( I BIAS − I TH )
Gain = η ⋅ ρ MON
7.2
I MOD
(re − 1)
Useful Optical Equations:
Parameter
Symbol
Average Power
PAVG
Extinction Ratio
re
Optical Amplitude
PP-P
P0 + P1
2
P
re = 1
P0
PAVG =
PP − P = P1 − P0
η=
Laser Slope
Efficiency
Laser to Monitor
Transfer
Relation / Definition
MON
ρ MON
PP − P
I MOD
I
= MD
PAVG
Bias Current
(DC-Coupled
IBIAS
I BIAS ≥ I TH
Monitor Diode
Current
IMD
I MD = ρ MON ⋅ PAVG
Modulation Current
IMOD
I MOD =
PP − P
η
Note: All equations assume a DC-coupled laser and a 50% Mark Density
Application Note HFDN-23.0 (Rev.2; 04/08)
Maxim Integrated
Page 8 of 9
8 Excel® Spreadsheet
The following spreadsheet can be down loaded at:
http://pdfserv.maxim-ic.com/arpdf/AppAttachments/1hfdn230.zip
References:
1. Data Sheet: “MAX3735: 2.7Gbps, Low
Power SFP Laser Driver.” - Maxim
Integrated Products, August 2002.
6. Application Note: “Choosing AC-Coupling
Capacitors.” – HFAN 01.1, Maxim
Integrated Products, September 2000.
2. Application Note: “Maintaining Average
Power and Extinction Ratio, Part 1, Slope
Efficiency and Threshold Current.” – HFAN
02.3.1, Maxim Integrated Products, May
2002.
7. Application Note: “NRZ Bandwidth – HF
Cutoff vs. SNR.” – HFAN 09.0.1, Maxim
Integrated Products, December 2001.
3. Application Note: “Maintaining Average
Power and Extinction Ratio, Part 2,
MAX3893 Laser Driver and DS1847 Digital
Resistor.” – HFAN 02.3.2, Maxim
Integrated Products, May 2002.
4. B.
Sklar,
Digital
Communications:
Fundamentals and Applications, Englewood
Cliff, New Jersey: Prentice Hall pp.78-82
5. Application Note: “NRZ Bandwidth – LF
Cutoff and Baseline Wander.” – HFAN
09.0.4, Maxim Integrated Products, August
2002.
Application Note HFDN-23.0 (Rev.2; 04/08)
Maxim Integrated
Page 9 of 9