Stability Analysis Tool
User's Guide
For use with Board Mounted
DC-DC converters
V1.3
TYCO ELECTRONICS POWER SYSTEMS 3000 SKYLINE DRIVE MESQUITE, TX 75149
No oral or written information or advice given by Tyco Electronics or its
distributors, agents or employees will operate to create any warranty or
guarantee or vary any provision or information herein, and you may not rely on
any such information or advice. Tyco Electronics reserves the right to change
any portion of this data, and to change the Information, at any time without
notice.
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1
Introduction
The Stability Analysis Tool (SAT) is a Microsoft Excel-based program that
provides a Bode plot of the voltage loop gain of a DC-DC converter for a variety of
external loads. From this plot, information such as crossover frequency and gain and
phase margins can be obtained.
In classical control theory, the stability of a feedback system is assessed by
evaluating its gain and phase margin which are read directly from the Bode plot of
the loop gain. The loop gain of a DC-DC converter depends not only on the converter
characteristics but also on the load characteristics and the output voltage sense
location. This dependence of loop gain on load and sense location makes it
impossible for the power converter manufacturer to determine stability margins in an
actual application, since the load (especially the number, type and location of output
bulk capacitors, parasitic inductances, etc.) and the output voltage sense location are
unknown. Due to this, in the past if the customer wanted to determine stability
margins, the loop gain would have to be measured using a breadboard of the power-
supply and the load network using a network analyzer.
The Stability Analysis Tool decouples the combined converter+load system into
two subsystems; one representing the converter and the other representing the load.
Tyco Electronics Power Systems provides converter data files on its web site. The
customer can download the converter data file and import it into the SAT. SAT
allows choosing one of five different configurations to best represent the combination
of load representation and voltage sense location. The tool then allows assessment
of the stability characteristics without the user having to build a prototype of the
power supply and the load network and avoids making measurements.
System Requirements
SAT v1.3 runs under the following systems:
1) Windows 95, 98, 2000 or Windows NT version 4 operating systems
2) Microsoft Excel 97 SR-2 or Excel 2000
3) Intel Pentium class or above processor and at least 64 MB of RAM
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Installation and Usage
You should first read and accept the terms of the SAT usage.
ꢀ Download the file SAT_v1.3.xls from the Tyco Electronics Power Systems
web site (given below) to a directory on your computer.
ꢀ Download one or more module data file(s) to the same directory.
ꢀ You can start up the tool by following the usual procedures to open an
Excel Worksheet and follow the directions on the screen. Make sure that
the Analysis Toolpak Add-ins are enabled in Excel. Go to Tools menu in
Excel and click on Add-Ins. Check (tick) on Analysis Toolpack and
Analysis Toolpack – VBA.
Technical Support
For technical support, please contact us at
USA
Tyco Electronics Power Systems
3000 Skyline Drive
Mesquite, TX 75149
USA
Phone - 800-526-7819
Fax - 888-315-5182
Outside
U.S.A.: Refer to our Web site below for Service and Support in other regions of
the world
Web:
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2
Using SAT
When you start SAT, you will see the window shown in Figure 1.
Fig. 1. SAT Introduction and Module Selection page
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ꢀ There are two sheets, "Module Selection" and "Configuration Menu" shown
initially at the bottom left-hand section of the Excel spreadsheet. Each session
should start at the "Module Selection" sheet.
Load Module Data File
ꢀ Click on the button
This will bring the module data file
import window as shown below in Figure 2.
Note that all module data files have .pwr extensions. If you have not already
downloaded the module data files for the particular modules you wish to analyze,
they will need to be downloaded before you can use the tool.
ꢀ Choose the module that you want to use in your application by selecting the
corresponding module data file. In this guide, we will use the JFW050A module
as an example.
ꢀ After highlighting the JFW050A.pwr file, click on the "OK" button or hit "ENTER".
SAT will load the module data file and move to the Configuration Menu as
shown in Figure 3. You may want to save SAT_v1.3.xls file under a different
name so that the original one that you downloaded remains unchanged.
Fig. 2. Module data file import window
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ꢀ If you want to choose a different module data file, you can always go back to the
Module Selection sheet to change it.
ꢀ The Configuration Menu lists five choices for representing the load circuit
topology.
ꢁ The first configuration is a simple one where the output voltage is sensed
directly at the output pins of the module. The capacitor is modeled as a series
combination of equivalent series resistance (ESR) and equivalent series
inductance (ESL). If all the capacitors are the same type (e.g. aluminum
electrolytic) and capacitance value (e.g. 6800 µF), then this is a reasonable
Configuration Menu
Please click on the appropriate box to choose the configuration for your application
SENSE
SENSE
DC/DC
CONVERTER
DC/DC
CONVERTER
CONFIGURATION
1
CONFIGURATION
2
RL
RL
SENSE
DC/DC
CONVERTER
CONFIGURATION
3
RL
RL
RL
SENSE
DC/DC
CONVERTER
CONFIGURATION
4
SENSE
DC/DC
CONVERTER
CONFIGURATION
5
Fig. 3. Circuit configuration
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model of the capacitor bank. The load is modeled by the resistance RL.
ꢁ The second configuration is similar to the first one except that the voltage sense
location is moved from the output pins of the module to the load. In this case,
the voltage sensed and regulated is not the module output voltage but the
voltage across the load, a situation commonly referred to as "remote sensing".
ꢁ The remaining three configurations (3, 4 and 5) allow the inclusion of more
detailed models of the capacitor banks and parasitic elements between the
module and the load. In some applications, the power module is mounted on a
separate printed circuit board and supplies a number of loads on different
PCBs. In this case, it is common to have one capacitor bank on the power
board and another one on the load board.
The first capacitor bank, which is a parallel combination of three capacitors, is
usually located as close as possible to the module output pins. It conveniently allows
for modeling different types of capacitors such as aluminum and tantalum
electrolytics and ceramics. When the size and type of capacitors used in a bank are
different, their individual frequency responses vary greatly from one another and
hence they cannot be modeled as a lumped capacitor as shown in the first two
configurations. Note that if you only have one or two types of capacitors, you can still
use the model by setting the values corresponding to the other capacitor to zero.
The second capacitor bank is typically placed as close as possible across the
load terminals to improve dynamic response during load transients by minimizing the
voltage overshoot and undershoot. The capability of modeling two capacitors with
their ESR and ESL are provided to model different types and sizes of capacitors.
The three configurations also allow for modeling various sense points for the
feedback voltage. Feedback voltage can be sensed across the load (case 3), across
the capacitor bank (case 2), or across the module output.
ꢀ Click on the configuration picture suitable for your application. In this example, we
will choose Configuration 4. Clicking on the picture will bring that configuration's
page as shown in Figure 4.
ꢀ The top left section shows the configuration circuit with the feedback voltage
sense path depicted in red. Underneath the configuration circuit diagram, circuit
parameters are listed with default values that can be edited in blue. The
JFW050A module is a 5V, 10A output module and hence in this example, the
load resistance is set at 0.5 ohms, indicating a 10A load. You should set the load
resistance value corresponding to the actual load in your application. The
resistors Ra1, through Ra3, and Rb1 through Rb3 are the ESRs of the capacitors
and the inductances La1 through Lb3 are the ESLs.
ꢀ Enter all circuit parameters of your application. When you finish editing the
parameter values, click on the
button.
Click to Calculate Stability
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SAT draws the Bode plot of the voltage loop gain on the right half of the page as
shown in Figure 5. The phase margin, which is a measure of stability, and the gain
crossover frequency, which is a measure of fast transient response, are also
calculated and presented below the Bode plot.
You can enter your notes under the "Notepad Area for JFW050A Module" section
in the left lower corner of the page. You can also edit the circuit parameters and
simulate various what-if scenarios and record the results on the same page. Figure 6
below compares two scenarios where the value of Cb2 is changed from 1000 µF to
6800 µF.
ꢀ To investigate a different configuration, click on the Configuration Menu tab at
the bottom of the Excel worksheet which will take you back to the configuration-
selection page. If you click on the circuit diagram for Configuration 2, the page for
that configuration will appear in the window and the Configuration 4 page will
disappear (Figure 7). You can now repeat the analysis in a manner similar to the
previous case. There is no need to re-load the module data file for JFW050A to
perform an analysis for another configuration.
Stability Analysis Tool
LS1
RS1
Ra1
LS2
RS2
SENSE
Magnitude of the Loop Gain
60
40
20
0
Ra2
Ca2
Ra3
Ca3
Rb1
Rb2
Cb2
DC/DC
CONVERTER
Ca1
La1
Cb1
Lb1
RL
La2
Lb2
La3
-20
-40
Please enter the circuit parameters below
Rload = 0.5
ohm
Rs1 = 1
Rs2 = 5
mohm
nH
10
100
1000
10000
100000
Frequency (Hz)
Ls1
Ra1
La1
=
=
=
Ls2
Rb1
Lb1
=
=
=
4
100
10
Ra2
La2
Ca2 = 10
=
=
Ra3
La3
Ca3 = 1000
=
=
Rb2
Lb2
Cb2 = 1000
=
=
100
1
100
1
10
1
10
10
mohm
nH
10
Phase of the Loop Gain
µ
F
Ca1 = 10
Cb1 = 1000
180
120
60
Click to Calculate Stability
0
Notepad Area for JFW050A Module
-60
-120
-180
10
100
1000
Frequency (Hz)
10000
100000
Hz
degrees
Gain crossover frequency:
Phase Margin:
Fig. 4. Page for entering and editing circuit parameters, shown for the case of
configuration 4.
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Stability Analysis Tool
LS1
RS1
Ra1
LS2
RS2
SENSE
Magnitude of the Loop Gain
40
20
Ra2
Ca2
Ra3
Ca3
Rb1
Cb1
Rb2
Cb2
DC/DC
CONVERTER
Ca1
La1
RL
0
La2
Lb2
La3
Lb1
-20
-40
-60
Please enter the circuit parameters below
Rload = 0.5
ohm
Rs1
Ls1 = 4
Ra1
=
Rs2
Ls2 = 100
Rb1
=
1
5
mohm
nH
100
1000
10000
100000
Frequency (Hz)
=
Ra2
=
Ra3
=
=
Rb2
=
100
100
10
10
10
mohm
La1 = 1
Ca1 = 10
La2 = 1
Ca2 = 10
La3 = 1
Ca3 = 1000
Lb1 = 10
Cb1 = 1000
Lb2 = 10
Cb2 = 1000
nH
µF
Phase of the Loop Gain
180
120
60
Click to Calculate Stability
0
Notepad Area for JFW050A Module
-60
-120
-180
100
1000
10000
100000
Frequency (Hz)
696.6 Hz
Gain crossover frequency:
Phase Margin:
52.06 degrees
Fig. 5. Voltage-loop-response Bode plot with phase margin and gain crossover
frequency calculated and displayed.
Stability Analysis Tool
LS1
RS1
Ra1
LS2
RS2
SENSE
Magnitude of the Loop Gain
40
20
Ra2
Ca2
Ra3
Ca3
Rb1
Rb2
Cb2
DC /DC
CONVERTER
Ca1
La1
Cb1
Lb1
RL
0
La2
Lb2
La3
-20
-40
-60
Please enter the circuit parameters below
Rload = 0.5
ohm
Rs1 = 1
Rs2 = 5
mohm
nH
100
1000
10000
100000
Frequency (Hz)
Ls1 = 4
Ra1 = 100
La1 = 1
Ls2 = 100
Rb1 = 10
Lb1 = 10
Cb1 = 1000
Ra2 = 100
La2 = 1
Ca2 = 10
Ra3 = 10
La3 = 1
Ca3 = 1000
Rb2 = 10
Lb2 = 10
Cb2 = 6800
mohm
nH
µF
Phase of the Loop Gain
Ca1 = 10
180
120
60
Click to Calculate Stability
0
Notepad Area for JFW050A Module
-60
-120
-180
100
1000
10000
100000
Frequency (Hz)
399.5
Hz
Gain crossover frequency:
Phase Margin:
42.8 degrees
Fig. 6. Voltage loop response Bode plot when Cb2=6800 µF
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ꢀ To analyze a different module, you should select the Module Selection tab at
the bottom of the Excel Worksheet to go back to the first page and load the data
file for the new module. Note that the new data file will overwrite the old one
belonging to the JFW050A. If you want to keep your analysis results for the
JFW050A module, you should save SAT_v1.3.xls under a different name, e.g.
JFW050A.xls.
Stability Analysis Tool
LS1
RS1
Ra1
SENSE
Magnitude of the Loop Gain
40
20
DC/DC
CONVERTER
Ca1
RL
0
La1
-20
-40
-60
-80
Please enter the circuit parameters below
Rload
Rs1
Ls1
=
=
=
0.054 ohm
1
mohm
nH
100
1000
10000
100000
Frequency (Hz)
28
Ra1 = 9
mohm
La1 = 0
Ca1 = 10000
nH
µF
Phase of the Loop Gain
180
120
60
Click to Calculate Stability
0
Notepad Area for JFW050A Module
-60
-120
-180
100
1000
10000
100000
Frequency (Hz)
229.1 Hz
Gain crossover frequency:
Phase Margin:
52.93 degrees
Fig. 7. Stability analysis of the JFW050A for Configuration 2.
Paralleled Modules
Paralleled modules can also be analyzed using SAT. Typically, in systems
with paralleled modules, active current sharing is used to distribute the stresses
evenly between modules. As described in [1], such a system can be analyzed
separately for common-mode stability (which is solely dependent on the number of
modules, the characteristics of the modules and the load), and differential-mode
stability (which only depends on the current-sharing loop and is independent of the
number of modules paralleled or the load). Since differential-mode stability is
independent of the load, the manufacturer of the module is able to ensure that the
current-sharing loop is stable. However, common-mode stability depends both on
the number of modules paralleled and the load, both of which are controlled by the
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customer application.
SAT can be used to assess the common-mode stability characteristics of a
paralleled converter system by analyzing an equivalent single-module system. The
single-module equivalent is obtained by scaling the load by the number of
paralleled modules. For example, in a two module parallel system, the load is
scaled by a factor of two by doubling the load resistance, ESR’s and ESLs, and
reducing the capacitances by half. The results from SAT are then valid for the
paralleled converter system as well
This method assumes that the layout is symmetrical in the sense that all
parasitic impedances between the modules and the load are substantially equal
and the sense locations of all modules are the same. If there is any discrepancy,
then the single equivalent module approach will yield a different answer than the
actual paralleled system.
References
[1] V. Joseph Thottuvelil, George C. Verghese, “Analysis and Control Design of Paralleled DC/DC
Converters with Current Sharing”, IEEE Trans. On Power Electronics, July 1998, pp. 635-644.
[2] Cahit Gezgin, Wayne C. Bowman, V. Joseph Thottuvelil, “A Stability Analysis Tool for DC-DC
Converters”, IEEE Applied Power Electronics Conference 2002, vol.1, pp. 367-373.
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3
Limitations of SAT
Although SAT is a powerful tool, please keep in mind the following :
1. The loop gain Bode plot and phase margin predicted by SAT are valid when the
module is operating in continuous conduction mode (CCM). Therefore, make
sure that RL is sufficiently low enough to guarantee a load current that leads to
CCM operation. Modules with synchronous rectifier based output stages operate
in CCM throughout the entire load current range.
2. It is assumed that the module input voltage is at the nominal value, e.g. 48V for
xWxxx, 24V for xCxx modules, etc. The loop response and phase margin will be
different if the input voltage is not at the nominal value. However, for stability
assessment purposes, since there are usually requirements for margins of >45°
and 12dB, performing a stability analysis at nominal voltage of 48V is typically
sufficient.
3. For buck derived converter topologies, the sensitivity of voltage loop response on
load variations is small. Therefore, SAT captures the loop response over load
variations, from CCM limit to full load, with reasonable accuracy. Future releases
of SAT will address the effect of input voltage variations on the stability margins.
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4
Troubleshooting
If you encounter the following message when running SAT,
there are two possibilities for the error message.
1. Some of the parameters you entered for your network are nonnumeric.
2. You have not enabled the Analysis Toolpack and Analysis Toolpack – VBA in
your Excel environment as desribed in page 5 of this document under
“Installation and Usage”. If you cannot see Analysis Toolpack and Analysis
Toolpack – VBA under the Tools/AddIns tab in Excel, then you have to
reinstall Excel with those options checked during installation.
Make sure that you have the correct Excel settings and numeric data for the network
parameters.
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