Improved Dynamic Voltage Sharing in MultilevelConverters Through Diode Characterization

Juan D. RamirezGE Healthcare

Waukesha, WI 53188Email: Juan.D.Ramirez@ge.com

Luke A. SolomonGE Power

Cranberry Township, PA 16066Email: Luke.Solomon@ge.com

Daniel F. OpilaUnited States Naval Academy

Annapolis, MD 21402Email: Opila@usna.edu

Abstract—Power converter topologies with series-connecteddevices must maintain repeatable blocking voltages across thedevices to ensure reliability. Effective voltage sharing requiresconsistent diode reverse recovery charges, which is not guaran-teed with commercially produced devices. To evaluate this effect,this paper measures and statistically quantifies the variation inreverse recovery characteristics of diodes from one manufacturer.Statistics are provided for various groupings by date code,shipment tube, and back- and front-end epitaxy processes. Thedevices are then matched for reverse recovery charge and series-connected in a medium-voltage five-level power converter. Voltagesharing is significantly better than a similar test with deviceschosen at random. However, the device voltage mismatch exceedspredictions based solely on charge mismatch.

Index Terms—Inverters, Motor drives, Power conversion,Diodes, Voltage sharing.

I. INTRODUCTION

Semiconductor devices are often connected in series in orderto achieve a higher effective voltage rating [1]–[4]. In orderto realize the potential rating of series-connected devices,the power electronics designer must deal with the static anddynamic voltage sharing issues that arise from connectingdevices in series that do not have identical characteristics.Much work as been done to mitigate voltage sharing issuesassociated with series-connected IGBTs due to the possiblecontrol actions on the gate terminal [5]–[11]; however, not asmuch investigation has been conducted regarding the seriesconnection of diodes [12].

One challenge with using diodes connected in series istheir voltage sharing during switching events [13]. Diodereverse recovery is a phenomenon in which a diode conductscurrent in reverse bias when hard-switched off [14]. Thisreverse recovery current is generally unwanted because itincreases switching losses and generates resonant currents andvoltages in a power converter [15]. It causes particular concernfor series-connected diodes because variations directly affectvoltage sharing among the devices.

Snubber circuits are used to assist with dynamic voltagesharing, but they create a separate conduction path for thereverse recovery current of the diodes as shown in Fig. 1.Series-connected diodes with poorly matched reverse recov-ery charges will create imbalances in the snubber capacitorvoltages during switching events and therefore a mismatch ofdiode voltages. While it is possible to increase the snubber

D2V

L

R2

D1

C2

R1

C1

D3

R3

C3

Fig. 1. Reverse recovery of series-connected diodes with snubbers.

capacitance to reduce the voltage mismatch across series-connected devices due to reverse recovery charge mismatch,this is undesirable because the switching losses in the circuitdue to the snubber are linearly proportional to snubber capac-itance for a given switching frequency.

An alternative method to improve the voltage sharing perfor-mance is to use diodes with closely matched reverse recoverycharges. While nominal diode reverse recovery charge ispublished on diode manufacturers’ datasheets, typically noinformation is given regarding the statistical distribution ofthe reverse recovery charge.

This paper uses a test circuit to characterize the reverserecovery charge of diodes from one manufacturer; 14,543devices were tested in total. Manufacturers would like tocontrol these charge variations without testing every device,possibly by ensuring diodes come from identical groups.To investigate this possibility, distributions and statistics arepresented for various groupings of these diodes that representthe same lot code, shipping tube, and the same front- andback-end processing.

For deployment in a full scale converter, the diodes werethen sorted by reverse recovery charge matching and statisticaloutliers were removed. The diodes were then installed in seriesin a medium voltage power converter to verify voltage sharing

DDUT

V Cbulk

Lloop

Lload

IGBT Gate Circuit

(Double Pulse)

Fig. 2. Double pulse test circuit used for diode characterization. The singlediode under test is on the right side of the figure.

in their final configuration and confirm the performance of thecharacterization and binning process.

While measuring diode reverse recovery charge is straight-forward for a small number of diodes, it is more difficult toperform at scale. Dynamic switching performance testing toquantify reverse recovery is not typically conducted duringthe diode fabrication process. However, diode forward voltagedrop is often measured. To investigate the feasibility of large-scale device sorting by reverse recovery charge, a number ofdiodes were characterized for both reverse recovery chargeand forward voltage drop. The results show a strong inversecorrelation between these parameters, which would allowsorting or binning by reverse recovery charge based only ona forward voltage measurement.

This paper is organized as follows: the characterizationmethods are discussed in Section II with the parameter resultsin Section III. The measured reverse recovery charge and snub-ber design are used to predict the statistical distributions ofpossible voltage mismatch in Section IV. Finally, experimentalresults in a full power converter are described in Section Vfollowed by conclusions.

II. METHODS FOR DIODE REVERSE RECOVERYCHARACTERIZATION

The diodes were characterized for their reverse recoverycharge before installation into converters. Each diode wasindividually tested using a double pulse test circuit as shownin Fig. 2 [16], [17]. The first gate pulse activates the switch tocharge the reactor. When the switch is turned off the reactorfreewheels through the diode. During the rising-edge of thesecond gate pulse, the diode is hard switched off forcing itto reverse recover. The rate of change of the diode currentis governed by the supply voltage and the commutation loopinductance [18]. A Rogowski coil is used to measure the diodecurrent. An ISF file with the data points is exported from theoscilloscope and a Python script is run against the data todetermine the first two times where the current crosses zero.These times indicate the start and end of reverse recovery.The current waveform is integrated between those two points

0 100 200 300 400 500 600 700 800

Time (ns)

-50

0

50

100

Cur

rent

(A

)

Diode CurrentIGBT Current

0 100 200 300 400 500 600 700 800

Time (ns)

-100

0

100

200

300

Vol

tage

(V

)

Diode VoltageIGBT Voltage

Fig. 3. Waveforms for a 60A test at −500 Aµs

and 105V showing the diodeand IGBT collector current (top) and the diode and IGBT collector-emittervoltage (bottom) during the rising edge of the second pulse. The device testedunder those operating conditions has a reverse recovery charge of 2.082µC.

in time to calculate the charge. A typical test waveform isshown in Fig. 3.

To maximize test repeatability, the same dc power supply,Rogowski coil, and oscilloscope were used for all tests. Alltest equipment was fixed to the test stand so that the position ofeach piece of equipment did not change from test to test. Thedouble pulse test circuit board was designed with pin socketsfor the diode. The Python script used to calculate the reverserecovery charge performed a dc offset calibration on the dataeach time by calculating a dc offset when current is known tobe zero.

III. REVERSE RECOVERY PARAMETER MEASUREMENTS

The three primary operating conditions that affect diodereverse recovery charge are rate of current change (dIdt ) at turn-off, steady-state diode current prior to being hard-switchedoff, and junction temperature. Although analysis was doneon the test results of different dI

dt and steady-state currentparameters, the results in this paper are for a steady-statecurrent of 60A, dI

dt of −500 Aµs , and junction temperature of

25C. These values are standard test conditions for the deviceshown in the datasheet.

A total of 14,543 diodes were tested from one manufacturerto understand the statistical variation in reverse recoverycharge. Fig. 4 shows the statistical charge distribution for dif-ferent device categories. Three groupings were used: devicesfrom the same back-end lot (same date code), devices from

300 Devices From The Same Back-End Lot

1.4 1.6 1.8 2 2.2 2.40

0.1

0.2

0.3

Prob

abili

ty

30 Devices From The Same Shipping Tube

1.4 1.6 1.8 2 2.2 2.40

0.1

0.2

0.3

Prob

abili

ty

300 Devices from the same Front-End and Back-End Lots

1.4 1.6 1.8 2 2.2 2.40

0.1

0.2

0.3

Prob

abili

ty

Fig. 4. Histograms of reverse recovery charge for randomly selected diodesfrom one manufacturers back-end lot (top), one shipment tube (middle), andback- and front-end epitaxy processes (bottom).

TABLE IREVERSE RECOVERY CHARGE VARIATION

Group Mean Std. Deviation Normalizedµ σ σ/µ

Back-End Lot 2.0178 0.1799 8.91%Shipping Tube 2.0519 0.1473 7.18%Front- and Back-End Lot 1.6916 0.0777 4.60%

the same back-end lot and packaging tube, and devices fromthe same front-end and back-end lots. Table I shows the mean,standard deviation, and standard deviation normalized by themean for the three different groupings as shown in the figure.The population mean for the first two groups (back-end lotand shipping tube) matches the datasheet value within 2%.The final group was a carefully controlled manufacturing runand produced much tighter distributions, but with a differentmean reverse recovery charge.

IV. PREDICTED PERFORMANCE WITH EFFECTIVELYMATCHED DIODES

This work was motivated by the construction of a five-level4160V ac drive with a 6.4kV dc bus [19] as shown in Fig.5c. The power module shown in Fig. 5b is comprised ofa five-level neutral point piloted topology, as shown in Fig.5a, based on discrete semiconductors and has many instancesof series-connected IGBTs and diodes. The voltage deviation

from nominal is first predicted analytically and then tested inSection V.

A. General Case

The voltage on any individual series diode Vx can bepredicted based on the total blocking voltage Vm, the snubbercapacitances Cx, the reverse recovery charge Qx for diodex, and similar parameters for the remaining n − 1 diodes ofan arbitrarily long series-connected diode string as shown inFig. 6. The number of diodes is denoted n, and the diodeoutput capacitance is neglected for simplicity. This derivationincludes variation in both the reverse recovery charge and thesnubber capacitors. These equations are general, but the worst-case prediction is made by assuming Dx has the lowest reverserecovery charge (and hence it turns off first) and the remainingdiodes all have the maximum charge [20].

The device voltage difference from the expected nominal is

∆Vx = Vx − Vnominal = Vx −1

nVm. (1)

The total charge flow through each diode-snubber stage QT

is the same for all stages, so the voltage across each diode is

Vx =QT −Qx

Cx. (2)

The stage voltages must sum to the total blocking voltage

Vm =

n∑i=1

QT −Qi

Ci= QT

n∑i=1

1

Ci−

n∑i=1

Qi

Ci, (3)

which leaves an expression for the total charge flow througheach stage

QT =Vm +

∑ni=1

Qi

Ci∑ni=1

1Ci

. (4)

We can then substitute into (2) to find an expression for thediode voltage Vx

Vx =1

Cx

[Vm +

∑ni=1

Qi

Ci∑ni=1

1Ci

−Qx

]. (5)

B. Identical Snubber Capacitors

In the special case where all the snubber capacitors Cx areidentical, this reduces to

Vx =Vmn−

Qx − 1n

∑ni=1 Qi

C. (6)

We can intuitively define a device’s reverse recovery chargedeviation from the string average as

∆Qx = Qx −1

n

n∑i=1

Qi =1

n

n∑i=1

(Qx −Qi), (7)

which is also the average difference in charge between thedevice x and all others. This leaves the simple expression

Vx =Vmn− ∆Qx

C. (8)

Vout

(a) Schematic

(b) Power Module

(c) Drive system

Fig. 5. Power stage schematic, power module and drive system for five-level4160V ac drive with 6.4kV dc bridge.

D2D1 Dn

Vm

CC C

...

V1 V2 Vn

Fig. 6. Series-connected diode string with n diodes and snubber capacitanceC.

Finally, our voltage deviation from nominal for identicalsnubbers is

∆Vx = −∆Qx

C, (9)

clearly indicating tighter control of the variation in reverserecovery directly yields better voltage control.

C. Analysis for this Converter

The converter section considered in this paper has 3 diodesin series, but is slightly more complex. The diode for eachstage in Fig. 6 is comprised of four diodes in parallel. Thismeans the reverse recovery charge in the preceding analysisis actually the sum of the charges for four of the diodes astested in Fig. 4.

In addition, the snubber capacitor for each stage is com-prised of a network of 14 capacitors, with 7 parallel sets of 2in series. So in total, each stage have 4 diodes in parallel and14 capacitors in series/parallel.

The capacitors are nominally ±10% tolerance, so we as-sume a normal distribution with 95% of components falling inthat range, yielding a standard deviation of 5%. The equivalentcapacitance of the network decreases like 1/

√N , so the

standard deviation of the whole network is more like 1.4%.Monte Carlo simulation was conducted to study the voltage

sharing distributions. For each case, diodes were randomlyselected from the populations in Fig. 4 (4 per stage, 3 in series,12 total) and capacitors from the assumed normal distribution(14 per stage, 42 total). The predicted voltages of each diodeare shown in Fig. 8a as a histogram for diodes in variousdistributions, and the peak diode voltage for each case isshown in Fig. 8b.

As expected, devices with a lower variance of reverserecovery charge yield better voltage sharing performance. Thecapacitor variation produces only imperceptible differences inthe figure. The statistical data for the voltage deviations in thefigure is shown in Table II. The data are based on variationfrom nominal and thus has zero mean. Also shown is thevariation with perfectly matched capacitors, which only showsvery minor improvement.

TABLE IIPREDICTED VOLTAGE VARIATION FROM NOMINAL

Group Std. Deviation Normalizedσ σ/µ

With Capacitor VariationBack-End Lot 38.58 7.23%Shipping Tube 31.32 5.87%Front- and Back-End Lot 17.48 3.28%With Identical CapacitorsBack-End Lot 38.08 7.14%Shipping Tube 30.73 5.76%Front- and Back-End Lot 16.46 3.09%

Histogram of Diode Tube X (30 Diodes)

1.4 1.6 1.8 2 2.2 2.40

0.1

0.2

0.3

0.4

Prob

abili

ty

Histogram of Diode Tube X After Removing 4 Outliers

1.4 1.6 1.8 2 2.2 2.40

0.1

0.2

0.3

0.4

Prob

abili

ty

Fig. 7. Histogram of reverse recovery charge after manual matching.

V. EXPERIMENTAL PERFORMANCE WITH EFFECTIVELYMATCHED DIODES

A. Analytical Validation

To experimentally validate the predictions for improvedvoltage sharing with reverse recovery charge control, two setsof diodes were tested in the bridge shown in Fig. 5a usingthree diodes in series. One set was chosen at random, while thesecond set of diodes were hand selected for matched reverserecovery characteristics. To select the matched diodes, onlytubes with ranges of 250nC or lower were used. When tubeshad only one or two diodes that were increasing the rangeabove 250nC, those diodes were removed. Fig. 7 shows thehistogram of a given tube before and after removing fourdiodes that were outliers with respect to the average. TableIII shows the statistics for the same data.

TABLE IIIREVERSE RECOVERY CHARGE AFTER MANUAL MATCHING

Group Mean Std. Deviation Normalizedµ σ σ/µ

30 Diodes Tube X 2.0026 0.1542 7.70%Outliers Removed 2.0561 0.0441 2.14%

The test performed on the power module is a doublepulse test similar to the test done for diode reverse recoverycharacterization, with the difference being that the pulses aresent to each of the levels. Fig. 9 is a typical test waveformshowing the voltage across each of the three series-connecteddiodes on the second level for a power module using randomand matched diodes. For this power module, diode voltagemismatches of about 380V between the highest and lowestdiode voltages were decreased to lower than 40V under fullvoltage and load. The testing was performed on more than20 power modules in each case and the results consistentlyshow mismatch between the highest and lowest diode voltagesdecreasing by an order of magnitude when using closelymatched diodes. These results are shown in Fig. 8c. Designerstypically study the worst case, so the peak voltage mismatchin each string is shown in Fig. 8d.

On the whole, the experimental voltage mismatch (Figs.8c and 8d) is worse than the predicted values (Figs. 8aand 8b). This is most likely due to reverse recovery chargemagnitude being inversely proportional to reverse blockingvoltage; if a diode in a series-connected string begins to takeless voltage due to its relatively large reverse recovery chargecompared to the remaining devices in the string, its effectivereverse recovery charge will increase due to the reduction inreverse blocking voltage for the particular switching event.This phenomenon was not included in our model. In any case,the test data indicate that reduced variation in reverse recoverycharge does improve voltage sharing, but the improvement isnot as strong as predicted based on reverse recovery chargeand snubber capacitance.

B. Extension to Large Scale Production

In order to begin initial investigation into the feasibilityof large-scale device sorting by reverse recovery charge, anumber of diodes were characterized for both reverse recoverycharge and forward voltage drop. As expected, this testingrevealed a strong correlation between reverse recovery chargeand forward voltage drop as shown in Fig. 10. The resultsalso indicate large variation in reverse recovery charge fora relatively small variation in forward voltage drop. Testingfor reverse recovery charge as done here is cumbersome; thiscorrelation may allow manufacturers to ensure tight controlof reverse recovery charge using only a forward voltagemeasurement during production.

VI. CONCLUSIONS AND FUTURE WORK

In this paper, power diodes were characterized for their re-verse recovery charge to quantify the improved voltage sharingwhen using matched diodes in series-connected configurations.Better voltage sharing allows tighter design margins and moreconsistent wear-out of series-connected components. Testingon a medium-voltage multilevel power converter showed largeimprovements in voltage sharing, but not as much as predictedsolely based on reverse recovery charge matching. While therelationship between charge and voltage sharing is not new,the novelty here is the statistical evaluation of controlled

300 Devices From The Same Back-End Lot

-300 -200 -100 0 100 200 3000

0.05

0.1

0.15

Prob

abili

ty

30 Devices From The Same Shipping Tube

-300 -200 -100 0 100 200 3000

0.05

0.1

0.15

Prob

abili

ty

300 Devices from the same Front-End and Back-End Lots

-300 -200 -100 0 100 200 300

Device Voltage Mismatch in Series Connected Three String (V)

0

0.05

0.1

0.15

Prob

abili

ty

(a) Predicted device voltage deviation from nominal with randomly selecteddiodes from one manufacturers back-end lot (top), one shipment tube(middle), and back- and front-end epitaxy processes (bottom).

300 Devices From The Same Back-End Lot

0 50 100 150 200 250 3000

0.1

0.2

0.3

Prob

abili

ty

30 Devices From The Same Shipping Tube

0 50 100 150 200 250 3000

0.1

0.2

0.3

Prob

abili

ty

300 Devices from the same Front-End and Back-End Lots

0 50 100 150 200 250 300

Peak Device Voltage in Series Connected Three String (V)

0

0.1

0.2

0.3

Prob

abili

ty

(b) Predicted peak voltage deviation from nominal with randomly selecteddiodes from one manufacturers back-end lot (top), one shipment tube(middle), and back- and front-end epitaxy processes (bottom).

Randomly Selected Devices

-300 -200 -100 0 100 200 3000

0.1

0.2

0.3

Prob

abili

ty

X Strings From Device Pool Binned at 250 nC

-300 -200 -100 0 100 200 300

Device Voltage Mismatch in Series Connected Three String (V)

0

0.1

0.2

0.3

Prob

abili

ty

(c) Experimental device voltage deviation from nominal for random (top)and matched (bottom) diodes.

Randomly Selected Devices

0 50 100 150 200 250 3000

0.1

0.2

0.3

Prob

abili

ty

X Strings From Device Pool Binned at 250 nC

0 50 100 150 200 250 300

Peak Device Voltage Mismatch in Series Connected Three String (V)

0

0.1

0.2

0.3

Prob

abili

ty

(d) Experimental peak device voltage deviation from nominal for random(top) and matched (bottom) diodes.

Fig. 8. Histograms of predicted (top) and actual (bottom) voltage mismatch from nominal for a string of three diodes in series from one manufacturer. Theplots on the left show the distributions of all the device voltages, and those on the right show the peak positive deviation for each string. For the predictions,devices were selected randomly from one manufacturers back-end lot, one shipment tube, and back- and front-end epitaxy processes. For the actual experimentsdevices were either selected randomly or manually matched.

0 0.5 1 1.5 2 2.5 3 3.5−400

−200

0

200

400

600

800

1000

Time (µs)

Vol

tage

(V

)

(a) Diodes chosen at random

0 0.5 1 1.5 2 2.5 3 3.5−400

−200

0

200

400

600

800

1000

Time (µs)V

olta

ge (

V)

(b) Diodes with closely matched reverse recovery characteristics

Fig. 9. Voltage sharing of three string of diodes at 60A current and -500A/µs per device.

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.11.15

1.2

1.25

1.3

1.35

1.4

Forw

ard

Vol

tage

Dro

p (V

)

Fig. 10. Diode reverse recovery charge vs forward voltage.

groups of commonly purchased parts and their effectivenessin improving voltage sharing in a real converter. We alsopresented a possible method to execute this reverse recoverycharge matching in volume production using only the forwardvoltage drop.

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