TP-para

TP-para
Paralleling Of Power MOSFETs For Higher Power Output
James B. Forsythe, Member IEEE
International Rectifier, E1 Segundo, California
Abstract - Dynamic current and transition energy unbalance resulting from parameter mismatch between parallel
MOSFET branches are mapped over wide operating ranges. Unbalance generator magnitudes are given for HEXFET
Power MOSFET data sheet ant typical production batch extremes.
Limit functions are defined for unbalance due to ON resistance, gain and threshold voltage mismatch. Q loci
are utilized for mapping dynamic load lines and transition energy. A critical product, average gate current times
commutation inductance, and a critical inductance ratio, common source to commutation inductances, are identified.
For worst case parameter mismatch, modest levels of unbalance are predicted through the use of minimum
gate decoupling, dynamic load lines with high Q values, common source inductance or high yield screening. Each
technique is evaluated in terms of current unbalance, transition energy, peak turn-off voltage and parasitic oscillations,
as appropriate, for various pulse duty cycles and frequency ranges. Results are predicted for a worst case clamped
inductive load circuit with an arbitrary number of paralleled IRF150 HEXFET Power MOSFETs.
I. INTRODUCTION
Concepts and design aids are presented for understanding and controlling the steady-state and dynamic
current balance between parallel MOSFETs. Dynamic balance is important in power systems employing high frequency, requiring high efficiency or utilizing large pulse currents.
The paper is an extension of earlier work which dealt primarily with the effects of threshold voltage and
transconductance (gain) mismatch on current and switching energy unbalance1, 2, 3. Current unbalance limit functions are derived herein for threshold voltage, gain and ON resistance mismatches. The latter includes temperature
compensation. The effects of MOSFET gate-source and Miller capacitance mismatches and gate decoupling resistance (including parasitics) are evaluated. Non-MOSFET parameter mismatches for drain inductance, common source
inductance and gate decoupling resistance are evaluated. Many of the results are generalized for an arbitrary number
of parallel devices.
The concept of Q loci is introduced and utilized for mapping dynamic load lines and transition energies.
These loci provide a complete generalization that interrelates the MOSFET, its gate driver and the power circuit. The
turn-on and turn-off switching loci and corresponding transition energies for a given circuit are easily determined
through the use of a simple equation and four graphs.
Unlike other switches4, parallel MOSFETs do not require additional sharing resistors, dynamic current
balancing transformers or active feedback to the driver. It is demonstrated that MOSFET generated unbalance can be
held to acceptable levels through appropriate driver design or power circuit design or parameter screening. The degree
of control necessary is a function of the application. Most of this work is highly predictable and the paper reviews the
relevant factors. A list of recommendations is given at the end of section IV.
Guidelines are developed in Section IV for reducing unbalance if the predicted limits for given mismatch(es) are considered
excessive. Current unbalance and transition energy ratios are evaluated for three different techniques in terms of pulse duty cycle
and frequency.
I (b) Analysis Model
The information presented in this paper has been generated for the widely used power circuit in Figure 1 consisting of a voltage
source, lead inductance, paralleled switches and a current source with an ideal freewheel diode to represent a clamped inductive
load. Transition energies are significant for this configuration.
A worst case representation is used for MOSFET parameter mismatch. N parallel devices are divided into two circuit branches:
the first contains a single device with adverse identical parameter mismatch (es); the second contains N-1 devices with identical
parameter values.
5, 6, 7
The MOSFET model used for analysis is given by the following classical equations
that describe the switching plane of
Figure 2(a):
Active Region —
2
iD = GF ( VGS - VT) ,
VDS ≥ VGS - VT ≥ 0
(1)
Ohmic Region —
iD = GF VDS {2(VGS - VT) - VDS }
VGS - VT ≥ VDS ≥ 0
where
(2)
iD = drain-to-source current
VGS = gate-to-source voltage
VT = VGS threshold or cut-off value
VDS = drain-to-source voltage
GF = device gain factor (proportional to
transconductance, gfs)
The applicability of these equations depends on the
specific MOSFET being considered. Certain
modifications for power MOSFETs have been
6
reported in the literature for the IRF150 used in this
paper. A more generalized set of equations would be
2
useful. However, with GF = 1.75 A/V , these
equations provide a reasonably accurate prediction for
the drain current in the active region (equation (1),
Figure 2 (b), 25°C and predict the RDS(on) quoted in
the data sheet (equation(2), VGS = 10V, iD = 14A).
The main variation from the data sheet occurs in the
ohmic region where the IRF150 resistance decreases
more rapidly with increasing gate voltage than the
equations predict.
DRAIN
CGD
VGS
GATE
+
G
+ VDS
ID
CGS
IL
-S
IL
VL
SOURCE
ICR
NOTE (2) OPERATION
NOTE (1) MOSFET MODEL
ICR
LSS1
+
VL
+
IL
IS
LD1
CGD1
VGS1
(N-1)CGD2
+ VDS1
ID1
+
CGS1
RG1
-
LD2/N-1
+ VDS2
VGS2 +
-
RGS/N-1
LS1
(N-1)ID2
LSS/N-1
(N-1)IG2
IG1
LSS2
Experimental results to support the predictions in this
paper are not yet available. An experimental test
circuit rated at 5KVA intended for operation in the
radio frequency range has been built and tested. Results will be published as they become available.
VDS
IS
(N-1)CGD2
RGC
+ VDR
-
Figure 1 . Clamped Inductive Load MOSFET Power Circuit
Containing N Parallel Branches: N-1 Identical; One with
Parameter Mismatch (es)
OHMIC
DRAIN
CURRENT
ID DRAIN CURRENT (AMPERES)
30
ACTIVE
ONX
VGS
ID
DRAIN-SOURCE VOLTAGE, VDS
X
OFF
VGS - VT
Figure 2(a)
: Combined Switching Plane Illustrating Active Region, Equation (1),
and Ohmic Region, Equation (2)
25
VDS -25V
20
15
TJ = + 1250C
TJ = 250C
10
TJ = -550C
5
0
1
2
3
4
5
6
7
8
VGS GATE-TO-SOURCE VOLTAGE (VOLTS)
Figure 2(b) : IRF150 Data Sheet Active Region
Transfer Characteristics For Deriving Gain Factor
(GF) and Threshold Voltage (VT) in Equation (1)
Figure 2: MOSFET Transfer Characteristics
A Fortran listing of the simulation program used to generate the data in this paper is available upon request.
I (c) Potential Causes of Unbalance
There are several conceivable causes for current unbalance that may result in a particular device exceeding its peak current or
continuous thermal ratings. Unbalance may be generated by:
(i) device parameter mismatch
- ON resistance mismatch RDS
- threshold voltage (VT)
(on)
- gain factor (GF, ∝ gfs )
- capacitance mismatch (CGD, gate-to-drain (Miller) or CGS, gate-to-source)
(ii) gate driver mismatch
- decoupling resistor (RG)
- gate loop inductance (LG)
(iii) power circuit mismatch
- branch inductance (LD, excluding LS)
- source inductance common to power and gate circuit (LS)
Individually or in combination, mismatch between these parameters may produce serious unbalance. For example, consider the
circuit of Figure 1 in which eleven IRF150's are sharing a pulse current (IL) from a clamped inductive load. The first parallel
branch contains the mismatched parameters causing the unbalance. The other ten branches are identical and, therefore, equally
share load and gate current. Because of the relatively large number of identical parallel branches, typical values are used for the
parameters of these branches (refer Table 1).
iD: maximum 70 A (IDM) continuous 28 A
VT: typical 3 V minimum 2 V
gfs: typical 10 A/V minimum 6 A/V
equivalent to
2
GF: typical 1.75A/ V minimum 1.05A/ V
CGS: 2650 pf
CGD: 350 pf
Table l: IRF150 Data
2
Consider the unbalance that occurs in branch #1 if its HEXFET Power MOSFET has a VT of 2.0 volt (2/3 typical) and a GF of
2
2.45 A/ V , (40% more than typical). Remaining parameters are:
VDR = 11V
RGC = 5.2Ω
RG1 = RG2 = 0
LDl = LD2 = 100 nh
LS1 = LS2 = 10 nh
LSSl + LSS2 = 9.1 nh
VSS = 50V
IL = 385A
Initially, the 385A load is circulating in the freewheel diode. At t = 0, VDR is stepped from zero to 11V, remains at this value for
700 nsec and then is reset to zero volt. The resulting current distribution and switching energy are illustrated in Figure 3. For this
example, the peak current in #1 HEXFET Power MOSFET is 61A or 75% greater than the balance current of 35A. The
transition energy dissipated in #l is more than 100% greater due to unbalance. This example illustrates several important factors.
First, even though the 61A peak current represents a large unbalance current in #1 HEXFET Power MOSFET, it is still within
the device SOA which allows a 70A peak current. Secondly, it is the differential current established during turn-on that sets the
initial unbalance for the constant current portion of the pulse. Unbalance losses due to turn-on differentials will be significant in
applications where conduction losses dominate the thermal design (e.g. high duty cycle pulses). Thirdly, the current differentials
established during turn-off generates energy differentials that will be significant in high frequency applications where switching
or transition losses dominate the thermal design. Note also that for threshold voltage or gain mismatch, the differential current
development during turn-off is a continuation of the process generating the differential during turn-on. Generally, maximum
differentials are established in the active region.
The extensive list of interacting unbalance generators given above illustrates that the evaluation of the effects may be a complex
task. To clarify the response of parallel MOSFETs to ON resistance, gain, and threshold voltage mismatch, unbalance limit
functions are derived. Although the following analyses concentrate on MOSFET generated unbalance, other parameters must be
included. The Q-locus mapping technique simplifies the quantification of current and transition energy unbalance by identifying
key parameter products and ratios.
iD1
60
1200
iD
TRANSITION ENERGY
iD2
40
800
JOULE
x10-6
IL/ N
AMP
#1
VDS iDdt
ET
20
#2
400
0
0
400
800
1200
t1 NSEC
Figure 3(a) : Drain Current Unbalance
0
0
400
800
1200
t1 NSEC
Figure 3(b): Transition Energy Unbalance
Figure 3: Unbalance Effects Due to Threshold Voltage and Gain Factor Mismatch
II. SUMMARY OF RESULTS
The primary results reported in this paper are summarized as follows:
(1) Unlike other switches parallel MOSFET current unbalance is inherently limited over wide operating ranges - for both steadystate and dynamic operations, 'runaway' conditions do not occur.
(2) These limits, however, can lead to excessive junction temperature or operation outside the SOA depending on specific power
circuit and gate driver parameters.
(3) The designer has several 'open loop' options that will reduce unbalance to acceptable levels without introducing complex or
expensive hardware.
(4) It is possible to limit pulse turn-on current unbalance to approximately 15% for certain applications without any device
screening through appropriate design of the gate driver.
(5) Switching transition energy ratios for wide ranges of unbalance are shown to typically be in the range 1.5 to 2.5 - the
importance of energy unbalance depends on application factors such as duty cycle, frequency and cooling system type.
Starting from the unbalance limits for given parameter mismatch(es), it is shown that if these limits are unacceptable for a given
application, the dynamic unbalance can be reduced to acceptable levels by one or more of the following:
•
•
restrict the dynamic load line to certain areas of the switching plane - by controlling the IG • LX product and/or the LS / LX
ratio;
use of a three parameter screening test with a 90% yield.
Basically, MOSFET current and switching energy unbalance can be restricted to levels whereby the use of current sharing
resistors, balancing transformers and/or active power circuit feedback is avoided.
Table 1 lists all of the causes and effects of unbalance evaluated on this paper. Current differentials are monitored for SOA.
Losses are monitored for junction temperature (TJ) constraints. It is assumed that the gate-source voltages of the parallel
MOSFETs are identical except for a minor degree of decoupling for control of parasitic oscillations. Some of the results are as
expected from other switch technologies - a few of the results are new and unique to MOSFETs. A brief explanation follows.
•
•
•
•
Differential RDS (on) will cause current unbalance and extra conduction losses as expected, but these are limited due to the
positive temperature coefficient for MOSFET resistance. The thermal 'runaway' characteristic of other semiconductor technologies does not apply to MOSFETs.
Gain factor differentials (∆GF) result in limited current unbalance. In the extreme, which is difficult to realize in practice,
the current unbalance is limited to the gain ratio. Since turn-on differentials are very easy to control, the predominate loss
differential occurs during turn-off.
VT also results in limited current unbalance. Before the device with the lowest threshold voltage can conduct an excess
current, its gate voltage must be increased above the higher threshold voltages of the other devices - thereby limiting the
maximum current conducted by the lowest threshold voltage device. Note that MOSFETs do not turn fully ON at threshold.
Additional gate voltage or charge must be provided if the drain current is to be increased. This characteristic is unique to
MOSFETs in comparison with other contemporary power switch technology.
Differential gate-to-source capacitances (∆CGS) do not cause current unbalance since drain currents are controlled by the
gate-to-source voltage potentials. By directly connecting all gates and sources together, a common potential is ensured. This
result remains valid with a limited degree of gate decoupling resistance and common source inductance present. Typical
turn-on times are sufficiently short to preclude ∆CGS from generating current unbalance.
Primary Unbalance Result
Unbalance Generator
Current Differential
Energy (Loss) Differential
Device:
steady-state & Limited
conduction
- ∆RDS (on)
dynamic & limited
turn-off
- ∆GF
dynamic & limited
turn-off
- ∆VT
none
none
- ∆CGS
none
none
- ∆CGD
Power Circuit:
none
turn-on
- ∆LD
dynamic
turn-on & turn-off
- ∆LS
Gate Driver:
dynamic
turn-on & turn-off
- ∆RG
Table 2: Primary Effect of Unbalance Generator on MOSFET Current Level and Dissipated Energy
•
•
•
•
Differential Miller capacitances (∆CGD) will affect the time required for the drain-to-source voltage (VDS) to collapse.
However, the first device to reduce VDS also reduces the forward bias across other parallel devices causing them to turn-on
earlier. Consequently if the gates are not strongly decoupled, no significant current unbalance develops.
In the power circuit external to each device, differential branch inductance (LD), which excludes source inductance common
to both power ant gate driver circuits (LS), normally does not cause current unbalance. In comparison with other
technologies, this result is unusual and advantageous. Drain current is controlled by gate voltage during transitions.
However, ∆LD will cause differential drain-to-source voltages during transition ant therefore differential transition energy.
LS through feedback effects will cause differential currents and transition energies. As is shown in the paper, common source
inductance is a critical parameter in higher frequency applications and must be given careful attention. However, worst case
current differentials increase as the number of parallel devices increase - and for these designs, the presence of any LS > 0
tends to reduce current unbalance due to other causes.
Differential decoupling resistance in the gate driver will cause both current and transition energy unbalance if the gates are
strongly decoupled (RGC → 0)
III. QUANTIFYING UNBALANCE
In this section the magnitudes of unbalance generators are reviewed. Techniques for rapidly estimating the maximum resulting
current unbalance possible are presented. These techniques are also useful for setting screening levels. The realization of these
limits depends on which dynamic load lines are utilized for turn-on and for turn-off. Techniques for estimating the magnitude of
dynamic unbalance are included.
III (a) Parameter Variation Ranges
Paralleling unbalance is caused by differences between the MOSFET, power circuit components and layout and gate driver for
each parallel branch.
(i) For International Rectifier's HEXFET Power MOSFET devices, parameter ranges are given in the data sheet for each part
number. These ranges tend to be extreme and are not generally realized in practice. Table 3 lists these extremes for RDS (on),
GF(gfs) and VT of the largest (HEX 5) and second largest (HEX 3) chips mounted in TO-3 packages. The wide ranges tabulated
indicate the possibility of significant parameter mismatch between paralleled devices that in turn would be expected to generate
large unbalances.
It is well established that each production batch of these parameters. Most of the device parameters fall well within the data sheet
extremes so that the odds are high that devices from one batch (or date code) will have relatively modest parameter variations.
Parameter variations for 90% of the devices sampled from various production batches were constrained as listed on Table 3. This
information is very useful in parallel circuit design, in terms of setting parameter mismatch extremes for computation of expected
levels of unbalance or for determining degree of compensation (if required). Alternatively, it provides a guide to the minimum
yield one would expect from screening tests.
However, without some screening of devices placed in parallel, the data sheet extremes will occasionally be realized and as will
be shown, circuit design has to contend with or control the resulting unbalances. This trade-off between screening and circuit
design is discussed further in Section IV.
(ii) The primary contributors to unbalance in the power circuit are differential drain or branch inductance (LD) and common
source inductance (LS). These inductances are developed by interconnection wiring and possibly discrete components. Thus the
variation between branches is a function of layout symmetry (including nearby magnetics) and production tolerances. Experience
8, 9
indicates variations of 10 - 20% are common .
To be certain that most cases are covered, the following analysis spans 50% differentials in these inductances.
(iii) For the gate driver, if a common voltage source is used, the primary factor contributing to unbalance is mismatch between
decoupling resistors if they are used. Since ±20% resistors are common, the analysis includes a differential of 50%.
III (b) Current Unbalance Limits
Unlike other switching devices such as thyristors, switchgear or power bipolar transistors, parallel MOSFET generated current
unbalance has inherent limits provided the gate-to-source voltages are the same. Limit functions are derived for ON resistance,
gain and threshold voltage mismatch. Gate-source and Miller capacitance mismatches have negligible effect. The function for
ON resistance includes the effect of junction temperature changes.
III (b) (i) Steady-State Limits
When parallel MOSFETs are switched ON and VGS for each device reaches its final (identical) value, current unbalance caused
by the MOSFETs will be due to mismatch in RDS (on). A 'worst case' analysis of this current unbalance is given in Appendix A.
Referring to Figure 1, branch #1 has the minimum RDS (on) and the other N-1 devices have an identical, larger value of RDS (on).
Thus current unbalance is a maximum in branch #1 for a given mismatch in R DS (on).
For a large number of devices in parallel, equation 3 (refer equation A11) gives a simple quadratic for the maximum unbalance
current (ID1) expressed as a fraction of the balance current (IB) that would otherwise flow for no parameter mismatch.
−
 I D1  
 I D1  
R 1−25 
1

 − 1 −

 −  ∆T2JA • K •

R 2−25 
 I B   ∆T2JA • K  I B  
2
1
=0
(3)
Where K = temperature coefficient for MOSFET resistance (for HEXFET Power MOSFETs, 0.6 < K < 1.2% per °C for 100 to
500 volt ratings respectively)
th
Ri-25 = RDS (on) of the i branch device at 25°C (i.e. nominal) for the steady-state gate voltage selected
∆T2JA = design junction-to-ambient temperature rise for the nominal resistance
2
= Ri-25 IB TPNθJA (refer equation A12)
TPN = nomalized pulse duty cycle
θJA = junction-ambient thermal resistance
Parameter Range
Source
Threshold
Voltage, VT
2-4V
2V
Transconductance or
Gain Factor gfs, GF
60 - 140%
80%
ON Ressitance
RDS (on)
70 - 130%
60%
Data Sheet
Extremes min/max ∆ =
Maximum Differential (Spanning Mean) for
approximately 90% of production batch
0.7 V
20%
35%
Table 3: HEXFET Power MOSFET Maximum Parameter Ranges From (1) Data Sheet, (2) Single Production Batch/Date Code
Screening With 90% Typical Yield.
Figure 4 illustrates the variation in current unbalance with N → ∞ as a function of the nominal resistance ratio for two extreme
conditions:
(a) ∆A2JA = 0 which represents either neglecting the effect of temperature compensation or ensuring equal junction temperature;
(b) ∆A2JA • K = 0.336 which is representative of the rated junction temperature resistance increase from nominal for 55°C
ambient. (from A3 and Al2, 0.3 < ∆A2JA • K <0.41 for 100 to 500 volt ratings resp.)
A substantial reduction in current unbalance is predicted when temperature effects are considered for a large number of devices
in parallel.
For reduced numbers of parallel devices (N < ∞), current
unbalance is given by a cubic equation (refer to (A10)). The
variation in unbalance current for 5 and 2 paralleled devices is
illustrated in Figure 4. It is interesting to note that temperature
compensation has a reduced effect as N is reduced. For N-l
large, a decrease in branch #1 current (∆ID1) due to temperature increase causes a minor increase in the temperature of the
devices for which ∆ID2 = ∆ID1/(N-l). With 2 parallel devices,
the current increase in the second device is fully equal to the
decrease in the first branch which causes a relatively large
increase in branch #2 device temperature. This increase
inhibits current reduction due to temperature compensation.
However, for a given mismatch, temperature compensation is
most effective where it is most needed - with a large number of
parallel devices.
5.0
N=∞
4.0
ID1
IB
N=5
Data Sheet RDS (on)
Extrremes (D = 60%)
N
COMMON AMBIENT
∆ TJA • K = 0.336
3.0
2.0
N=2
1.0
0
0
Table 4 identifies 'worst case' current unbalance for the two
sets of parameter mismatch extremes given in Table 3. For two
devices from the same date code, the predicted 18% maximum
unbalance is reduced to 14% allowing for temperature
compensation. For N large and without screening, temperature
compensation reduces the predicted maximum unbalance from
85% to 56%. Note that these reductions assume a common
ambient temperature. If a common heatsink is used, the
reductions will not be as large (refer to condition (b) above).
For simplified heatsink design, see reference 10.
TJ1 = TJ2 = 250C
0.2
0.4
0.6
R1-25 / R2-25
0.8
1.0
Figure 4: Worst Case Current Unbalance Ratio For #1
Branch (ID1 / IB) Vs. Nominal ON Resistance
Mismatch Ratio Between #1 Branch and #2
Branch (R1-25 / R2-25) for N Parallel Devices
With: (1) Common Junction Temperature; (2)
Temperature Compensation From Common
Ambient
Production Batch /Date Code
RDS (on) Extremes (D = 35%)
Large
TJ
Equal
1.85
TJ
Compensated
1.56
TJ
Equal
1.43
TJ
Compensated
1.30
5
1.59
1.43
1.32
1.23
2
1.30
1.27
1.18
1.14
Table 4: Maximum Current Unbalance (I1/IB) Due to RDS (on) Mismatch For Various Numbers of Paralleled Devices (N), With
and Without Junction Temperature (TJ) Compensation
III (b) (ii) Dynamic Limits
There are upper limits to the magnitude of current unbalance caused by threshold voltage or gain mismatch These limits could be
realized by relatively slow transition times and occur at the boundary of the active/ohmic regions.
It is instructive to consider an illustration of these limits for the example of a large number of devices in parallel. From Appendix
B, an expression for the worst case unbalance current in branch # 1 is given by (refer equation B10):
2
I D1 
IB 
=  ∆V +

GF1  T
GF2 
(4)
A convenient normalizing factor that will allow this expression to represent any device is IDM/GF where IDM is the rated pulse
current and GF is the absolute gain from equation (1). The normalized expression is (refer equation B14):
2
I D1N 
I BN 
=  ∆V +

GF1N  TN
GF2N 
(5)
Table 5 lists the relevant parameters and normalizing factors for all of the International Rectifier HEX-5 and HEX-3 TO-3
packaged devices. Figure 5 illustrates the variation of IDlN over the parameter ranges given in the table.
This figure is immediately useful for:
(1) rapidly estimating the potential unbalance resulting from a given mismatch;
(2) determining screening levels for threshold voltage.
PART
NO.
IDM
A
GF
A/V2
(250C)
VT
V
(250C)
IDM/GF
IDM / GF
DVTN
max.
GF1N
max.
GF2N
min.
GF1 / GF2
max.
Series
IRF150, 1
152, 3
IRF250, 1
252, 3
IRF350, 1
352, 3
IRF450, 1
452, 3
IRF130, 1
132, 3
IRF230, 1
232, 3
IRF330, 1
332, 3
IRF430, 1
432, 3
IRF9130, 1
9132, 3
70
1.4
0.6
2.33
1.75
3.00
40.0
6.32
0.316
60
34.3
5.86
0.341
60
1.33
0.67
2.0
3.40
3.10
17.65
4.20
0.476
50
14.71
3.83
0.522
25
1.44
0.56
2.6
2.63
3.00
9.51
3.08
0.650
20
7.60
2.76
0.725
25
1.4
0.6
2.33
5.5
3.40
4.55
2.13
0.940
20
3.64
1.91
1.05
30
1.4
0.6
2.33
1.00
2.90
30.0
5.48
0.365
25
25.0
5.00
0.40
15
1.44
0.56
2.6
1.45
3.30
10.34
3.22
0.621
12
8.28
2.88
0.695
8
1.43
0.57
2.5
1.45
3.25
5.52
2.35
0.852
7
4.83
2.20
0.910
7
1.4
0.60
2.33
1.25
3.25
5.60
2.37
0.845
6
4.80
2.19
0.914
-30
1.43
0.57
2.5
-0.55
-3.00
54.5
7.38
0.407
-25
45.5
6.74
0.445
Table 5: Gain Factor Constant (GF), Maximum Gain Factor Ratio (GF1/GF2) and Normalized Threshold Voltage (∆VTN) ant
Gain Factor Ranges (GF1N, GF2N) For International Rectifier HEX-5 and HEX-3 TO-3 Packaged Devices
For example, consider the maximum unbalance that could occur from one IRF150 device turning on early due to the lowest VT
(2V) and a remaining large number of devices turning on at the typical VT (3V). Here ∆VTN = (3-2)/6.32 = 0.158. From Figure
5 the maximum unbalance for GF1N = GF2N = 1.0 occurs at maximum IBN (1.0) and is equal to approximately 35% (ID1N =
1.35).
Maximum current unbalance resulting solely from gain mismatch (i.e., ∆VTN = 0) is simply the gain ratio (ID1N = GF1N
•IB/GF2N from Figure 5) with a large number of devices. With one device assigned the highest gain (+40%) and all others
assigned the typical value (1.0), then the maximum current unbalance is simply 1.4 or 40%.
Consider the screening levels for threshold voltage and gain of the IRF150 where the maximum potential current unbalance is
limited to 20% (with a balance current IBN = 0.75). The nominal value for ID1N is 0.9. For the gain range allowed by the data
sheet, ±40%, the limits for ID1N/GF1N are 1.5 and 0.64. Similarly, IBN/GF2N limits are 1.25 and 0.54. Other limits, due to
threshold voltage are given by the VTN = 0 and VTN = 0.318 loci.
The above limits define a solution region as shown in Figure 5 (shaded region) for a maximum 20% current unbalance potential
with a large number of parallel devices. Any combination of screening levels for gain and threshold values that locates a point in
the solution region will not cause unbalance in excess of 20%.
N = N1 (<∞),∆VTN=1.0
0.6
0.4
0.2
∞, ∆V
2.0
ID1N
0.
15
8
GF1N
=
INCREASING
GF1N/GF2N
∞
,∆
VT
N
1.0
N
GF1N
0.
4
1.5
∆ VTN = 0
N = N1
∆ VTN = 0.0
∞,
∆V
TN
=
N
0.
31
8
2.0
ID1N
N = N1
∆ VTN=0.4
DECREASING
N
0.4
0.8
TN
1.0
= 1.0
2.5
1.0
N
N=∞
0.5
DEVICE
NORMALIZING
FACTOR: IDM / GF
0
0
0.5
1.0
1.5
DEVICE NORMALIZING
FACTOR: IDM/GF
2.0
IBN / GF2N
Figure 5: Normalized Worst Case #1 Branch
Drain Current (ID1N) Vs. Balance Current (IBN)
For Various Gain Factor Mismatches (GF1N, GF2N)
and Threshold Voltage Differentials (∆ VTN)
Between #1 and #2 Branches (Figure 1)
With a Large Number of Parallel Devices.
0
0
1.0
IBN/GF2N
2.0
Figure 6: Illustration of the Reduction in Unbalance
Current (ID1N) for a Finite Number of Parallel Devices
For a smaller number of devices (N < ∞), screening levels can be opened up for a given performance criterion. The potential
unbalance magnitude decreases with the number of parallel devices. A somewhat more complex expression describes the
unbalance current for N < ∞ (refer equation Bl5). Figure 6 shows that the effect of reducing the number of parallel devices is
generally to reduce ID1N for a given set of parameter mismatches. Each locus for VTN in Figure 5 breaks into a new family of loci
for N < ∞ that are generated by the gain ratio, GF1N/GF2N.
Table 6 lists the variation in maximum current unbalance limits as the number of paralleled devices is decreased. The variation
in limit magnitude is slightly more than two-to-one for 2 < N < ∞.
Unbalance Cause
N
GF1N / GF2N = 1.4
∆ VTN & ∆ GF
∆ VTN = 0.158
89%
40%
35%
Large
62%
30%
28%
5
36%
18%
16%
2
Table 6: 'Static' Limits For Dynamic Current Unbalance, (ID1 - IB)/ IB %, Vs. Number of Parallel Devices for Threshold Voltage
and Gain Mismatch Parameters: #1 Branch - Data Sheet Extremes; 82 Branch - Typical. (IBN = 1.0)
Although the effects of junction temperature on dynamic balance have not been rigorously analyzed, trends may be inferred from
Figure 2(b). As temperature increases, VT decreases (-6 mV per °C) and GF decreases. This results in two trends. For the initial
pulse current, the hotter device has a higher drain current for a particular V GS, but as the pulse develops, this device will have a
lower drain current (particularly for lower voltage rating devices). The effects of temperature on dynamic balance may
compensate each other.
III (c) Realizable Dynamic Unbalance
Limits have been identified for MOSFET generated current unbalance. Whether or not these limits are realized depends on the
dynamic load lines for turn-on and turn-off selected by the designer.
In the first part of this section, dynamic current unbalance and transition energy differentials are mapped for two general series
using worst case analysis for each:
Series #1: Analysis for eleven parallel devices for which a single device in branch #1 is assigned worst case adverse data sheet
extremes. The other ten devices, equivalent to a large number selected over many production batches, are assumed identical and
assigned typical parameter values.
Series #2: Analysis for two parallel devices in which each is assigned data sheet parameter extremes to maximize current
unbalance in #1 branch. Single production batch/date code extremes are also evaluated.
In the second part, unbalance generators other than MOSFETs are reviewed.
The influence of specific dynamic load lines on current unbalance and transition energy differentials have been evaluated by
computer simulations based on 4th order Runge-Kutta numerical techniques. To quantify the nature of the transitions from OFFON-OFF, the switching plane has been mapped using Q-loci (refer Appendix C) where the product of average translation gate
current (IG) and commutation inductance (LX) uniquely determines a base dynamic load line in the switching plane. From
Appendix C,
Q = IG • L X
(6)
The basic dynamic load line or Q-locus is deflected towards a higher transition energy or slower transition time as the ratio LS /
LX is increased (refer Figures C2a and C3a in Appendix C). The switching transition energies dissipated by the device are also
mapped by Q-loci for the IRF150 (refer Figures C2b and C3b).
-9
-9
-9
Three Q loci, 4X10 (Q0), 20X20 (Q1) and 100X10 9 (Q2) amp-henry, span a wide range in the switching plane for the
IRF150 and are the basis for the following analysis. The switching transition each locus represents is characterized as follows:
Q0: relatively slow transition or high switch energy dissipation, with low peak turn-off voltage.
Q1: intermediate transition.
Q2: relatively fast transition or low switch energy dissipation, with high peak turn-off voltage.
Series #1: Dynamic Unbalance For Eleven Parallel Devices
#1 HEXFET Power MOSFET drain current increase and transition energy for the parameter mismatches listed in Table 7 are
illustrated as a function of Q and LX in Figures 7 and 8.
A 40% mismatch in gain in Figure 7(a) results in a maximum increase in the #l HEXFET Power MOSFET current of 12.4A or
35%. This limit is the same as the static limit predicted by equation (Bl5) for eleven devices in parallel. The Q0 locus realizes
this limit. As Q is increased, the unbalance current decreases.
The ratios of transition energy dissipated for #1 HEXFET Power MOSFET compared with #2 are illustrated in Figure 7(b). They
range between 1.2 and 1.5 except during turn-on for the Q1 and Q2 loci. The ratio becomes indeterminate as the energy values
become very small. Even though the energy ratio is greater than unity throughout the switching plane, the absolute transition
energy for #1 HEXFET Power MOSFET with the increased unbalance current decreases as Q is increased for both ON and OFF
transitions.
The results of a two-thirds threshold mismatch are illustrated in Figures 7(a) and 7(b). The maximum drain current increase is
44% and occurs for the Q0 locus. For switching loci with higher values of Q, the dynamic current unbalance is reduced as
illustrated. The transition energy ratios range between 1.2 and 1.7. Loci with higher values of Q have lower transition energy.
Dynamic current unbalance for the simultaneous mismatch of both gain and threshold voltage are illustrated in Figure 8(a). The
peak increase in #1 HEXFET Power MOSFET current is 32.6 A or 93% above the matched parameter value.
This value is equal to that derived from the product of the current ratios for the individual mismatches. Transition energies are
illustrated in Figure 8(b).
The ratios are higher, ranging between 1.5
and 2.5. Higher valued Q loci are associated
with lower turn-on and turn-off transition
energies.
GF1=2.45A/V2, GF2=1.75 A/V2
20
(57%)
49% 'STATIC' LIMIT
39% 'STATIC' LIMIT
#1 DRAIN
CURRENT
INCREASE
Series #2: Dynamic Unbalance For Two
Parallel Devices
VT1 = 2V, VT2 = 3V
Q0
10
Q0
(29%)
Q2OFF
AMP
In each of the following analyses, the clamped
inductive load is 70 A giving each device a
balance current of 35 A. The switch comprised
of two IRFl50's is considered ON when the
total switch current is equal to 70 A, each
device is in the ohmic region and has a gateto-source voltage of at least 10 V.
Q2ON
0
0
100
200
0
LX, nh
GAIN FACTOR
MISMATCH
100
200
LX, nh
THRESHOLD VOLTAGE
MISMATCH
Figure 7(a): #1 IRF150 Drain Current Increase Range Above Balance
Current (IB = 35 A) For Q0 < Q < Q2
2
Q1 OFF
Q0 OFF
TRANSITION
ENERGY
RATIO
#1 / #2
1
Q2 OFF
Q1 ON
0
0
100
200
0
LX, nh
GAIN FACTOR
MISMATCH
100
200
LX, nh
THRESHOLD VOLTAGE
MISMATCH
Nominal values for VSS, LX and LD are 50V,
200nh and 100nh, respectively. Two sets of four
general cases are analyzed. For each set, two
values of LS/LX are used: LS = 20nh, LS/LX =
10%, a value that could be appropriate for the TO3 package with a common lead to the source pin;
LS = lnh, LS/LX = 0.5%, a minimum value that
could be associated with dual source connections
to the MOSFET chip. For each LS/LX, two basic
dynamic load lines are analyzed (Q1 and Q2 loci,
refer Appendix C).
Figure 7(b): Transition Energy Ratio Band For Q 0 < Q < Q2
Figure 7(a) & 7(b): HEXFET Power MOSFET IRF150 Current and Transition Energy Unbalance Vs. Dynamic Load Line (Q
Locus) and Commutation Inductance (LX) for (1) Gain Factor Mismatch, (2) Threshold Voltage Mismatch. (N = 11, IB = 0.5
IDM, LS/LX ≤ 5%)
BRANCH
#1
N
VT
1
2
GF
2.45
V
VSS = 50
A
IL = 385
V
BRANCH VDR =11
CGS = 2,650 µfd
#2
10
CGD = 350 µfd
3V
LX RANGE
= 20-200 nh
2
1.75A/V
Q RANGE = 4-100 x 10 - 9 A-h
Table 7: Parameters For Worst Case Dynamic Current Unbalance Study With N = 11.
III (c) (i) Effect of Decoupling Resistance (RG)
There is a preferred level of gate decoupling that eliminates parasitic oscillations without significantly increasing unbalance due
to parameter mismatch. With no gate decoupling (RG = 0, Figure l), high frequency current oscillations (20-100MHz) are
predicted through the Miller capacitance. To avoid oscillations, analysis indicates RG/N should be greater than 5% of the total
driver resistance.
An upper limit for RG/N is given by unbalance
considerations. In comparing current unbalance
due to threshold voltage and/or gain mismatch, no
changes are noted between RG/N equal to 0% or
100%.
93% 'STATIC' LIMIT
30
(86%)
20
(57%)
#1 DRAIN
CURRENT
INCREASE
For device capacitance mismatch, significant
current unbalance occurs for RG/N = 100% (refer
Table 8). With RG/N = 0%, no unbalance occurs
for either gate-source or Miller capacitance
unbalance.
Q0
GF1=2.45A/V2, GF2=1.75 A/V2
VT1 = 2V, VT2 = 3V
AMP
10
(29%)
Q2ON
Therefore, it is recommended that RG/N be set at
approximately 10% of the total driver resistance.
Unless otherwise noted, this value is used for the
remaining analysis in the paper.
0
100
0
200
LX, nh
Figure 8(a): #1 IRF150 Drain Current Increase Range Above Balance
Current (IB = 35 A) For Q0 < Q < Q2
3
Q1 OFF
Figure 8(a) & 8(b): HEXFET Power MOSFET
IRF150 Current and Transition Energy
Unbalance Vs. Dynamic Load Line (Q
Locus) and Commutation Inductance
(LX) For Combined Gain Factor and
Threshold Voltage Mismatch (N = 11,
IB = 0.5 IDM, LS/LX ≤ 5%).
2
TRANSITION
ENERGY
RATIO
#1 / /#2
Q2OFF
1
0
100
0
200
LX, nh
Figure 8(b): Transition Energy Ratio Band For Q0 < Q < Q2
Q1
∆ CGD
2.7A
(8%)
0.5%
7.3
(21%)
Table 8: Current Unbalance, ID1 - IB, Due to Device Capacitance Mismatch
(Refer Table 9) With Completely Decoupled Gates. (N = 2, IB = 0.5 IDM, RG/N = 100%)
LS / LX
10%
∆ CGS
8.1A
(23%)
14.2
(41%)
Q2
∆ CGD
9.6A
927%)
17.1
(49%)
∆ CGS
3.1A
(9%)
2.8
(8%)
III (c) (ii) MOSFET Generated Unbalance
In this next set of analysis, the dynamic current and transition energy unbalances due to extreme data sheet parameter variation
are examined (refer Table 3). The analysis is based on the worst case of simultaneous extreme for VT, GF, CGS and CGD
variations for the IRF150 (refer Table 9). Because this combination is rare, the analysis is restricted to two parallel devices.
Device
#1
#2
GF
(A/V2)
VT
(V)
CGS
(pf)
CGD
(pf)
2.0
2.45
1500.
200.
4.0
1.05
3800.
500.
Table 9: IRF150 Parameter Extremes From Data Sheet
Current (∆I) ant transition energy (ET) unbalance resulting from these simultaneous mismatches are listed in the first two rows of
Table 10. The maximum differential current occurs for minimum LS/LX ant for the minimum value of Q (Q1). At 76%, this is
slightly greater than the 'static' limit and is attributed to gate voltage decoupling caused by RG/N equal to 10%.
Minimum current unbalance (18%) during turn-on occurs for minimum LS/LX and maximum Q (Q2). The low value for LS/LX
causes a relatively high unbalance (67%) during turn-off. Figure 9(a) illustrates the drain current for each device. If RDS(on) is
matched, the differential current established during turn-on will decay as indicated by the dashed lines at a rate determined by
the parallel loop L/R time constant.
During turn-off, the peak drain-source voltage would reach 217V. Figure 9(b) illustrates the turn-off with the voltage clamped at
100V.
The switching energy unbalance covers a wide range for these cases. The maximum ratio (8:1) occurs with an intermediate level
of current unbalance (59%).
The next set of analysis is based on the simultaneous mismatch extremes for threshold voltage and gain to be expected from a
single production batch (refer Table 3). Table 11 lists the production batch extremes (90% screening yields) for the IRF150 used
in this analysis. Due to insufficient capacitance data, the data sheet extremes of Table 9 are used - the resulting current unbalance
is minimal due to the weak degree of gate decoupling.
Turn-On
∆ I, A
Unbalance
Generator
Data Sheet
Extremes
(Table 3)
Turn-Off
∆ I, A
ET, µJ
ET, µJ
LS / LX
'Static'
Limit
Q1
Q2
Q1
Q2
Q1
Q2
Q1
Q2
10%
25.9A
(74%)
20.1
(57%)
11.3
(32%)
230/120
21/47
20.8
(59%)
13.3
(38%)
1200/150
610/130
0.5%
25.9
26.6
(76%)
6.4
(18%)
81/22
4/4
26.6
(76%)
23.5
(67%)
960/130
490/100
(150/91,
VZ=100V
Single
7.4
4.2
7.4
4.2
220/170 28/36
740/420
410/260
Production
10%
8.4
(21%)
(12%)
(12%)
(12%)
Batch Typical
(24%)
Extremes For
11.8
4.0
11.0
4.0
110/60
620/420
320/220
90% Yield
0.5%
8.4
5/3
(34%)
(11%)
(31%)
(11%)
(Table 3)
Table 10: Current Unbalance (∆I = ID1 - IB) and HEXFET Power MOSFET Transition Energy Unbalance ( ET, #1/#2) Vs. LS/LX
and Q for Two Sources of Parameter Mismatch (N = 2, IB = 35A, RG/N = 10%).
Results of this analysis are listed in the latter part of Table 10. Maximum current unbalance occurs as expected with minimum
LS/ LX and Q. However, the current excess at 34% is greater than the 24% allowed by the static limit. This excess is due to the
10% gate decoupling. Without gate decoupling or without capacitance mismatch, current unbalance drops to 20%, within the
'static' limit. The percentage effect of 10% gate decoupling increases as the unbalance magnitude decreases.
Minimum current unbalance of 11% occurs for the Q2 loci. Switching transition energy ratios are generally in the range of 1.5:1.
These unbalance results are substantially lower than those computed for data sheet extremes.
EOFF
ONLY
VDS1 MAX
= 217V
iDM = 70A
80
X10-6 J
iD1
60
iB MAX
= 35A
DRAIN 40
CURRENT,
AMP
600
ET1
400
iD2
20
200
ET2
0
50
100
150
200
T
T + 100
T + 200
TIME, N SEC
Figure 9(a): Unristricted Drain-Source Voltage (VDS) During Turn-Off
VZ = 100V
iD1
400
200
iD2
ET1
ET2
T
T + 100
T + 200
(b) Drain-Source Voltage Clamped At
Rated Value (VZ = 100V)
III (c) (iii) Non-Device Parameter Differentials
LD ± 25%: Mismatch between the drain inductance (LD) of parallel branches does not cause current unbalance for LS/LX greater
than 1% and Q less than Q2. Unlike other switches, during turn-on and turn-off, drain current is controlled by gate-to-source
voltage. It is not normally controlled by individual branch inductance.
Variations in LD will affect the drain-source voltage and thus transition energy is unbalanced. Table 12 illustrates transition
energy unbalance for N = 2. The differentials increase for large values of N. As LS/LX is decreased or, as Q is increased during
turn-on, the unbalance increases but the absolute energy level decreases. During turn-off, the differentials are relatively
unaffected by LS/LX or Q. For this example, LD/LX is 50% such that differential LD is lost in the larger absolute turn-off energy.
Device
VT
GF
#1
#2
(V)
2.65
3.35
(A/V2)
1.93
1.57
Table 11: IRF150 Parameter Extremes Expected From Single Production Batch/Date Code.
Transition Energy
ON
LS / LX
10%
0.5%
OFF
Q1
210/180
110/67
Q2
51/19
6/3
Q1
540/580
470/520
Q2
320/340
270/270
Table 12: Transition Energy Unbalance (#1 device/ #2 device, microjoules) Due to Drain Inductance Unbalance, LD ± 25%: LDl
= 75%; LD2 = 125% (N = 2, IB = 35A, RG/N = 10%)
LS ± 25%: Mismatch in common source inductance results in both current and transition energy unbalance during turn-on as
shown in Table 13.
For a nominal value of 10% for LS/LX, current unbalance is approximately 15% for N = 2 and 33% for N = 11. For LS/LX =
0.5%, the unbalance is negligible due to the low relative magnitude of source inductance.
The higher value for Q results in a slightly higher level of unbalance. This result is the opposite of that for all other sources of
unbalance where increasing Q results in lower current unbalance. In this case, the cause of unbalance is amplified by increasing
Q which offsets the reduced time in the active region.
Turn-On
N
2
11
LS / LX
Nominal
10%
0.5%
10%
0.5%
∆I
Q1
5.0 (14%)
0.8 (2%)
10.2 (29%)
1.4 (4%)
Turn-Off
ET
ET
Q2
5.9 (17%)
0.3 (1%)
12.5 (36%)
0.5 (1%)
Q1
220/170
88/85
280/220
90/87
Q2
24/31
4/4
59/57
4/4
Q1
540/580
490/500
560/580
490/500
Q2
360/300
270/280
410/340
260/270
Table 13: Current (∆I, amp) and Transition Energy (ET, #1/#2, Microjoules) Unbalance Due to Common Source Inductance
Unbalance, LS ± 25%: LS1 = 75%, LS2 = 125%. (N = 2, IB = 35A, RG/N = 10%)
Transition energy unbalance proportion is less than the original ± variation in LS.
RG ± 25%: To determine the maximum unbalance due to gate resistor mismatch, RGC is set equal to zero. Table 14 shows the
maximum current unbalance of 23% occurs for minimum L RS and Q. For minimum LS the turn-off transition energy variation
approaches ± 25%.
The current unbalance results are comparable with those listed in Table 8 for gate-source capacitance mismatch of ±43%. For the
Q1 locus, the mismatch is not significant. For the Q1 locus, the current unbalance due to capacitance mismatch is proportionately
greater . For all of the non-device parameter mismatches, the effect of the adverse mismatch on device #1 during turn-on is to
deflect the Q locus to the right in the switching plane (refer Figure C2a) which is a higher transition energy region for other
factors remaining equal. During turn-off, the Q locus is also deflected to the right, but this results in lower transition energy.
Consequently adverse current unbalance also increases peak drain-source voltage during turn-off.
Turn-On
∆I
LS / LX
10%
0.5%
Q1
5.0 (15%)
8.2 (23%)
Turn-Off
ET
ET
Q2
3.1 (9%)
3.7 (11%)
Q1
100/69
23/15
Q2
38/29
5/4
Q1
390/460
290/470
Q2
320/350
220/350
Table 14: Current (∆I, %) and Transition Energy (ET , #1, #2, microjoules) Unbalance Due to De-Coupling, Resistance (RGC=0)
Unbalance, RG ± 25%: RG1 = 75%, RG2 = 125%. (N = 2, IB = 35A).
III (d) Summary
This completes the current and transition energy unbalance mapping for mismatch between parallel branch parameters. Two sets
of HEXFET Power MOSFET parameter mismatch extremes from data sheet and single production batch (date code) sources are
identified. Estimates are given for non-MOSFET parameter mismatch. The results are summarized as follows.
(i) Unbalance is limited for ON resistance, gain or threshold voltage mismatch.
•
•
N → ∞: ID1/IB < R2/R1 (steady-state)
< GF1/GF2 (dynamic)
< 44% per volt for IRF150 AVT (dynamic)
N < ∞: Generally, the larger the unbalance for N → ∞, the greater the unbalance reduction as N is reduced.
(ii) Significant reductions from the above limits are possible. Dynamic current unbalance realized from the above and from other
causes is a function of the dynamic load line as described by a base Q locus (Q = IG • LX) and a deflection dependent on the
LS/LX ratio. Switching time and transition energy increases as LX/IG and/or LS/LX increase. Peak device voltage during turnoff
increases as Q increases or as LS/LX decreases.
•
•
•
Increasing Q reduces turn-on and turn-off current unbalance.
For the higher Q values, decreasing LS/LX reduces turn-on unbalance and increases turn-off unbalance.
For lower Q values, turn-on and turn-off current unbalance tend to be equal and both are reduced as LS/LX is increased.
(iii) With HEXFET Power MOSFET data sheet parameter mismatch extremes, turn-on current unbalance is limited to 15% for Q
= Q2 and LS/LX = 0.5%.
(iv) With fully decoupled gates (RGC = 0), current unbalance due to device capacitance mismatch is maximized. For weakly
decoupled gates (RGC/N < 5% driver resistance, parasitic current oscillations occur in the Miller capacitance.
(v) Current unbalance sensitivity to threshold voltage mismatch increases as the device voltage rating increases.
(vi) Current unbalance due to ON resistance mismatch is reduced by allowing different junction temperatures. This reduction is
maximized for a large number of devices.
(vii) With current unbalance present, the peak turn-off voltage increases as the L D/LX ratio is increased.
(viii) For N large, the transition energy increase ranges between 50 and 150%.
IV. GUIDELINES FOR CONTROLLING DYNAMIC UNBALANCE BETWEEN
PARALLEL BRANCHES
Different techniques are available for controlling current unbalance. The most effective combination will consider:
(1) allowable level of unbalance - depends on the application
(2) options available for control.
There are wide ranges for both of these categories such that no single recommendation is generally useful. In this section, items
(1) and (2) are reviewed to highlight the salient features of MOSFETs with respect to paralleling. Guidelines are developed for
ensuring acceptable levels of unbalance.
IV (a) Application Factors
The optimum approach for a given user depends in part on the application. In particular, the transition-to-conduction energy
ratio (ET/EC), the pulse duration-to-loop time constant ratio (TP/τ) and the number of paralleled devices influences the technique
chosen to control current balance.
Table 15 lists typical values of ET/EC for different pulse duty cycles and frequencies. It indicates that a high duty cycle, low
repetition rate pulse could tolerate dynamic current balancing techniques that increased transition energy (within limits) since
this would not initially increase the thermal loading on the cooling system. Conversely, low duty cycle, high repetition rate pulses
would prefer current balancing techniques that maintained or reduced transition energy.
Frequency
Low
High
Duty Cycle
High
Low
<<1
~1
~1
>> 1
Table 15: Typical Transition (ET) to Conduction (EC) Energy Ratios (ET/EC) Vs. Pulse Characteristics
Current unbalance developed between parallel branches through the turn-on transition decays during the constant switch current
interval at a rate determined by the time constant (τ) of the parallel loop. For pulse duty cycles in the range 50-100%, the balance
current (IB) is typically ≤ 50% of IDM, the rated peak current (refer Figure 10(a)), due to rms current or thermal constraints.
Therefore, for long pulses (Tp >> τ), a relatively large dynamic current unbalance during turn-on case be tolerated due to the
large SOA margin and to the relatively short duration of the excess current. Similarly, during turn-off, a relatively large current
different is permissible.
With short duty cycle pulses, IB may approach IDM (refer Figure 10 (b)) thereby eliminating the excess SOA margin. For both
turn-on and turn-off, margin for dynamic current unbalance is minimized.
For MOSFET parameter mismatch, the relative degree of resulting current unbalance is summarized in Table 16.
Two or three devices screened with 90% yield from a given production batch result in low current unbalance. Conversely, a large
number of paralleled devices reflecting data sheet parameter extremes with only a few of these adversely mismatched could
develop large unbalance currents - but the probability of the combination occurring is very low.
IV (b) Dynamic Balancing options
At least three approaches can be applied to improve dynamic unbalance (refer Table 17):
A - eliminate the cause by matching the parameters listed in I(c) (i), (ii) and (iii) above, i.e. realize a balanced system
through screening;
B - modify the power circuit to compensate for or cancel the effect of the mismatch, i.e. minimize the magnitude of
resulting unbalance;
C - modify the gate driver to offset the effects of parameter mismatch, i.e. minimize the duration of unbalance.
Techniques A & B have been previously reported.
100
1, 2, 8, 9
100
IDM
80
DRAIN 60
CURRENT,
40
AMP
20
IBMAX1
0
ID
(CONTINOUS RATING)
T1
Figure 10a. Intermediate to High Duty Cycle Pulses
Provide Large Peak Current Margin
IDM
IBMAX1
80
DRAIN 60
CURRENT,
40
AMP
20
ID
0
T2
Figure 10b. Short Duty Cycle Pulses May Leave Small
Peak Current Margin
Figure 10. Variation In IRF150 Peak Current Margin for Current Pulses of Equal RMS Drain Current
Device Unbalance
Generator
Number of Parallel Devices
Low
High
(<5)
(>10)
Data Sheet Extremes
Single Production Batch
moderate
low
large (improbable)
moderate
Table 16: Relative Magnitude of Devices Generated Current Unbalance
IV (b) (i) Screening
From Section III(b) technique A derives screening limits for X given application based on permissible unbalance and the degree
of parameter mismatch allowable for that unbalance. Various combinations are possible.
The mismatch limits set the screening levels and the next step is to evaluate each combination.
(A) Screen Parameters
- GF (gfs)
- VT
- CGS
- CGD
(B) Modify Power Circuit
- Current Balancing Transformers (LD)
- Active Feedback to Gate Driver
- LS/LX
(C) Modify Gate Driver
- LD
- LS
- RG
- RG
- IG
Table 17: Three General Approaches for Dynamic Current Balancing
The data of Table 10 shows that current unbalance can be reduced by more than a factor of two by using HEXFET Power
MOSFETs from a single date code and setting the 90% yield screening limits of Table 3. With this technique current unbalance
for two parallel devices ranges between 11 and 34% depending on how the MOSFETs are applied.
For the remaining parameters in Table 17, LD ant LS differentials can be minimized by ensuring symmetrical layouts (include
nearby magnetic). For MOSFETs, ∆LD affects only transition energy and is significant only for larger values of parallel devices.
For unusually fast drivers (Q > Q2), ∆LD will affect current balance. RG differentials are minimized by specifying close tolerance
resistors. However if RG/N is ≤ 10% of the total driver resistance the effect of mismatched RG will be minimal.
IV (b) (ii) Comparison of Techniques B and C
Technique B is may be implemented by adding current balancing transformers to the power circuit (SCR and Darlington circuits)
or by adding current transformers and modifying the device driver to accept current feedback from the power circuit (power
bipolar circuits). With MOSFETs, a third approach is effective. This utilizes source inductance as a simple method of reducing
current unbalance. In the following, the characteristics of techniques B and C will be compared. For technique B, one method for
reducing current unbalance is to introduce source inductance that is common to both the gate driver ant the train-source power
circuit (LS in Figure 1). Additional di/dt due to current hogging modifies the gate voltage of the unbalanced device in a direction
to inhibit further unbalance. There are side effects to this approach, however.
Consider the effect of LS on the Q loci in Figure C2(a) in Appendix C. The introduction of common inductance to the gate and
power circuit results in increased drain-to-source voltage during turn-on and therefore a higher transition energy Figure C2b
maps the increase in turn-on energy for increased values of LS. Similarly during turn-off the addition of common source
inductance in Figure C3b increases the transition energy dissipated by the device. However as shown in Figure C3a the peak
drain-to-source voltage is reduced during turn-off. These results are consistent since the lower drain-to-source voltage means a
longer time is required to commutate the current in the external power circuit inductance L X. Therefore the greater amount of
energy drawn from the supply during this increased time contributes to the increased device transition energy.
A primary reason for limiting current unbalance magnitude is to control the thermal load of each device. Technique (C) allows
an alternate method for limiting excess thermal load due to current unbalance. In a given power circuit the total transition energy
dissipated in each device can be reduced by increasing the Q value of the switching loci during turn-on and turn-off. This is
accomplished by increasing the average gate current during the active region transition increase VDR and/or reduce RGC. Figures
C2b and C3b show the substantial reductions possible in transition energy for a given power circuit design (i.e. given LX). To
maximize this energy reduction, LS should be minimized. However during turn-off the combination of a high Q value ant low
value for LS may result in excessive drain-to-source voltage (Figure C3a). To remain within the SOA at lease two choices are
available:
(1) relatively small increase in LS with a corresponding increase in transition energy (on and off) that must be
dissipated by the device;
(2) locate a diverter circuit that will limit the peak drain-to-source voltage and absorb more than the resulting increase
in turn-off transition energy.
The diverter may be a zener diode or a diode-capacitor clamp with a resistor to return supply energy to the supply. The choice
between techniques B and C for controlling the effects of current unbalance may be dictated by the frequency and/or loading the
MOSFET switch operates at.
( i i ) Turn-Off
( i ) Turn-On
60
VDS1
iD1
iD1
100
RATED
iD
VDS , VOLT
AMP
INCREASE
Q
40
iD2
IL / N
50
VSS
INCREASE LS
iD2
20
INCREASE LS
INCREASE
Q
iD1
0
0
400
0
200
400
t1 , NSEC
600
800
0
200
t1 , NSEC
400
t1 , NSEC
Figure 11(a): Drain Current and Voltage for #1 and #2 HEXFETs
1500
(i) Turn-On
INCREASE
LS
(ii) Turn-Off
( Original, Figure 3)
1000
x10-6
JOULES
INCREASE
Q
500
( With VDS Clamp )
t, NSEC
0
0
200
400
600
0
200
400
600
800
Figure 11(b): Transition Energy for #1 HEXFET
Figure 11. Comparison of Methods for Reducing Peak Dynamic Current Unbalance: Technique B Increasing Common Source Inductance, LS / LX = 20%, Q =Q1 (RGC = 5.24 Ω); Technique C Increasing Q by Reducing RGC, LS / LX = 5%, Q = Q2 (RGC = 1.29)
600
800
Returning to the dynamic current unbalance example of Figure 3 the above information is applied to reduce the unbalance. Using
technique B the common source inductance, LS, is increased from 10 to 40 nh. This modifies the basic Q1 switching loci in
Figures C2 and C3 from the original LS = 5% to LS = 20%. The transition energies increase. The impact of this change is
illustrated in Figure 11. The original current unbalance differentials of 23A during turn-on ant 29A during turn-off are reduced
to 13A and 22A differentials, respectively. The total transition energy dissipated by the device increases by 33% from 1330 to
1780 microjoules. It is interesting to note that for a case temperature of 87 °C, the device would be limited to an operating
frequency of 42kHz due to these transition losses alone.
To apply technique C, the basic Q locus is shifted. Consider the results of increasing Q from Q 1 to Q2 by reducing RGC from 5.24
to 1.29Ω. For Q2 with LS = 5%, Figures C2 and C3 predict significantly lower transition energies and an increase to peak turnoff voltage to 125V.
The effect on dynamic current unbalance is shown in Figure 11(a). The original differentials of 23A during turn-on and 29A
during turn-off are reduced to 5A and 22A differentials, respectively. Figure 11(b) shows that the transition energies are reduced
as expected. Figure 11(a) also confirms a higher than rated peak drain-source voltage (VDS1) during turn-off. The effect of
including an energy diverter circuit such as a zener diode or a diode-capacitor-return resistor is also illustrated (dashed). With
the HEXFET Power MOSFET voltage clamped at 100V, the drain current reduces more rapidly. This results in a further
reduction of the total HEXFET Power MOSFET transition energy to 360 microjoules. Excluding other losses this would raise the
operating frequency limit from 42kHz using technique B to 155kHz for technique C. The diverter circuit increases the turn-off
energy due to the lower turn-off voltage from 620 to 890 microjoules for #1 branch in this example. Part of this increase can be
returned to the supply, depending on the diverter circuit design.
IV (b) (iii) Limiting Unbalance with the Gate Driver
It has been generally shown that increasing the Q value of the dynamic load line reduces current unbalance, particularly during
turn-on Technique C is most effective for larger pulse duty cycles where IB ~ 0.5 IDM (Figure 10(a)).
By increasing Q sufficiently, it has been shown in Table 10 that the peak dynamic current unbalance generated by data sheet
parameter extremes can be held to approximately 15% during turn-on By matching RDS(on), this unbalance limit can be held until
turn-off.
Technique C requires a very low LS/LX ratio and as shown in Figure 9, it results in a large unbalance current and high peak
voltage during turn-off. For higher duty cycle pulses the unbalance current can be accommodated within the SOA. An energy
diverter circuit may be added to clamp the voltage. Alternatively , depending on E T/EC, a lower value for Q may be used for turnoff.
As given in equation (6), Q may be increased by raising the average gate driver current or the commutation inductance. This
choice may be dictated by operating frequency since the former reduces transition energy whereas the latter raises it.
For medium to high duty cycle current pulses, applied over wide frequency range, parallel current unbalance can be constrained
to modest levels by appropriate gate driver design without any device (HEXFET Power MOSFET) screening except for RDS(on).
IV (b) (iv) Combined Techniques For Minimum Overall Unbalances
For the shorter pulse of Figure 10(b) in which IB approaches the SOA limit of IDM, both turn-on and turn-off dynamic current
unbalance must be limited.
To minimize the device unbalance generators, the designer can minimize gate decoupling resistance and screen devices from a
given production batch (date code) with 90% yield limits. For practical reasons LS/LX may approach 10%. This tends to equate
turn-on and turn-off unbalance and also raise transition energy which is significant in short pulses. To limit transition energy
increased Q through an augmented gate driver may be used.
Figure 12 illustrates current and energy balance using the above techniques. This is predicted without the use of current
balancing transformers drain current feedback to the driver circuit or current sharing resistors.
IV (c) Summary of Recommendations for Balancing Parallel MOSFET Currents
The following recommendations are generally applicable. For certain extreme operating conditions such as very high frequency,
large numbers of parallel devices, ultra fast gate drivers, some recommendations may not apply (refer to paper).
IV (c) (i) General
Screening, Parameter Matching
•
•
•
•
•
MOSFET gate-to-source and Miller capacitance mismatch are not significant provided decoupling resistance is
limited to less than 10% of total driver resistance
Branch inductance and decoupling resistance (for above recommendation) mismatch are not significant.
Matching common source inductance (for LS/LX > 1%) assists dynamic current balance.
Screening MOSFET RDS(on) is sufficient for steady-state current balance.
MOSFET threshold voltage and gain factor (transconductance) screens are effective for dynamic current balance.
Power Circuit Modifications
•
•
Additional series resistance, current balancing transformers or feedback to the gate driver are not needed for current
balance.
Increasing common source inductance assists dynamic current balance. This also increases transition energy.
Gate Driver Modifications
•
•
Minimizing decoupling resistance assists dynamic current balance by reducing differential gate-source voltages
between parallel MOSFETs Partial gate decoupling (approximately 10%) may be required for parasitic oscillation
control.
Increasing the dynamic load line Q value assists dynamic current balance. This reduces transition energy, but
increases peak turn-off voltage Restrict Q value to not more than Q2 for turn-on, otherwise differential branch
inductance may contribute to current unbalance.
80
iDM = 70A
EON + EOFF
X10-6 J
iD1
60
ET1
1,000
40
iD2
iB MAX = 56A
ET2
500
20
0 0
200
400
TIME, N SEC
T
T + 200
0
Figure 12: IRF150 Current and Energy Unbalance For N=2 With Techniques A, B and C
Combined For Short Pulse Duty Cycle-Single Production Batch Parameter Mismatch
(Tables 3 and 11), LS/LX=10%, RG/N 10%, Q=Q2
IV (c) (ii) Pulse Duty Cycle > 30%
Starting from a general set of parameter mismatch to balance turn-on current, minimize LS/LX and increase Q to Q2. For low
frequency applications with ET/EC << 1, reduce Q to Q1 during turn-off to alleviate turn-off voltage stress For high frequencies,
with ETlEc >> 1, use Q2 and an energy diverter circuit for turn-off.
IV (c) (iii) Pulse Duty Cycle < 30%
To minimize turn-on and turn-off current differentials, increase LS/LX and increase Q to Q2. For high frequency, with ET/EC >>
1, the value for LS/LX required to offset parameter mismatch may generate excessive losses. Some screening or matching may be
require to allow a lower LS/LX ratio.
References
1.
"A 48V, 200A Chopper For Motor Speed Control With Regenerative Braking Capability, Using Power HEXFETs,"
S. Clemente ant B. Pelly, IEEE - IAS Conference — Record, October, 1980.
2. "A Chopper For Motor Speed Control Using Parallel Connected Power HEXFETs," S. Clemente ant B. Pelly,
International Rectifier Application Note AN-941.
3. "Techniques For Controlling Dynamic Current Balance In Parallel Power MOSFET Confiagrations," J. Forsythe,
Powercon U.S.A. 1981.
4. "How to Use Silicon Controlled Rectifiers in Series or Parallel" A. Mulica, Control Engineering, May 1964.
5. "Switching Transients in High-Frequency, High Power Converters Using Power MOSFETs", T. Sloane, H. Owen,
T. Wilson, International Rectifier Application Note AN933.
6. "A High Power MOSFET Computer Model," H. Niehaus, J. Bowers and P. Harren, Jr., PESC, 1980.
7. "Characterization and Implementation of Power MOSFETs in Switching Converters," R. Erickson, B.
8. Behen, R. Middlebrook, S. Cuk, Powercon U.S.A., 1980
9. "Methods of Achieving Balance In Diode Type Rectifiers," D. T. Bewley, IEEE Conference Paper 63 - 374,
January, 1963.
10. "Operation of Unmatched Rectifier Diodes In Parallel Without Artificial Balancing Means", A. Ludbrook, IEEE
Conference Paper 63 - 1169, June, 1963.
11. "Simplified HEXFET Power Dissipation and Junction Temperature Calculation Speeds Heatsink Design",
12. Severns, International Rectifier Application Note AN942.
APPENDIX A
Current Unbalance Limits for ON Resistance Mismatch
Equations ant graphs describing
parallel branch current unbalance
due to mismatched ON-state
drain-source resistancesmRDS(on)
are derived for the 'worst case'
circuit of Figure 1. The first
branch is assigned a reduced
resistance and the remaining N-1
branches are assigned identical
values (refer Figure A-1).
IS
ONE HEXFETS
WITH
MINIMUM R
( N-1 )HEXFETS
IN PARALLEL,
ALL WITH R2
ID1
R1
R2
( N -1 )
( N-1 ) ID2
Current unbalance graphs are
derived for two general cases
(refer Figure 4):
(1) 0 < RDS(on1) < RDS(on2) < 1.0;
N = 2, 5, ∞; TJ held constant
at 25°C.
Figure A1 : Equivalent Circuit for Computing Worst Case Steady-State
Current Unbalance Due To RDS ON Mismatch
(2) for above parameter range, the unbalance current is corrected for junction temperature change with the junction-to-ambient
design temperature rise set at 56°C.
For the circuit (Figure A1),
IS = ID1 + (N-1) ID2
(A1)
with equal voltage drop:
ID1R1T = ID2R2T
(A2)
where the subscript ‘T’ indicates the resistance value at temperature, T.
2
RiT = Ri-25 {1 + [(TA-25) + I
DiRiTθJA]K}
(A3)
th
where Ri-25 is the i branch limiting maximum value of ON resistance at 25°C, θJA is the total junction-to-ambient resistance
in deg. C/W, and K is the per unit change of ON resistance per °C.
Solving (A3) for RiT and substituting into (A2),
I D1 ⋅
R 1− 25
1 − R 1− 25 I D1 2θ JA K
= I D2 ⋅
R 2− 25
(A5)
1 − R 2− 25 I D 2 2θ JA K
The balanced current (IB) for each device is,
IB = IS/N
(A6)
Substituting from (A6) and (A1) into (A5),
I D1 ⋅
R 1− 25
1 − R 1− 25 I D1 θ JA K
2
=
NI B − 1
⋅
N−1
R 2− 25
1 − ( NI B − I D1 ) ⋅
2
R 2− 25θ JA K
(A7)
( N − 1) 2
Expressed as a cubic equation of ID1, (A7) becomes,
R 1− 25 R 2− 25θ JA KN
⋅ I D1 3 −
R 1− 25 R 2− 25 θ JA KN( N + 1) I B
⋅ I D1 2
( N − 1)
( N − 1)


θ JA KR 2− 25 ( NI B ) 2 
R 2− 25 NI B
1 
 R 2− 25 +  ( N − 1) −
−
=0
R 1− 25  ⋅ I D1 +
N − 1 
( N − 1)
N−1



2
2
(A8)
3
Dividing (A8) by IB , R2-25, θJAK, rearranging terms and setting the design junction-to-ambient temperature rise for nominal
resistance (∆T2JA) equal to,
2
∆T2JA = R2-25 IB θJAK
(A9)
equation (A8) becomes,
3
2
 I D1 
 I D1 
 I D1  
R 2− 25 
N − 1
1

 − ( N + 1)
 + N −
N − 1 +
⋅


N 
R 1− 25  ∆T2JA ⋅ K  I B 
 IB 
 IB  

R 2− 25 
+ ( N − 1) ∆T2JA ⋅ K ⋅
=0
R 1− 25 

For N → ∞, (A10) reduces to a quadratic,
(A10)
−1
 I D1  2 
 I D1  
R 1− 25 
1
⋅K ⋅

 − 1 −

 −  ∆T
 =0
R 2− 25 
∆T2 JA ⋅ K  I B   2JA
 IB  
(A11)
Since rms current determines average junction temperature, for pulse currents with peak current I B and normalized duty cycle
TPN, equation (A9) becomes,
2
∆T2JA = R2-25 IB TPN θJA
(A12)
APPENDIX B
Current Unbalance Limits For Gate and Threshold Voltage Mismatch
Maximum current differentials for gain and/or threshold voltage
mismatch(es) occur in the active region during relatively slow transitions
in which common source inductance (LS) voltage drops are negligible.
( N-1 ) ID2
This current unbalance has limits which may be derived by holding the
switch current (iS) at the maximum value for a given transition (IS) and
computing the maximum unbalance current. For worst case unbalance
between paralleled devices, assume N MOSFETs are arranged so that one
device with adverse parameter mismatch is in the first branch and N-l
identical devices are located in the remaining branches as illustrated in
Figure Bl.
ID1
ID2
+
-
From Figure Bl,
IS = ID1 + (N - l) ID2
VGS
Figure B1 : Equivalent Circuit for
Determination of Worst Case 'Static'
Unbalance Current Limits
(Bl)
Substituting from equation (1) and rearranging (Bl),
ID1 = IS - (N-1) GF2 (VGS - VT2)
2
= GF1 (VGS - VT1)
2
(B2)
(B3)
Then, from (B2) and (B3),
VGS 2 −
2[GF1 VT1 + ( N − 1)GF2 VT 2 ]
GF1 + ( N − 1)GF2
⋅ VGS
GF1 VT1 2 + ( N − 1)GF2 VT 2 2 − I S
+
=0
GF1 + ( N − 1)GF2
(B4)
Solving for VGS,
VGS =
GF1 VT1 + ( N − 1)GF2 VT 2
GF1 + ( N − 1)GF2
− ( N − 1)GF1GF2 [ VT1 − VT 2 ] + [GF1 + ( N − 1)GF2 ] I S
(B5)
2
+
[GF1 + ( N − 1)GF2 ] 2
ID2
=0
The balance current for each device is given by,
IB = IS/N
(B6)
Also, let the differential threshold voltage be,
VT1 - VT2 = ∆VT
(B7)
Substituting from equations (B5), (B6) ant (B7) into equation (l),
I D1 = GF1 ( VGS − VT1 ) 2
=
GF1
[GF1 + ( N − 1)GF2 ] 2
(B8)
{
⋅ ( N − 1)GF2 ∆VT + N[GF1 + ( N − 1)GF2 ]I B − ( N − 1)GF1GF2 ∆VT 2
}
Then,
I D1
GF1



( N − 1)
=
⋅ ∆VT +
 GF1 + ( N − 1)
 GF2




2
IB
( N − 1) ∆VT
N

⋅
−
2
GF1
GF2 


GF1
GF2
+ ( N − 1)

 
GF2
+ ( N − 1)
GF1  
 GF2

(B9)
For a large number of parallel devices, the worst case current unbalance for branch #1 (with adverse parameter mismatch) is
given by,
I D1
GF1
N→∞
2

IB 
=  ∆VT +

GF2 

(B10)
A convenient normalizing factor for this equation is IDM/GF where for a given device,
IDM = rated peak pulse current
GF = active region gain (from equation (l))
Let
I D1N
I
I
= D1 ÷ DM
GF1N GF1 GF
(B11)
I BN
I
I
= B ÷ DM
GF2N GF2 GF
(Bl2)
∆VTN = ∆VT ÷
I DM
GF
(Bl3)
Then the normalized maximum unbalance current for N → ∞ is given by,
2
I D1N 
I BN 

=  ∆V +
GF1N  TN
GF2N 
(Bl4)
For N < ∞, from equation (B9)
I D1N
GF1N



( N − 1)
=
⋅ ∆VTN +
 GF1N + N − 1
 GF2N

I BN
( N − 1) ∆VTN 2
⋅
−
GF2N  GF
GF2N
+N−1
1N
+ ( N − 1)

GF1N
 GF2N
N
GF1N
GF2N
2



2 
 
 
(Bl5)
APPENDIX C
Dynamic Load Lines and Transition Energy
For MOSFETs, dynamic load lines can be generalized by introducing a concept that relates the device and its gate driver to the
power circuit. The concept of 'Q' loci, although not precise, allows one to organize significant factors influencing switching loci
into simple groupings that are very useful for prediction. Q loci are used to map dynamic load lines and transition energies.
The Q locus for a MOSFET relates its average gate current during transition through the active region to the external circuit
inductance (LX) that is, in part, controlling the transition time (see Figure C1). In reference to Figure 1:
Q = IG • LX
(C1)
where LX is the commutation inductance,
LX = LD + (LSS1 + LSS2) • N,
and IG equals the average device gate current during the active region transition.
Source inductance common to the gate ant drain power circuits (LS, refer Figure 1) has been omitted from equation (C1). It is
given separate treatment later. Dynamic load lines for the IRF150 are mapped by Q loci (solid lines) in Figure C2a ant C3a. For
low values of Q, the device supports the supply voltage during the turn-on transition. During turn-off, the device develops a
relatively Low voltage in excess of the supply to reduce the branch current. Loci for high Q values indicate that the external
inductance supports the supply voltage during turn-on. Also, the device develops a large voltage to drive the branch current to
zero during turn-off.
Equation C1 states that the switching locus in the active region depends only on the product of average gate current and the
power circuit inductance controlling the transition. The transition time will vary depending on the specific inductance value.
However, for a given value of inductance, a higher Q value means shorter transition time ant lower switching energy as shown by
the solid lines in Figures C2b ant C3b. The introduction of common source inductance (LS) to the gate and power circuit results
in increased drain-to-source voltage during turn-on and therefore a higher transition energy. The dashed lines in Figures C2a and
b map the dynamic load line deflection and the increase in turn-on energy for increased values of LS/LX.
Similarly, during turn-off, the addition of common source inductance in Figure C3b increases the transition energy dissipated by
the device. However, as shown in Figure C3a, the peak drain-to-source voltage is reduced during turn-off. These results are
consistent since the lower drain-to-source voltage means a longer time is required to commutate the current in the external power
circuit inductance, LX. Therefore, the greater amount of energy drawn from the supply during this increased time contributes to
the increased device transition energy.
To determine the value of RGC, the following procedure is used:
+
-
+ -
+
+ +
- -
+-
+
IL
+
-
LOAD
VS
+
IL
VDS
VS
-
+
+
- +
-
+
+
+
-
-
+
+
VDS
-
-
+
-
-
LOAD
-
+
-
+
+
-
VDS ON = VS - Σ VLi
VDS ON = V0 - Σ VLi
VDS OFF = VS + Σ VLi
VDS OFF = V0+ Σ VLi
LX = Σ Li
LX = Σ Li
(a) BUCK CIRCUIT
(b) BOOST CIRCUIT
V0
Figure C1: Illustration of Commutation Inductance, LX , for Two Common Circuits LX Controls Current Transfer Between the Two Branches
OHMIC
Q0 = 4 x 10 - 9 AMP-HENRY
40
Q1 = 20 x 10 - 9 AMP-HENRY
ACTIVE
Q2 = 100 x 10 - 9 AMP-HENRY
ON
LS / LX
= 150%
iD
AMP
Q0
Q1
20
30%
20%
Q2
OFF
0
0
25
VDS , VOLT
50
Figure C2(a): Dynamic Load Line Mapping By Q Loci Including Deflection By LS / LX
From equation C1:
IG2 =
Q
LX
 VT 2 + VB 

VDR − 


2
≅
R G2
(C2)
where VB is the value of VGS2 at the active/ohmic region boundary for the specific Q locus (VGS2 = VDS + VT2, refer Figure C2a).
150%
400
30%
LS / LX = 20%
Q0
TRANSITION
ENERGY
x 10 - 6 JOULE
Figure C2(a) & C2(b): Q-Loci For IRF150
Turn-On
200
Q1
Q2
0
0
200
400
LX , nh
Figure C2(b): Transition Energy Mapping By Q Loci
R G2
 VT 2 + VB 

VDR − 

2

≅
L X (C3)
Q
40
IL/N
PEAK CONTINUOUS
VOLTAGE RATING
ON
X
20%
30%
For 100% decoupling between N parallel
devices, let
RGC = RG2/N
and set RGi equal to zero.
Q2
iD
AMP 20
LS / LX = 150%
(C4)
Q0
Q1
OFF
0
0
50
VDS VOLT
100
Figure C3(a): Dynamic Load Line Mapping By Q Loci
Including Deflection By LS / LX
150
30%
150%
Q0
800
LS / LX = 20%
Q1
Q2
TRANSITION
ENERGY
400
x 10 - 6 JOULE
Q2 : VZ = 100V; HEXFET OR
DIVERTER CIRCUIT
0
0
200
LX , nh
Figure C3(b): Transition Energy Mapping By Q Loci
Figure C3(a) & C3(b): Q-Loci For IRF150 Turn-Off
400
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