Chapter 4. Switch Realization
4.1. Switch applications
Single-, two-, and four-quadrant switches. Synchronous rectifiers
4.2. A brief survey of power semiconductor devices
Power diodes, MOSFETs, BJTs, IGBTs, and thyristors
4.3. Switching loss
Transistor switching with clamped inductive load. Diode
recovered charge. Stray capacitances and inductances, and
ringing. Efficiency vs. switching frequency.
4.4. Summary of key points
Fundamentals of Power Electronics
1
Chapter 4: Switch realization
SPST (single-pole single-throw) switches
SPST switch, with
voltage and current
polarities defined
Buck converter
with SPDT switch:
L
1
iL(t)
+
1
+
i
2
+
–
Vg
C
R
V
–
v
–
with two SPST switches:
0
iA
A
L
iL(t)
+
+ vA –
All power semiconductor
devices function as SPST
switches.
Fundamentals of Power Electronics
+
–
Vg
2
–
vB
+
B
iB
C
R
V
–
Chapter 4: Switch realization
Realization of SPDT switch using two SPST switches
G
G
G
G
A nontrivial step: two SPST switches are not exactly equivalent to one
SPDT switch
It is possible for both SPST switches to be simultaneously ON or OFF
Behavior of converter is then significantly modified
—discontinuous conduction modes (chapter 5)
Conducting state of SPST switch may depend on applied voltage or
current —for example: diode
Fundamentals of Power Electronics
3
Chapter 4: Switch realization
Quadrants of SPST switch operation
1
+
i
Switch
on state
current
A single-quadrant
switch example:
v
ON-state: i > 0
–
OFF-state: v > 0
0
Switch
off state voltage
Fundamentals of Power Electronics
4
Chapter 4: Switch realization
Some basic switch applications
Singlequadrant
switch
switch
on-state
current
Currentbidirectional
two-quadrant
switch
switch
off-state voltage
switch
on-state
current
Voltagebidirectional
two-quadrant
switch
Fundamentals of Power Electronics
switch
on-state
current
switch
off-state
voltage
switch
on-state
current
Fourquadrant
switch
switch
off-state
voltage
5
switch
off-state
voltage
Chapter 4: Switch realization
4.1.1. Single-quadrant switches
1
+
i
Active switch: Switch state is controlled exclusively
by a third terminal (control terminal).
Passive switch: Switch state is controlled by the
applied current and/or voltage at terminals 1 and 2.
v
–
0
SCR: A special case — turn-on transition is active,
while turn-off transition is passive.
Single-quadrant switch: on-state i(t) and off-state v(t)
are unipolar.
Fundamentals of Power Electronics
6
Chapter 4: Switch realization
The diode
• A passive switch
i
• Single-quadrant switch:
1
+
• can conduct positive onstate current
on
i
v
off
v
–
0
Symbol
instantaneous i-v characteristic
Fundamentals of Power Electronics
7
• can block negative offstate voltage
• provided that the intended
on-state and off-state
operating points lie on the
diode i-v characteristic,
then switch can be
realized using a diode
Chapter 4: Switch realization
The Bipolar Junction Transistor (BJT) and the
Insulated Gate Bipolar Transistor (IGBT)
BJT
C
1
i +
• An active switch, controlled
by terminal C
i
v
• Single-quadrant switch:
on
–
off
0
IGBT
v
• can block positive off-state
voltage
1
i +
C
v
–
0
• can conduct positive onstate current
instantaneous i-v characteristic
Fundamentals of Power Electronics
8
• provided that the intended
on-state and off-state
operating points lie on the
transistor i-v characteristic,
then switch can be realized
using a BJT or IGBT
Chapter 4: Switch realization
The Metal-Oxide Semiconductor Field Effect
Transistor (MOSFET)
• An active switch, controlled by
terminal C
i
on
1
i +
C
• Normally operated as singlequadrant switch:
v
off
v
–
on
(reverse conduction)
0
• can conduct positive on-state
current (can also conduct
negative current in some
circumstances)
• can block positive off-state
voltage
Symbol
instantaneous i-v characteristic
Fundamentals of Power Electronics
9
• provided that the intended onstate and off-state operating
points lie on the MOSFET i-v
characteristic, then switch can
be realized using a MOSFET
Chapter 4: Switch realization
Realization of switch using
transistors and diodes
Buck converter example
iA
A
L
iL(t)
+
+ vA –
Vg
+
–
–
vB
B
C
R
V
+
Switch A: transistor
iB
–
Switch B: diode
iA
SPST switch
operating points
Switch A
on
iB
Switch B
iL
on
Switch A
Switch B
off
off
Vg
vA
Switch A
Fundamentals of Power Electronics
–Vg
iL
vB
Switch B
10
Chapter 4: Switch realization
Realization of buck converter
using single-quadrant switches
iA
+
vA
L
–
+
Vg
–
vB
+
+
–
iL(t)
vL(t)
–
iB
iA
Switch A
on
iB
Switch B
iL
on
Switch A
Switch B
off
off
Vg
Fundamentals of Power Electronics
vA
–Vg
11
iL
vB
Chapter 4: Switch realization
4.1.2. Current-bidirectional
two-quadrant switches
• Usually an active switch,
controlled by terminal C
i
1
i
on
(transistor conducts)
+
C
v
–
0
BJT / anti-parallel
diode realization
Fundamentals of Power Electronics
v
off
on
(diode conducts)
instantaneous i-v
characteristic
12
• Normally operated as twoquadrant switch:
• can conduct positive or
negative on-state current
• can block positive off-state
voltage
• provided that the intended onstate and off-state operating
points lie on the composite i-v
characteristic, then switch can
be realized as shown
Chapter 4: Switch realization
Two quadrant switches
switch
on-state
current
i
1
+
on
(transistor conducts)
i
v
off
v
switch
off-state
voltage
–
0
Fundamentals of Power Electronics
on
(diode conducts)
13
Chapter 4: Switch realization
MOSFET body diode
i
1
i
on
(transistor conducts)
+
off
v
C
v
–
on
(diode conducts)
0
Power MOSFET
characteristics
Fundamentals of Power Electronics
Power MOSFET,
and its integral
body diode
14
Use of external diodes
to prevent conduction
of body diode
Chapter 4: Switch realization
A simple inverter
iA
+
Vg
+
–
Q1
D1 vA
–
v0(t) = (2D – 1) Vg
L
iL
+
+
Vg
+
–
Q2
D2 v
B
–
C
R
v0
–
iB
Fundamentals of Power Electronics
15
Chapter 4: Switch realization
Inverter: sinusoidal modulation of D
v0(t) = (2D – 1) Vg
v0
Sinusoidal modulation to
produce ac output:
Vg
D(t) = 0.5 + Dm sin (ωt)
D
0
0.5
1
–Vg
The resulting inductor
current variation is also
sinusoidal:
iL(t) =
Vg
v0(t)
= (2D – 1)
R
R
Hence, current-bidirectional
two-quadrant switches are
required.
Fundamentals of Power Electronics
16
Chapter 4: Switch realization
The dc-3øac voltage source inverter (VSI)
ia
Vg
+
–
ib
ic
Switches must block dc input voltage, and conduct ac load current.
Fundamentals of Power Electronics
17
Chapter 4: Switch realization
Bidirectional battery charger/discharger
D1
L
+
+
Q1
vbus
vbatt
D2
spacecraft
main power bus
–
Q2
–
vbus > vbatt
A dc-dc converter with bidirectional power flow.
Fundamentals of Power Electronics
18
Chapter 4: Switch realization
4.1.3. Voltage-bidirectional two-quadrant switches
• Usually an active switch,
controlled by terminal C
+
i
• Normally operated as twoquadrant switch:
i
1
on
v
v
C
off
off
(diode
blocks voltage)
(transistor
blocks voltage)
–
0
BJT / series
diode realization
instantaneous i-v
characteristic
• can conduct positive on-state
current
• can block positive or negative
off-state voltage
• provided that the intended onstate and off-state operating
points lie on the composite i-v
characteristic, then switch can
be realized as shown
• The SCR is such a device,
without controlled turn-off
Fundamentals of Power Electronics
19
Chapter 4: Switch realization
Two-quadrant switches
1
i
+
switch
on-state
current
i
v
on
–
0
v
1
i
+
off
off
(diode
blocks voltage)
(transistor
blocks voltage)
switch
off-state
voltage
v
C
–
0
Fundamentals of Power Electronics
20
Chapter 4: Switch realization
A dc-3øac buck-boost inverter
φa
iL
+
vab(t)
–
φb
Vg
–
+
+
vbc(t)
–
φc
Requires voltage-bidirectional two-quadrant switches.
Another example: boost-type inverter, or current-source inverter (CSI).
Fundamentals of Power Electronics
21
Chapter 4: Switch realization
4.1.4. Four-quadrant switches
switch
on-state
current
• Usually an active switch,
controlled by terminal C
• can conduct positive or
negative on-state current
switch
off-state
voltage
Fundamentals of Power Electronics
22
• can block positive or negative
off-state voltage
Chapter 4: Switch realization
Three ways to realize a four-quadrant switch
1
1
i
i
1
+
1
i
+
+
v
v
v
–
–
–
+
i
v
–
0
0
Fundamentals of Power Electronics
0
23
0
Chapter 4: Switch realization
A 3øac-3øac matrix converter
3øac input
3øac output
ia
van(t)
+
–
vbn(t)
+
–
ib
+
–
vcn(t)
ic
• All voltages and currents are ac; hence, four-quadrant switches are required.
• Requires nine four-quadrant switches
Fundamentals of Power Electronics
24
Chapter 4: Switch realization
4.1.5. Synchronous rectifiers
Replacement of diode with a backwards-connected MOSFET,
to obtain reduced conduction loss
i
+
1
1
i
i
+
1
i +
C
v
v
v
–
–
–
ideal switch
conventional
diode rectifier
Fundamentals of Power Electronics
(reverse conduction)
v
off
on
0
0
0
on
MOSFET as
synchronous
rectifier
25
instantaneous i-v
characteristic
Chapter 4: Switch realization
Buck converter with synchronous rectifier
iA
+
vA
L
–
iL(t)
Q1
Vg
+
–
–
vB
+
C
C
Q2
• MOSFET Q2 is
controlled to turn on
when diode would
normally conduct
• Semiconductor
conduction loss can
be made arbitrarily
small, by reduction
of MOSFET onresistances
iB
• Useful in low-voltage
high-current
applications
Fundamentals of Power Electronics
26
Chapter 4: Switch realization
4.2. A brief survey of power semiconductor devices
!
!
!
!
!
!
Power diodes
Power MOSFETs
Bipolar Junction Transistors (BJTs)
Insulated Gate Bipolar Transistors (IGBTs)
On resistance vs. breakdown voltage vs. switching times
Minority carrier and majority carrier devices
Fundamentals of Power Electronics
27
Chapter 4: Switch realization
4.3.1. Transistor switching with clamped inductive load
iA
+
vA
iL(t)
–
physical
MOSFET
+
–
vB
gate +
driver
+
–
Vg
–
DTs
Ts
transistor
waveforms
L
iL
iA(t)
ideal
diode
0
0
iL
iB
iB(t)
0
transistor turn-off
transition
1
2
t
–Vg
pA(t)
W off =
0
vB(t)
Vg iL
= vA iA
area
Woff
VgiL (t 2 – t 0)
t0
Fundamentals of Power Electronics
t
diode
waveforms
Buck converter example
vB(t) = vA(t) – Vg
i A(t) + iB(t) = iL
Vg
vA(t)
28
t1
t2
t
Chapter 4: Switch realization
Switching loss induced by transistor turn-off transition
Energy lost during transistor turn-off transition:
W off =
1
2
VgiL (t 2 – t 0)
Similar result during transistor turn-on transition.
Average power loss:
Psw = 1
Ts
Fundamentals of Power Electronics
pA(t) dt = (W on + W off ) fs
switching
transitions
29
Chapter 4: Switch realization
p–n junction!
Junction diode consisting of!
• p-doped silicon!
• n-doped silicon!
• A p-n junction where the p- and n-material meet !
+
v
p
+
+
+
–
+
–
+
+
+
–
n
–
–
–
+
+
–
–
–
–
p material contains
n material contains
mobile holes!
mobile electrons!
vo +
p–n–junction!
p
+
+
Fundamentals of Power Electronics!
+
+
+
+
+
+
+
–
–
1!
–
–
–
+
+
+
+
+
E
–
–
n
–
–Chapter 4: Switch realization!
–
–
–
–
–
+
v
–
p Formation
n
–
region"
+
+ of depletion
–
–
also called+ “space charge layer”!–
+
+
+
+
–
+
+
–
–
–
–
• At the junction, the concentrations of holes and electrons changes abruptly!
• The holes and electrons diffuse in the direction of reducing concentration!
Hole diffusion!
Electron diffusion!
p
+
+
+
+
+
+
+
+
+
– vo +
–+
–+
–+
–+
–+
–
–
n
–
–
–
–
–
–
–
E
• These holes and electrons leave behind charged atoms—a “depletion
region”!
– vo +
• An electric
in the vicinity
– –of+the
+ junction!
p field forms
n
–
+
+
– opposes
• This electric field constitutes an energy
barrier that
diffusion!
– –++
–
–
+
+ –
– + the
+ voltage
+
• The device+ comes to equilibrium
when
vo across the depletion
–
– – + +of charges across
region is enough to stop further diffusion
the junction!
–
+
Fundamentals of Power Electronics!
+
+
– –2! + +
E
–
–
–
Chapter 4: Switch realization!
+
+
+
–
+
+
+
–
+
–
–
–
+
+
–
–
–
–
The diode under reverse
bias conditions!
–v +
o
–+ –
n
–
–+
–
–
+
+
–+
+
+
–
–
+
• Application of an external
voltage to the diode– causes
+
+ reverse
+
– the depletion
–
–
–+
region to increase!
p
+
+
• The external voltage is blocked by the
E depletion region!
• Increasing the reverse voltage requires that charge is added to the depletion
region!
– v +
p
+
+
+
+
+
+
+
+
+
–
–
–
–
–
–
–
–
–
–
o
+
+
+
+
+
+
+
+
+
+
–
–
n
–
–
–
–
–
–
–
E
+
–
• “Junction capacitance”: depletion region charge vs. voltage characteristic!
– vo +
p
n
–
+
+
–
–3! +
Fundamentals of Power Electronics!
Chapter 4: Switch realization!
–
–
+
+
–+ – –
+
+
–+
–
+
+
+
–
–
E
p
+
+
+
+
+
+
+
+
+
–
–
–
–
+
+
+
+
–
–
n
–
–
–
–
–
–
–
E
– v +
The diode under forward
bias conditions!
o
––++ –
n
–
––++
–
–
+
+ – – + +
+
+
–
––++
–
+
+ positive,
+
–
• When the diode voltage
is
depletion
is not large
–
– region voltage
– –the
++
enough to prevent diffusion of charge across the junction!
E the junction, and become minority
• Holes from the p-region diffuse across
carriers in the n-region, whose energy state is high enough to enable them
to conduct!
p
+
+
+
–
• Similarly, electrons from n-region diffuse across the junction and become
minority carriers in the p-region!
– vo +
p
n
–
+
+
–
–+
–
–
+
+
–+ – –
+
+
–+
–
+
+
+
–
–
E
Fundamentals of Power Electronics!
4!
Chapter 4: Switch realization!
– vo +
p
n
– vo +
p
+
+
+
+
+
+
–+
–+
–+
charge
Minority-carrier
stored
+
+
+
–
–
–
n
–
–
–
in forward-biased
diode!
–
–
–
E
Under forward-biased conditions, a hole enters the p-material from the external
circuit. It then either (a) diffuses across junction, then recombines with an
electron in the n-region, or (b) recombines in the p-region with a minority-carrier
electron!
– vo +
p
n
+
–
+
–
Electron concentration
Hole concentration
The forward current of the diode consists entirely of recombination, either in
the p- or n-region. The forward current continues as long as there is minority
charge. To turn off the diode, the minority charge must be eliminated.!
Fundamentals of Power Electronics!
5!
Chapter 4: Switch realization!
– vo +
p
n
+
–
+
–
Charge-controlled behavior of the diode!
The diode equation:!
q(t) = Q0 e
v(t)
Hole concentration
+
–
Electron concentration
i
v
–1
p
n
+
Charge control equation:!
q(t)
dq(t)
= i(t) –
dt
L
–
+
–
Electron concentration
Hole concentration
with:!
 = 1/(26 mV) at 300 K!
Area = total stored minority charge q!
L = minority carrier lifetime!
(above equations don t
include current that charges
depletion region capacitance)!
In equilibrium: dq/dt = 0, and hence!
i(t) =
q(t)
L
(lumped-element charge
control model with 1 lump)!
Fundamentals of Power Electronics!
6!
=
Q0
L
e
v(t)
– 1 = I0 e
v(t)
–1
Chapter 4: Switch realization!
Removal of stored charge during reverse recovery!
v(t)
Distribution of minority charge on
one side of p-n junction during
reverse recovery!
t0
t1
t2
t3 t4
t
Minority
charge
t = t0
t1
0 x0
Voff
i(t)
t2
x3
t = t3
Ion
0
x
Slope determines diffusion rate and
hence current!
Fundamentals of Power Electronics!
7!
Chapter 4: Switch realization!
Charge-control in the diode:"
Discussion!
•
The familiar i–v curve of the diode is an equilibrium relationship
that can be violated during transient conditions!
•
During the turn-on and turn-off switching transients, the current
deviates substantially from the equilibrium i–v curve, because of
change in the stored charge and change in the charge within the
reverse-bias depletion region!
•
The reverse-recovery time tr is the time required to remove the
stored charge in the diode and enable it to block the full applied
negative voltage. The area of the negative diode current during
reverse recovery is the recovered charge Qr!
Fundamentals of Power Electronics!
8!
Chapter 4: Switch realization!
Inclusion of Switching Loss in the
Averaged Equivalent Circuit Model
The methods of Chapter 3 can be extended to include switching loss in
the converter equivalent circuit model
•
Include switching transitions in the converter waveforms
•
Model effects of diode reverse recovery, etc.
To obtain tractable results, the waveforms during the switching
transitions must usually be approximated
Things that can substantially change the results:
•
Ringing caused by parasitic tank circuits
•
Snubber circuits
•
These are modeled in ECEN 5817, Resonant and SoftSwitching Phenomena in Power Electronics
1
The Modeling Approach
Extension of Chapter 3 Methods
Sketch the converter waveforms
– Including the switching transitions (idealizing assumptions
are made to lead to tractable results)
– In particular, sketch inductor voltage, capacitor current, and
input current waveforms
The usual steady-state relationships:
vL = 0, iC = 0, ig = Ig
Use the resulting equations to construct an equivalent
circuit model, as usual
2
Buck Converter Example
•
•
•
•
Ideal MOSFET, p–n diode with reverse recovery
Neglect semiconductor device capacitances, MOSFET
switching times, etc.
Neglect conduction losses
Neglect ripple in inductor current and capacitor voltage
3
Assumed
waveforms
Diode recovered charge Qr,
reverse recovery time tr
These waveforms assume
that the diode voltage
changes at the end of the
reverse recovery transient
• a “snappy” diode
• Voltage of soft-recovery
diodes changes sooner
• Leads to a pessimistic
estimate of induced
switching loss
4
Inductor volt-second balance
and capacitor charge balance
As usual: vL = 0 = DVg – V
Also as usual: iC = 0 = IL – V/R
5
Average input current
ig = Ig = (area under curve)/Ts
= (DTsIL + trIL + Qr)/Ts
= DIL + trIL /Ts + Qr /Ts
6
Construction of Equivalent Circuit Model
From inductor volt-second balance: vL = 0 = DVg – V
From capacitor charge balance: iC = 0 = IL – V/R
7
Input port of model
ig = Ig = DIL + trIL /Ts + Qr /Ts
8
Combine for complete model
The two independent current sources consume power
Vg (trIL /Ts + Qr /Ts)
equal to the switching loss induced by diode reverse recovery
9
Solution of model
Output:
V = DVg
Efficiency: = Pout / Pin
Pout = VIL
Pin = Vg (DIL + trIL /Ts + Qr /Ts)
Combine and simplify:
= 1 / [1 + fs (tr /D + Qr R /D2Vg )]
10
Predicted Efficiency vs Duty Cycle
Switching frequency 100 kHz
Input voltage 24 V
Load resistance 15 Recovered charge 0.75 µCoul
Reverse recovery time 75 nsec
Buck converter with diode reverse recovery
100.00%
90.00%
80.00%
(no attempt is made here to
model how the reverse
recovery process varies with
inductor current)
• Substantial degradation of
efficiency
• Poor efficiency at low duty
cycle
Efficiency
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
0
0.2
0.4
0.6
Duty cycle
11
0.8
1
Boost Converter Example
Model same effects as in previous buck converter example:
• Ideal MOSFET, p–n diode with reverse recovery
• Neglect semiconductor device capacitances, MOSFET
switching times, etc.
• Neglect conduction losses
• Neglect ripple in inductor current and capacitor voltage
12
Boost
converter
Transistor and diode
waveforms have same
shapes as in buck
example, but depend
on different quantities
13
Inductor volt-second balance
and average input current
As usual: vL = 0 = Vg – DV
Also as usual: ig = IL
14
Capacitor
charge balance
iC = id – V/R = 0
= – V/R + IL(DTs – tr)/Ts – Qr /Ts
Collect terms: V/R = IL(DTs – tr)/Ts – Qr /Ts
15
Construct model
The result is:
The two independent current sources consume power
V (trIL /Ts + Qr /Ts)
equal to the switching loss induced by diode reverse recovery
16
Predicted V/Vg vs duty cycle
Boost converter with diode reverse recovery
8
7
With RL only
6
5
V/Vg
Switching frequency 100 kHz
Input voltage 24 V
Load resistance 60 Recovered charge 5 µCoul
Reverse recovery time 100 nsec
Inductor resistance RL = 0.3 (inductor resistance also inserted
into averaged model here)
4
3
2
1
With RL and diode reverse recovery
0
0
0.2
0.4
0.6
Duty cycle
17
0.8
1
Summary
The averaged modeling approach can be extended to
include effects of switching loss
Transistor and diode waveforms are constructed,
including the switching transitions. The effects of the
switching transitions on the inductor, capacitor, and
input current waveforms can then be determined
Inductor volt-second balance and capacitor charge
balance are applied
Converter input current is averaged
Equivalent circuit corresponding to the the averaged
equations is constructed
18
4.2.1. Power diodes!
A power diode, under reverse-biased conditions:!
v
+
–
p
+
+
+
{ {
low doping concentration
n-
–
E
v
+
n
–
–
–
depletion region, reverse-biased
Fundamentals of Power Electronics!
9!
Chapter 4: Switch realization!
Forward-biased power diode!
v
+
–
i
{
conductivity modulation
n-
p
+
–
+
+
+
n
+
–
+
–
minority carrier injection
Fundamentals of Power Electronics!
10!
Chapter 4: Switch realization!
Diode in OFF state:"
reversed-biased, blocking voltage!
v(t)
v
+
–
t
n–
p
i(t)
+
0
{
–
E
v
n
t
Depletion region, reverse-biased
• Diode is reverse-biased!
• No stored minority charge: q = 0!
(1)
• Depletion region blocks applied
reverse voltage; charge is stored in
capacitance of depletion region!
Fundamentals of Power Electronics!
12!
Chapter 4: Switch realization!
Turn-on transient!
v(t)
Diode conducts with low on-resistance
t
• charge to increase
voltage across
depletion region!
Diode is forward-biased. Supply minority
charge to n– region to reduce on-resistance
Charge depletion region
i(t)
On-state current determined by converter circuit
t
(1)
(2)
Fundamentals of Power Electronics!
13!
The current i(t) is
determined by the
converter circuit. This
current supplies: !
• charge needed to
support the on-state
current!
• charge to reduce onresistance of n–
region!
Chapter 4: Switch realization!
Turn-off transient!
v
+
–
i (< 0)
n-
p
n
+
+
+
+
+
+
+
+
}
Removal of stored minority charge q
Fundamentals of Power Electronics!
14!
Chapter 4: Switch realization!
Diode turn-off transient"
continued!
v(t)
t
(4) Diode remains forward-biased.
Remove stored charge in n– region
(5) Diode is reverse-biased.
Charge depletion region
capacitance.
i(t)
tr
0
t
di
dt
Area
–Qr
(1)
(2)
Fundamentals of Power Electronics!
(3)
(4)
15!
(5)
(6)
Chapter 4: Switch realization!
The diode switching transients induce
switching loss in the transistor!
iA
+
vA
–
fast
transistor
+
–
–
+
–
Vg
iL(t)
vB
+
L
transistor
waveforms
Qr
Vg
silicon
diode
0
0
t
diode
waveforms
• Diode recovered stored charge
Qr flows through transistor
during transistor turn-on
transition, inducing switching
loss!
• Qr depends on diode on-state
forward current, and on the
rate-of-change of diode current
during diode turn-off transition!
iL
vA(t)
iB
Fundamentals of Power Electronics!
see Section 4.3.2!
iA(t)
iL
iB(t)
vB(t)
0
0
t
area
–Qr
–Vg
tr
pA(t)
= vA iA
area
~QrVg
area
~iLVgtr
16!
t0
t1 t2
t
Chapter 4: Switch realization!
Types of power diodes!
Standard recovery!
Reverse recovery time not specified, intended for 50/60Hz!
Fast recovery and ultra-fast recovery!
Reverse recovery time and recovered charge specified!
Intended for converter applications!
Schottky diode!
A majority carrier device!
Essentially no recovered charge!
Model with equilibrium i-v characteristic, in parallel with
depletion region capacitance!
Restricted to low voltage (few devices can block 100V or more)!
Fundamentals of Power Electronics!
18!
Chapter 4: Switch realization!
Paralleling diodes!
Attempts to parallel diodes, and share the
current so that i1 = i2 = i/2, generally donʼt
work.!
i
i1
i2
Reason: thermal instability caused by
temperature dependence of the diode
equation.!
+
+
v1
v2
Increased temperature leads to increased
current, or reduced voltage.!
–
–
One diode will hog the current.!
To get the diodes to share the current, heroic
measures are required:!
• Select matched devices!
• Package on common thermal substrate!
• Build external circuitry that forces the currents to balance!
Fundamentals of Power Electronics!
20!
Chapter 4: Switch realization!
Ringing induced by diode stored charge!
see Section 4.3.3!
iL(t)
L
vi(t)
+
–
vL(t)
vi(t) +
–
silicon
diode
iB(t)
+
vB(t)
–
V1
t
0
–V2
C
iL(t)
• Diode is forward-biased while iL(t) > 0
• Negative inductor current removes diode
stored charge Qr!
• When diode becomes reverse-biased,
negative inductor current flows through
capacitor C.!
• Ringing of L-C network is damped by
parasitic losses. Ringing energy is lost.!
Fundamentals of Power Electronics!
21!
0
t
area
– Qr
vB(t)
t
0
–V2
t1
t2
t3
Chapter 4: Switch realization!
Energy associated with ringing!
Recovered charge is!
Qr = –
t3
t2
iL(t) dt
vi(t)
V1
t
0
Energy stored in inductor during interval
t2 ≤ t ≤ t3 :!
t3
WL =
vL(t) iL(t) dt
t2
Applied inductor voltage during interval
t2 ≤ t ≤ t3 :!
di (t)
vL(t) = L L = – V2
dt
Hence,!
t3
t3
diL(t)
WL =
L
i (t) dt =
( – V2) iL(t) dt
dt L
t2
t2
–V2
iL(t)
0
vB(t)
t
0
–V2
W L = 12 L i 2L(t 3) = V2 Qr
t1
Fundamentals of Power Electronics!
t
area
– Qr
22!
t2
t3
Chapter 4: Switch realization!
4.2.2. The Power MOSFET
Source
• Gate lengths
approaching one
micron
Gate
n
p
n
n
p
nn
n
• Consists of many
small enhancementmode parallelconnected MOSFET
cells, covering the
surface of the silicon
wafer
• Vertical current flow
• n-channel device is
shown
Drain
Fundamentals of Power Electronics
46
Chapter 4: Switch realization
MOSFET: Off state
source
n
p
–
n
• p-n- junction is
reverse-biased
n
p
n
• off-state voltage
appears across nregion
depletion region
nn
drain
Fundamentals of Power Electronics
+
47
Chapter 4: Switch realization
MOSFET: on state
• p-n- junction is
slightly reversebiased
source
n
p
n
n
p
• drain current flows
through n- region
and conducting
channel
channel
nn
drain
Fundamentals of Power Electronics
n
• positive gate voltage
induces conducting
channel
drain current
48
• on resistance = total
resistances of nregion, conducting
channel, source and
drain contacts, etc.
Chapter 4: Switch realization
MOSFET body diode
• p-n- junction forms
an effective diode, in
parallel with the
channel
source
n
p
n
n
p
Body diode
• negative drain-tosource voltage can
forward-bias the
body diode
• diode can conduct
the full MOSFET
rated current
nn
• diode switching
speed not optimized
—body diode is
slow, Qr is large
drain
Fundamentals of Power Electronics
n
49
Chapter 4: Switch realization
=1
DS
• On state: VGS >> Vth
V
V
=2
DS
V
10A
• Off state: VGS < Vth
0V
00V
Typical MOSFET characteristics
V DS
ID
=2
• MOSFET can
conduct peak
currents well in
excess of average
current rating
—characteristics are
unchanged
on state
5A
V DS =
off
state
1V
V DS = 0.5V
0A
0V
5V
10V
VGS
Fundamentals of Power Electronics
50
15V
• on-resistance has
positive temperature
coefficient, hence
easy to parallel
Chapter 4: Switch realization
A simple MOSFET equivalent circuit
D
• Cgs : large, essentially constant
• Cgd : small, highly nonlinear
Cgd
G
• Cds : intermediate in value, highly
nonlinear
Cds
• switching times determined by rate
at which gate driver
charges/discharges Cgs and Cgd
Cgs
S
Cds(vds) =
Fundamentals of Power Electronics
C0
Cds(vds) ≈ C0
v
1 + ds
V0
51
V0
C '0
vds = vds
Chapter 4: Switch realization
Switching loss caused by
semiconductor output capacitances
Buck converter example
Cds
+
–
Cj
+
–
Vg
Energy lost during MOSFET turn-on transition
(assuming linear capacitances):
W C = 12 (Cds + C j) V 2g
Fundamentals of Power Electronics
52
Chapter 4: Switch realization
MOSFET nonlinear Cds
Approximate dependence of incremental Cds on vds :
Cds(vds) ≈ C0
C '0
V0
vds = vds
Energy stored in Cds at vds = VDS :
V DS
W Cds =
vds i C dt =
vds C ds(vds) dvds
0
V DS
W Cds =
0
C '0(vds) vds dvds = 23 Cds(VDS) V 2DS
— same energy loss as linear capacitor having value
Fundamentals of Power Electronics
53
4
3
Cds(VDS)
Chapter 4: Switch realization
Characteristics of several commercial power MOSFETs
Rated max voltage
Rated avg current
R on
Qg (typical)
IRFZ48
60V
50A
0.018Ω
110nC
IRF510
100V
5.6A
0.54Ω
8.3nC
IRF540
100V
28A
0.077Ω
72nC
APT10M25BNR
100V
75A
0.025Ω
171nC
IRF740
400V
10A
0.55Ω
63nC
MTM15N40E
400V
15A
0.3Ω
110nC
APT5025BN
500V
23A
0.25Ω
83nC
APT1001RBNR
1000V
11A
1.0Ω
150nC
Part number
Fundamentals of Power Electronics
54
Chapter 4: Switch realization
MOSFET: conclusions
G
G
G
G
G
G
G
A majority-carrier device: fast switching speed
Typical switching frequencies: tens and hundreds of kHz
On-resistance increases rapidly with rated blocking voltage
Easy to drive
The device of choice for blocking voltages less than 500V
1000V devices are available, but are useful only at low power levels
(100W)
Part number is selected on the basis of on-resistance rather than
current rating
Fundamentals of Power Electronics
55
Chapter 4: Switch realization
Synchronous buck converter
Q1
Main switch Q1
Synchronous rectifier Q2
D1
Gate driver circuitry:
L
Vg
+
–
+
vs(t)
Q2
D2
–
iL
• Source of Q2 is connected to ground
• Source of Q1 is connected to switch node
Half-bridge gate driver
+ 12 V
Q1
D1
Half-bridge gate driver:
L
+
–
+
iL
• Gate of Q2 is driven by low-side driver
• Gate of Q1 is driven by high-side driver
• High-side driver is powered by bootstrap
power supply circuit
• High voltage integrated circuit
+ 12 V
vs(t)
Q2
D2
–
Logic input
Logic input:
• Commands ON/OFF state of MOSFETs
• When Q1 is on, Q2 must be off, and viceversa
• High-side control signal must be level-shifted
• Non-overlapping control: insert dead times
Modeling and understanding the gate driver circuit
+ 12 V
Rth
Thevenin
equivalent
model
vth(t)
A simple Thevenin-equivalent circuit:
• vth(t) is open-circuit voltage produced by
gate driver
• Rth is effective output resistance of driver,
approximately given by on-resistance of
output-stage transistors within the driver
• For a driver rated at 12 V and 1 A,
= (12essentially
V)/(1 A) = 12
Ω
• CgsR: thlarge,
constant
+
–
A simple MOSFET equivalent circuit
D
• Cgd : small, highly nonlinear
MOSFET, with
capacitances and body
diode explicitly shown
Cgd
G
• Cds : intermediate in value, highly
nonlinear
Cds
• switching times determined by rate
at which gate driver
charges/discharges Cgs and Cgd
Cgs
S
Cds(vds) =
Fundamentals of Power Electronics
C0
Cds(vds) 5 C0
v
1 + ds
V0
51
V0
C '0
vds = vds
Chapter 4: Switch realization
Switching transitions
+ 12 V
Q1
vth(t)
D1
L
+
–
+
Rth
Cgd
+
Cgs
vth(t) +
(t)
v
gs
–
–
Gate driver
model
iL
vgs(t)
vs(t)
–
vs(t)
MOSFET
model
t
4.2.3. Bipolar Junction Transistor (BJT)
Base
• Interdigitated base and
emitter contacts
Emitter
• Vertical current flow
n
p
n
n
• minority carrier device
• on-state: base-emitter
and collector-base
junctions are both
forward-biased
nn
• on-state: substantial
minority charge in p and
n- regions, conductivity
modulation
Collector
Fundamentals of Power Electronics
• npn device is shown
56
Chapter 4: Switch realization
BJT switching times
vs(t)
Vs2
–Vs1
VCC
vBE(t)
0.7V
RL
iC(t)
iB(t)
vs(t)
+
–
RB
+
vBE(t)
–
–Vs1
+
iB(t)
IB1
vCE(t)
0
–
–IB2
vCE(t)
VCC
IConRon
iC(t)
ICon
0
(1) (2) (3)
Fundamentals of Power Electronics
57
(4)
(5)
(6)
(7)
(8)
(9)
t
Chapter 4: Switch realization
Ideal base current waveform
iB(t)
IB1
IBon
0
t
–IB2
Fundamentals of Power Electronics
58
Chapter 4: Switch realization
Current crowding due to excessive IB2
Base
Emitter
–IB2
p
–
–
n
–
+
+
–
–
n-
–
p
can lead to
formation of hot
spots and device
failure
n
Collector
Fundamentals of Power Electronics
59
Chapter 4: Switch realization
BJT characteristics
IC
n
egio
r
e
v
acti
10A
tion
a
satur
i
s
a
u
q
CE
V CE = 5V
saturation region
slope
=β
5A
V CE = 200V
V = 20V
VCE = 0.5V
• Off state: IB = 0
• On state: IB > IC /β
• Current gain β decreases
rapidly at high current. Device
should not be operated at
instantaneous currents
exceeding the rated value
VCE = 0.2V
cutoff
0A
0V
5V
10V
15V
IB
Fundamentals of Power Electronics
60
Chapter 4: Switch realization
Darlington-connected BJT
• Increased current gain, for high-voltage
applications
Q1
Q2
D1
Fundamentals of Power Electronics
• In a monolithic Darlington device,
transistors Q1 and Q2 are integrated on the
same silicon wafer
• Diode D1 speeds up the turn-off process,
by allowing the base driver to actively
remove the stored charge of both Q1 and
Q2 during the turn-off transition
62
Chapter 4: Switch realization
Conclusions: BJT
G
G
G
BJT has been replaced by MOSFET in low-voltage (<500V)
applications
BJT is being replaced by IGBT in applications at voltages above
500V
A minority-carrier device: compared with MOSFET, the BJT
exhibits slower switching, but lower on-resistance at high
voltages
Fundamentals of Power Electronics
63
Chapter 4: Switch realization
4.2.4. The Insulated Gate Bipolar Transistor (IGBT)
• A four-layer device
Emitter
• Similar in construction to
MOSFET, except extra p
region
Gate
n
p
n
n
n-
n
p
minority carrier
injection
• compared with MOSFET:
slower switching times,
lower on-resistance, useful
at higher voltages (up to
1700V)
p
Collector
Fundamentals of Power Electronics
• On-state: minority carriers
are injected into n- region,
leading to conductivity
modulation
64
Chapter 4: Switch realization
The IGBT
collector
Symbol
gate
Location of equivalent devices
emitter
C
n
Equivalent
circuit
n
p
i2
n
p
n
i1
n-
G
i1
p
i2
E
Fundamentals of Power Electronics
65
Chapter 4: Switch realization
Current tailing in IGBTs
IGBT
waveforms
iL
Vg
vA(t)
iA(t)
C
curr
ent t
}
ail
0
0
iL
t
diode
waveforms
iB(t)
0
G
0
t
vB(t)
i1
–Vg
i2
pA(t)
E
Vg iL
= vA iA
area Woff
t
t0
Fundamentals of Power Electronics
66
t1
t2
t3
Chapter 4: Switch realization
Switching loss due to current-tailing in IGBT
+
vA
iL(t)
–
iL
physical
IGBT
vB
+
–
Vg
–
+
–
DTs
Ts
L
gate +
driver
Vg
vA(t)
iA(t)
curr
ent t
ideal
diode
ail
}
iA
IGBT
waveforms
0
0
iB
iL
t
diode
waveforms
Example: buck converter with IGBT
iB(t)
0
t
vB(t)
transistor turn-off
transition
–Vg
pA(t)
Psw = 1
Ts
0
Vg iL
= vA iA
pA(t) dt = (W on + W off ) fs
switching
transitions
area Woff
t0
Fundamentals of Power Electronics
67
t1
t2
t3
t
Chapter 4: Switch realization
Characteristics of several commercial devices
Part number
Rated max voltage
Rated avg current
V F (typical)
tf (typical)
S i ng l e-chi p dev i ces
HGTG32N60E2
600V
32A
2.4V
0.62µs
HGTG30N120D2
1200V
30A
3.2A
0.58µs
M ul t i p l e-chi p p o w er m o dul es
CM400HA-12E
600V
400A
2.7V
0.3µs
CM300HA-24E
1200V
300A
2.7V
0.3µs
Fundamentals of Power Electronics
68
Chapter 4: Switch realization
Conclusions: IGBT
G
G
G
G
G
G
G
Becoming the device of choice in 500 to 1700V+ applications, at
power levels of 1-1000kW
Positive temperature coefficient at high current —easy to parallel
and construct modules
Forward voltage drop: diode in series with on-resistance. 2-4V
typical
Easy to drive —similar to MOSFET
Slower than MOSFET, but faster than Darlington, GTO, SCR
Typical switching frequencies: 3-30kHz
IGBT technology is rapidly advancing:
G
G
3300 V devices: HVIGBTs
150 kHz switching frequencies in 600 V devices
Fundamentals of Power Electronics
69
Chapter 4: Switch realization
4.3.4. Efficiency vs. switching frequency
Add up all of the energies lost during the switching transitions of one
switching period:
W tot = W on + W off + W D + W C + W L + ...
Average switching power loss is
Psw = W tot fsw
Total converter loss can be expressed as
Ploss = Pcond + Pfixed + W tot fsw
where
Fundamentals of Power Electronics
Pfixed = fixed losses (independent of load and fsw)
Pcond = conduction losses
89
Chapter 4: Switch realization
Efficiency vs. switching frequency
Ploss = Pcond + Pfixed + W tot fsw
Switching losses are equal to
the other converter losses at the
critical frequency
100%
dc asymptote
fcrit
90%
fcrit =
80%
η
This can be taken as a rough
upper limit on the switching
frequency of a practical
converter. For fsw > fcrit, the
efficiency decreases rapidly
with frequency.
70%
60%
50%
10kHz
Pcond + Pfixed
W tot
100kHz
1MHz
fsw
Fundamentals of Power Electronics
90
Chapter 4: Switch realization
Wide Bandgap Semiconductor Devices
Why wide bandgap semiconductor materials can significantly
improve the tradeoff between breakdown voltage, forward
voltage drop, and switching speed
Silicon Carbide (SiC) power devices
•
•
Schottky diode
MOSFET
Gallium Nitride (GaN) power devices
•
HEMT
Fundamentals of Power Electronics
i
Specific on-resistance Ron as a function of breakdown voltage VB
Majority-carrier device:
A
VB
Ec
µn
es
University of Colorado Boulder
𝐴𝐴𝑅𝑅#$
𝑘𝑘
/
=
𝑉𝑉
, .
𝜇𝜇$ 𝜀𝜀) 𝐸𝐸+
device area
device breakdown voltage
critical electric field for avalanche breakdown
electron mobility
semiconductor permittivity
1
Comparison of Power Semiconductor Materials
Material
Bandgap [eV]
Electron
mobility µn
[cm2/Vs]
Critical field
Ec [V/cm]
Thermal
conductivity
[W/moK]
Si
SiC
GaN
1.12
2.36-3.25
3.44
1400
300-900
1500-2000
(AlGaN/GaN
2DEG)
3 x 105
1.3-3.2 x 106
3.0-3.5 x 106
130
700
110
Wide-bandgap device advantages
• Much larger Ec, hence much lower specific Ron at high breakdown voltages
• Majority carrier devices: no current tail, no reverse recovery
• Capability of operation at increased junction temperature
University of Colorado Boulder
2
Comparison of Power Semiconductor Materials
Material
Bandgap [eV]
Electron
mobility µn
[cm2/Vs]
Critical field
Ec [V/cm]
Thermal
conductivity
[W/moK]
Si
SiC
GaN
1.12
2.36-3.25
3.44
1400
300-900
1500-2000
(AlGaN/GaN
2DEG)
3 x 105
1.3-3.2 x 106
3.0-3.5 x 106
130
700
110
But:
• SiC is inferior to Si at sub-600V voltages because of lower electron mobility
• GaN devices are lateral (not vertical), more difficult to scale to higher
voltages and currents
• GaN substrate issues: GaN-on-Si
University of Colorado Boulder
3
The SiC Schottky Diode
Available at 600 V, 1200 V, and higher
No reverse recovery
Forward voltage drop 1.5 V – 2 V
Comparison with p–n Si diode at same voltage:
•
•
•
•
Much lower switching loss
Higher conduction loss
Overall higher efficiency
More expensive
Note that silicon Schottky diodes are restricted to < 100V
Fundamentals of Power Electronics
4
The SiC MOSFET
We have silicon MOSFETs at up to 600-700 V
SiC MOSFETs now are available at 600V – 10kV
104
• Properties are similar to Si MOSFETs, but with low Ron at
these higher voltages
• p–n body diode has VF of 3-4 V
Realization
• Switch
Allows
much higher switching frequency than Si IGBT
Table 4.4
Part number
C3M0030090K
C3M0075120K
C2M0045170D
SCT3022AL
CPM3-0900-0010A
Characteristics of several commercial SiC MOSFETs
Rated maximum voltage
Rated average current
Ron
Qg (typical)
900 V
1200 V
1700 V
650 V
900 V
63 A
30 A
72 A
93 A
196 A
30 m⌦
75 m⌦
45 m⌦
22 m⌦
10 m⌦
87 nC
51 nC
188 nC
133 nC
68 nC
Additionally,
a wide bandgap directly influences
the impact on switching time because
5
Fundamentals
of Power Electronics
improvement in specific on-resistance allows a reduction in device area while maintaining the
Power GaN HEMT
High Electron Mobility Transistor (HEMT)
A heterojunction field effect transistor
Source
Gate
Lateral device
No oxide layers
Drain
AlGaN
n-type
AlGaN: low bandgap
GaN: high bandgap
GaN
intrinsic
Substrate
Fundamentals of Power Electronics
6
The Two-Dimensional Electron Gas
(2DEG)
Source
Gate
Drain
–
–
–
+
–
+
–
+
–
–
– – –
AlGaN
n-type
+ + + +
– – – –
2DEG
+
+
+ +
Substrate
Fundamentals of Power Electronics
GaN
intrinsic
+ + +
7
The energy band diagram
takes a step at the
heterojunction. Under the
correct conditions, a
2DEG forms at the
surface of the GaN layer.
These electronics exhibit
very low resistivity (high
mobility), and can
conduct current between
source and drain.
A majority carrier device
having:
• High breakdown field
• Low on resistance
The HEMT is a JFET
The basic device is a depletion-mode junction field-effect
transistor:
• Normally on
• To turn off, reverse-bias gate
• Gate-channel junction is a diode that can conduct
current when forward-biased
Additional semiconductor design can shift threshold
voltage:
• Enhancement-mode JFETs are available
• Then device is off when vgs = 0
Fundamentals of Power Electronics
8
D
G
S
Electrical Considerations
On state:
• vgs > Vth with Vth ~ 3.5 V
• But don’t apply vgs that is too large: gate-source
diode will become forward-biased and conduct
large current.
Off state:
• vgs ≤ 0
Reverse conduction:
• No body diode
• Channel can conduct current in either direction
• With vgs = 0, a negative vds (< – Vth) can turn
device on
• Behavior is similar to having a body diode,
except
• Large forward drop ~ Vth
• No reverse recovery
Fundamentals of Power Electronics
9
D
G
S
State of the Art Device Comparison Example
Voltage rating
Ron at 25oC-150oC
Qg at VDS = 400V
Coss (energy eq.)
Coss (time eq.)
VSD
Qrr
trr
University of Colorado Boulder
Si MOSFET
600 V
24-60 mW
123 nC (10V)
184 pF
1900 pF
0.8 V
8.7 uC
440 ns
GaN
650 V
25-65 mW
12 nC (6V)
177 pF
284 pF
4V
-
10
State of the Art Device Comparison Example
Voltage rating
Ron at 25oC-150oC
Qg at VDS = 400V
Coss (energy eq.)
Coss (time eq.)
VSD
Qrr
trr
Si MOSFET body diode
reverse recovery
University of Colorado Boulder
Si MOSFET
600 V
24-60 mW
123 nC (10V)
184 pF
1900 pF
0.8 V
8.7 µC
440 ns
GaN
650 V
25-65 mW
12 nC (6V)
177 pF
284 pF
4V
-
Qrr VDS fs = 350 W
at 400V, 100 kHz
11