Buck Converter
Design
Buck Converter Design
Before reading this section, please read the
introduction.
All of
the circuits in this tutorial can be simulated in
LTspice^{®}. If you are new to
LTspice, please have a
look at my
LTspice Tutorial
In order to efficiently reduce a high voltage to a
lower voltage, a buck dc/dc converter is needed.
Consider the circuit of FIG 1
**
FIG 1**
The top MOSFET switches on creating a short circuit
between the input voltage (IN) and the left hand
side of the inductor, L1. The inductor current ramps
up according to the equation
where V is the voltage __across__ the
inductor, L is the inductance value and di/dt is the
__change__ in current with time through
the inductor. Thus with a fixed input voltage and a
fixed output voltage, there is a fixed voltage
across the inductor thus the change in current with
time is constant (i.e. a ramp waveform).
The output voltage on startup is 0V, so the initial
voltage across the inductor is equal to the input
voltage. However, as the output voltage changes (and
then reaches regulation) the above equation becomes
The peak inductor current is sensed by a small
series resistor, R4, and when the voltage across
this resistor equals a certain value (see the
specific converter’s datasheet) the IC switches off
the top MOSFET.
Now, inductors do not like having their current
interrupted, so when the top MOSFET switches off,
the inductor behaves like a battery to try to
maintain the current flow. Referring to FIG 1,
output side of the inductor tries to fly positive
(to push current out of the right hand side of the
inductor) and its switched side (the left hand side)
flies negative (to try and sink current into its
left hand side) – in an effort to maintain the left
to right current flow. Since the output side of the
inductor is clamped by a capacitor, the left hand
side flies negative. At this point the IC switches
on the bottom MOSFET, Q2, to clamp the left hand
side of the inductor to ground and enable the
inductor to maintain its current flow.
Thus a current flows __up__ MOSFET Q2,
from left to right through the inductor and down
into the output capacitor, thus charging the output
capacitor.
When MOSFET Q2 switches on, it also provides a short
circuit to 0V at the bottom of capacitor C6. Since
the top of C6 is connected to the LTC3891’s internal
linear regulator (INTVCC) via diode D1, this
capacitor charges to INTVCC – 0.3V. The voltage on
this capacitor is then used to provide a voltage
higher than the input voltage to enable the top
MOSFET to be switched on. Indeed, at startup, Q2
actually switches on before Q1 to charge the flying
capacitor, C6, to enable Q1 to be switched on.
The process then starts again, with Q1 switching
back on again and recharging the inductor.
The discharge cycle of the inductor is governed by
the same equation as the charge cycle:
where V is the voltage across the inductor and is
equal to the output voltage (since the left hand
side of the inductor is clamped to 0V by MOSFET Q2)
The LTspice model of FIG 1 can be downloaded here
(right click over the link and save as a '.asc'
file):
LTC3854 buck converter.
The datasheet of the
LTC3854 can be downloaded here:
LTC3854 datasheet.
Considering FIG1, the input voltage is 12V, the
output voltage (in regulation) is 5V and the
inductor value is 6uH
Thus from
we can determine that change in current when the
inductor is charging is
or 1,166,666 Amps per second.
When the inductor is discharging (when Q2 is
on), the inductor discharges according to the
equation
or
which equates to 833,333 Amps per second.
**
FIG 2**
FIG 2 shows an LTspice simulation with the current ramping from 4.378A to
5.604A over 1.08us, a change of 1,135,185 Amps per
second – not too far off what was calculated
above.
During discharge, the current ramps down from 5.604A
to 4.378A, but over 1.438us, a change of 852,573A –
close to what we calculated.
The discrepancy in the above is because each MOSFET
does not present a perfect short circuit and
actually has about 50mV across it when fully
activated.
It is interesting to note that the value of *di/dt
*is determined ONLY by the inductance
value and the voltage across the inductor. The controller IC has nothing to do with
setting the inductor ramp current.
It is also useful to calculate the duty cycle of the
converter. The duty cycle is the ratio of the ON
time of the top MOSFET to the total period of
oscillation.
The inductor charges according to
and discharges according to
(here dt_{1} is the ON time of the top
MOSFET and dt_{2} is the ON time of the
bottom MOSFET)
In steady state, as can be seen in FIG 2 the charge
current is equal to the discharge current, so
From this we can see that
so
so
and if Duty Cycle (DC) is a ratio of dt_{1}
to (dt_{1} +dt_{2}) then
So the duty cycle is equal to the ratio of Vout to
Vin.
It is interesting to note that the duty cycle is
purely dependent on the input and output voltages
and has nothing to do with the controller IC or
inductor value.
The above is true as long as the inductor current
does not fall to zero. The converter is then said to
be operating in continuous conduction mode (CCM). If
the inductor current ramps down to zero, the
converter is then in discontinuous conduction mode
(DCM).
In CCM if the load current changes, the duty cycle
of the converter and the amplitude of the ripple
current remain the same. The circuit responds to a
change in load current by changing the midpoint of
the inductor current (its dc offset). Indeed it is
also true that the *average inductor current in a
buck converter is equal to the load current*.
In FIG 2 we can see that the midpoint of the
inductor current is 5A and it can be seen from FIG 1
that our load is 1 Ohm, thus the load current is 5A.
If the load resistance were increased to 2 Ohms, the
ripple current and duty cycle would remain unchanged
(in the steady state), but the dc offset current
would fall to 2.5A.
__
Buck Converter Design
Procedure__
We are going to use the LTC3891 to design a buck
converter that converts from 24V to 5V and can
supply a load of 2A. The LTC3891 datasheet can be
downloaded here:
LTC3891 Datasheet
The outline schematic is shown in FIG 3
**
FIG3**
With a 24V input and a 5V output, the duty cycle of
the converter is
The LTC3891 has a selectable fixed frequency
operation. Tying the FREQ pin to INTVCC (see datasheet)
sets the frequency to 535kHz, thus a switching
period of 1.87us. Thus the ON time of the top MOSFET
will be 21% of 1.87us, or 389ns. At this point it is
wise to check that the converter has a minimum ON
time of less than 389ns. The LTC3891 has a minimum
ON time of 95ns, so we are well within spec.
If the input voltage is very close to the output
voltage, the duty cycle will be very high. In this
case, it is worth checking that the calculated duty
cycle does not violate the maximum duty cycle spec
of the part. In any dc/dc converter with a high side
N channel MOSFET (Q1 in FIG1), the bottom MOSFET
must switch on to enable the flying capacitor (C6 in
FIG1) to refresh and it is this refresh cycle that
determines the maximum duty cycle of the converter.
__
Inductor Choice__
It is good design practice to keep the inductor
ripple current (*di*) to about 40% of the
output current, so with a 2A load this implies a
ripple current of 800mA. Increasing the ripple
current increases the switching losses and output
ripple, but means we can use a smaller value and
size of inductor. Decreasing the ripple current
means the circuit will be less responsive to load
transients.
The current ramp in the inductor during charging is
represented by
We know Vin, Vout, dt1 and the inductor ripple, *
di*, so can work out the optimum inductor value.
which implies and inductor value of 9.24uH. A 10uH
inductor should be suitable.
We know that the average inductor current is equal
to the output current, so our peak inductor current
is equal to the output current plus half the ripple
current. For a 2A load, the peak inductor current
will be 2.4A.
We need to pick a 10uH inductor with a saturation
current rating of at least 2.4A. If too much current
flows in the inductor, the ferrite that the inductor
is wound on saturates and the inductor loses its
inductive properties causing the inductor value to
fall. From the equation
if the inductor value falls, the current ramp
increases causing the ferrite to further saturate,
causing more current to flow…
Therefore we must make sure that the inductor never
saturates.
Using
the
Wurth Electronics Component Simulation Software,
we can see the 10uH, 3.5A saturation current
74404064100
is a good fit:
74404064100 datasheet
Regarding the placement of Wurth inductors on the
PCB, the 'dot' on the inductor package represents
the start of the winding. Therefore it is advisable
to connect the dot end of the inductor closest to
the FETs as this is the end that will undergo the
most dv/dt and hence generate the most interference.
If the non-dot end is connected to the output
voltage (at dc) and the windings closest to the
output voltage are wound over the dot end, they will
give a degree of shielding to the inner (switched)
end of the inductor.
__
Rsense Calculation__
The sense resistor (R4 in FIG 3) senses the inductor
current. The trip threshold on the current sense
comparator in the case of the LTC3891 is 50mV (if
the ILIM pin is tied to INTVCC), so a current sense
resistor of 16mOhms should ensure that the peak
current never rises above 3.1A – high enough that
our peak current demands can be met, but lower than
the saturation current of the inductor.
__
MOSFET Choice - General__
In nearly all applications the specification for the
top MOSFET is different from that for the bottom
MOSFET if maximum efficiency is to be achieved.
Both MOSFETs will be exposed to the input voltage at
some point during the switching cycle, so both
must have a drain-source breakdown voltage of at least
Vin. In our design, the input voltage is 24V, so a MOSFET rated with a breakdown voltage of at least
30V should suffice.
The peak current will occur just as the top MOSFET
switches off and the bottom MOSFET switches on and
the same magnitude of current flows through both
devices. Our current sense resistor sets the peak
current to 3.1A, so any MOSFET with a peak current
greater than 5A is suitable.
Looking at the block diagram of the LTC3891, we see
that the drive circuitry for the bottom MOSFET is
powered from INTVCC. The minimum voltage
specification on this voltage is 4.85V, so our
bottom MOSFET must have a gate turn on voltage of
significantly less than 4.85V. However, the drive to the top MOSFET is powered from
INTVCC – 0.3V (the voltage across the flying
capacitor) so the turn on voltage of the top MOSFET
needs to be significantly less than 4.55V. In either case, a logic level MOSFET, with a turn on
voltage of 1V - 2V is suitable.
The above parameters represent the bare minimum
characteristics of the MOSFETs. However, to get a
good design, we must ensure that the losses in the
MOSFETs are as low as possible.
__
MOSFET Choice – Switching and Conduction Losses__
The MOSFETs present two losses in the
circuit: switching losses and conduction losses.
The switching losses result from current flowing
through the MOSFET at the same time that a voltage
is across the MOSFET (so power is generated in the
MOSFET), during the turn on and turn off times of
the MOSFET. For a given gate drive coming out of the
controller IC, the lower the Gate-Source capacitance
of the MOSFET, the quicker the MOSFET will turn on.
Thus the Qg specification of the MOSFET is important
and should be as low as possible. The Qg of the
MOSFET will also have an impact on the heat
dissipation of the chip, especially if the input
voltage to the chip is high.
Charge is dictated by the equation:
Charge (Q) = Current (I) x Time (s)
Since Frequency is the inverse of Time, we can write
So we can calculate the current needed to flow into
the chip, just to charge the gate capacitance of the
FETs. Since heat is the product of voltage and
current, if the gate charge is high and/or the
switching frequency is high, the heat dissipation in
the chip will be high if the input voltage is high.
Once the MOSFET has switched on, the MOSFET presents
a small dc resistance between its Drain and Source
terminals. This is the MOSFETs ‘Drain Source ON
resistance’ or RDSON. Again, this needs to be as low
as possible.
Now, MOSFET manufacturers reduce the ON resistance
of the MOSFET by constructing many parallel
conduction paths between the Drain and Source. Thus,
like connecting resistors in parallel, the ON
resistance comes down with more parallel paths.
However, in connecting Drain Source paths in
parallel, a negative effect is that the Gate Source
capacitance (Qg) is also connected in parallel, so a
low ON resistance (and hence low conduction loss)
sometimes implies a high gate source capacitance
(hence high switching loss). Thus the MOSFET that is
chosen should be a compromise between these two
characteristics. In addition, high current MOSFETs
tend to come in much larger packages, so meeting the
ideals of low ON resistance and low Qg might violate
a space requirement spec, so the selection process
has to start over. Engineering, as ever, is a
compromise.
Indeed looking at the selection tables of the MOSFET
manufacturers, it is better to select a MOSFET with
a low ON resistance (less than 10mOhms), then filter
this selection to remove MOSFETs with a Qg of
greater than 10nC, then select a MOSFET from this
list, as long as the Gate turn on voltage, Vds and
Id can be met. Starting by selecting MOSFETs with a
Vds of between 20V and 30V might rule out some
higher voltage FETs that are better suited to lower
voltage designs.
Failing that, download all the results to a
spreadsheet and sort from there. I have never had
much luck with the parametric searches on MOSFET
websites.
Alternatively, download all the MOSFET
characteristics into a spreadsheet, remove the ones
that don't meet the VDS and ID requirements, then
add a column called FOM (Figure of Merit). This
column should contain the value RDSON x QG. Then
sort by this column and pick the FET with the lowest
FOM. This part will be the best compromise between
RDSON and QG and ideal for the top MOSFET.
Just to
further complicate matters, if the application has a
high input voltage and a low output voltage, the
duty cycle will be low. Therefore the ON resistance
of the top FET will be less important since the top
FET will only be on for a short period of time. The
lower the duty cycle, the less important ON
resistance becomes. I designed a 12V to 1V buck
converter where I spent ages picking the top FET to
balance Qg and RDSON, only to get an efficiency of
84%. Changing the top FET to a low Qg one regardless
of RDSON (it was about 65mOhms) increased the
efficiency to 94%.
__
MOSFET Choice – Top MOSFET__
The Duty Cycle governs how long the top MOSFET
switches on for during each period of the switching
frequency. We have calculated that the duty cycle is
dictated by the ratio of Vout to Vin (for a buck
converter operating in continuous conduction mode).
So it can be argued that if the input voltage is
high and the output voltage is low (i.e. a low duty
cycle), conduction losses in the top MOSFET are not
important since the top MOSFET is only ON for a
short amount of time. Therefore for low duty cycle
circuits, a MOSFET with low Qg should be chosen,
almost regardless of RDSON. Although there is no
figure as to what constitutes a low duty cycle, any
circuit with a duty cycle of less than about 15%
warrants having its MOSFET optimised for low Qg with
RDSON being largely unimportant.
That said, our duty cycle is 21%, so unfortunately
we should strive to find a MOSFET with both low Qg
and low ON resistance.
Luckily the suggested LTspice circuit for the
LTC3891 comes with an extremely
good top MOSFET, the Renesas RJK0305. This
device has an RDSON of 6.7mOhms and a Qg of 8nC.
RJK0305 Datasheet
__
MOSFET Choice – Bottom MOSFET__
When the top MOSFET switches off, the voltage at the
left hand side of the inductor flies negative, thus
the voltage across the bottom MOSFET is nearly zero
when the bottom MOSFET switches on. Therefore the
switching losses of the bottom MOSFET are
negligible, so we do not have to worry about the Qg
specification of the bottom MOSFET. Only the RDSON
characteristic of the bottom MOSFET is important.
In fact, every MOSFET has a ‘body diode’. This is a
diode inherent in the structure of the MOSFET and in
an N channel FET, its anode is connected to the
source and the cathode is connected to the Drain.
When the inductor voltage flies negative, it is the
body diode that conducts first before the gate drive
to the MOSFET activates the Drain-Source channel.
FIG 4 shows a simulation of the switch node just as
the bottom MOSFET is switching on.
**
FIG 4**
We can see the switch node (V(sw)) falling to a
voltage below zero well before the drive to the
bottom MOSFET gate starts to rise. This is
indicative of the body diode starting to conduct and
indeed the negative voltage is approximately -0.6V.
When the body diode conducts, it stores charge in
the MOSFET that has to be removed before the MOSFET
can fully turn on, so body diode conduction can
affect the efficiency of the converter.
If optimum efficiency is desired, it is wise to
place a Schottky diode across the bottom MOSFET, so
the Schottky diode can conduct the inductor flyback voltage and not
the body diode. The resulting increase in efficiency
can be as much as 3%. The Schottky diode will
conduct the peak current flowing through the
inductor, but this current will only flow for a
short period of time (until the bottom MOSFET
switches on). Therefore, the current rating of the
diode can be a lot less than peak inductor current.
An MBRS340 has a reverse voltage rating of 40V, but
a non repetitive peak forward current of 40A.
MBRS340 Datasheet
For the bottom MOSFET, the Renesas RJK0301 has
2.3mOhms RDSON and a Qg of 32nC.
RJK0301 Datasheet
__
Output Capacitor Choice__
In continuous conduction mode, the capacitor has a
continual current flowing into it from the inductor.
Unlike a boost converter, the output capacitor in a
buck regulator does not have to hold up the output
while the inductor is being charged.
The output is made up of 2 components: the ripple
current from the inductor producing a voltage across
the effective series resistance (ESR) of the output
capacitor and the ripple current charging the output
capacitor according to the equation
Unlike a boost converter where the rectifier diode
current jumps from 0A to the peak inductor current
as the MOSFET switches off, the ripple in a buck
architecture is determined by the *ripple*
current amplitude, not the *peak* inductor
current.
Recent innovations in ceramic capacitor design mean
that very low ESR capacitors are available with high
capacitance values. Ceramic capacitors have a
typical ESR of 10mOhms.
Failing that, low ESR tantalum capacitors are
available in much higher capacitance values with ESRs of upwards of 50m Ohms. Of course capacitors can
also be paralleled to increase the capacitance and
reduce the ESR.
In our example the inductor ripple current is 800mA
and the ESR of a typical tantalum capacitor is
70m Ohms, giving an ESR ripple of 56mV. Two such
capacitors in parallel will yield an ESR ripple of
28mV.
To calculate the charging ripple, from the equation
above we can see
**
FIG 5**
FIG5, shows the inductor ripple current (in blue),
output voltage ripple (in green) and output
capacitor current (in red). For convenience, the
output capacitor ESR has been reduced to 0 Ohms to
illustrate the ripple due to capacitor discharge. It can be seen that the
capacitor current has the same amplitude as the
inductor ripple current, but does not have the dc
offset current (of approx. 5A). This is easy to
picture, since the output current is equal to the
average inductor current (i.e. a straight line drawn
through the middle of the inductor current) and any
current that does not flow into the load must flow
in and out of the capacitor. To obtain the capacitor
current, just subtract the output current.
Now, we can see that while the capacitor current is
positive (above the dotted white line) the output
capacitor voltage goes up and while it is negative,
the output capacitor voltage goes down. To work out
the amplitude of the ripple voltage on the output
capacitor, we must calculate the average of the
positive part of the capacitor current (above the
dotted white line). Since we know the peak to peak
ripple current (is equal to the inductor ripple
current), the peak ripple current is Iripple/2 and
hence the average of this current (since half of the
cycle is below zero) is Iripple/4. We can now work out the
charging ripple.
From
We can see that dt is equal to half the period, so
we can say
Since our capacitor current is positive for half the
ON time and half the OFF time, the above equation
holds true regardless of duty cycle.
Let’s assume we want a total ripple voltage of 1% (50mV).
We already have 28mV of ripple as a result of the
capacitor ESR, so we now have a budget for the charging
ripple of 22mV
If our ripple current is 800mA and we are operating
at a switching frequency of 535kHz, a capacitor of
8.5uF should suffice.
Our ESR ripple calculations assumed two capacitors
in parallel to reduce the ESR, so two 4.7uF
capacitors with an ESR of 70mOhms should ensure we
meet our total ripple budget of 50mV
__
Other Points__
The feedback resistor values can be calculated using
this spreadsheet:
Feedback Resistor Calculator
A
decoupling capacitor should also be placed on the
input rail. The positive terminal of this capacitor
should be situated physically close to the drain of
the top MOSFET and the negative terminal close to
the source of the bottom FET. When the MOSFETs
switch, high changes in current occur at the input
(probe the current into the drain of the top MOSFET
to see this in LTspice). The input capacitor
provides a local low impedance path for this current
and helps improve EMC performance.
If the
circuit is sensitive to fast current changes on the
input (if a radio transmitter, say, is connected to
the input rail), using a
SEPIC converter in a buck only mode will give
much quieter circuit operation.
The final LTspice circuit can be downloaded here (right
click over the link and save as a '.asc' file):
LTC3891 Buck Converter
Running the simulation, it can be seen that the
ripple current is 750mA, the switching frequency is
536kHz, the ON time is 401ns and the duty cycle is
21.6% (all measured using the cursors in LTspice).
This ties in closely with what we have designed for.
The output ripple was also measured at 30.7mV. The
ripple current and output voltage can be seen in FIG
6
**
FIG 6**
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