The previous page on the step-down switch-mode power supply circuit was described and analyzed assuming that the components used are ideal. The real diode and the MOSFET have some limitations and they have to be taken into account for designing a practical power supply. First, the characteristics of the diode are outlined first.
DIODE REVERSE RECOVERY CURRENT
Even if a fast-recovery or an ultra-fast recovery diode
is used for free-wheeling operation, the reverse-recovery characteristic
of the diode imposes some constraints. The circuit that can be used to
test the reverse recovery characteristic of a diode is shown in Fig. 1.
An applet, named the first applet, simulates the reverse recovery property
of the diode and is displayed below.
The operation of the test circuit is explained at first. The time constant due to load inductance and load resistance should be several times the time corresponding to the switching frequency. Then the current through the remains more or less steady and its value is given by:
When the MOSFET is ON, the load current flows through the transistor. When it is turned off, the current flows through the snubber circuit initially and then the free-wheeling diode, marked as DUT (device under test). When the MOSFET is switched ON again, the source tends to reverse the current through the diode. The current through the diode falls rapidly and reverses before it becomes zero. The reverse recovery has been simulated using the model of the diode shown in Fig. 1.
The reverse-recovery transient process depends on the diode itself and it also depends on the junction temperature of the diode, the forward current prior to being reverse biased, the rate of fall forward current and the source voltage that applies to the reverse bias to the diode. As the value of any one of these parameters rises with the other parameters remaining unchanged, the reverse recovery transient process becomes worse, reflected by an increase in the peak reverse current. The reverse recovery turn-off period starts once the diode current becomes negative and lasts till the reverse diode current increases in ampltidue first and then decays to about 10% of its reverse peak current. It represents the time that has to elapse before the diode recovers ability to block reverse voltage.
The manufacture specifies the reverse recovery transient period and the maximum reverse current for a set defined by its forward current, the rate of fall of forward current and the junction temperature. For many diodes, the maximum rate of fall forward current is specified to be 100 A/ms. This means the test inductance L should set be such that
If reverse recovery transient is to be minimized, it would be preferable to select L such that
where the rated current of diode is Irated,diode
and
diF/dt is the permissible ,axi,u, rate of fall of diode current.
It is difficult to select an inductor based on trr, its reverse
recovery transient period, because the inductor chosen based on the diF/dt
rating of the diode is more conservative. For example, the data sheet
for a diode with 30 A rating may have its diF/dt rating to be
100 A/ms and its turn-off time at 100o
C of junction temperature may be specified to be 150 ns. If
the diode is carrying 30 A when it is suddenly reverse-biased, a time interval
of 300 ns is required for its current to fall to zero and then a
further 150 ns
would need to elapse before the diode is off. It
is seen why the inductor is to be selected based on the diF/dt
rating of the diode. It is better that the inductor restricts the
rate of fall of diode current to a value lower than its diF/dt
rating in order to restrict the reverse-recovery current.
The applet simulates the reverse recovery transient. It is an approximation of the behaviour of the diode. No accuracy for this model is claimed, but it does show the dependence of recovery transient on the parameters mentioned. The model developed is a mathematical model, based purely on the turn-off time, load current, rated current, junction temperature, and the maximum rate of fall of current of the diode. No physical model has been developed, as is the common practice. The process that occurs within a diode during turn-off and turn-on is a complex one and it is difficult to develop a physical model that is stable as well as realistic. On the other hand, the mathematical model is easy to develop. When the MOSFET is turned on, the current through the diode falls, its rate of fall restricted by the inductor. In the process, diode current reduces and becomes negative. The peak reverse current that can occur is calculated based on the load current, the rate of fall of diode current,and the junction temperature. Once this peak reverse current is reached, the diode voltage builds up, depending on the reverse voltage rating, the junction temperature and the turn-off time and the diode current can be calculated once the diode voltage is determined.
The pull-down choice menu contains rated current of the diode, its turn-off period, its turn-on period, load current, source voltage, test inductance in nH, test resistance in Ohms and the junction temperature as its items. To change the value of a menu-item, pull down the menu, highlight the item, change its value in the adjacent text-field and then click on Set Value button. When the Run/More button is clicked, the program displays the diode current and the voltage across the diode for a period corresponding to 12 times the turn-off period. If the diode had not turned off by then, click again on the Run/More button, and the process that occurs for the next 12 times the turn-off period would be displayed. Whenever the rate of fall of forward current increases due to either lower test inductance or higher source voltage, the total period required for the diode to turn-off decreases, but there would a significant increase in the peak reverse current. In the plots shown by the applet, unit on the y-axis represents the rated current for the top plot and it represents the rated reverse voltage for the bottom plot.
APPLET FOR REVERSE RECOVERY TRANSIENT IN A DIODE
The turn-on transient in a diode is not as predominant as its turn-off process is, but nonetheless it affects the performance of the circuit in which it is placed. The circuit for simulating the turn-on transient process is shown in Fig.2 and the diode model used is the same as shown in Fig. 1.
In a practical circuit, it is often difficult to notice
the turn-on transient process, for two reasons. Firstly, the turn-on process
lasts only for a brief period. Secondly, the transient process of some
other device can often mask the turn-on process of a diode. For example,
the turn-off delay of the MOSFET can mask the turn-on process of the diode.
The simulation, shown in the second applet, makes the assumption that the
transistor is ideal and simulates the turn-on process in an approximate
manner. It is necessary to have a snubber capacitor across the FET
as shown in Fig. 2. Again a mathematical model is used. When
the FET is turned off, the snubber capacitor voltage builds up to the source
voltage due to load current charging it. After that, the diode current
rises at a predetermined rate, depending on the rated current, the turn-on
period and the junction temperature. After the diode current becomes
equal to the load current, the diode voltage exponentially decays, based
on its turn-on period. It is assumed that the diode current remains
constant.
In some circuits, such as the flyback converter to be described in one of the pages to follow, the turn-on delay of the diode is crucial. The only practical remedy to address this problem is to connect an RC snubber circuit across the diode.
APPLET FOR TURN-ON TRANSIENT IN A DIODE
TRANSIENT PROCESSES IN A MOSFET
For a MOSFET, three transient processes can be identified. The first is the turn-on transient process associated with the MOSFET and the second is its turn-off process and the third is the turn-off transient process associated with the body-diode of the MOSFET. The turn-on transient of the body diode is relatively fast and can be ignored.
For a fast MOSFET, the turn-on transient process is characterized by two time periods, one is the turn-on time delay and the second is the rise time. During the turn-on time delay, the gate-to-source voltage builds up to its threshold value and during the rise time, the device current rises to about 90% of its final value. There is a further delay before the drain-to-source voltage becomes equal to its conduction drop. The turn-on delay time can be reduced to some extent by a stiff gate drive signal. When the MOSFET is turned off, there is a delay period corresponding to the period in which the gate voltage reduces to its threshold level. It is followed by the cross-over period that includes a delay period and a fall period. During the delay period, the drain-to-source voltage rises from its conduction value to its blocking value. After this delay period has elapsed, the fall period follows during which the current through the MOSFET decreases. For a fast MOSFET, the total turn-on transient lasts for about 50 ns, whereas the turn-off process lasts for about 100 ns.
The turn-on characteristic of a MOSFET is shown below. The voltage and the current associated with the device can change in this manner and the datasheets display a similar turn-on characteristic. When the MOSFET is placed in a circuit, the rise in current and the fall in voltage get modified due to the influence of the external components.
The turn-off characteristic of a MOSFET is shown
below. The voltage and the current associated with the device can
change in this manner and the datasheets display a similar turn-off characteristic.
When the MOSFET is placed in a circuit, the fall in current and the rise
in voltage get modified due to the influence of the external components.
The body diode is comparatively slow. It turns on quite fast, but its turn-off process is quite slow, of the order of 500 ns. Hence when the MOSFET is to be operated at high frequency, it is preferable to use an external diode. In such a case, an additional diode may be required, that has to be connected in series with the MOSFET.
A circuit that can be used for simulating the transient
processes in a MOSFET is shown in Fig. 3. Here Q1 is turned on and off,
whereas Q2 remains off. When Q1 is turned off, the load current is diverted
through diode D2, the body diode of Q2 . When Q1 is turned on, both the
turn-on transient of Q1 and the reverse recovery transient of D2 occur.
The simulation that is displayed as applet 3 is again quite approximate.
The purpose is to illustrate how MOSFET functions as a switch. An air-cored
inductor, labeled L3 in Fig.3, is necessary to be used to reduce the reverse
recovery current of the diode. The time constant due L3 and R3 should be
much less compared with the cycle period corresponding to switching frequency.
The turn-on process of the MOSFET is quite slow, due to the slow turn-off
of the body diode D2. In applications where the MOSFET has to be switched
on and off at higher frequency of the order of 20 kHz and above, it is
the practice to bypass the body diode by an external diode. In this application,
such a technique is unnecessary because the body diode does not have to
conduct at all.
When the applet for simulating the dynamic characteristics of a MOSFET is run, the waveforms produced may appear to be bizarre. When the applet is run with the default values to simulate the turn-on process of the MOSFET, the waveforms produced are presented below.
The logic behind the waveforms is as follows. When
the MOSFET is turned on by applying a gate pulse,
theere is a turn-on delay. During this period,
the voltage across the FET remains equal to the source voltage and there
is no current through the FET. Then the rise period follows, during
which the FET current rises and the FET voltage is determined by the external
circuit. Here when the current the FET rises, inductor L3 absorbs
the voltage and the voltage across the FET is zero. The current
through the FET equals the load current well before the rise period elapses
and hence the voltage across the FET becomes equal to the source voltage
once the rate of rise FET current is zero. At the end of the rise
period, the body diode of Q2 contains still a large number of charge carriers
and it is predisposed to conduct in the reverse direction. As the
reverse recovery current increases, the FET voltage falls in some piecewise
linear fashion. There is some behind the simulation, even though
its accuracy is questionable.
Now the waveforms obtained for the turn-off process are explained.
When the MOSFET is turned off, there is a storage delay
period during which both the current and the voltage of the FET do not
change. After that, the FET voltage rises, with its current remaining
unchanged. Then the FET current falls. As the current falls, the
voltage across L3 changes polarity and the FET voltage is the sum of the
source voltage and the voltage across the inductor L3.
APPLET FOR TRANSIENT PROCESSES IN A MOSFET
The losses in a FET are due to three factors:
LOSSES IN ENERGY STORAGE ELEMENTS
The non-ideal properties of filter capacitor at the output and the inductor affect the performance of the circuit. The inductor is not lossless because of the winding resistance and the core loss. The model of the inductor can be changed to a series network containing a resistor reflecting its losses and an inductor. Due to the losses in the inductor, there is a slight reduction in the output voltage and also a drop in the efficiency of the circuit. Given a duty cycle and a steady input voltage, the output voltage is has been obtained in the previous page as:
The average inductor current is the same as the average load current. Then the average inductor current IL is:
If the internal resistance of the inductor is Rind, the drop in output voltage is approximately:
The effect of the ESR of capacitor is to increase the
ripple content in output. From the previous page, the change in capactor
current from its higheest value to its lowest value is:
The worst-case increase in peak-to-peak ripple in output
voltage can be obtained by just adding the ripple due to ESR with the previously
obtained value. If ESR of capavitor be Rcap, then
The actual peak-to-peak ripple would be less than the
value stated above.
It is necessary to modify the step-down SMPS if it is
to operate at relatively high voltage in the continuous conduction mode.
The problem with continuous conduction occurs when the MOSFET is turned
on with the diode still in conduction. To explain this aspect, Fig. 4 is
presented. When the MOSFET is turned on, the diode can act as a short circuit
till it recovers. To overcome this problem, the circuit in Fig. 4 is to
be modified.
The modifed circuit is presented in Fig. 5. This circuit, when designed properly, would well whether the conduction is continuous or discontinuous. This circuit contains a few additional components. The components added are an additional diode marked as D1 and an RC dissipating circuit for D1. Diode D3, inductor L2 and capacitor C2 are the same components, marked as D, L and C respectively in Fig. 4. The operation of the circuit in Fig. 5 is explained now. The circuit in Fig. 5 does not show the snubber circuit required for the diodes D1 and D2 and possibly MOSFET. Some MOSFETs do not need a snubber circuit, whereas a diode needs a snubber circuit. There is a separate page on design of snubber circuit.
The conduction path that exists when the MOSFET is ON is shown in red colour in Fig. 6. The current flow is through the MOSFET and the inductors.
When the MOSFET is turned off, the set of components in conduction varies. In mode 1 following immediately after the turn-off of the MOSFET, diode D1, inductor L1, capacitor C1, resistor R1 and components L2 C2 and RL are in conduction. The RC circuit in series with D1 conducts, the time constant associated with C1 and R1 being very small compared with the on-off periods of the MOSFET. During this mode, inductor L1 discharges its energy to R1 and C1. The components in conduction in mode 1 are shown in Fig. 7.
When mode 1 is over after inductor L1 has discharged its energy, mode 2 follows. Here only D2 continues to conduct, but L1 and D1 are not in conduction. This mode is illustrated in Fig. 8. During this phase, C1 would discharge any energy it may have acquired into R1. After the end of the period corresponding to the switching frequency, the MOSFET is turned ON again and the circuit reverts to the state shown in Fig. 9.
The circuit lasts in the state shown in Fig. 9 till the current through L1 becomes equal to that through L2. After that, the circuit reverts to the state shown in Fig. 6.
When the MOSFET is switched on, current through L1 rises gradually and current through D2 falls gradually. If inductor L1 is sufficiently large, there would be hardly any reverse recovery transient due to diode D2. Typically L1 should be such that the rate of rise current is less than 50% of the maximum rate of fall specified for diode D2. Inductor L1 can even be an air-core inductor, whereas inductor L2 has a ferrite-core with an air gap.
The complete power circuit along with the required snubber circuits is shwon in Fig. 10. The design of power circuit is described in a separate page. The snubber circuit for the MOSFET may not be required if a MOSFET that does not need a snubber is chosen.
The fourth applet presented below simulates the circuit in Fig. 5. It is assumed that the turn-on delay of diodes is negligible.The pull-down menu contains two items that are not shown explicitly in Fig.5. They are the equivalent-series resistance of capacitor C2 and the internal resistance of inductor L2. In practice, even with a fixed duty cycle, a fixed switching frequency and a steady-input voltage, the ripple content in output tends to be higher than the calculated value, mainly due to the ESR of C2. The default value of ESR of C2 is set to be zero. To see its effect, the type of response should be set as Statistics. Then when the program is run, the peak-to-peak ripple in output voltage is displayed. The program has to be run a few times in this mode before the peak-to-peak ripple in output settles down to its periodic value. For example, when ESR of C2 is increased to 0.1 W , it can be seen that the peak-to-peak ripple that results is much higher.
The internal resistance of L2 reflects the winding resistance and the core loss and the losses in inductor L2 tend to reduce the efficiency of this converter. The default value of internal resistance has been set to be zero. Its realistic value can be calculated by assuming a quality factor of about 100 at the switching frequency. For the value of inductor L2, an appropriate value of internal resistance of L2 can be set to be about 0.5 W. To see its effect, the type of response should be set as Statistics in the program.
When the type of response is Statistics, the program should be run a few times before the results become repetitive. Even then, the sum of output power and all the losses may not add upto the input power, due to errors in modelling and the presence of energy storage elements. The loss calculation of diode D1 in particular is quite incorrect, because the turn-on losses of a diode have been ignored. Even though the average current of D1 turns out to be small, its turn-on losses are quite significant and it is advisable to use the same diode selected to be used as D2. These diodes should be fast-switching diodes with a low reverse period of about 50 ns. It is likely that there will be some time delay before the selected response is displayed. In the meantime, the message that computing is going on will be flashed on the screen.
APPLET FOR PRACTICAL BUCK
CONVERTER IN FIG. 5
CURRENT MODE CONTROL: IDEAL CIRCUIT
Current mode control of a SMPS is a popular technique built into several PWM integrated-circuits nowadays. This topic should have been covered in the previous page, but has been held over and presented now.
The block diagram of the current-mode control is similar to that described the previous page on the ideal step-down SMPS circuit. The PI controller illustrated in Fig. 22 of the previous page can used be as it is. In the previous page, closed-loop control was effected by comparing the output of the PI controller with a ramp signal (Fig. 19). For current-mode control, the output of the PI controller should be compared with the signal reflecting the current though the inductor L2, with this signal suitably scaled. This signal is compared with the PI controller output and when the signal corresponding to inductor current tends to exceed the PI controller output, the MOSFET is turned off for the rest of the output cycle. At the start of each cycle, the MOSFET should be turned on.
With just this type of control, the pulse-width tends
to fluctuate from one cycle to the next, leading to oscillations in output.
Ideally duty cycle should be equal to the ratio of desired output
voltage to the source voltage, but the intersection of the PI controller
output and the signal reflecting inductor current may not always occur
after a time lapse from the start of a cycle that corresponds to the desired
duty cycle. To overcome this problem, a component proportional to
the time elapsed from the instant the cycle starts can be added to the
signal corresponding to the inductor current and this sum can be compared
with the output of the PI controller. Let us say that the maximum
of the PI controller output be 10 V and let the signal corresponding to
inductor current be 10 V when the inductor current is at nominal rated
value. Let also a ramp voltage be generated such that it rises from 0 V
to 10 V from the start to the end of a cycle. Then a fraction of
the ramp voltage can be added to the signal reflecting current, the fraction
being equal to the duty cycle which in turn is the ratio of desired output
voltage to the source voltage. When the source voltage tends to vary
over an input cycle, this fraction computed as the ratio of desired
output voltage to the source voltage automatically gets adjusted and the
correction to the signal reflecting the inductor current becomes the right
adjustment.
APPLET FOR PWM WITH CURRENT
CONTROL
This page has described the practical aspects of the step-down SMPS. The inductor design for the SMPS is also critical and it is described in one of the pages to follow.
The next page describes the operation of the step-up switch-mode
power supply circuit.
