Overview
Energy conversion systems inevitably involve energy consumption. Although 100% conversion efficiency cannot be achieved in actual applications, a high-quality power supply can achieve very high efficiency levels, approaching 95%. The operating efficiency of most power ICs can be measured under specific operating conditions, and these parameters are given in the data sheet. Generally, manufacturers will provide actual measured results, but we can only guarantee our own data. Figure 1 shows a circuit example of an SMPS step-down converter, which can achieve a conversion efficiency of 97%, and maintain a high efficiency even at light loads. What is the secret to achieving such high efficiency? It is best to start by understanding the common issues of SMPS losses. Most of the losses in a switching power supply come from the switching devices (MOSFET and diode), and a small part of the losses come from the inductor and capacitor. However, if very cheap inductors and capacitors (with higher resistance) are used, the losses will increase significantly. When selecting an IC, the architecture and internal components of the controller need to be considered in order to obtain high efficiency indicators. For example, Figure 1 uses a variety of methods to reduce losses, including: synchronous rectification, low on-resistance MOSFETs integrated inside the chip, low quiescent current and pulse skipping control mode. We will discuss the benefits of these measures in this article. Figure 1. The buck converter integrates low on-resistance MOSFETs and uses synchronous rectification. The efficiency curve is shown in the figure.
Buck-Down SMPS
Loss is a problem faced by any SMPS architecture. Here we take the buck (or step-down) converter shown in Figure 2 as an example for discussion. The switching waveforms at each point are marked in the figure for subsequent calculations. The main function of a buck converter is to convert a higher DC input voltage into a lower DC output voltage. To achieve this, the MOSFET is switched on and off at a fixed frequency (fS) under the control of a pulse width modulated signal (PWM). When the MOSFET is on, the input voltage charges the inductor and capacitor (L and COUT), through which energy is transferred to the load. During this period, the inductor current increases linearly, and the current loop is shown as loop 1 in Figure 2.
When the MOSFET is turned off, the input voltage is disconnected from the inductor, and the inductor and output capacitor supply power to the load. The inductor current decreases linearly and flows through the diode, and the current loop is shown as loop 2 in the figure. The on-time of the MOSFET is defined as the duty cycle (D) of the PWM signal. D divides each switching cycle into two parts: [D × tS] and [(1 - D) × tS], which correspond to the conduction time of the MOSFET (loop 1) and the conduction time of the diode (loop 2), respectively. All SMPS topologies (buck, inverting, etc.) divide the switching cycle in this way to achieve voltage conversion.
For the buck converter circuit, a larger duty cycle will transfer more energy to the load and increase the average output voltage. Conversely, when the duty cycle is lower, the average output voltage will also decrease. Based on this relationship, we can get the following ideal conversion formula for step-down SMPS (without considering the voltage drop of diode or MOSFET): VOUT = D × VIN IIN = D × IOUT62)]It is important to note that the longer any SMPS is in one state during a switching cycle, the greater the losses it will incur in that state. For a buck converter, the lower D (and therefore the lower VOUT), the greater the losses in loop 2.
Switching Device LossesMOSFET Conduction Losses
The MOSFET in Figure 2 (and most other DC-DC converter topologies) MOSFET and diode are the main factors causing power consumption. The relevant losses mainly include two parts: conduction loss and switching loss.
MOSFET and diode are switching elements. When the device is turned on, the current flows through the loop. When the device is turned on, the conduction loss is determined by the on-resistance (RDS(ON)) of the MOSFET and the forward voltage of the diode respectively.
The conduction loss of the MOSFET (PCOND(MOSFET)) is approximately equal to the product of the on-resistance RDS(ON), the duty cycle (D), and the average current of the MOSFET when it is on (IMOSFET(AVG)).
PCOND(MOSFET) (using average current) = IMOSFET(AVG)2 × RDS(ON) × D
The above equation gives an approximation of the MOSFET conduction losses in an SMPS, but it is only an estimate of the circuit losses because the power dissipated when the current is linearly rising is greater than the power dissipated by the average current. For "peak" currents, a more accurate calculation method is to integrate the square of the current waveform between the peak and valley current values (IV and IP in Figure 3).
Figure 3. Typical buck converter MOSFET current waveform, used to estimate the MOSFET conduction losses.
[p=null, 0, The following formula gives a more accurate method to estimate the loss, which uses the integral of the current waveform I2 between IP and IV instead of the simple I2 term. PCOND(MOSFET) = [(IP3 - IV3)/3] × RDS(ON) × D
= [(IP3 - IV3)/3] × RDS(ON) × VOUT/VIN
Where IP and IV correspond to the peak and valley values of the current waveform, respectively, as shown in Figure 3. The MOSFET current flows from IV Linearly ramp up to IP. For example, if IV is 0.25A, IP is 1.75A, RDS(ON) is 0.1Ω, and VOUT is VIN/2 (D = 0.5), the calculation based on the average current (1A) is:PCOND(MOSFET) (using average current) = 12 × 0.1 × 0.5 = 0.050W. Using waveform integration for a more accurate calculation: PCOND(MOSFET) (calculated using integration of current waveform) = [(1.753 - 0.253)/3] × 0.1 × 0.5 = 0.089W
or approximately 78%, which is higher than the result obtained by calculating based on the average current. For current waveforms with a small peak-to-average ratio, the difference between the two calculation results is small, and the average current calculation can meet the requirements.
Diode Conduction Losses
While the conduction losses of a MOSFET are proportional to RDS(ON), the conduction losses of a diode depend strongly on the forward voltage (VF). Diodes typically have greater losses than MOSFETs, and diode losses are proportional to the forward current, VF, and the conduction time. Since the diode is on when the MOSFET is off, the conduction loss of the diode (PCOND(DIODE)) is approximately:PCOND(DIODE) = IDIODE(ON) × VF × (1 - D)Where IDIODE(ON) is the average current during the diode conduction period. As shown in Figure 2, the average current during the diode conduction period is IOUT. Therefore, for the buck converter, PCOND(DIODE) can be estimated as follows:PCOND(DIODE) = IOUT × VF × (1 - VOUT/VIN)Unlike the MOSFET power calculation, using the average current can get a more accurate power consumption calculation result because the diode loss is proportional to I, not I2.
Obviously, the longer the MOSFET or diode is on, the greater the conduction losses. For a buck converter, the lower the output voltage, the greater the power dissipation in the diode since it is on longer.
Switching Dynamic Losses
Since the switching loss is caused by the non-ideal state of the switch, it is difficult to estimate the switching loss of MOSFET and diode. It takes a certain amount of time for the device to switch from fully on to fully off or from fully off to fully on, and power loss will be generated in this process. The relationship between the drain-source voltage (VDS) and the drain-source current (IDS) of the MOSFET shown in Figure 4 can well explain the switching loss of the MOSFET during the transition process. From the waveform in the upper half, it can be seen that the voltage and current transiently change during tSW(ON) and tSW(OFF), and the capacitance of the MOSFET is charged and discharged.
As shown in Figure 4, the full load current (ID) flows through the MOSFET before VDS drops to the final on-state (= ID × RDS(ON)). Conversely, during shutdown, VDS gradually rises to the final value of the off-state before the MOSFET current drops to zero. The overlap of voltage and current during the switching process is the source of switching losses, which can be clearly seen in Figure 4.
Figure 4. Switching loss occurs during the transition process of MOSFET on and off.
Switching loss increases with the SMPS It is easy to understand that as the switching frequency increases (the cycle shortens), the proportion of the switching transition time increases, thereby increasing the switching loss. During the switching conversion process, the switching time is one twentieth of the duty cycle, which has a much smaller impact on efficiency than the case where the switching time is one tenth of the duty cycle. Since the switching loss is closely related to the frequency, the switching loss will become the main loss factor when working at high frequencies. The switching loss (PSW(MOSFET)) of the MOSFET can be estimated according to the triangle wave shown in Figure 3, and the formula is as follows: PSW(MOSFET) = 0.5 × VD × ID × (tSW(ON) + tSW(OFF)) × fS 62)]Where VD is the drain-source voltage during the MOSFET off period, ID is the channel current during the MOSFET on period, and tSW(ON) and tSW(OFF) are the turn-on and turn-off times. For the buck circuit conversion, VIN is the voltage when the MOSFET is off, and the current when it is on is IOUT.
To verify the switching loss and conduction loss of the MOSFET, Figure 5 shows the typical waveforms of the integrated high-side MOSFET in the buck converter: VDS and IDS. The circuit parameters are: VIN = 10V, VOUT = 3.3V, IOUT = 500mA, RDS(ON) = 0.1Ω, fS = 1MHz, and the switching transient time (tON + tOFF) is 38ns in total.
As can be seen in Figure 5, the switching change is not instantaneous, and the overlapping parts of the current and voltage waveforms cause power loss. When the MOSFET is "on" (Figure 2), the current IDS flowing through the inductor increases linearly, and the switching loss at the off time is greater than that at the turn-on edge.
Using the above approximate calculation method, the MOSFET The average power loss can be calculated as follows: PT(MOSFET) = PCOND(MOSFET) + PSW(MOSFET) = [(I13 - I03)/3] × RDS(ON) × VOUT/VIN + 0.5 × VIN × IOUT × (tSW(ON) + tSW(OFF)) × fS This result is close to the 117.4mW measured in the lower curve of Figure 5. Note: in this case, fS is high enough and PSW (MOSFET) is the main factor in power consumption. Figure 5. Typical switching cycle of the high-side MOSFET of a buck converter, 10V input, 3.3V output (500mA output current). The switching frequency is 1MHz and the switching transition time is 38ns.
Like MOSFETs, diodes also have switching losses. This loss is largely determined by the reverse recovery time (tRR) of the diode. The diode switching loss occurs when the diode switches from forward conduction to reverse cutoff.
When a reverse voltage is applied across the diode, the accumulated charge generated by the forward current on the diode needs to be released, resulting in a reverse current spike (IRR(PEAK)) with a polarity opposite to that of the forward current, thereby causing V × I power loss, because during the reverse recovery period, the reverse voltage and reverse current exist simultaneously in the diode. Figure 6 shows a schematic diagram of the PN junction of a diode during reverse recovery.
Figure 6. When the diode junction is reverse biased, the accumulated charge during the forward conduction period needs to be released, resulting in a peak current (IRR(PEAK)).
Knowing the reverse recovery characteristics of the diode, the switching loss of the diode (PSW(DIODE)) can be estimated by the following formula:
PSW(DIODE) = 0.5 × VREVERSE × IRR(PEAK) × tRR2 × fS
Where VREVERSE is the reverse bias voltage of the diode, IRR(PEAK) is the peak value of the reverse recovery current, and tRR2 is the time from the reverse current peak IRR to the recovery current becoming positive. For the buck circuit, when the MOSFET is turned on, VIN is the MOSFET To verify the diode loss calculation formula, Figure 7 shows the switching waveform of the PN junction in a typical buck converter, VIN = 10V, VOUT = 3.3V, IRR(PEAK) = 250mA, IOUT = 500mA, fS = 1MHz, tRR2 = 28ns, VF = 0.9V. Using these values we get: 385477 This is close to the measured value of 358.7mW shown in Figure 7. Considering the large VF and long diode conduction period, the tRR time is very short and the switching loss (PSW(DIODE)) dominates the diode losses.
Figure 7. Switching waveforms of a PN junction switching diode in a buck converter, stepping down from 10V input to 3.3V output with an output current of 500mA. Other parameters include: fS of 1MHz, tRR2 of 28ns, and VF = 0.9V.
Improve efficiency
Based on the above discussion, what are the ways to reduce the switching loss of the power supply? The direct way is: choose a MOSFET with low on-resistance RDS(ON) and fast switching; choose a diode with low on-voltage drop VF and fast recovery. There are several factors that directly affect the on-resistance of a MOSFET. Generally, increasing the chip size and drain-source breakdown voltage (VBR(DSS)) helps to reduce the on-resistance RDS(ON) due to the increase in semiconductor material in the device. On the other hand, larger MOSFETs increase switching losses. Therefore, although large-size MOSFETs reduce RDS(ON), they also cause efficiency problems that can be avoided with small devices. When the die temperature increases, the on-resistance of the MOSFET increases accordingly. The junction temperature must be kept low so that the on-resistance RDS(ON) is not too large. The on-resistance RDS(ON) is inversely proportional to the gate-source bias voltage. Therefore, it is recommended to use a sufficiently large gate voltage to reduce RDS(ON) losses, but this will also increase gate drive losses. It is necessary to balance the benefits of reducing RDS(ON) with the disadvantages of increasing gate drive. MOSFET The switching losses are related to the device capacitance. Larger capacitance requires longer charging time, slowing down the switching process and consuming more energy.
The Miller capacitance is usually defined in MOSFET data sheets as the reverse transfer capacitance (CRSS) or gate-to-drain capacitance (CGD), and plays a decisive role in the switching process. The charging charge of the Miller capacitance is represented by QGD. In order to switch the MOSFET quickly, the Miller capacitance must be as low as possible. In general, MOSFET The capacitance of the diode is inversely proportional to the chip size, so a compromise must be made between switching losses and conduction losses, and the switching frequency of the circuit must also be carefully selected. For diodes, the on-state voltage drop must be reduced to reduce the resulting losses. For small-sized, low-rated voltage silicon diodes, the on-state voltage drop is generally between 0.7V and 1.5V. The size, process and voltage rating of the diode will affect the on-state voltage drop and reverse recovery time. Large-sized diodes usually have higher VF and tRR, which will cause relatively large losses. Switching diodes are generally divided by speed, divided into "high-speed", "very high-speed" and "ultra-high-speed" diodes, and the reverse recovery time decreases with increasing speed. The tRR of fast recovery diodes is hundreds of nanoseconds, while the tRR of ultra-fast recovery diodes is tens of nanoseconds. In low-power applications, an alternative to fast recovery diodes is Schottky diodes, which have an almost negligible recovery time and a reverse recovery voltage VF of only half that of fast recovery diodes (0.4V to 1V), but the rated voltage and current of Schottky diodes are much lower than those of fast recovery diodes, and they cannot be used in high voltage or high power applications. In addition, Schottky diodes have higher reverse leakage current than silicon diodes, but these factors do not limit their application in many power supplies. However, in some low voltage applications, even Schottky diodes with lower voltage drops have unacceptable conduction losses. For example, in a circuit with an output of 1.5V, even if a Schottky diode with a 0.5V on-state voltage drop VF is used, a 33% output voltage loss will occur when the diode is turned on! To solve this problem, a MOSFET with low on-resistance RDS(ON) can be selected to implement a synchronous control architecture. The diode is replaced by a MOSFET (compare the circuits of Figure 1 and Figure 2), which works synchronously with the main MOSFET of the power supply, so that only one is guaranteed to be turned on during the alternating switching process. The conducting diode is replaced by the conducting MOSFET, and the high on-state voltage drop VF of the diode is converted into the low on-state voltage drop of the MOSFET (MOSFET RDS(ON) × I), effectively reducing the conduction loss of the diode. Of course, synchronous rectification only reduces the voltage drop of MOSFET compared with diode. On the other hand, the power consumption of driving synchronous rectification MOSFET cannot be ignored. IC data sheet The above discusses two important factors that affect the efficiency of switching power supply (MOSFET and diode). Looking back at the buck circuit shown in Figure 1, the main factors that affect the working efficiency of controller IC can be obtained from the data sheet. First, the switch element is integrated inside the IC, which can save space and reduce parasitic losses. Second, the use of MOSFET with low on-resistance RDS(ON) can achieve 0.27Ω (typical value) and 0.19Ω (typical value) for NMOS and PMOS in small-size integrated buck IC (such as MAX1556). Finally, the synchronous rectification circuit used. For a 500mA load, the switching circuit with a duty cycle of 50% can reduce the loss of the low-side switch (or diode) from 225mW (assuming the diode voltage drop is 1V) to 34mW. Reasonable selection of SMPS IC Reasonable selection of SMPS IC packaging, control architecture, and reasonable design can effectively improve conversion efficiency.
Integrated power switch
Power switch integrated into IC When the switch is integrated into the chip, the cumbersome MOSFET or diode selection can be omitted, and the circuit can be made more compact. Due to the reduction of line loss and parasitic effects, the efficiency can be improved to a certain extent. According to the power level and voltage limit, the MOSFET and diode (or synchronous rectification MOSFET) can be integrated into the chip. Another advantage of integrating the switch into the chip is that the size of the gate drive circuit has been optimized for the on-chip MOSFET, so there is no need to waste time on unknown discrete MOSFETs.
Quiet Current
Battery-powered devices pay special attention to the quiescent current (IQ) in the IC specification. This is the current required to maintain circuit operation. Under heavy load conditions (greater than ten or a hundred times the quiescent current IQ), IQ The effect on efficiency is not obvious because the load current is much larger than IQ. As the load current decreases, the efficiency tends to decrease because the power corresponding to IQ accounts for a higher proportion of the total power. This is especially important for applications that are in sleep mode or other low-power modes most of the time. Many consumer products need to maintain keyboard scanning or other functions even when they are "off". At this time, it is undoubtedly necessary to choose a power supply with very low IQ.
Power architecture improves efficiency
[color=rgb(62, 62, SMPS control architecture is one of the key factors affecting the efficiency of switching power supplies. We have already discussed this in the synchronous rectification architecture. Since low on-resistance MOSFETs are used to replace the power-hungry switching diodes, the efficiency index can be effectively improved. Another important control architecture designed for light load operation or a wide load range is pulse skipping, also known as pulse frequency modulation (PFM). Unlike pure PWM switching operation, which uses a fixed switching frequency at both heavy and light loads, pulse skipping mode operates the converter in skipping switching cycles, which can save unnecessary switching operations and thus improve efficiency.
In pulse skipping mode, the inductor is discharged over a longer period of time, transferring energy from the inductor to the load to maintain the output voltage. Of course, as the load draws current, the output voltage will also drop. When the voltage drops to the set threshold, a new switching cycle will start to charge the inductor and replenish the output voltage.
It should be noted that pulse skipping mode will generate load-dependent output noise, which is difficult to filter out because it is distributed at different frequencies (unlike the fixed-frequency PWM control architecture).
Advanced SMPS ICs will reasonably take advantage of the advantages of both: using a constant PWM frequency when heavily loaded and using pulse skipping mode to improve efficiency when lightly loaded. The IC shown in Figure 1 provides such an operating mode.
When the load increases to a higher effective value, the pulse skipping waveform will switch to fixed PWM, and the noise is easily filtered under nominal load. In the entire operating range, the device selects pulse skipping mode and PWM mode as needed to maintain the overall highest efficiency (Figure 8).
The efficiency curves shown in curves D, E, and F in Figure 8 are low efficiency at light loads in fixed PWM mode, but can provide high conversion efficiency (up to 98%) at heavy loads. If the setting is to maintain fixed PWM operation mode at light loads, the IC will not change the operation mode according to the load conditions. In this case, the ripple can be kept at a fixed frequency, but a certain amount of power is wasted. At heavy loads, the additional power required to maintain PWM switching operation is small and far less than the output power. On the other hand, the efficiency curves in pulse-skipping "idle" mode (A, B, C in Figure 8) can remain high at light loads because the switch is only turned on when the load requires it. For the 7V input curve, efficiencies of more than 60% can be achieved in idle mode with a 1mA load. Figure 8. Buck converter efficiency curves in PWM and idle (pulse skipping) modes. Note that at light loads, the efficiency in idle mode is higher than that in PWM mode.
Optimizing SMPS
Switching power supplies are widely used due to their high efficiency indicators, but their efficiency is still restricted by some inherent losses in SMPS circuits. When designing a switching power supply, it is necessary to carefully study the sources of SMPS losses and reasonably select SMPS ICs to fully utilize the advantages of the device. In order to obtain an efficient SMPS while keeping the circuit cost as low as possible or even without increasing the circuit cost, engineers need to make comprehensive choices.
Passive Component Losses
We have already seen that MOSFETs and diodes contribute to SMPS losses. Using high-quality switching devices can greatly improve efficiency, but they are not the only components that can optimize power supply efficiency.
Figure 1 details the basic circuit of a typical buck converter IC. Two synchronous rectifier MOSFETs are integrated, low RDS(ON) MOSFETs, and high efficiency is achieved. In this circuit, the switching elements are integrated inside the IC and the components are pre-selected for the specific application. However, to further improve efficiency, designers also need to pay attention to the passive components—external inductors and capacitors—and understand their impact on power dissipation.
Inductor power consumption resistive loss
Inductor power consumption includes two basic factors: coil loss and core loss. Coil loss is attributed to the DC resistance (DCR) of the coil, and core loss is attributed to the magnetic characteristics of the inductor.
DCR is defined as the following resistance formula:
[p=null, 0,Left]
Where ρ is the resistivity of the coil material, l is the coil length, and A is the cross-sectional area of the coil.
DCR will increase with the increase of coil length and decrease with the increase of coil cross-sectional area. This principle can be used to judge the standard inductor and determine the required different inductance values and sizes. For a fixed inductance value, when the inductor size is small, in order to maintain the same number of turns, the cross-sectional area of the coil must be reduced, thus resulting in a DCR Increase; for a given inductor size, a smaller inductor value generally corresponds to a smaller DCR, because fewer turns reduce the coil length and allow the use of thicker wire.
Given the DCR and average inductor current (which depends on the SMPS topology), the inductor's resistive losses (PL(DCR)) can be estimated as follows:
PL(DCR) = LAVG2× DCR
Here, IL(AVG) is the average DC current flowing through the inductor. For a buck converter, the average inductor current is the DC output current. Although the size of DCR directly affects the power dissipation in the inductor resistance, which is proportional to the square of the inductor current, it is necessary to reduce DCR.
Also, it should be noted that when the average current of the inductor is used to calculate PL(DCR) (as shown in the above formula), the result is slightly lower than the actual loss because the actual inductor current is a triangular wave. In the MOSFET conduction loss calculation introduced earlier in this article, a more accurate result can be obtained by integrating the inductor current waveform. A more accurate and of course more complex calculation formula is as follows:
PL(DCR) = (IP3 - IV3)/3 × DCR
Where IP and IV are the peak and valley values of the inductor current waveform.
Core loss
Core loss is not as easy to estimate as conduction loss and is difficult to estimate. It consists of hysteresis and eddy current losses, which directly affect the alternating flux of the core.SMPS In the figure, although the average DC current flows through the inductor, the ripple current generated by the change of the switching voltage across the inductor causes the core's magnetic flux to change periodically.
Hysteresis losses are caused by the power consumed by the rearrangement of the core dipoles in each AC cycle. It can be regarded as the "friction" loss caused by the dipoles rubbing against each other when the magnetic field polarity changes, which is proportional to the frequency and flux density.
In contrast, eddy current losses are introduced by the time-varying magnetic flux in the core. From Faraday's law, we know that alternating flux produces alternating voltage. Therefore, this alternating voltage will generate local currents, resulting in I2R losses in the core resistance.
The core material has a great influence on the core loss. The inductor commonly used in SMPS power supplies is iron powder core. Iron nickel molybdenum powder core (MPP) has the lowest loss. Iron powder core has the lowest cost, but the core loss is relatively large.
Core loss can be estimated by calculating the maximum change in core flux density (B), and then looking at a graph of flux density and core loss (and frequency) provided by the inductor or core manufacturer. Peak flux density can be calculated in several ways, and the formula can be found in the core loss curve in the inductor data sheet.
Accordingly, if the core area and number of turns are known, the peak flux can be estimated using the following formula:
[p=null, 0,Here, B is the peak flux density (Gauss), L is the coil inductance (henry), ΔI is the peak-to-peak value of the inductor ripple current (ampere), A is the core cross-sectional area (cm2), and N is the number of coil turns.
With the popularization of the Internet, it is easy to download information and search for device information from the Internet. Some manufacturers provide interactive inductor power consumption calculation software to help designers estimate power consumption. Using these tools, you can quickly and accurately estimate the power loss in the application circuit. For example, Coilcraft provides an online inductor core loss and copper loss calculation formula. Simply enter some data to get the core loss and copper loss of the selected inductor.
Capacitor Losses
Contrary to the ideal capacitor model, the actual physical characteristics of capacitor components lead to several losses. Capacitors mainly play the role of voltage regulation and input/output noise filtering in SMPS circuits (Figure 1). These losses of capacitors reduce the efficiency of the switching power supply. These losses are mainly manifested in three aspects: equivalent series resistance loss, leakage current loss and dielectric loss.
Resistive losses in capacitors are straightforward. Since current flows in and out of the capacitor with each switching cycle, the inherent resistance (RC) of the capacitor will cause some power dissipation. Leakage losses are power losses caused by the resistance (RL) of the capacitor's insulating material causing a small current to flow through the capacitor. Dielectric losses are more complex and are caused by the polarization of the dielectric molecules due to the change in the electric field of the capacitor when an AC voltage is applied across it.
Figure 9. Capacitor loss models are typically simplified to an equivalent series resistance (ESR)
All three losses are represented in the typical loss model for a capacitor (left portion of Figure 9), with each loss represented by a resistance. The power associated with each loss associated with the energy stored in the capacitor is represented by the loss factor (DF), or loss tangent (δ). The DF for each loss can be found by taking the ratio of the real to imaginary part of the capacitor impedance, and each loss can be plugged into the model separately.
To simplify the loss model, the contact resistance loss, leakage current loss, and dielectric loss in Figure 9 are lumped together into an equivalent series resistance (ESR). ESR is defined as the portion of the capacitor impedance that consumes active power.
When extrapolating the capacitor impedance model and calculating the ESR (the real part of the result), the ESR is a function of frequency. This dependence can be demonstrated in the following simplified ESR equation:385483where DFR, DFL, and DFD are the power dissipation factors for contact resistance, leakage current, and dielectric losses.
Using this equation, we can observe that as the signal frequency increases, both leakage and dielectric losses decrease until, at a higher frequency, contact resistance losses begin to dominate. Above this frequency (which is not included in the equation), the ESR tends to increase due to the skin effect of high frequency AC currents.
Many capacitor manufacturers provide ESR graphs that plot ESR vs. frequency. For example, TDK provides ESR curves for most of its capacitor products. These graphs can be used to determine the ESR value versus switching frequency.
However, if an ESR graph is not available, a rough estimate of ESR can be obtained from the DF specification in the capacitor data sheet. DF is the overall DF of the capacitor (including all losses), or the ESR can be estimated as follows:
Whichever method is used to arrive at the ESR value, our intuition tells us that high ESR will reduce the efficiency of a switching power supply, since the input and output capacitors are charged and discharged through the ESR during each switching cycle. This results in I2 × RESR power losses. This loss (PCAP(ESR)) can be calculated as follows:
PCAP(ESR) = ICAP(RMS)2 × RESR
Where ICAP(RMS) is the RMS value of the AC current flowing through the capacitor. For the output capacitor of the buck circuit, the RMS value of the inductor ripple current can be used. The calculation of the RMS current of the input filter capacitor is relatively complicated, and a reasonable estimate can be obtained according to the following formula:
ICIN(RMS) = IOUT/VIN × [VOUT (VIN - VOUT)]1/2
Obviously, in order to reduce the power loss of the capacitor, a low ESR capacitor should be selected, which helps the SMPS power supply reduce the ripple current. ESR is the main cause of output voltage ripple, so choosing a low ESR capacitor is a good choice. In general, capacitors with different types of dielectrics have different ESR ratings. For a given capacitance and voltage rating, aluminum electrolytic and tantalum capacitors have higher ESR values than ceramic capacitors. Polyester and polypropylene capacitors have ESR values between them, but these capacitors are larger and are rarely used in SMPS.
For a given type of capacitor, a larger capacitance and lower fS can provide a lower ESR. Larger capacitors generally also reduce ESR, but electrolytic capacitors introduce a larger equivalent series inductance. Ceramic capacitors are considered a good compromise, and lower capacitor voltage ratings can also help reduce ESR for a given capacitance value.
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