“There must be energy consumption in the energy conversion system. Although the conversion efficiency of 100% cannot be obtained in practical applications, the efficiency of a high-quality power supply can reach a very high level, and the efficiency is close to 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 give actual measurement results, but we can only guarantee our own data.

“

There must be energy consumption in the energy conversion system. Although the conversion efficiency of 100% cannot be obtained in practical applications, the efficiency of a high-quality power supply can reach a very high level, and the efficiency is close to 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 give actual measurement results, but we can only guarantee our own data. Figure 1 shows a circuit example of an SMPS buck converter, which can achieve a conversion efficiency of 97% and maintain high efficiency even at light loads. What is the secret to achieving such high efficiency? It is good to start by understanding the common problem of SMPS losses, most of the losses in switching power supply are from the switching devices (MOSFETs and diodes), and a small part of the losses are from the inductors and capacitors. However, using very cheap inductors and capacitors (with higher resistances) will result in significantly higher losses. When choosing an IC, the controller architecture and internal components need to be considered for efficiency metrics. For example, Figure 1 uses a variety of methods to reduce losses, including: synchronous rectification, low on-resistance MOSFETs integrated on-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 SMPS**

Losses are an issue for any SMPS architecture, and we discuss here using the step-down (or buck) converter shown in Figure 2 as an example, where the switching waveforms at various points are marked for subsequent calculations.

The main function of a buck converter is to convert a higher DC input voltage to a lower DC output voltage. To meet this requirement, the MOSFET is switched on and off under the control of a pulse-width modulated signal (PWM) at a fixed frequency (fS). When the MOSFET is turned on, the input voltage charges the Inductor and capacitors (L and COUT), which transfer energy to the load through them. During this period, the inductor current rises 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 power the load. The inductor current drops linearly, and the current 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[D × tS]and[(1 – D) × tS]Two parts, which correspond to the conduction time of the MOSFET (Loop 1) and the conduction time of the diode (Loop 2). All SMPS topologies (buck, anti-equal) divide the switching cycle in this way for voltage conversion.

For a buck conversion circuit, a larger duty cycle will deliver more energy to the load, increasing the average output voltage. Conversely, when the duty cycle is low, the average output voltage also decreases. From this relationship, the following conversion equation for a buck SMPS under ideal conditions (without considering the voltage drop of the diode or MOSFET) can be obtained:

VOUT = D × VIN

IIN = D × IOUT

It is important to note that the longer any SMPS is in a certain state during a switching cycle, the more losses it will cause in that state. For a buck converter, the lower D (and correspondingly lower VOUT), the higher the losses due to loop 2.

**1. Loss of switching device MOSFET conduction loss**

The MOSFETs and diodes in Figure 2 (and most other DC-DC converter topologies) are the main contributors to power dissipation. The relevant loss mainly includes two parts: conduction loss and switching loss.

MOSFETs and diodes are switching elements, and current flows through the loop when turned on. When the device is on, conduction losses are 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 during conduction (IMOSFET(AVG)).

PCOND(MOSFET) (using average current) = IMOSFET(AVG)? × RDS(ON) × D

The above equation gives an approximation of the conduction losses of the MOSFETs in the SMPS, but it is only an estimate of the circuit losses because the power dissipation when the current rises linearly is greater than the power dissipation calculated from the average current. For “peak” currents, a more accurate calculation is to obtain an estimate by integrating the square of the current waveform between the peak and valley values of the current (IV and IP in Figure 3).

Figure 3. MOSFET current waveform for a typical buck converter to estimate MOSFET conduction losses.

The following equation gives a more accurate method for estimating losses, using the integration of the current waveform I? between IP and IV instead of the simple I? 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. MOSFET current rises linearly from IV to IP, for example: if IV is 0.25A, IP is 1.75A, RDS(ON) is 0.1Ω, VOUT is VIN/2 (D = 0.5), calculated based on average current (1A) for:

PCOND(MOSFET) (using average current) = 12 × 0.1 × 0.5 = 0.050W

Use waveform integration for more accurate calculations:

PCOND(MOSFET) (calculated using current waveform integration) = [(1.753 – 0.253)/3] × 0.1 × 0.5 = 0.089W

or approximately 78%, which is higher than that calculated from the average current. For the current waveform with small peak-to-average ratio, the difference between the two calculation results is very small, and the average current calculation can meet the requirements.

**2. Diode conduction loss**

The conduction loss of a MOSFET is proportional to RDS(ON), and the conduction loss of a diode is strongly dependent on the forward voltage (VF). Diodes typically have larger losses than MOSFETs, and diode losses are proportional to forward current, VF, and on-time. Since the diode conducts when the MOSFET is off, the diode conduction loss (PCOND(DIODE)) is approximately:

PCOND(DIODE) = IDIODE(ON) × VF × (1 – D)

where IDIODE(ON) is the average current during diode conduction. As shown in Figure 2, the average current during diode conduction is IOUT, so for a buck converter, PCOND(DIODE) can be estimated as:

PCOND(DIODE) = IOUT × VF × (1 – VOUT/VIN)

Unlike MOSFET power dissipation calculations, more accurate power dissipation calculations can be obtained using average current because diode losses are proportional to I, not I2.

Obviously, the longer the conduction time of the MOSFET or diode, the greater the conduction losses. For a buck converter, the lower the output voltage, the more power dissipation the diode produces because it remains on for longer.

**3. Switching dynamic loss**

Since switching losses are caused by the non-ideal state of the switch, it is difficult to estimate the switching losses of MOSFETs and diodes, it takes a certain amount of time for the device to go from fully on to fully off or from fully off to fully on, and power is generated in the process loss. The graph of drain-source voltage (VDS) and drain-source current (IDS) of the MOSFET shown in Figure 4 can well explain the switching losses of the MOSFET during the transition process. As can be seen from the upper half of the waveform, tSW(ON) and Voltage and current transients occur during 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 until VDS falls to the final on-state (= ID × RDS(ON)). Conversely, during turn-off, VDS gradually rises to its final value in the off-state before the MOSFET current drops to zero. During switching, the overlap of voltage and current is the source of switching losses, as can be clearly seen in Figure 4.

Figure 4. Transition of switching losses during MOSFET on and off transitions

It is easy to understand that switching losses increase as the SMPS frequency increases, as the switching frequency increases (the period decreases) the proportion of the switching transition time increases, thus increasing the switching losses. During the switching conversion process, the effect of switching time being one-twentieth of the duty cycle on efficiency is much smaller than that of switching time being one-tenth of the duty cycle. Since switching loss has a great relationship with frequency, when working at high frequency, switching loss will become the main loss factor. The switching loss of the MOSFET (PSW(MOSFET)) can be estimated according to the triangular wave shown in Figure 3 with the following formula:

PSW(MOSFET) = 0.5 × VD × ID × (tSW(ON) + tSW(OFF)) × fS

where VD is the drain-source voltage during the off period of the MOSFET, ID is the channel current during the on period of the MOSFET, and tSW(ON) and tSW(OFF) are the on and off times. For buck circuit conversion, VIN is the voltage at which the MOSFET is turned off, and the current is IOUT when it is turned on.

In order to verify the switching and conduction losses of the MOSFET, Figure 5 shows the typical waveforms of the integrated high-side MOSFET in a buck converter: VDS and IDS. The circuit parameters are: VIN = 10V, VOUT = 3.3V, IOUT = 500mA, RDS(ON) = 0.1Ω, fS = 1MHz, and the total switching transient time (tON + tOFF) is 38ns.

As can be seen in Figure 5, the switching change is not instantaneous, and the overlap of the current and voltage waveforms results in power loss. When the MOSFET is “on” (Figure 2), the current through the inductor, IDS, rises linearly, and switching losses are greater at the turn-off than at the turn-on edge.

Using the approximation above, the average loss of a MOSFET can be calculated as:

PT(MOSFET) = PCOND(MOSFET) + PSW(MOSFET)

= [(I13 – I03)/3] × RDS(ON) × VOUT/VIN + 0.5 × VIN × IOUT × (tSW(ON) + tSW(OFF)) × fS

= [(13 – 03)/3] × 0.1 × 3.3/10 + 0.5 × 10 × 0.5 × (38 × 10-9) × 1 × 106

= 0.011 + 0.095 = 106mW

This result is close to the 117.4mW measured in the lower curve of Figure 5, note: In this case, fS is high enough that PSW (MOSFET) is the dominant factor in power dissipation.

Typical switching cycle of a buck converter high-side MOSFET, input 10V, output 3.3V (output current 500mA). The switching frequency is 1MHz, and the switching transition time is 38ns.

Like MOSFETs, diodes have switching losses. This loss is largely dependent on the diode’s reverse recovery time (tRR), and diode switching losses occur during the diode’s transition from forward conduction to reverse cutoff.

When the reverse voltage is applied across the diode, the accumulated charge generated by the forward conduction current on the diode needs to be released, resulting in a reverse current spike (IRR(PEAK)), the polarity of which is opposite to the forward conduction current, resulting in V × I power loss because both reverse voltage and reverse current exist in the diode during reverse recovery. Figure 6 shows a schematic diagram of the diode’s PN junction during reverse recovery.

When the diode junction is reverse biased, it is necessary to release the accumulated charge during the forward conduction period, resulting in a peak current (IRR(PEAK)).

Knowing the reverse recovery characteristics of the diode, the switching loss (PSW(DIODE)) of the diode can be estimated by the following equation:

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 peak value IRR of the reverse current to the positive recovery current. For a buck circuit, when the MOSFET is on, VIN is the reverse bias voltage of the diode when the MOSFET is on.

To verify the diode loss calculation formula, Figure 7 shows the switching waveforms of a PN junction in a typical buck converter, VIN = 10V, VOUT =3.3V, measured IRR(PEAK) = 250mA, IOUT = 500mA, fS = 1MHz, tRR2 = 28ns, VF = 0.9V. Using these values we get:

This result is close to the measurement shown in Figure 7 at 358.7mW. Considering the large VF and long diode conduction period, the tRR time is very short and switching losses (PSW(DIODE)) dominate the diode losses.

Switching waveform of a PN junction switching diode in a buck converter, from 10V input to 3.3V output, with an output current of 500mA. Other parameters include: fS at 1MHz, tRR2 is 28ns, 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 low on-resistance RDS(ON), fast switching MOSFET; choose low on-voltage drop VF, fast recovery diode.

There are several factors that directly affect the on-resistance of a MOSFET, usually increasing the die size and drain-source breakdown voltage (VBR(DSS)), which helps reduce the on-resistance RDS(ON) due to the increased semiconductor material in the device . On the other hand, larger MOSFETs increase switching losses. Therefore, while large size MOSFETs reduce RDS(ON), they also cause efficiency problems that can be avoided with small devices. As 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 gate voltage that is large enough to reduce the RDS(ON) loss, but it will also increase the gate drive loss at this time. It is necessary to balance the reduction of RDS (ON) benefits and disadvantages of increasing gate drive. The switching loss of a MOSFET is related to the device capacitance. A larger capacitance requires a longer charging time, making the switching slower and consuming more energy. Miller capacitance, usually defined in MOSFET data sheets as reverse transfer capacitance (CRSS) or gate-drain capacitance (CGD), determines the switching time during switching. The charging charge of the Miller capacitor is denoted by QGD, and for fast switching of the MOSFET, the lowest possible Miller capacitance is required. In general, the capacitance of a MOSFET is inversely proportional to the die size, so a compromise must be taken between switching and conduction losses, and the switching frequency of the circuit must be chosen carefully.

For diodes, the on-voltage drop must be reduced to reduce the resulting losses. For small, lower voltage rated silicon diodes, the on-voltage drop is typically between 0.7V and 1.5V. Diode size, process and withstand voltage level will affect the turn-on 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 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 fast recovery diodes is tens of nanoseconds. An alternative to fast recovery diodes in low power applications is Schottky diodes, which have negligible recovery time and half the reverse recovery voltage VF of fast recovery diodes (0.4V to 1V), but Schottky diodes have far lower voltage and current ratings than fast recovery diodes and cannot be used in high voltage or high power applications. In addition, Schottky diodes have higher reverse leakage current compared to silicon diodes, but these factors do not limit their use in many power supplies. However, in some low voltage applications, even a Schottky diode with a lower voltage drop produces unacceptable conduction losses. For example, in a circuit with an output of 1.5V, even using a Schottky diode with a 0.5V turn-on voltage drop VF, there will be a 33% output voltage loss when the diode is turned on! To solve this problem, MOSFETs with low on-resistance RDS(ON) can be selected to implement a synchronous control architecture. Replacing the diode with a MOSFET (compare the circuits of Figure 1 and Figure 2), it works synchronously with the main MOSFET of the power supply, so during the alternate switching process, only one is guaranteed to be on. The conducting diode is replaced by the conducting MOSFET, and the high on-voltage drop VF of the diode is converted into the low on-voltage drop of the MOSFET (MOSFET RDS(ON) × I), which effectively reduces the conduction loss of the diode. Of course, compared with the diode, synchronous rectification only reduces the voltage drop of the MOSFET. On the other hand, the power consumption of driving the synchronous rectification MOSFET cannot be ignored. IC Data Sheets Two important factors (MOSFETs and diodes) that affect the efficiency of switching power supplies are discussed above. Reviewing the step-down circuit shown in Figure 1, the main factors affecting the efficiency of the controller IC can be obtained from the data sheet. First, the switching elements are integrated inside the IC, which saves space and reduces parasitic losses. Second, using MOSFETs with low on-resistance RDS(ON), in small-scale integrated step-down ICs (such as MAX1556), the on-resistance of NMOS and PMOS can reach 0.27Ω (typ.) and 0.19Ω (typ.) . After that, use the synchronous rectifier circuit. For a 500mA load, a switching circuit with a 50% duty cycle reduces the losses in the low-side switch (or diode) from 225mW (assuming a diode drop of 1V) to 34mW. Reasonable selection of SMPS IC Reasonable selection of SMPS IC packaging, control structure, and reasonable design can effectively improve the conversion efficiency.

**4. Integrated power switch**

Integrating the power switch into the IC eliminates the need for cumbersome MOSFET or diode selection and makes the circuit more compact, which can improve efficiency to some extent due to reduced line losses and parasitics. Depending on the power level and voltage constraints, MOSFETs, diodes (or synchronous rectifier MOSFETs) can be integrated into the chip. Another benefit of integrating the switch inside the chip is that the size of the gate drive circuit is already optimized for the on-chip MOSFET, eliminating the need to waste time on unknown discrete MOSFETs.

**Quiescent Current**

Battery-powered devices are particularly concerned about quiescent current (IQ) in IC specifications, which is the current required to maintain circuit operation. In the case of heavy load (more than ten or hundred times the quiescent current IQ), the effect of IQ on efficiency is not obvious, because the load current is much larger than IQ, and as the load current decreases, the efficiency tends to decrease, because IQ corresponds to The ratio of power to total power is increased. This is especially important for applications that spend most of the time in sleep mode or other low-power modes. Many consumer products need to maintain power for keyboard scanning or other functions even in the “off” state. Very low IQ power supply.

**Power Architecture Improves Efficiency**

The control architecture of SMPS is one of the key factors affecting the efficiency of switching power supplies. We have already discussed this in the synchronous rectification architecture, which can effectively improve the efficiency index due to the use of low on-resistance MOSFETs instead of switching diodes that consume more power.

Another important control architecture is designed for light-load operation or a wide load range, pulse-skipping mode, also known as pulse frequency modulation (PFM). Unlike pure PWM switching, which uses a fixed switching frequency at heavy and light loads, the converter operates in skipped switching cycles in pulse-skipping mode, which saves unnecessary switching and improves efficiency.

In pulse skip mode, the inductor discharges for an extended 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 also drops. When the voltage drops to the set gate, a new switching cycle is started, charging the inductor and replenishing the output voltage.

It should be noted that the pulse-skipping mode generates load-dependent output noise that is difficult to filter due to its distribution at different frequencies (unlike fixed frequency PWM control architectures).

Advanced SMPS ICs take advantage of both: a constant PWM frequency at heavy loads and a pulse-skipping mode at light loads to improve efficiency, as the IC shown in Figure 1 provides.

When the load increases to a higher rms value, the skipped pulse waveform will switch to fixed PWM, and the noise is easily filtered out at the nominal load. Over the entire operating range, the device selects pulse-skipping and PWM modes as needed to maintain overall high efficiency (Figure 8).

The efficiency curves shown in curves D, E, and F are in fixed PWM mode, which are less efficient at light loads, but can provide high conversion efficiency (up to 98%) at heavy loads. If set to keep fixed PWM operation mode at light load, the IC will not change the operation mode according to the load condition. 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 the PWM switching operation is small and much lower than the output power. On the other hand, the efficiency curves in pulse-skipping “idle” mode (A, B, C in Figure 8) can be kept high at light loads because the switch is only turned on when the load requires it. For the 7V input curve, more than 60% efficiency can be obtained in idle mode with a 1mA load.

Buck Converter Efficiency Curves in PWM and Idle (Pulse Skipping) Mode, Note: Idle mode is more efficient than PWM mode at light loads.

**Optimize SMPS**

Switching power supplies are widely used because of their high efficiency indicators, but their efficiency is still limited by some inherent losses in SMPS circuits. When designing a switching power supply, it is necessary to carefully study the source of SMPS loss, select SMPS IC reasonably, and make full use of the advantages of the device. In order to keep the circuit cost as low as possible without even increasing the circuit cost, engineers A comprehensive choice needs to be made.

**5. Loss of passive components**

We have seen that MOSFETs and diodes contribute to SMPS losses. Using high-quality switching devices can greatly improve efficiency, but they are not components that optimize power efficiency.

The basic circuit of a typical step-down converter IC is described in detail. Two synchronous rectifier MOSFETs are integrated, low RDS(ON) MOSFETs for high efficiency. In this circuit, the switching elements are integrated inside the IC, and the components have been pre-selected for the specific application. However, in order to further improve efficiency, designers also need to pay attention to passive components – external inductors and capacitors, to understand their impact on power consumption.

**6. Inductor power dissipation resistive loss**

Inductor power dissipation includes two basic factors, coil loss and core loss. The coil loss is attributed to the direct current resistance (DCR) of the coil, and the core loss is attributed to the magnetic properties of the inductor.

ρ is the resistivity of the coil material, l is the length of the coil, and A is the cross-sectional area of the coil.

DCR will increase as the coil length increases and decrease as the coil cross-sectional area increases. This principle can be used to judge the standard inductance and determine the different inductance values and sizes required. For a fixed inductance value, small inductance sizes require a smaller coil cross-sectional area to maintain the same number of turns, thus resulting in increased DCR; for a given inductor size, a small inductance value usually corresponds to a small DCR, because A smaller number of coils reduces coil length, allowing the use of larger diameter wire.

Knowing the DCR and the average inductor current (depending on the SMPS topology), the resistive loss of the inductor (PL(DCR)) can be estimated as:

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 the DCR directly affects the power dissipation of the inductor resistor, the power dissipation is proportional to the square of the inductor current, so it is necessary to reduce the DCR.

Also, it should be noted that when calculating PL(DCR) using the average inductor current (as 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 calculations described earlier in this article, a more accurate result can be obtained by integrating the waveform of the inductor current. more acurrate. Of course, the 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.

**7. Core loss**

Core loss is not as easy to estimate as conduction loss, it is difficult to estimate. It consists of hysteresis and eddy current losses, which directly affect the alternating magnetic flux of the iron core. In SMPS, although the average DC current flows through the inductor, the ripple current due to the change of the switching voltage through the inductor causes the periodic magnetic flux change of the magnetic core.

Hysteresis losses arise from the power dissipated by the rearrangement of the core dipoles during each AC cycle, and can be thought of as “frictional” losses due to the dipoles rubbing against each other as the magnetic field polarity changes, proportional to frequency and magnetic pass density.

Conversely, eddy current losses are introduced by the time-varying magnetic flux in the core. According to Faraday’s law, alternating magnetic flux produces alternating voltage. Therefore, this alternating voltage creates a localized current that creates I2R losses in the core resistance.

The core material has a large effect on the core loss. Iron powder cores are commonly used inductors in SMPS power supplies. Iron-nickel-molybdenum powder cores (MPP) have low losses, and iron powder cores have low cost, but larger core losses.

Core loss can be estimated by calculating the large variation in core flux density (B), then looking at the flux density and core loss (and frequency) graphs provided by the inductor or core manufacturer. Peak flux density can be calculated in several ways, the formula can be found in the core loss curve in the inductor data sheet.

Accordingly, if the core area and the number of coils are known, the peak flux can be estimated using:

Here, B is the peak flux density (Gauss), L is the coil inductance (Henry), ΔI is the peak-to-peak inductor ripple current (Amps), A is the core cross-sectional area (cm2), and N is the number of coil turns.

With the popularity of the Internet, it is easy to search for device information from online materials. Some manufacturers provide interactive inductive power consumption calculation software to help designers estimate power consumption. Use these tools to quickly and accurately estimate power losses in application circuits. For example, the online inductor core loss and copper loss calculation formulas provided by Coilcraft, simply enter some data to get the core loss and copper loss of the selected inductor.

**8. Capacitor loss**

Contrary to the ideal capacitance model, the actual physics of the capacitive element causes several losses. Capacitors in SMPS circuits mainly play a role in voltage regulation and filtering of input/output noise (Figure 1). These losses in capacitors reduce the efficiency of switching power supplies. These losses are mainly manifested in three aspects: equivalent series resistance loss, leakage current loss and dielectric loss.

The resistive losses of the capacitor are obvious. Since current flows into and out of the capacitor every switching cycle, the inherent resistance (RC) of the capacitor will cause some power dissipation. Leakage current loss is the power loss due to the resistance (RL) of the insulating material of the capacitor causing a small current to flow through the capacitor. Dielectric loss is more complicated. Due to the AC voltage applied across the capacitor, the electric field of the capacitor changes, which causes the polarization of the dielectric molecules to cause power loss.

Capacitive loss models are generally simplified to an equivalent series resistance (ESR)

All three losses are represented in a typical loss model for capacitors (left part of Figure 9), with resistors representing each loss. The power of each loss associated with capacitive energy storage is expressed as a power dissipation factor (DF), or loss tangent (δ). The DF for each loss can be derived from the ratio of the real to imaginary parts of the capacitor impedance, which can be inserted into the model separately.

To simplify the loss model, the contact resistance losses, leakage current losses, and dielectric losses in Figure 9 are concentrated as an equivalent series resistance (ESR). ESR is defined as the portion of capacitive impedance that dissipates active power.

When estimating the capacitive impedance model, calculating the ESR (real part of the result), the ESR is a function of frequency. This correlation can be demonstrated in the following simplified ESR equation:

where DFR, DFL, and DFD are power dissipation coefficients for contact resistance, leakage current, and dielectric loss.

Using this equation, we can observe that both leakage current losses and dielectric losses decrease as the signal frequency increases until the contact resistance losses dominate from a higher frequency point. Above this frequency point (this parameter is not included in the formula), the ESR tends to increase due to the skin effect of the high-frequency alternating current.

Many capacitor manufacturers provide ESR graphs showing ESR versus frequency. For example, TDK provides ESR curves for most of its capacitor products. Refer to these graphs against switching frequency to get the ESR value.

However, if an ESR graph is not available, a rough estimate of the ESR can be obtained from the DF specification in the capacitor data sheet. DF is the overall DF of the capacitor (including all losses), and the ESR can also be estimated as:

No matter which method is used to get the ESR value, our intuition is that high ESR will reduce the efficiency of 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 loss. This loss (PCAP(ESR)) can be calculated as:

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 step-down circuit, the RMS value of the inductor ripple current can be used. The calculation of the RMS current of the input filter capacitor is 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 will help the SMPS power supply to reduce the ripple current. ESR is the main cause of output voltage ripple, so choosing capacitors with low ESR not only improves efficiency, but also provides other benefits.

In general, capacitors with different types of dielectrics have different ESR ratings. For a given capacity and voltage rating, aluminum electrolytic and tantalum capacitors have higher ESR values than ceramic capacitors. Polyester and polypropylene capacitors have ESR values in between, but these capacitors are larger in size and rarely used in SMPS.

For a given type of capacitor, larger capacitance, lower fS can provide lower ESR. Larger size capacitors also generally reduce ESR, but electrolytic capacitors introduce larger equivalent series inductance. Ceramic capacitors are seen as a good compromise. In addition, lower capacitor voltage ratings can also help reduce ESR for a given capacitance value.

The Links: **LC260W01-A5K3** **LM64C142**