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Switched Mode Power Supply Design: SMPS Power Loss & Efficiency

Warm hint: The word in this article is about 1500 words and reading time is about 5 minutes

Catalogues1. Which components are your power wasters?2.4 Switch transistor turn-on/off processes-forward output power supply3.2 Magnetic hystersis loop of unipolar switch mode power supply transformer core
2. Switch transistor loss2.5 Effect of switching time on switching loss
2.1 Equivalent circuit of switch transistor2.6 Method of shortening switching time3.3 Hysteresis loop of various transformer cores
2.2 Switch transistor turn-on/off processes-pure resistive load3. Switch mode power supply transformer loss3.4 The selection of the transformer core
2.3 Switch transistor turn-on/off processes-flyback output power supply3.1 Switch mode power supply transformer loss


Introduction

1. Which components are your power wasters?

The losses of switching power supply mainly come from three components: switch transistor, transformer and rectifier diode. 

Switch transistor loss is mainly divided into turn-on/off losses two aspects. The loss of the switching transformer mainly includes hysteresis loss, eddy current loss and copper loss. The loss of rectifier diodes is mainly composed of two parts: forward conduction loss and reverse recovery loss.

The loss of the switch transistor is mainly related to the on/off switching times, as well as the operating frequency and load characteristics.

If the switching time is doubled, the loss of the switch tube will increase by about 2~3 times, and the loss of the switch transistor is directly proportional to the operating frequency of the switching power supply. The eddy current loss of the switching transformer and the copper loss of the transformer coil are directly proportional to the square of the operating frequency, while the hysteresis loss is proportional to the magnetic flux density raised to the 1.6 power in addition to the operating frequency. The forward loss of the rectifier diode is related to the forward voltage drop of the rectifier diode, while the reverse recovery loss is related to the reverse recovery time of the diode.

The above three losses account for more than 20% of the total loss of switching power supply. How to reduce the loss of switch transistors and transformers to improve the efficiency is a problem that every designer should consider.


Details & Analyses

2. Switch transistor loss

The losses of the switch transistor mainly include turn-on and turn-off losses.

FIG.1_20180614.jpg

FIG.1 Switch transistor circuit

2.1 Equivalent circuit of switch transistor

FIG.2_20180614.jpg

FIG.2 Equivalent circuit of switch transistor

The transistor (or MOSFET) input can be equivalent to a capacitor in parallel with a resistor, and its input voltage is:

EUA.1_20180614.jpg

When the transistor (or MOSFET) is on, the output end can be equivalent to an inductor in parallel with a resistors; when the transistor is off, it can be equivalent to a capacitor in parallel with a resistor; and its output voltage is:

EUA.2_20180614.jpg

The collector current is:

EUA.3_20180614.jpg

2.2 Switch transistor turn-on/off processes-pure resistive load

FIG.3_20180614.jpg

FIG.3 Purely resistive switching circuit

Transistor switching characteristic parameters:

  1. 1. Delay time td

  2. The time required for the collector current Ic to rise to 10% of its maximum value Icm, when the input signal Vin becomes positive.

  3. 2. Rise time tr

  4. The time taken by the collector current Ic to rise from 10% to 90% of its maximum value Icm.

  5. 3. Storage time ts

  6. The time required for the peak collector current Icm to drop to 90% of its value, when the input signal Vin becomes negative.

  7. 4. Fall time tf

  8. The time taken by the collector current Ic to drop from 90% to 10% of its maximum value Icm.

FIG.4_20180614.jpg

FIG.4 Switching loss with purely resistive load

2.3 Switch transistor turn-on/off processes-flyback output power supply

FIG.5_20180614.jpg

FIG.5 Flyback switching power supply

With a flyback switching power supply, the current flowing through the switch transistor is a sawtooth wave. At first the switch transistor is turned on, the current flowing through the primary coil of the transformer is small, but just before the transformer is turned off it becomes very large. Therefore, the loss of the transistor during the on-time (td and tr) is small, and the loss during the off-time (ts and tf) is very large, which is a difference of several tens of times.

FIG.6_20180614.jpg

FIG.6 Switching loss of flyback switch mode power supply

2.4 Switch transistor turn-on/off processes-forward output power supply

FIG.7_20180614.jpg

FIG.7 Forward switching power supply

With a forward switching power supply, the current flowing through the switch transistor is a trapezoidal waveform. At first the switch tube is turned on, the current flowing through the primary coil of the transformer is relatively large. It becomes larger just before the transistor is turned off. Therefore, the loss of the switch transistor during the initial conduction period (td and tr) and the turn-off period (ts and tf) is all larger than that of the flyback switch-mode power supply.

One way to reduce the switching losses is to minimize the turn-on/off time of the transistor as much as possible, especially the turn-off time,  and the other is to reduce the operating frequency.

FIG.8_20180614.jpg

FIG.8 Switching loss of forward switch-mode power supply

2.5 Effect of switching time on switching loss

FIG.9_20180614.jpg

FIG.9 Increasing the turn-on/off time will meanwhile increase the switching loss

The switching loss of the purely resistive load is proportional to the four switching times of the switch transistor. So increasing the turn-on/off time of the transistor will meanwhile reduce the voltage and current rise rates of the switched circuit. It is also beneficial to reduce the radiation interference of the switching power supply, but it will increase the switching loss of the transistor.

In inductive loads, the switching losses of forward and flyback switching power supply are different.

FIG.10_20180614.jpg

FIG.10 Waveforms and losses at various points of the switch circuit

2.6 Method of shortening switching time

FIG.11_20180614.jpg

FIG.11 A method to shorten the switching time

The most effective way to reduce the loss of the switch transistor is to reduce the turn-on/off time of it. The figure above shows a method to reduce the turn-on/off time of the transistor.

Like the figure shows, C is a speed-up capacitor. When the signal is positive, a large base current can be provided to the transistor to accelerate the conduction of it; when the signal is negative, the voltage across the capacitor can be discharged back to the switch transistor to speed up the shutdown of it. The role of D1 is to prevent the capacitor from discharging through Rb, so that the reverse voltage of the capacitor is all added to the pin B-E of the transistor. D2 is an anti-saturation diode. When the base potential is higher than the collector potential, D2 will be turned on to prevent the transistor switch into deep saturation, causing the transistor to rapidly exit the saturation region at the moment of shutdown. If the operating frequency of the switching power supply is relatively low, D2 can be cancelled, now that a high saturation voltage drop also increases the switching loss.

FIG.12_20180614.jpg

FIG.12 Reducing switching loss by shortening switching time

3. Switch mode power supply transformer loss

The switch mode power supply transformer loss is divided into hysteresis loss and eddy current loss.

3.1 Switch mode power supply transformer loss

FIG.13_20180614.jpg

FIG.13 Hysteresis loss and eddy current loss of switch mode power supply transformer

The hysteresis loss of the switch mode power supply transformer is proportional to the area of the hysteresis loop:

EUA.4_20180614.jpg

The eddy current loss of transformer core is proportional to the square of magnetic inductance:

EUA.5_20180614.jpg

In the above formula, Kh and Ke are the coefficients related to the material and structure of the transformer core respectively, Bm is the magnetic induction intensity, f is the working frequency and V is the volume of the iron core. The exponent n is related to the magnetic induction intensity Bm value, and n is approximately equal to 1.6 to 2, which is related to the shape factor of magnetic hystersis loop. The copper loss of the transformer is related to the diameter of the varnished wire. Generally, the current density of the varnished wire cannot exceed 5A/mm2.

3.2 Magnetic hystersis loop of unipolar switch mode power supply transformer core

FIG.14_20180614.jpg

FIG.14 Magnetic hystersis loop of unipolar switch mode power supply transformer core

The figure above shows the magnetization curve (hysteresis loop) of the transformer core when the unipolar switch-mode power supply is in normal operating condition. When the excitation current magnetizates the core, the magnetic flux density changes along the magnetization curve abc. In this case, the magnetic flux density increases with the magnetic field strength. When demagnetizing, the magnetic flux density and magnetic field strength change along the magnetization curve cda. In this case, the magnetic flux density decreases with the magnetic field strength.

On the one hand, when the pulse width is constant, the magnetic field strengths generated by the excitation current and the demagnetization current are equal in magnitude but opposite to the direction, so that the two terminals (a and c) of the hysteresis loop are substantially stable. on the other hand, both ends of the magnetic hysteresis loop will change with the pulse width.

3.3 Hysteresis loop of various transformer cores

FIG.15_20180614.jpg

FIG.15 Technology performance comparison of various transformer core 

The above diagram is about the magnetization curve (hysteresis loop) of various transformer cores, which shows the application of various magnetic materials to different technical requirements in the design of switching power supply.

These are some of the parameters of transformer core that we should considered in the design of switching power supply: the maximum magnetic flux density Bm (or magnetic saturation flux density Bs), the maximum magnetic permeability μm or effective magnetic permeability μe, the coercivity Hm and eddy current loss, etc.

3.4 The selection of the transformer core

FIG.16_20180614.jpg

FIG.16 Working frequency range of various transformer cores

Regarding the selection of transformer core, we mainly consider the following aspects, such as volume, working efficiency, reliability, cost and so on, which will inevitably involve many parameters of transformer core, such as: maximum magnetic flux density Bm (or magnetic saturation flux density Bs), the maximum magnetic permeability μm, effective magnetic permeability μe, the coercivity Hm and eddy current loss, etc. These parameters are basically related to the operating frequency, especially the eddy current loss Pe and hysteresis loss Ph.


Switch Mode Power Supply Measurements and Analysis


Book Recommendation

Switch-Mode Power Supplies Spice Simulations and Practical Designs

It is a comprehensive resource on using SPICE as a power conversion design companion. This book uniquely bridges analysis and market reality to teach the development and marketing of state-of-the art switching converters. Invaluable to both the graduating student and the experienced design engineer, this guide explains how to derive founding equations of the most popular converters…design safe, reliable converters through numerous practical examples…and utilize SPICE simulations to virtually breadboard a converter on the PC before using the soldering iron.

by Christophe Basso

Power Converters with Digital Filter Feedback Control 1st Edition

This book presents a logical sequence that leads to the identification, extraction, formulation, conversion, and implementation for the control function needed in electrical power equipment systems. Also it builds a bridge for moving a power converter with conventional analog feedback to one with modern digital filter control and enlists the state space averaging technique to identify the core control function in analytical, close form in s-domain (Laplace). It is a useful reference for all professionals and electrical engineers engaged in electrical power equipment/systems design, integration, and management.

by Keng C. Wu


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