2. Р. Т. Krein, Elements of Power Electronics, Oxford University Press, New York, 1998.

3. T. M. Jahns and E. L. Owen, Ac adjustable-speed drives at the millenium: how did we get here? in Proc. IEEE Applied Power Electronics Conf, 2000, pp. 18-26.

4. C. C. Herskind and W. McMurray, History of the Static Power Converter Committee, IEEE Trans. Industry Applications IA-20:4, 1069-1072 (1984).

5. E. L. Owen, Origins of the inverter, IEEE Industry Applications Mag. 2: 64 (1996).

6. J. D. Van Wyk and F. C. Lee, Power electronics technology at the dawn of the new millenium - status and future, in Rec, IEEE Power Electronics Specialists Conf, 1999, pp. 3-12.

7. P. Wood, Switching Power Converters, Van Nostrand Reinhold, New York 1981.

8. R. Erickson, Fundamentals of Power Electronics, Chapman and Hall, New York, 1997.

9. P. T. Krein and D. C. Hamill, Smoothing circuits, in Wiley Encyclopedia of Electrical and Electronics Engineering, J. Webster, ed., John Wiley, New York, 1999.

The Power Diode

Dr. All I. Maswood, Associate Professor

School of EEE, Nanyang

Technological University, Nanyang Avenue, Singapore-639798

2.1 Diode as a Switch................................................................................. 15

2.2 Some Properties of PN Junction............................................................. 15

2.3 Common Diode Types.......................................................................... 17

2.4 Typical Diode Ratings........................................................................... 17

2.4.1 Voltage Ratings 2.4.2 Current Ratings

2.5 Snubber Circuits for Diode.................................................................... 19

2.6 Standard Datasheet for Diode Selection................................................... 19

Tutorial 2.1. Reverse recovery and overvoltages Tutorial 2.2. Ideal diode operation, mathematical analysis and PSPICE simulation

2.7 Typical Applications of Diodes............................................................... 23

2.8 Standard Datasheet for Diode Selection................................................... 23

2.8.1 General-Use Rectifier Diodes

References........................................................................................... 25

2.1 Diode as a Switch

Among all the static switching devices used in power electronics (PE), the power diode is perhaps the simplest. Its circuit symbol, shown in Fig. 2.1, is a two terminal device, and with terminal A known as the anode and terminal К known as the cathode. If terminal A experiences a higher potential compared to terminal K, the device is said to be forward biased and a forward current (Ip) will flow through the device in the direction as shown. This causes a small voltage drop across the device (<1V), which under ideal conditions is usually ignored. By contrast, when a diode is reverse biased, it does not conduct and the diode then experiences a small current flowing in the reverse direction called the leakage current. Both forward voltage drop and leakage current are ignored in an ideal diode. In PE applications a diode is usually considered to be an ideal static switch.

The characteristics of a practical diode depart from the ideals of zero forward and infinite reverse impedance, as shown in Fig. 2.2a. In the forward direction, a potential barrier associated with the distribution of charges in the vicinity of the junction, together with other effects, leads to a voltage drop. In the case of silicon this is in the range of 1V for currents in the normal range. In the reverse direction, within the normal voltage operating range, a very small current flows that is largely independent of the voltage. For practical purposes the static characteristics are often repre-

sented as shown in Fig. 2.2b. In Fig. 2.2b the forward characteristic is expressed as a threshold voltage Vq with a linear incremental or slope resistance r. The reverse characteristic remains the same over the range of possible leakage currents irrespective of voltage within the normal working range.

2.2 Some Properties of PN Junction

From the forward and reverse-biased condition characteristics, one notices that when the diode is forward biased, current rises rapidly as the voltage is increased. Current in the reverse-biased region is significantly small until the breakdown voltage of the diode is reached. Once the applied voltage is over this limit, the current will increase rapidly to a very high value limited only by an external resistance.

DC Diode parameters. The most important are the following:

Forward voltage Vp is the voltage drop of a diode across A and К at a defined current level when it is forward biased.

Breakdown voltage is the voltage drop across the diode at a defined current level when it is beyond reverse-biased level. This is known as avalanche.

Reverse current Ij is the current at a particular voltage, and which is below the breakdown voltage.

Copyright © 2001 by Academic Press.

All rights of reproduction in any form reserved.

Metal

Ceramic Insulator

К

(a) (b) (c)

figure 2.1 Power diode: (a) symbol; (b) and (c) types of packaging.

AC Diode parameters. Very common are the following:

Forward recovery time is the time required for the diode voltage to drop to a particular value after the forward current starts to flow.

Reverse recovery time tj is the time interval between the application of reverse voltage and the reverse current dropped to a particular value as shown in Fig. 2.2. Parameter is the interval between the zero crossing of the diode current and when it becomes Ijj. On the other hand, ty is the time interval from the maximum reverse recovery current to 0.25 of I. The ratio of the

two parameters and % is known as the softness factor SF. Diodes with abrupt recovery characteristics are used for high-frequency switching. See Fig. 2.3 for soft and abrupt recovery.

In practice, a design engineer frequently needs to calculate reverse recovery time in order to evaluate the possibility of high-frequency switching. As a rule of thumb, the lower t is, the faster the diode can be switched [ 1 ].

trr = ta + tb

(2.1)

If % is negligible compared to (which commonly occurs), then the following expression is vahd:

trr =

di/dt

from which the reverse recovery current

figure 2.2a Typical static characteristic of a power diode (forward and reverse have different scale).

where Q is the storage charged, and can be calculated from the area enclosed by the path of the recovery current.

Example 2.1 The manufacturer of a selected diode gives the rate of fall of the diode current di/dt = 20A/is, and a reverse recovery time of t = 5 is. What value of peak reverse current do you expect?

Solution. The peak reverse current is given as:

di Jt

Irr = J-2QRR

The storage charge Qjj is calculated as Q = di/ dtt 1/2 X 20 A/is X (5 X 10-) = 50 iC. Hence

figure 2.2b Practical representation of the static characteristic of a power diode.

L = /20-х2х50цС = 44.72А

figure 2.3 Diode reverse recovery process with various softness factors, (a) Soft recovery; and (b) abrupt recovery.

Diode Capacitance C, is the net diode capacitance including the junction (Cj) plus package capacitance (Cp).

In high-frequency pulse switching a parameter known as transient thermal resistance is of vital importance because it indicates the instantaneous junction temperature as a function of time under constant input power.

2.3 Common Diode Types

Depending on their applications, diodes can be segregated into the following major divisions:

Small Signal Diode. These are the semiconductor devices used most often in a wide variety of applications. In general purpose apphcations, they are used as a switch in rectifiers, limiters, capacitors, and in wave shaping. The common diode parameters a designer needs to know include forward voltage, reverse breakdown voltage, reverse leakage current, and recovery time.

Silicon Rectifier Diode. These are the diodes that have high forward-current carrying capability, typically up to several hundred amperes. They usually have a forward resistance of only a fraction of an ohm while their reverse resistance is in the megaohm range. Their primary application is in power conversion, such as for power supplies, UPS, rectifiers/inver-inverters etc. In case of current exceeding the rated value, their case temperature will rise. For stud mounted diodes, their thermal resistance is between 0.1 to 1° C/W.

Zener Diode. Its primary applications are in the voltage reference or regulation. However, its ability to maintain a certain voltage depends on its temperature coefficient and impedance. The voltage reference or regulation application of Zener diodes are based on their avalanche properties. In the reverse-biased mode, at a certain voltage the resistance of these devices may suddenly drop. This occurs at the Zener voltage Vx, a parameter the designer knows beforehand.

Figure 2.4 shows a circuit in which a Zener diode is used to control the reference voltage of a linear power supply. Under normal operating conditions, the transistor will transmit power to the load (output) circuit. The output power level will depend on the transistor base current. A very high base

InputO

Zener

Diode,

О

Regulator l-transistor

QOutput

figure 2.4 Voltage regulator with a Zener diode for reference.

current will impose a large voltage across the Zener and it may attain Zener voltage V, at which point it will crush and limit the power supply to the load.

Photodiode. When a semiconductor junction is exposed to light, photons generate hole-electron pairs. When these charges diffuse across the junction, they produce photo current. Hence this device acts as a source of current that increases with the intensity of light.

Light-Emitting Diode (LED). Power diodes used in PE circuits are high-power versions of the commonly used devices employed in analog and digital circuits. They are manufactured in many varieties and ranges. The current rating can be from a few amperes to several hundreds while the voltage rating varies from tens of volts to several thousand volts.

2.4 Typical Diode Ratings 2.4.1 Voltage Ratings

For power diodes, a data sheet will give two voltage ratings. One is the repetitive peak inverse voltage ( Vrrm) and the other is the nonrepetitive peak inverse voltage. The nonrepetitive voltage (Vjm) is the diodes capability to block a reverse voltage that may occur occasionally due to an overvoltage surge. On the other hand, repetitive voltage is apphed on the diode in a sustained manner. To understand this, let us look at the circuit in Fig. 2.5a.

\Zdi

figure 2.5 (a) The circuit.

Example 2.2. Two equal source voltages of 220 V peak and phase-shifted from each other by 180° supply a common load: (a) Show the load voltage; (b) describe when diode Dl will experience Vrrm and (c) determine the Vrrm magnitude considering a safety factor of 1.5.

Solution, (a)The Input voltages, load voltage, and the voltage across Dl when it is not conducting (Vrrm) shown in Fig. 2.5b.

(b) Diode Dl will experience Vrrm when it is not conducting. This happens when the applied voltage VI across it is in the negative region (from 70 to 80 ms as shown in Fig. 2.5b) and consequently the diode is reverse biased. The actual ideal voltage across it is the peak value of the two input voltages 220 x 2 = 440 V. This is because when Dl is not conducting, D2 is. Hence, Vn bn is also apphed across it because D2 is practically shorted.

(c) The Vrrm = 440 V is the value under ideal circumstances. In practice, however, higher voltages may occur due to stray circuit inductances and/or transients due to the reverse recovery of the diode. These are hard to estimate. Hence, a design engineer would always use a

safety factor to cater to these overvoltages, that is, a diode with a 220 X 2 X 1.5 = 660 V rating.

2.4.2 Current Ratings

Power diodes are usually mounted on a heat sink. This effectively dissipates the heat arising due to continuous conduction. Current ratings are estimated based on temperature rise considerations. The data sheet of a diode normally specifies three different current ratings. These are: (1) the average current; (2) the rms current; and (3) the peak current. A design engineer must ensure that each of these values are never exceeded. To do that, the actual current (average, rms, and peak) in the circuit must be evaluated either by calculation, simulation, or measurement. These values must be checked against the ones given in the data sheet for that selected diode. The calculated values must be less than or equal to the data sheet values. The following example shows this technique.

Example 2.3 The current waveform passing through a diode switch in a switch-mode power-supply application is shown in Fig. 2.6. Find the average, rms and peak currents.

Solution. The current pulse duration is shown to be 0.2 ms within a period of 1 ms and with a peak amph-tude of 50 A. Hence the required currents are:

laverage = 50 X = 10 A

I = ,/502x = 22.36A

Irms = 50 A

Sometimes, a surge current rating and its permissible duration are also given in a data sheet. For protection of diodes and other semiconductor devices, a fast acting fuse is required.

Input Voltages

I V(V2: + ) < V(V1: + )

Load Voltage

1 V(R1:1,R1:2)

SEL 500V 60ms

70ms 80ms

figure 2.5 (b) The waveforms.

50An

0.2 ms

Times (ms)

figure 2.6 The current waveform in Example 2.3.

These fuses are selected based on their It rating, which is normally specified in a data sheet for a selected diode.

2.5 Snubber Circuits for Diode

Snubber circuits are essential for diodes used in switching circuits. It can save a diode from overvoltage spikes, which may arise during the reverse recovery process. A very common snubber circuit for a power diode consists of a capacitor and a resistor connected in parallel with the diode as shown in Fig. 2.7.

When the reverse recovery current decreases, the capacitor by virtue of its property will try to retain the voltage across it, which is approximately the voltage across the diode. The resistor, on the other hand, will help to dissipate some of the energy stored in the inductor, which forms the I loop. The dv/dt across a diode can be calculated as:

dv 0.632*5 0.632*5

и~ T RcCc

(2.2)

where is the voltage applied across the diode.

Usually the dv/dt rating of a diode is given in manufacturer datasheets. By knowing dv/dt and R, one can choose the value of the snubber capacitor Q. Here R can be calculated from the diode reverse recovery current:

(2.3)

The designed dv/dt value must always be equal or lower than the dv/dt value found from the data sheet.

Emitter

Gate

-ЛЛЛг-

n- drift

p+ substrate

Collector

С

N-MOSFET

2.6 Series and Parallel Connection of Power Diodes

For specific applications when the voltage or current rating of a chosen diode is not enough to meet the designed rating, diodes can be connected in series or in parallel. Connecting them in series will give the structure a high voltage rating that may be necessary for high-voltage applications [2]. However, one must ensure that the diodes are properly matched, especially in terms of their reverse recovery properties. Otherwise, during reverse recovery there may be large voltage unbalances between the series-connected diodes. Additionally, due to differences in reverse recovery times, some diodes may recover from the phenomenon earlier than the others, thereby causing them to bear the full reverse voltage. All of these problems can effectively be overcome by connecting a bank of a capacitor and a resistor in parallel with each diodes as shown in Fig. 2.8.

If a selected diode cannot match the required current rating, one may connect several diodes in parallel. In order to ensure equal current sharing, the designer must choose diodes with the same forward voltage drop properties. It is also important to ensure that the diodes are mounted on similar heat sinks and are cooled (if necessary) equally. This will affect the temperatures of the individual diodes, which in turn may change the diode forward characteristics.

figure 2.7 A typical snubber circuit.

figure 2.8 Series-connected diodes with necessary protection.

Tutorial 2.1 Reverse Recovery and Overvoltages

Figure 2.9 shows a simple switch mode power supply. The switch (1-2) is closed at t = OS. When the switch is open, a freewheehng current = 20A flows through the load (RL), freewheehng diode (DF), and the large load circuit inductance (LL). The diode reverse recovery current is 20 A and it then

from time zero to time the current will decay at a rate of 20A/S and will be zero at = 20/20 = l/iS. The reverse recovery current starts at this point and according to the given condition becomes 20 A at From this point on, the rate of change remains unchanged at 20A/iS. Period 2 - is found:

20 A 20 A/iS

= 1 iS

From 2 to % the current decays to zero at the rate of 20A/iS. The required time is

figure 2.9

diode.

A simple switch mode power supply with freewheeling

decays to zero at the rate of 10 A/iS. The load is rated at 10 Q and the forward on-state voltage drop is neglected.

(a) Draw the current waveform during the reverse recovery (/) and find its time (t).

(b) Calculate the maximum voltage across the diode during this process (/).

Solution, (a) A typical current waveform during reverse recovery process is shown in Fig. 2.10 for an ideal diode.

When the switch is closed, the steady-state current is = 200 V/10 Q = 20 A, because under the steady-state condition the inductor is shorted. When the switch is open, the reverse recovery current flows in the right-hand side loop consisting of LL, RL, and DF. The load inductance LL is assumed to be shorted. Hence, when the switch is closed, the loop equation is [3]:

dis V

V = L

from which

= - = = 20A/,S

At the moment the switch is open, the same current keeps flowing in the right-hand side loop. Hence,

did dis

= --=-20 A/iS dt

h-h =

20 A 10 A/iS

= 2iS

Hence the actual reverse recovery time: (1 + 1 + 2) - 1 = 3 iS.

(b) The diode experiences the maximum voltage only when the switch is open. This is due to both the source voltage 200 V and the newly formed voltage caused by the change in current through inductor L The voltage across the diode.

y = -yj L- = -200 + (10 X 10 )(-20 x 10) dt

= -400 V

Tutorial 2.2 Ideal Diode Operation,

Mathematical Analysis and PSPICE Modelling

This tutorial illustrates the operation of an ideal diode circuit. Most of the power electronic applications operate at a relatively high voltage and, in such cases, the voltage drop across the power diode is usually small. It is quite often justifiable to use the ideal diode model. An ideal diode has a zero conduction drop when it is forward-biased and has zero current when it is reverse-biased. The equations and the analysis presented here are based on an ideal diode model.

figure 2.10 Current through the freewheeling diode during reverse recovery.

figure 2.11 Circuit diagram.

Circuit Operation A circuit with a single diode and a very common RL load is shown in Fig. 2.11. The source is an alternating sinusoidal source. Suppose = sin(a;t). is positive when 0 < wt < n, and is negative when n < cot < In. When Vs starts to become positive, the diode begins conducting and the positive source keeps the diode in conduction until (Dt reaches n radians. At that instant (defined by cot = я radians), the current through the circuit is not zero and there is some energy stored in the inductor. The voltage across an inductor is positive when the current through it is on the increase and it becomes negative when the current through it tends to fall. When the voltage across the inductor is negative, it is in such a direction as to forward bias the diode. The polarity of voltage across the inductor is as shown in Figs. 2.12 and 2.13.

When Vs changes from a positive to a negative value, there is current through the load at the instant cot = n radians and the diode continues to conduct until the energy stored in the inductor becomes zero. After that the current tends to flow in the reverse direction and the diode blocks conduction. The entire applied voltage now appears across the diode.

Circuit Analysis The expression for the current through the diode can be obtained from the following mathematical analysis [7]. It is assumed that the current flows for 0 < (Dt < where P > n, when the diode conducts, and the

figure 2.12 Current rising, 0 < wt < л/2.

driving function for the differential equation is the sinusoidal function defining the source voltage. During the period defined by P < cot < 2n, the diode blocks the current and acts as an open switch. For this period, there is no equation defining the behavior of the circuit. For 0 < cot < P, Eq. (2.4) applies [7].

L + Ri = sm(e), where - 0 < 9 < P (2.4) dt

LRi = 0 dt

(2.5)

(2.6)

i(0) = Ae

-RO (dL

Assuming a linear differential equation, the solution is found in two parts. The homogeneous equation is defined by Eq. (2.5). It is preferable to express the equation in terms of the angle в instead of t. As в = (Dt, then dO = CD.dt. Then Eq. (2.5) is converted to Eq. (2.6). Equation (2.7) is the solution to this homogeneous equation and is called the complementary integral.

The value of constant A in the complementary solution is to be calculated. The particular solution is the steady-state response and Eq. (2.8) expresses it. The steady-state response is the current that would flow in steady-state in a circuit that contains only the source, the resistor, and the inductor as shown in the circuit in Fig. 2.11, where the only element missing is the diode. This response can be obtained using the differential equation, the Laplace transform, or the ac sinusoidal circuit analysis. The total solution is the sum of both the complementary and the particular solution. It is shown in Eq. (2.9). The value of A is obtained using the initial condition. As the diode starts conducting at cot = 0 and the current starts building up from zero, i(0) = 0. The value of A is expressed by Eq. (2.10).

Once the value of A is found, the expression for current is known. After evaluating A, current can be evaluated at different values of cot, starting from cot = я. As wt increases, the current continues to decrease. For some value of cot, say , the current would be zero. If cot > , the current would drop to a negative value. As the diode blocks current in the reverse direction, the diode stops conducting when cot is reached. Then an expression for the average output voltage can be obtained. Because the average voltage across the inductor has to be zero, the average voltage across the resistor and at the cathode of the diode are the same. This average value can be obtained as shown in Eq. (2.11).

figure 2.13 Current falling, %/2 < wt < %.

41)

sin(cot - a)

(2.8)

where a = atan, and = -\- coP

= [z)

(2.9) (2.10)

Hence, the average output voltage: E

oavg-

sme.de = -[l-cos(l])]

(2.11)

figure 2.14 PSPICE circuit to study the diode R-L circuit.

PSPICE Modelling: For modelling the ideal diode using PSPICE, the circuit used is shown in Fig. 2.14. Here the nodes are numbered. The ac source is connected between nodes 1 and 0. The diode is connected between nodes 1 and 2 and the inductor hnks nodes 2 and 3. The resistor is connected from 3 to the reference node, that is, node 0.

The PSPICE program in text form is presented here:

*Half-wave rectifier with RL load *An exercise to find the diode current VIN 1 0 sin(0 100 V 50 Hz) Dl 1 2 Dbreak LI 2 3 10 mH Rl 3 0 5Q

.MODEL Dbreak D(IS=10N N=1 BV=1200 IBV=10E-3 VJ=0.6)

.TRAN 10is 100 is 60is 100 is

.PROBE

.OPTIONS (ABSTOL=lN RELTOL=.01 VNTOL=lMV) .END

The diode is characterized using the MODEL statement. The TRAN statement controls the transient operation for a period of 100 ms at an interval of 10 ms. The OPTIONS statement sets limits for tolerances. The output can be viewed on the screen because of the PROBE statement. A snapshot of various voltages/currents are presented in Fig. 2.15.

It is evident from Fig. 2.15 that the current lags the source voltage. This is a typical phenomenon in any inductive circuit and is associated with the energy storage property of the inductor. This property of the inductor causes the current to change slowly, governed by the time constant т = tan~(a; i). Analytically, this is calculated by the expression in Eq. 2.8.

figure 2.15 Voltage/current waveforms at various points in the circuit.