## Cem Cem Cem Cem

Only 3 external components 2.56 > 90 efficiencies over wide iout range (1mA to 225mA) 2.96 > 90 efficiencies over wide l0ut range, drives external 1.60 P-channel FET Same as MAX649 651 but 96.5 duty cycle and only 100mV 1.60 current sense limit High power, few external components 4.52 6.83 High power, few external components 3.00 High power, few external components 3.00 High power, few external components 3.00 High power, few external components 3.00

## Symbols Units and Conversion Factors

Symbols Frequently Used in This Book Ab Winding area of a core bobbin (usually given in square inches) Ae Effective core area (usually given in square centimeters) Aj Inductance of core (usually given in millihenries per 1000 turns Br Remanence flux density of a core material (flux density at zero oer Bs Saturation flux density of a core material Dcma Current density in wire (usually expressed in circular mils per rms ampere) lm Effective path length of a magnetic core (usually quoted in...

## 0 V

Figure 2.10 Forward converter topology. Showing feedback loop closed around one master No , which is regulated against line and load changes. Also two semiregulated slaves ('Vtl and Vs2) which are regulated against line changes only. The topology is an outgrowth of the push-pull circuit of Fig. 2.1 but does not suffer from the latter's major shortcoming of flux imbalance. Since it has one rather than two transistors, compared to the push-pull, it is more economical in dollars and required...

## 000025

And from Eq. 15.5, for an Ipmd of 0.25 mA, an Ipl of 4.61 A, and an Rs of 0.25 ft And to minimize drift in EA2 (Fig. 15.7), R3 is set equal to R2. 15.4.5 Boost switching frequency with the UC 3854 In addition to determining the current out of the M& D at pin 5, because of internal circuit details, R1A also sets the boost switching frequency. Once R1A has been fixed, the boost switching frequency is fixed by where Cll is the capacitor to ground at pin 14. For7 14 in ohms and Cll in farads, F...

## 0075

The remaining height in bobbin must accommodate primary-to-secondary insulation plus the filament wires (about one turn of no. 22 wire at 0.0281-in diameter). Obviously the E625 core is marginal of the other two, the ETD44 appears preferable. 16.6.7 Toroidal core transformer for current-fed topology The circumference of the inside diameter (ID) of a toroid (it X ID) is much greater than the bobbin width of an EE core of roughly equal Ae. Hence the toroid permits more turns per layer than the EE...

## 01

Figure 4.8 Circuit during Q1 and Q2 off time. Current Ix, stored in Lm during Ql, Q2 on time, also flows through leakage inductance L,. During the off time, energy stored in Lm must be delivered to the secondary load as reflected into the primary across Lm. But also flows through Lh and during the off time, the energy it represents VzL , I2) is returned to the input source Vdc through diodes Di, D2. This robs energy which should have been delivered to the output load and continues to rob energy...

## 015 011

Figure 4.2 Inductance per 1000 turns (Alg) for various ferrite cores with various air gaps. Also the point in ampere turns cliff' point where saturation commences. (Courtesy Ferroxcube Corporation.) Figure 4.2 Inductance per 1000 turns (Alg) for various ferrite cores with various air gaps. Also the point in ampere turns cliff' point where saturation commences. (Courtesy Ferroxcube Corporation.) available for all cores at various air gaps, Eq. 4.14 would give the number of turns for any selected...

## 02

2.0 Figure 13.10 Gain curve for the zero-voltage-switching circuit of Fig. 13.(Courtesy Jovanovic, Tabisz, Lee) no current industry-wide consensus on the future or even the present value of resonant power supplies. It is of interest to consider the pros and cons on the subject. First, it is interesting to note that to the author's knowledge, resonant power supplies are not listed in any of the major manufacturers' catalogs. This may indicate that resonant supplies are presently not...

## 02 X 141p 0282p

Now select V as 10 percent above V the sine wave peak at maximum rms input voltage. Then - ( V> T T 1--I (15.12) But Vp Vp VrmJVrms. And taking V , 90 V and V 250 V from Eq. 15.12, ( Ilf o 0-67371 (1513) Thus for Vrms 90 V, frequency 100 kHz (t 10 xs), e 85 percent, and po - 250 W, from Eq. 15.14 i-i 3.37(902)(10 X 10 6)(0.85) QOQ L1 _ 928 15.4.7 Selection of boost output capacitor Refer to Fig. 15.10. The boost capacitor Co usually feeds a DC DC converter generally a half bridge for output...

## 025r1

Since the doubled-frequency forward converter has twice the rms current, it will have twice the wire area of the original converter of half the output power. And since it has half the number of primary turns, its resistance is one-fourth the resistance of the original forward converter. With twice the rms current, its I2R losses are equal to that of the original forward converter of half the output power. 7.3.3 Derivation of output power relations for half-bridge topology The half bridge is...

## 03

Figure 10.2 Toshiba MB amorphous core, BH loop at 100 kHz. In magnetic-amplifier operation, the core moves along a minor loop 01234567890. In going from 1 to 4, the core is on the steep part of the hysteresis loop and the MA has high impedance. At point 4, the core saturates and the MA has essentially zero impedance. At the end of the Q1 on time (Fig. 10.1), the core is reset to Bv The time to move from Bx to +B, is the switch-open time. The further down Bx is pushed, the longer the blocking or...

## 04

Figure 8.17 Direct coupling from emitter of output transistor in PWM chip. When Ql is on, totem-pole driver Q2 turns on power transistor Q4 with base current limiting determined by R2, Z1. Capacitor Cl takes on a charge equal to the zener voltage ( - 3.3 V). When Ql turns off, Q3 emitter falls to about +0.6 V and right-hand side of Cl forces Q4 base down to about - 3 V, turning it off rapidly. emitter bias and is off. On the way down, when Q3 is turning on, Q2 has a 0.6-V reverse base-emitter...

## 05

Frequency (kHz) Figure 10.5d (Continued) for Metglas 2714A are shown in Fig. 10.5c. Data comparing core loss versus frequency at a peak flux density of 2000 G for Toshiba MA, MB material and 1-mil Permalloy are given in Fig. 10.5< i. Note that figure gives loss in watts per cubic centimeter. For MA, MB density of 8.0 g cm3, loss in watts per pound is 56.8 x loss in watts per cubic centimeter. The BH loops at 100 kHz for Toshiba MA, MB material and Vfe-mil Permalloy are shown in Fig. 10.6a....

## 05 1 0 15 2 0 2 5 3 0 J

150 200 250 300 350 400 450 DC GATE TRIGGER CURRENT(IaT) -mA 150 200 250 300 350 400 450 DC GATE TRIGGER CURRENT(IaT) -mA Figure 6.3 (a) Switching times. Typical switching time t , td, tr versus gate-trigger current. (6) Relationship between off-state voltage, on-state current, and gate-trigger voltage showing reference points for definition of turnon time t Note Figure 6.3a, 6.36 illustrate the original RCA S7310 a type of SCR very similar to the Marconi type ACR25U.)

## 050

Expensive, may be able to operate at the desired current with no heat sink at all. The next criterion for selection is the operating frequency. Higher-frequency devices can use smaller inductors (LI, Fig. 17.1a), which is important as this is likely to be the largest and, next to the regulator, the most expensive component. 17.2.6 Component selection for boost regulators3 Once the regulator chip has been selected, the major components whose magnitude is to be chosen are (Fig. 17.1a), LI, D1,...

## 053 T1

P0 Eff(Vdc)(0.4)(2Ip) Forward converter VDE specifications generally require three layers of 1-mil-thick insulating material if secondaries are to be sandwiched in between halves of the primary (as usually done to reduce proximity-effect copper losses), that wastes 6 mils of bobbin height. Finally, there is the practical problem that it is difficult to safely assemble the core and bobbin if the full bobbin height is fully utilized. 3. Primary current waveshape is as shown in Fig. 7.3. At...

## 073

Thus the Baker clamp has satisfactorily solved two significant problems. It prevents a sufficient forward bias on the base-to-collector junction to cause appreciable storage time. It also permits the circuit to work equally well with large changes in load current and over a large production spread in transistor beta because of the redistribution of input currents between D2 and D3 as base current demands change. However, it is still desired to provide reverse base current to at the instant of...

## 074

If the 3019 ferrite core is selected, its bobbin width is 0.459 in and height is 0.198 in. For a no. 26 wire diameter of 0.0182 in, the number of turns per width is 0.459 0.0182 25. The number of layers per bobbin height is 0.198 0.0182 10. Thus the 138 turns could be accommodated within six layers. If any of the above toroidal cores were selected, the 138 turns could easily be accommodated in three layers. The skin effect is no problem as the AC amplitude is small, and Table 7.6 shows...

## 08t 2t

But the rms value of a rectangular waveform of amplitude 7pft, duty cycle of 0.4, is rms IpilV0A or pft 1.58 rms. Then AT time, s for this flux change 0.471 At Vdc(min), AB AT fimax 0.4r. Then for f l T from Eq. 7.2 1.265NpBmaxAef x 10 8( rms) (7.3) Now assume that primary and all secondaries operate at the same current density Dcma in circular mils per rms ampere. Bobbin area occupied by the reset winding is assumed negligible as it carries only magnetizing current and its wire size is usually...

## 1

The feedback loop regulates against DC input voltage changes by decreasing Ton as Vdc increases, or increasing toa as Vdc decreases. 4.4.2.2 Input, output current-power relations. In Fig. 4.6, the output power is equal to the output voltage times the average of the secondary current pulses. For equal to the current at the center of the ramp in the secondary current pulse Figure 4.6 Current-on-time relations in a continuous-mode flyback. Current is delivered to the load only during the off time....

## 1 6 V

Tr 16 x 106 2tt (L1 + L2)Ci and from Eqs. 6.14a, 6.15a, C 0.024 xF, Lx + L2 275 xH. A choice of a lower value for tjtt would have yielded a lower maximum SCR voltage stress (Table 6.1) and hence possibly greater reliability. But it would have resulted in larger values of tt (lower trigger frequencies), and at low output power, the resulting value of tt (Eq. 6.12) would have brought trigger frequency down far into the audible frequency range. 6.5 Cuk Converter Topology Introduction14 16 In its...

## 1 ka und i VNArtL

The first integrated-circuit pulse-width-modulating control chip. (Courtesy Silicon General Corp.) Figure 5.2 (b) PWM UC1846. The first integrated-circuit current-mode control chip. (Courtesy Unitrode Corp.) Figure 5.2 (b) PWM UC1846. The first integrated-circuit current-mode control chip. (Courtesy Unitrode Corp.)

## 1 Ut

Or 1 JT 0.5934 and t 11.87 xs, ioff 8.13 xs and from Eq. 4.19 and the average of the secondary current pulse which should equal the DC output current is I (secondary average) csr(i0ff ') 24.59 x 8.13 20 10.0 A, which checks. From Eq. 4.20 7cpr 1.25 x 501 (38X11.86 20) 2.77 A. From Eq. 4.22, for the minimum input power of 5 W at the minimum DC input voltage of 38 V, Lp 37 x 38(11.86)2 x 1012 2.5 x 5 x 20 x 10 6 791 ixH. The contrast between the discontinuous and continuous mode can now be seen...

## 1 V

It can be seen from Eq. 17.7 or 17.8 that for a constant toS, as Vn goes up, to keep V constant, frequency f must go up. Regulation can be seen as follows (Fig. 17.12). When Q1 is on, P drive, pin 1 is low, keeping the P-channel MOS-FET on. And N drive, pin 14 is also low, keeping the iV-channel MOS-FET off. The four elements No, II, Na, 12 form a set-reset flip-flop (FF1), and hence the P and N drive outputs remain locked in the low state, keeping Ql on and Q2 off until the flip-flop is reset....

## 10

Figure 10.12 Toshiba amorphous MB cores. Temperature rise versus core losses. (Courtesy Toshiba Corp.) Now the number of turns on MA and its iron area must be chosen to block 51 V. But they will be chosen to block not for the 1 xs of minimum blocking time, but for the full 4 p.s corresponding to the maximum duration of Vsp on the assumption that the MA may be used to force the slave output voltage completely down to zero. Assume that for a 100-kHz magnetic amplifier, an amorphous core such as...

## 100

Note Skin depths are taken from Table 7.5 RJRic from Eq. 7.21. Note Skin depths are taken from Table 7.5 RJRic from Eq. 7.21. However, Table 7.6 should not be misinterpreted. Although Fig. 7.6 shows that Rac Rdc increases as wire diameter increases (d S increases), Rac actually decreases as wire diameter increases and larger wire sizes will yield lesser core losses. This, of course, is because Rdc is inversely proportional to d2 and decreases more rapidly than Rac decreases as a result of...

## 1000

Note Data are for bipolar magnetic circuits (first- and third-quadrant operation). For unipolar circuits (forward converter, flyback), divide by 2. Association (MMPA)5'6 and IEC publications from the American National Standards Institute.7 The various core geometries shown in Fig. 7.2 are pot or cup cores, RM cores, EE cores, PQ cores, UU or UI cores. The pot core is shown in Fig. 7.2e. It is used mostly at low power levels up to 125 W and usually in DC DC converters. Its major advantage is...

## 101 Introduction

In Sees. 2.2.1 and 2.3.3, multi-output-voltage push-pull and forward converter topologies were discussed. As was described, in either circuit, a feedback loop is closed around a main or master (usually the highest-current or 5-V) output. The feedback loop keeps the master output constant against line or load changes. Additional secondaries on the power transformer yield slave output voltages whose magnitudes are proportional to their respective numbers of turns. These slaves are operated...

## 102 Linear and Buck Regulator Postregulators

A linear regulating postregulator is the best approach for output currents up to 1.5 A. The 1.5-A limit comes about because of low cost and low internal dissipation. Linear regulators with up to 1.5 A of output current are available as integrated circuits in plastic T0220 packages at a cost of about 500. They require no additional external components other than a small filter capacitor. They are usually specified as requiring 2 V (typically, 3 V for the worst case) minimum input-output...

## 1033 Magneticamplifier core resetting and voltage regulation

Thus far only the transition of the core from its starting point Bl up to saturation has been discussed. During tf, the MA impedance is essentially zero and it delivers the characteristic ramp-on-a-step current waveform demanded by the output LC filter. At the end of the Q on time and prior to the start of the next on time, the core must be restored to the B1 level on the hysteresis loop, which yields the correct blocking time on the next switching cycle. If no current is delivered into MA in...

## 1034 Slave output voltage shutdown with magnetic amplifiers

Heretofore, the magnetic amplifier was presented only as a means of voltage regulating the slave output voltage. That was done by controlling the flux level to which the core is reset at the end of the power transistor on time. The further down Bx was pushed, the longer the blocking time tb, the shorter the firing time tf, and hence the lower the DC output voltage. The magnetic amplifier can also be used to shut down the DC output voltage completely. This is done by pushing the initial flux...

## 1036 Core loss and temperature rise calculations

Toshiba provides curves useful in calculating core temperature rise for each of its cores. Figures 10.9, 10.10, and 10.11 show core loss versus toted flux change in maxwells for its three largest MB cores. Recall that flux change in maxwells equals flux density change in gauss multiplied by core area in square centimeters. Thus, dividing the maxwells shown in the curves by the core area gives the flux density change in gauss. The maximum maxwells shown on the curves then correspond to the total...

## 1037 Design examplemagneticamplifier postregulator

Design a magnetic-amplifier postregulator for the output of the forward converter shown in Fig. 10.13a. Specifications are Forward converter switching frequency 100 kHz Slave output voltage 15 V The main output voltage is Vom Vdc(Nsm Np)(tOQ T). The main feedback loop, in keeping Vom constant, then must keep the product Vdcton constant. Thus ton is a maximum when Vdc is a minimum. In the usual case, the number of turns on the T1 reset winding Nr is set equal to the turns on the power winding...

## 1038 Magneticamplifier gain

When the MA has fired, it has close to zero impedance and the DC current through it is determined only by the DC output impedance and the slave output voltage. That is simply the specified DC output current. But to bring the MA to its fired state, a current equal to twice the coercive current Ic is required to force the core from the left to the right side of the hysteresis loop (Fig. 10.2). That current comes from the transformer secondary Vsp. Similarly, when the core is reset to the left...

## 104 Magnetic Amplifier Pulse Width Modulator and Error Amplifier

Thus far, in this chapter, magnetic amplifiers as postregulators only have been considered. In this section, an interesting example of the use of a magnetic amplifier used simultaneously as a pulse-width modulator and error amplifier is described.9 It may be puzzling why, with the current enormous proliferation of inexpensive semiconductor pulse-width modulating chips with their built-in width modulators and error amplifiers, there is interest in magnetic elements to perform these functions....

## 111 Introduction

In topologies which have a transformer in series with their power transistor (all except the buck regulator), switching losses due to the overlap of falling current and rising voltage across the power transistor during the turnoff interval account for most of the losses. The integral JI(t)V(t)dt over the turnoff interval, which may last anywhere from 0.2 to 2 xs (for bipolar transistors), generally has a very high peak value. Even averaged by the turnoff duty cycle, it can be two to four times...

## 113 RCD Turnoff Snubber Operation

In Fig. 11.1a, when the Q1 base receives its turnoff command, the transformer leakage inductance attempts to maintain the peak on current which had been flowing just before the turnoff command. That peak current divides in some way between the off-turning collector and CI through diode D1 which has latched in. The amount of current IC1 flowing into CI slows up the collector voltage rise time, and by making CI large enough, the rising collector voltage and falling collector current intersect so...

## 114 Selection of Capacitor Size in RCD Snubber

Equation 11.2 shows that power dissipation in i l is proportional to CI. Hence there must be some procedure to select CI large enough to adequately slow up collector voltage rise time and yet not cause excessive dissipation in i l. There is no best way to select CI. It is done in different ways by different designers who make different assumptions as to how much of the peak current in Q1 is available to charge CI, how much the Ql collector voltage rise time is to be slowed up, and how fast the...

## 115 Design ExampleRCD Snubber

Design the RCD snubber for the forward converter of Sec. 11.2. Recall that the peak current Ip just before turnoff was 3.45 A, transistor fall time was 0.3 xs, and transistor dissipation without a snubber was 19 W. From Eq. 11.3 _ (3.45 2)(0.3 x 106) 2 x 184 0.0014 (juF But recall that a forward converter transformer is designed so that maximum transistor on time is at minimum DC voltage and will be forced to be 0.8772. For a switching frequency of 100 kHz, this is 4 xs. But in Sec. 11.2,...

## 1151 rcd snubber returned to positive supply rail

The RCD snubber is often (and preferably) returned to the positive supply rail as shown in Fig. 11.3. It works exactly in the same way as when it is returned to ground as in Fig. 11.1. At turnoff, D1 latches in and CI slows up collector voltage rise time with its charging current flowing into Vdc. At the following turnon, CI is discharged through Ql and the supply source Vdc. The advantage of returning i l, D1 to Vdc instead of to ground is Figure 11.3 When snubber is returned to positive rail,...

## 117 Snubber Reduction of Leakage Inductance Spike to Avoid Second Breakdown

The snubber offers a second very important advantage in addition to slowing up voltage rise time and thus decreasing average transistor dissipation. It prevents second breakdown, which occurs if the instantaneous voltage and current cross the reverse-bias safe operating area (RBSOA) boundary given in the manufacturer's data sheets (Fig. 11.5). This boundary can be crossed by the omnipresent leakage inductance spike (Fig. 2.10) which occurs at the instant of turnoff. Transistor manufacturers...

## 120220 V Ac

Figure 13.4 (a) A series-loaded resonant half bridge. Inductance Lr resonates with capacitance Cr The load is reflected by 71 in series with the resonant circuit. Transistors are turned off directly after the end of the first half cycle of resonant current to achieve zero current switching. In series loading, the output filter is capacitive. (6) A parallel-loaded resonant half bridge. Inductance Lr resonates with capacitance C The load is reflected by T1 in shunt with the resonating capacitor....

## 121 Introduction

Before going into the details of stabilizing a feedback loop, it is of interest to consider in a semiquantitative way, why a feedback loop may oscillate. Consider the negative-feedback loop for a typical forward converter in Fig. 12.1. The essential error-amplifier and PWM functions are contained in all pulse-width-modulating chip. The chip also provide many other functions, but for understanding the stability problem, only the error amplifier and pulse-width modulator need be considered. For...

## 1210 Type 3 Error Amplifier When Used and Transfer Function

In Sec. 2.3.11.2, it was pointed out that the output ripple Vor Ra dl where Ra is the ESR of the filter output capacitor Ca and dl is twice the minimum DC current. Now most aluminum electrolytic capacitors do have an ESR. Study of many capacitor manufacturers' catalogs indicates that for such capacitors, R0C0 is constant and equal to an average value of 65 x 10 6. Thus, using conventional aluminum electrolytic capacitors, the only way to reduce output ripple is to decrease Ra, which can be done...

## 1211 Phase Lag through a Type 3 Error Amplifier as Function of Zero and Pole Locations

In Sec. 12.7, it was pointed out that the phase boost at a frequency Fco due to a zero at a frequency Fz is 0zb taxx 1(FcJFz) tan-1 K (Eq. 12.4). If there are two zeros at the frequency Fz, the boosts are additive. Thus boost at Fco due to two zeros at the same frequency Fz is e2zb 2 tan-1 K. Similarly, the lag at Fco due to a pole at Fp is 9Jp tan-1(lIK) (Eq. 12.5). The lags due to two poles at Fp are also additive. Thus lag at Fco due to two poles at Fp is 012p 2 tan_1(l ifj. The lag and...

## 1212 Type 3 Error Amplifier Schematic Transfer Function and Zero and Pole Locations

The schematic of a circuit which has the gain-versus-frequency characteristic of Fig. 12.146 is shown in Fig. 12.15. Its transfer function can be derived in the manner described in Sec. 12.6 for the Type 2 error amplifier. Impedances of the feedback and input arm are expressed in terms of the s operator, and the transfer function is simply G(s) Z2(s) Zl(s). Algebraic manipulation yields the following expression for the transfer function dV0 (1 + sR2Cl) l + s(Rl + R3)C3 G(S) dV sRl(Cl + C2)(l +...

## 1213 Design Example Stabilizing a Forward Converter Feedback Loop with a Type 3 Error Amplifier

Design the feedback loop for a forward converter having the following specifications Switching frequency 50 kHz Output ripple (peak to peak) < 20 mV Assume that the output capacitor is zero ESR. First the output LC filter and its Refer to Fig. 12.15. From Eq. 2.47 of the type advertised as having corner frequency are calculated. Now it was assumed that the output capacitor had zero ESR so that ripple due to ESR should be zero. But there is a small capacitive ripple component (Sec. 1.2.7)....

## 1214 Component Selection to Yield Desired Type 3 Error Amplifier Gain Curve

There are six components to be selected CR1, R2, R3, CI, C2, C3) and four equations for zero and pole frequencies (Eqs. 12.12 to 12.15). Arbitrarily choose R1 1000 ft. Now the first zero (at 2000 Hz) occurs when R2 Xcl and the impedance of the feedback arm at that frequency is mainly that of R2 itself. Thus gain at 2000 Hz is R2 R1. From Fig. 12.16, gain of the error amplifier at 2000 Hz is +37 dB or a numerical gain of 70.8. Then for Rl IK, R2 70.8K, from Eq. 12.12, we obtain l 2u(0.08 x...

## 1215 Conditional Stability in Feedback Loops

A feedback loop may be stable under normal operating conditions when it is up and running, but can be shocked into continuous oscillation at turnon or by a line input transient. This odd situation, called conditional stability, can be understood from Fig. 12.17a and 12.176. Figure 12.17aand 12.176 contains plots of total open-loop phase shift and total open-loop gain versus frequency, respectively. Conditional stability may arise if there are two frequencies (points A and C) at which the total...

## 1216 Stabilizing a Discontinuous Mode Flyback Converter

12.16.1 DC gain from error-amplifier output to output voltage node The essential elements of the loop are shown in Fig. 12.18a. The first step in designing the feedback loop is to calculate its DC or low-frequency gain from the error-amplifier output to the output voltage node. Assume an efficiency of 80 percent. Then from Eq. 4.2a

## 1217 Error Amplifier Transfer Function for Discontinuous Mode Flyback

In Fig. 12.19, for Ro(min), on curve EFGH, Fm will be established at one-fifth the switching frequency (point PI) as stated in Sec. 12.3. Most often, Fc0 will occur on the horizontal slope of the output circuit transfer function. To force Fco to be at the desired point, the error amplifier will be designed to have a gain at Fco (point PI) equal and opposite to the output circuit loss at point PI. Since the slope of EFGH at Fco is horizon tal, the error-amplifier gain slope must be -1 (in the...

## 124 Error Amplifier Transfer Function Poles and Zeros

The circuit of an operational amplifier with a complex impedance Zx input arm and a complex impedance Z2 feedback arm is shown in Fig. 12.9. Its gain is Z2jZ1. If Zx is a pure resistor i l and Z2 is a pure re- Figure 12.8 Where to locate break frequencies Fz and Fp. The farther apart Fz and Fp are spread, the greater the phase margin. But spreading them further apart reduces low-frequency gain, which reduces the degeneration of low-frequency line ripple. It also increases high gain, which...

## 125 Rules for Gain Slope Changes Due to Zero and Pole Frequencies

The zero and pole frequencies represent points where the error-amplifier gain slope changes. A zero represents a +1 change in gain slope. Thus (Fig. 12.10a), if a zero appears at a point in frequency where the gain slope is zero, it turns the gain into a +1 slope. If it appears where the original gain slope is -1 (Fig. 12.106), it turns the gain slope to zero. Or if there are two zeros at the same frequency (two factors in the numerator of Eq. 12.3 having the same RC product) where the original...

## 127 Calculation of Type 2 Error Amplifier Phase Shift from Its Zero and Pole Locations

Adopting Venable's scheme,1 the ratio Fco Fz if will be chosen equal to Fp Fco K. Now a zero, like an RC differentiator (Fig. 12.26), causes a phase lead. A pole, like an RC integrator (Fig. 12.2a), causes a phase lag. The phase lead at a frequency F due to a zero at a frequency Fz is But we are interested in the phase lead at Fco due to a zero at a frequency Fz. This is 9ld(ati 0) tan1 (12.5) The phase lag at a frequency F due to a pole at a frequency Fp is and we are interested in the lag at...

## 128Phase Shift through LC Filter Having ESR in Its Output Capacitor

The total open-loop phase shift consists of that through the error amplifier plus that through the output LC filter. Figure 12.36 showed for Rn 20 VE CQ and no ESR in the filter capacitor, the lag through the filter itself is already 175 at 1.2F0. This lag is modified significantly if the output capacitor has an ESR table 12.1 Phase Lag through a Type 2 Error Amplifier for Various Values of K( FJFZ VFco) table 12.1 Phase Lag through a Type 2 Error Amplifier for Various Values of K( FJFZ VFco)

## 133 Resonant Converter Operating Modes

13.3.1 Discontinuous and continuous above resonance and below resonance operating modes Operating modes can be discontinuous as in Fig. 13.1. In the discontinuous mode (DCM), as noted, output voltage regulation is accomplished by varying the switching frequency. Power is delivered to the load as sequence of discrete current or power pulses separated by times long compared to their duration. If the output voltage must be raised because Vdc has gone down or DC load current has been increased, the...

## 14

MPP cores OD 0.8 in, ID 0.5 in, height 0.25 in, lm 5.09 cm. All inductances in microhenries. Note Magnetics Inc. MPP cores OD 0.8 in, ID 0.5 in, height 0.25 in, lm 5.09 cm. All inductances in microhenries. table 4.3 Maximum Number of Turns and Maximum Inductance at Those Turns for Various Peak Currents lp at a Maximum Inductance Falloff of 10 Percent from Zero Current Level

## 141v T

Then from Eq. 15.19, Ipk t 2.82PJEVrms Now assume nominal, minimum, and maximum rms input voltages of 120, 92, and 138 V. For V . 92 V, Pa 80 W, and E 0.95, (92)2 X 0.95T L1 H O 50To* (5'21) If a Ton of 10 xs is selected, LI is 500 (jlH from Eq. 15.21 which is reasonably small for a peak ramp current of I k t 1.41 X 92 x 10 X 10-6 (500 X 106) 2.59 A. Now the boosted voltage must be above the sine wave peak at maximum line input. For Vrms 138 V, the sine wave peak is 1.41 X 138 195 V. If it is...

## 142 Forward Converter Waveshapes

The circuit schematic for these waveshapes is shown in Fig. 14.1. It is a 125-kHz forward converter designed for 100 W, and waveshapes are shown at 80 and 40 percent of full load. Full-load outputs are 5 V at 10 A and 13 V at 3.8 A. Waveshapes are shown for nominal input volt- C, 160 HF, 100 V C2 3200 HF, 16 V C3 1500 (IF, 25 V C4. Cs 1.0 HF. 50 V D2, D3 MBR 1045 D4, 06 MBR 415 D,. 1N 4937 Q,. RFP 12N18 Vde 38-60 V C, 1.0 (iF Tl core-782E272-3F3 (Ferroxcube) Np-13 Turns, 2 18 in parallel N5-5...

## 144

This procedure was followed for three tentatively usable cores with the results shown in Table 16.7. It can be seen that although all three cores could be used, the E625 would be questionable because there would be marginally sufficient vertical height left in the bobbin for the secondary and filament winding after laying down the two half primaries. Thus, the secondary feeds two lamps at 0.43 rms A each. For a total of 0.86 rms A at 500 cmils rms A, the required area for the secondary wire is...

## 16

2.3.9.1 First-quadrant operation only. The transformer core in the forward converter operates in the first quadrant of the hysteresis loop only. This can be seen in Fig. 2.10. When Q1 is on, the dot end of T1 is positive with respect to the no-dot end and the core is driven, say, in a positive direction on the hysteresis loop and the magnetizing current ramps up linearly in the magnetizing inductance. When Q1 turns off, stored current in the magnetizing inductance reverses the polarity of...

## 170

Thus, guessing first at the 2616 pot core and proceeding to the 3019 pot core yields Table 16.4. Table 16.4 shows that the 2616 cannot be used because even with a 32-mil gap which requires 200 turns, the maximum ampere-turns at 1 A of current just barely rest at the saturation cliff. Increasing the gap would probably put NImax inside the cliff, but would require significantly more than 153 turns. Most likely, the core bobbin could not then accommodate the required turns of the appropriate wire...

## 172

Devices similar to Linear Technology regulators from the other major supplier of such IC regulators requiring only a minimum number of components external to the package. Control Package Temp. 1000-up Number_(VI_IV)_max ttyp) (mAtyp) Scheme Options* EV Kit Ranges** Features_( )

## 1a

Ground, and RA and D2 in series charge the positive end of C2 up to one diode drop below V0. Thus if the drops in Dl and D2 are almost equal, C2 is charged up to a voltage closely equal to V. Now the voltage across C2 moves up and down with the negative end of the internal reference voltage (GND pin), and it is that voltage which is regulated. Regulators like those in Fig. 17.16 are designed as buck regulators with the internal power transistor emitter connected to the Vsw pin so that it can...

## 2 4 6 810

Figure 16.2 Fluorescent lamp light output in lumens per watt. For T12(1.5-in lamp diameter) and T17(1.88-in lamp diameter) versus frequency. (From High-Frequency Fluorescent Lamps, Campbell, Schultz, Kershaw, Illumination Engineering, Feb. 1953.) smaller and lighter, had no audible noise, and was less expensive. And at this high frequency, the lamp showed no flicker and conducted and radiated EMI was easier to suppress. These advantages of high-frequency operation, though significant, could not...

## 2 B

For DC output current of 10 A, MA will be carrying the 10 A for a maximum of only 3 xs (maximum tf) at low DC input. Maximum rms current is then 10V3 10 5.48 A. At 500 circular mils per rms ampere, a wire area of 2739 circular mils is required. Two No. 19 wires in parallel provide 2 x 1290 or 2580 circular mils, which is close enough. The inner periphery of the Toshiba MB21 x 14 x 4.5 core is -it x 0.55 1.73 in. For the 0.0391-in diameter of No. 19 wire, the inner periphery can hold 1.73 0.0391...

## 2 Ll

Where E is in joules, Lx is in henries, and Ip is in amperes. During the Ql on time, the output current is supplied entirely from C0, which is chosen large enough to supply the load current for the time ton with the minimum specified droop. When Ql turns off, since the current in an inductor cannot change instantaneously, the current in LI reverses in an attempt to maintain the current constant. Now the no-dot end of LI is positive with respect to the dot end, and since the dot end is at Vdc,...

## 2 P

Thus for ymhu V - 70 370 - 70 300 V, Thu 30 ms, from Eq. 15.15, And for Pc 250 W and Ec 0.85, from Eq. 15.16, Co 0.88(429 X lO-6) 378, say, 400 mF Now the transformer in the DC DC converter must be designed so that the outputs remain within specification at the above-specified Vmhu or 300 V. This will be safely achieved, as discussed in Sec. 3.2.2.1, if the number of secondary turns is sufficient to yield high enough secondary voltages that the required output voltages are obtained at an on...

## 2 T

Figure 12.18 Discontinuous-mode flyback feedback loop. Figure 12.18 Discontinuous-mode flyback feedback loop. Referring to Fig. 12.186, it is seen that the PWM compares the output of the error amplifier Vea to a 0- to 3-V triangle. It generates a rectangular pulse whose width (Ton Fig. 12.18c) is equal to the time from the start of the triangle to its intersection with DC voltage level Veii. This Ton will be the on time of power transistor Ql. It is seen in Fig. 12.186 that Vea 3 T0JT or Ton...

## 200 X 1q6

Sprague 673D, 674D aluminum electrolytics Now assume a regulator boosting from +5 to +15 V with 25-W (1.66-A) output. Assume a Mallory VPR 200 mF capacitor rated at 25 V. Then from the above relation Then from the above relation, the peak-to-peak ripple is V r 4 dco (ESR) 4 X 1.66 X 0.145 0.963 V. Modern tantalum capacitors may have lower ESR and yield lower ripple. Ripple may be reduced by increasing capacitance, using capacitors with higher voltage ratings or paralleling capacitors. All these...

## 2000

10.0 100.0 POWER DISSIPATION (WATTS) 10.0 100.0 POWER DISSIPATION (WATTS) also calculated as above, is 1.90 in2. Also from Fig. 7.4c, neglecting copper losses, its temperature rise is only 57 C. It is thus verified that it is easier for smaller cores to deliver the powers shown in Fig. 7.2a and 1.2b at 1600 G and high frequency. It is of interest to compare the thermal resistance of some cores as measured by the manufacturer and as calculated Rt 80A0'70) from Fig. 7.4a (see Table 7,4). 7.5...

## 2045

Note From Eq. 7.7, P 0.00050Bmtu AeAiyDcmB, where P is in watts, Bmax in gauss, Ae and Ab in square centimeters, f in hertz, Z> cmtl in circular mils per rms ampere, bobbin winding space factor 40 percent. For Bm< UI 1600 G. For other Bm , multiply by Bm 1600. For ),, , 500 circular mils rms ampere. For other > , , multiply by 500 Dom . For push-pull topology, multiply powers by a factor of 2. Note From Eq. 7.7, P 0.00050Bmtu AeAiyDcmB, where P is in watts, Bmax in gauss, Ae and Ab in...

## 24

MPP cores OD 1.84 in, ID 0.95 in, height 0.71 in, lm 10.74 in. All inductances in microhenries. Note Magnetics Inc. MPP cores OD 1.84 in, ID 0.95 in, height 0.71 in, lm 10.74 in. All inductances in microhenries. the on time, that primary peak current, multiplied by the turns ratio Np Ns is driven into the secondary where it decays linearly as shown in Fig. 4.1c. In most cases, output voltages are low and input voltages are higher, resulting in a large Np Ns ratio and a...

## 2500

Figure 16.10 Fluorescent lamp operating voltages and currents. The source impedance and ballast impedance determine the ballast operating voltage at the manufacturer's specified operating current. Operating at currents lower than the manufacturer's specified value results in less input and less light power output. At higher currents than specified, power input and light power output increase but lamp lifetime is decreased. (From Fluorescent Lamp Light Sources, Illumination Engineering...

## 3

Or + L3) C3 - '8Vdc,mil- Thus from Eq. 6.1, which gives the product of (L3 + Lx), (C3), and Eq. 6.8, which gives their ratio, values of the resonating elements (L3 + L ) or (L3 + L2) and C3 are fixed for specified values of Vdc(min) and the maximum output current 7o(dc). The transformer turns ratio is fixed from Eq. 6.3. The ratio of L i L1 is chosen to minimize off-voltage stress on the SCRs. A smaller ratio is in the direction of lesser off stress and lesser dV dt stress. The precise ratio is...

## 3 13p

Pin 1.25 P0 Vdc(0.47pft) or 7ptt - (2.28) This is a valuable relation. It gives the equivalent peak flat-topped primary current pulse amplitude in terms of what is known at the outset the minimum DC input voltage and the total output power. This permits an immediate selection of a transistor with adequate current rating and gain if it is a bipolar transistor or with sufficiently low on resistance if it is a MOSFET type. It can be seen that for a forward converter, Eq. 2.28 shows 7pft is twice...

## 3 40

Figure 12.2 (a) An RC integrator has a gain dVa dVin of -20 dB decade beyond Fp VvnRlCl. If the scales are such that 20 dB is the same linear distance as 1 decade in frequency, a gain slope of - 20 dB decade has a -1 slope. Such a circuit is referred to as a -1 slope circuit. (6) An RC differentiator has a gain of +20 dB decade. At Fz H2-R2C2, where XC2 R2, gain asymptotically approaches 0 dB. If scales are such that 20 dB is the same linear distance as 1 decade in frequency, a gain slope of +...

## 3 6 91215

Figure 2.3 Hysteresis loop of a typical ferrite core material (Ferroxcube 3C8). Flux excursions are generally limited to 2000 G up to about 30 kHz by requirement to stay on the linear part of the loop. At frequencies of 100 to 300 kHz, peak flux excursions must be reduced to about 1200 or 800 G because of core losses at these higher frequencies. of the push-pull topology or to applications where simple and inexpensive fixes could avoid the problem. This subtle failure mode in push-pull...

## 3000

But in forward converters and flybacks, operation is over the first quadrant only. Since ferrite core losses are hysteresis losses only and these losses are proportional to the area of the hysteresis loop, it might be thought that in unipolar magnetic circuits where only half of the hysteresis loop is traversed, core losses would be half those given for bipolar circuits at the same peak flux density. There is considerable difference of opinion among...

## 350

250 300 350 400 450 500 550 600 650 700 750 Wavelength (nanometers) Figure 16.4 Spectral energy distribution from a 40-Wo white fluorescent lamp. In microwatts per nanometer (1 nm 10 A). The smooth curve is the continuous spectrum of energy generated by the white phosphorous. The discrete bands, 10 nm wide, represent energy generated by the mercury atoms in transition from a high to a low energy level. (Courtesy General Electric Bulletin Fluorescent Lamps.) 250 300 350 400 450 500 550 600 650...

## 38

With its large distributed air gap, it can tolerate a large DC current bias without saturating. It is available in a large range of different geometries. (Courtesy Magnetics Inc.) Figure 4.4 Falloff in permeability or A1 for MPP cores of various permeabilities versus DC magnetizing force in oersteds. (Courtesy Magnetics Inc.) Figure 4.4 Falloff in permeability or A1 for MPP cores of various permeabilities versus DC magnetizing force in oersteds. (Courtesy...

## 38 V 49 V

Lp (calculated in Sec. 4.3.2.7) 56.6 p,H Recall from Sec. 4.3.2.7 that Ca was calculated as 2000 i,F. But it was pointed out there that at the instant of turnoff, the peak secondary current of 66 A would cause a thin spike of 66 x 0.03 2 V across the anticipated ESR of 0.03 V for a 2000- xF capacitor. It was noted that either this thin spike could be integrated away with a small LC circuit or CD could be increased to lower its ESR. Here, both will be done. Capacitance Ca will be increased to...

## 4

Figure 5.7 Slope compensation in the UC1846 current-mode control chip. A positive ramp voltage is taken off the top of the timing capacitor, scaled by resistors i x, R2 and added to the voltage at the top of the current resistor R,. By choosing Rlt R2 to make the slope of the voltage added to V, equal to half the downslope of the output inductor current, reflected into the primary and multiplied by R the output inductor average current is rendered independent of power transistor on times....

## 401

Skin depth S 2837 Vf-, S in mils for F in hertz. *From Eq. 7.19. Skin depth S 2837 Vf-, S in mils for F in hertz. Thus Eq. 7.21 indicates that the wire's AC-to-DC resistance RaJ Rdc (1 + F) is dependent only on the ratio of wire diameter to skin depth. Figure 7.6 plots RaJRdc against the ratio d S from Eq. 7.21. 7.5.4 AC DC resistance ratio for various wire sizes at various frequencies Because of skin effect, the AC-to-DC resistance of round wire is dependent on the ratio of the...

## 46

Figure 16.11 (a) American National Standards Institute (ANSI) specifications for various fluorescent lamps (6) volt ampere characteristics at different operating currents for various hot cold cathode lamps. Figure 16.12 Block diagram of a modern fluorescent lamp light source. Output frequency of the DC AC inverter is set by a series or parallel self-resonant oscillator in the range of 20 to 50 kHz. The ballast is usually a capacitor or the controlled source impedance of a series LC resonant...

## 5

All cores have outer diameter (OD) 1.060 in, inner diameter (ID) 0.58 in, height 0.44 in, lm 6.35 cm. All inductances in microhenries. greater than the desired value is reached. The core at that point is the only one which can yield the desired inductance with only a 10 percent swing. The number of turns Nd on that core for a desired inductance Ld is within 5 percent given by where Al is the value in column 3 in Table 4.1. If, moving vertically, no core can be...

## 50

DT 50 PDRth VisionlIdRth or Id -- Figure 9.13 Typical DC current gain for the 2N6542 3 bipolar transistor. Gain of a bipolar transistor falls off with increasing output current, but that of a MOSFET does not. Maximum current in a MOSFET is limited only by junction temperature rise. (Courtesy Motorola Inc.) Figure 9.13 Typical DC current gain for the 2N6542 3 bipolar transistor. Gain of a bipolar transistor falls off with increasing output current, but that of a MOSFET does not. Maximum current...

## 6

Peak primary current from Eq. 4.9 is _ 38 x 9.49 x 1Q-6 p 52 x 10 6 6.9 A and the front end of the secondary current triangle is Isipeak, (Np Ns)Ip 9 x 6.9 62 A Tr (0.8 x 20) - 9.49 6.5 o,s, and the average value of the secondary current triangle (which should equal the DC output current of 10 A is

## 600

KoolMu 77439 Core OD 1-.84 in ID 0.94 in Ht 0.71 in Micrometal T250-26 Core OD 2.5 in ID 1.25 in Ht 1.0 in KoolMu 77439 Core OD 1-.84 in ID 0.94 in Ht 0.71 in Micrometal T250-26 Core OD 2.5 in ID 1.25 in Ht 1.0 in Figure 16.17 Geometry of candidates for core for current feed inductor LCF of Fig. 16.14a. The final choice, then, is based on a cost versus engineering performance comparison. The KoolMu 77439 (Fig. 16.17a) is smaller, has lower dissipation, but costs more. Its outside diameter (OD)...

## 656

Figure 6.27 Waveforms and data on the current-fed Royer driven from a buck regulator. Feedback is from the buck output. Same circuit as in Fig. 6.26. The material is produced in a thin ribbon tape, wound on a toroidal core and then encased in either aluminum or some nonmetallic case. The tape is available in either 1- or V2-m.il thickness. Core losses increase rapidly with frequency, and just as with power transformers, where higher frequencies require thinner laminations to minimize losses,...

## 710

It thus can be seen that at higher DC output voltages, the efficiency is significantly higher than at lower voltages. When realistic input line ripple voltages are assumed, efficiency for 5-V output for input line tolerances of 15 percent are in the range 32 to 35 percent. 1.2.4 Linear regulator efficiency versus output voltage When ripple is taken into account, the minimum headroom of 2.5 V must be guaranteed at the bottom of the ripple triangle at the low tolerance limit of the input AC...

## 724

Figure 14.19 Significant waveforms in 50-kHz flyback supply of Fig. 14.18. Figure 14.19 Significant waveforms in 50-kHz flyback supply of Fig. 14.18. large enough to limit the spike to a safe amplitude without causing too much dissipation ( 0.5C2(Vpeak)2 Tr) in snubber resistor i l. The waveforms show that as Vdc increases the pulse width required to maintain a constant master output voltage decreases. This of course is what the feedback loop will do when connected in. It is also seen that the...

## 727

The transistor currents shown in Fig. 6.24 show no sign of an end of on-time spike. The numerical data of Fig. 6.24 are summarized in Table 6.2. It is seen from Table 6.2 that efficiency has averaged about 71 percent with a constant load over the 38- to 60-V range of telephone industry specifications for power supplies. This compares to the 50.6 percent efficiency for the same Royer with the same 49.8-il load resistor without the series input inductor (Fig. 6.23). The voltage drop down to zero...

## 734

Operating Temp. 105 C Winding Area .188 in2. Mean Length of Turn 3.08 in. Flammability UL94-V2 Figure 16.19 Dimensions of the E21 core and bobbin. This core is a potential candidate for the current-fed parallel resonant push-pull topology of Fig. 16.14a. But its magnetizing inductance is the resonant inductor of the resonant tank circuit. Since there are constraints on how small the resonant capacitor is, this limits the magnetizing inductance to a relatively...

## 747

Figure 14.20 Significant waveforms in 50-kHz flyback supply of Fig. 14.18. Figure 14.20 Significant waveforms in 50-kHz flyback supply of Fig. 14.18. Voltage and current into 15 V rectifier (03, Fig. 14.18) Voltage and current into 5 V rectifier (D2, Fig. 14.18) Voltage and current into 15 V rectifier (03, Fig. 14.18) V15 current 0.39 A, voltage 19.39 V V5 current 2.08 A, voltage 5.00 V Voltage and current into 5 V rectifier (D2, Fig. 14.18) V,5 current 0.39 A, voltage 19.39 V V5 current 2.08...

## 756 Proximity effect

Proximity effect11-15 is caused by alternating magnetic fields arising from currents in adjacent wires or, more seriously, from currents in adjacent winding layers in a multilayer coil. It is more serious than skin effect because the latter increases copper losses only by restricting the conducting area of the wire to a thin skin on its surface. But it does not change the magnitude of the currents flowing only the current density at the wire surfaces. In contrast, in proximity effect, eddy...

## 780

Figure 14.13 Transformer center tap current and drain-to-source voltage (Q2i at minimum (photo PP13), nominal (photo PP14), and maximum (photo PP15) input voltage for one-fifth of maximum output currents. ing current or for a given maximum magnetizing current, from too low a total DC output current. The magnetizing current can become larger than originally specified if the two transformer halves inadvertently separate slightly, thus decreasing the magnetizing inductance and increasing the...

## 8

And at 500 cmils rms A, this would require wire of 966-cmil area. Possible wire choices are shown in Table 16.6. It is seen in Table 16.6 that the 7 primary could only barely fit inside the E21 bobbin using no. 20 wire which has somewhat more than the required circular-mil area. Since it requires 136 turns and using no. 20 wire, the bobbin can hold only 20 X 7 140 turns. With no. 21 wire, each half primary could be handled in three layers (23, 23, and 22 turns). This would leave 0.256 - 6 X...

## 81 Introduction

Over the past 5 to 8 years, bipolar power transistors have increasingly been replaced by MOSFET transistors in switching power supplies. New designs in the coming years will most frequently be done with MOSFETs. There will nevertheless remain some niche areas (perhaps low power applications, because of their lower cost) which will continue using bipolars. Thus because of some small remaining areas where bipolar transistors still offer some advantages and because the vast majority of the...

## 819

Figure 14.10 Significant waveforms in 200-kHz 85-W converter of Fig. 14.8. The assumption that the amplitude measured with a current probe in the drain as for photo PP6 is more valid than the measurement with the same probe in the transformer center tap (as photos PP1 to PP3) is verified by measuring voltage drop across a small current-monitoring resistor in series in the transistor source. Measurement with a current probe in series in the drain gives exactly the same absolute currents as does...