## 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...

## 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...

## 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....

## How To Repair Tektronix Switch Mode Powersupply

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...

## 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.) 406 Magnetics and Circuits Design . N 406 Magnetics and Circuits Design . N Figure 10.13 Design example of magnetic-amplifier postregulator. Magnetic amplifier blocks Vs< ) for a time tb and is a zero-impedance short circuit for a time tr. Then Vos Veo (UT). Time tf s controlled in a negative-feedback loop by the current that Q2 forces into MA via Dm. That current is controlled by error...

## 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...

## 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)....

## 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...

## 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...

## 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...

## 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...

## 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. 7.18, P 0.0014Bm fAeAJDaM, where P0 is in watts, Bmaj< in gauss, and Ab in square centimeters, in hertz, Dctlla in circular mils per rms ampere, bobbin winding space factor - 40 percent. For 3 . , 1600 G. For other Bm , multiply by B . 1600. For D 500 .11.1,1 , mila rms ampere. For other 1 > , ___multiply by r,00 > , ema Note From Eq. 7.18, P 0.0014Bm fAeAJDaM, where P0 is in watts, Bmaj< in gauss, and Ab in square centimeters, in hertz, Dctlla in circular mils per rms...

## 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 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...

## 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...

## 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)...

## 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...

## 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...

## 822 A spike of high base input current b1 at instant of turnon

To ensure fast collector current turnon, there should be a short spike of base current about two to three times the average value during the on time. This spike need last only about 2 to 3 percent of the minimum on time (Fig. 8.2a). The effect of this turnon overdrive can be seen in Fig. 8.26. If turnon speed is not a factor, base input current Ibl) for a desired collector current (Jcl)need be only that required to bottom Vce to the saturation voltage Vce(sat) at the intersection of the...

## 823 A spike of high reverse base current a at the instant of turnoff Fig 82a

If base input current is simply dropped to zero when it is desired to turn off, collector current will remain unchanged for a certain time (storage time ts). Collector voltage will remain at its low Vce(sat) value of about 0.5 V and when it finally rises, will have a relatively slow rise time. This comes about because the base-to-emitter circuit acts like a charged capacitor. Collector current keeps flowing until the stored base charges drain away through the external base-to-emitter resistor....

## 83 Baker clamps

The transformer-driven Baker clamp1-4 is a widely used base drive scheme. It is inexpensive in dollars, is low in component count, and provides all six features described in Sees. 8.2.1 to 8.2.6. Since it is transformer-driven, it also nicely solves the problem of coupling a width-modulated pulse originating on output ground (where the PWM chip and housekeeping supply are best located for off-the-AC-line supplies) to the base of the power transistor on input ground (see Fig. 6.19 and Sec....

## 831 Baker clamp operation

In Fig. 8.6, a large current Ix of the desired pulse width is provided at the anode of D2. The current is large enough and has a sufficient overdrive to turn on the maximum current in Ql with the desired speed when Ql is a minimum beta transistor. As Ql commences turning on, D3 is reverse-biased, draws no current, and is effectively out of the circuit. All the 71 flows through D2 into the base, yielding very fast rise time. However, when the collector voltage has fallen low enough to...

## 832 Transformer coupling into a Baker clamp

8.3.2.1 Transformer supply voltage, turns ratio selection, and primary and secondary current limiting. The circuit of Fig. 8.7 provides all the required drive characteristics for the Baker clamp high forward and reverse base drive for Q2 at relatively low primary current drawn from the housekeeping supply Vh. It also provides the reverse Q2 base voltage which permits it to tolerate its Vcov rating. It works as follows. First, the T1 turns ratio Np Ns is chosen as large as conveniently possible...

## 8354 Base drive transformer primary inductance and core selection At

The start of the Q1 on time, Vc is at Vh and at the end of the on time, it is desired that Vc collapse to ground so as to store a current in Np. Now assume that Vc falls linearly from Vh to ground in the minimum Q1 on time ion(min). Then at the end of the on time, Np must be carrying a current Figure 8.13 Fast CI recharge circuit for proportional base drive. In Fig. 8.12, if CI cannot be recharged to Vh in the minimum Q2 on time, emitter-follower Q3 is interposed between R1 and CI for fast...

## 836 Miscellaneous base drive schemes

A wide variety of specialized bipolar base drive schemes have evolved through the years. They are more often used at lower power levels and, by various circuit tricks, seek to achieve two common goals. (1) a low-parts-count scheme to obtain substantial reverse base voltage, reverse base current, or a base-emitter short circuit at turnoff and at turnon and (2) forward base current adequate to drive lowest beta transistors at maximum current without long storage times for high beta transistors at...

## 838

Figure 14.16 Significant waveforms in 200-kHz converter of Fig. 14.8. Figure 14.16 Significant waveforms in 200-kHz converter of Fig. 14.8. drains down to ground. However, A1 and SI are fictitious turnons. At those times, the drain is driven down to ground by the positive drain bump after turnoff of the opposite transistor. This phenomenon is an extreme example of the situation seen in photo PP13 obtained by increasing the primary magnetizing current by increasing the transformer gap at low DC...

## 861

Figure 14.2 The 125-kHz 100-W forward converter of Fig. 14.1 at 80 percent full load. Drain-to-source voltages also appear as they should be theoretically. Transistor on time at low line (Vdc 38 V) is seen to be very close to 80 percent of a half period as discussed in Sec. 2.3.2. It is not always exactly that because of the inevitable rounding up or rounding down of fractional secondary turns to the nearest integral number. In this transformer, the calculated 4.5 turns on the secondary were...

## 91

Figure 14.3 The 125-kHz 100-W forward converter of Fig. 14.1 at 40 percent full load. they come at a high repetition rate, their average dissipation can be high and can exceed the conduction dissipation of VdsIdston T. The overlap dissipation at turnon is not as serious as at turnoff. At turnon, the power transformer leakage inductance presents an infinite impedance for a short time and causes a very fast drain-to-source voltage fall time. The same leakage inductance does not permit a very fast...

## 918

P - type MOSFET showing inherent body diode Figure 9.18 Inherent body diodes in N- and P-type MOSFETs. In the N-channel MOSFET, the diode prevents a negative drain-to-source voltage. In the P-channel MOSFET, the diode prevents a positive drain-to-source voltage. P - type MOSFET showing inherent body diode Figure 9.18 Inherent body diodes in N- and P-type MOSFETs. In the N-channel MOSFET, the diode prevents a negative drain-to-source voltage. In the P-channel MOSFET, the diode prevents a...

## 92

Its length and resistance in ohms per foot as read from the wire tables for the selected wire size. It was also assumed that 7rms is the rms current as calculated from its waveshape (Sees. 2.2.10.2, 2.3.10.4). There are two effects, skin and proximity effects, which can cause the winding losses to be significantly greater than (Irms)2Rdc Both skin and proximity effects arise from eddy currents which are induced by varying magnetic fields in the coil. Skin effect is caused by eddy currents...

## 9212 Mosfet draintosource body diode

Inherently in solid-state structure of a MOSFET, a parasitic body diode is located across the drain-source terminals as shown in Fig. The diode polarity is such as to prevent reverse voltage across the MOSFET. The forward current handling capability and reverse voltage rating of the diode are identical to those of the MOSFET itself. Its reverse recovery time is faster than a conventional AC power rectifier diode, but not as fast as discrete fast-recovery types. Manufacturers' data sheets show...

## 923 Mosfet gate rise and fall times for desired drain current rise and fall times

Very rapid drain current rise and fall times are undesirable as they cause large L di dt spikes on ground buses, supply rails, and large C dV dt capacitatively coupled spikes into adjacent wires or nodes. The question thus arises as to what gate voltage rise time is required to yield a desired drain current rise time. This can be seen from the transfer characteristics shown in Fig. 9.36 and 9.3d. In a MOSFET, switching time between zero and a drain current Id is only the times required for the...

## 925 Mosfet flda temperature characteristics and safe operating area limits45

The most common failure mode in bipolar transistors second breakdown comes about because their on-voltage drop Vce(sat) decreases with temperature. This imposes limits (RBSOA curve of Fig. 8.4) on the Ic - Vce trajectory the transistor may not cross during the turnoff transition. Manufacturers state that only a single crossing of this limit curve may cause the bipolar to fail in the second-breakdown mode. However, MOSFETs, because their on-voltage drop or r(jg increases with temperature, do not...

## 927 Mosfet switching speed and temperature characteristics

MOSFET switching speed is significantly independent of temperature. Drain current rise and fall times depend only on the time required for the gate voltage to cross the narrow boundary between the gate threshold voltage (Vgsth) and VgI in Fig. 9.36. This depends on the output resistance of the source-sink driver and the effective gate input capacity. The source-sink output resistance is usually a discrete exter- nal resistance which has a low-temperature coefficient. Further, since gate input...

## 928 Mosfet current ratings

For bipolar transistors, maximum output current is limited by the fact that current gain falls drastically as output current rises. Thus unac-ceptably high base input currents are required as output current increases. This is shown in Fig. 9.13 for the 2N6542 a typical 5-A, 400-V bipolar transistor. With MOSFETs, however, output-input gain (transconductance or dIdJdVgs) does not decrease with output current, as can be seen in Fig. 9.14. Thus the only limitation on drain current is power...

## 929 Paralleling MOSFETs7

In paralleling MOSFETs, two situations must be considered (1) whether the paralleled devices share current equally in the static case when they are fully on and (2) whether they share current equally during the dynamic turnon-to-turnoff transition. With paralleled MOSFETs, in either the static or dynamic case, the concern is that if one MOSFET hogs a disproportionate part of the current, it will run hotter, and long-term reliability will decrease or, in the short run, will fail. Unequal static...

## A

Where h effective round wire height 0.866 (wire diameter d) 0.866d Ft copper layer factor Ntd w (where Nl number of turns per layer, w layer width, d wire diameter note Ft 1 for foil) The ratio is given for a number of different values of a variable p, which is the number of coil layers per portion. A portion is defined as a region where the low-frequency magnetomotive force H dl OA-aNI) ranges from zero to a peak. This portion often misinterpreted is clarified thus. Consider that the primary...

## Ampere Turns

Figure 8.9 Inductance per 1000 turns At for Ferroxcube 1408PA3C8 pot core. A small core suitable for the transformer T1 of Fig. 8.7. It can be a 2N2222A an 800-mA 40-V device whose rise and fall times are under 60 ns. It comes in a small T018 package and cost is under 25 By changing the circuit of Fig. 8.7 to the simpler one of Fig. 8.10, greatly improved performance with all the advantages of Baker clamping is achieved. Current gain in T1 can be doubled without increasing Vh, and better...

## C

Transformer secondary plus output rectif iers and filter Figure 2.6 Output rectifiers serve as free-wheeling diodes in a push-pull circuit. Secondaries carry the normal free-wheeling ledge current during the 20 percent dead time. This should be considered in estimating secondary copper losses. in the buck regulator of Fig. 1.4. In the buck, the free-wheeling diode was essential as a return path for inductor current when the transistor turned off. When the transistor turned off, the polarity...

## D wv v514bl

5.6.7.10 Turns ratio selection in overlapping mode. Equation 5.14a gives the relation between output input voltage and on time for the overlapping mode for a preselected choice of 7 turns ratio Nv As good a choice for Nx is the value calculated from Eq. 5.14a, which makes D 0.5 at the nominal value of input voltage Vdcn. Then for all DC input voltages less than Vdcn, there will be overlapping on times (D > 0.5) and the output voltage-on-time relation is given by Eq. 5.14a for that calculated...

## D2

Figure 6.22 (a) Basic Royer oscillator. (b) Square hysteresis loop of T1 core, (c) Characteristic high current spikes at end of on time. These spikes are major drawbacks in Royer oscillators. As long as the core is on the vertical part of its hysteresis loop, the positive feedback from Np to Nb widings keeps a transistor on and in saturation. When the core has moved to either the top or the bottom of its hysteresis loop, coupling between the collector and base windings immediately drops to zero...