A HIGH P E R F O R M A N C E LINE REGULATOR G. I. Cardwell and D. J. Packard Hughes Aircraft CompanyEl Segundo, California ABSTRACT A. high performance 10 k H z switching line regulator featuring isolated drive with full dynamic range is described. Also described are a wide-band isolated output sense circuit and suitable compensation extended transient response beyond the resonant frequency of the output filter. This switching regulator w a s designed and developed as part of a p r o g r a m sponsored by N A S A Lewis Research Center, Contract N o . N A S 3-17223, under the direction of Jim Sovey. INTRODUCTION This paper describes the design of a 10 k H z 500 W switching buck type regulator used as a line regulator in a power conditioner for an ion thruster. The design specifications w e r e to regulate a 200 to 400 volt solar panel input to a 180 volt output with 1 percent regulation for line and load variation. Additional constraints w e r e that the regulator be able to respond rapidly to large load transients requiring a full dynamic range of operation and a wide bandwidth. A wide bandwidth w a s necessary because the regulator is used to provide an input to an inverter whose output is supplying magnetic amplifier loads (Figure 1). Since each magnetic amplifier load has a c o m m a n d a b l e reference with its o w n closed loop negative feedback control, it reflects a neg­ ative impedance to the output of the switching regulator at low frequencies. Often a negative impedance load causes a negative resistance type oscillation w h e n attached to a resonant L C filter source such as an L C filtered switching regulator. T o stabilize this network, a resistor m a y be added in series with the output filter capacitor. H o w e v e r , the large resistor can cause an unac­ ceptable voltage ripple on the output of the regu­ lator. In the case discussed in this paper, the bandwidth of the magnetic amplifier could not be significantly reduced. Therefore, it w a s neces­ sary to raise the frequency response of the switching regulator to a frequency beyond the resonant frequency of the output L C filter to pro­ duce a positive total network impedance and pre­ vent the negative resistance oscillation discussed above. A n analytical treatment of this problem is included in this paper. 1 0 6 - P E S C 74 R E C O R D A further design constraint w a s that the control electronics be isolated to greater than 2000 volts from the power switch, requiring both an isolated power transistor drive circuit and an isolated feedback sense circuit. Finally, the goal w a s for an efficiency of greater than 93 per­ cent full load with a weight of less than 2. 0 pounds. The following is a description of the approach taken to m e e t these requirements on drive and sense circuitry and wide band compensation. Since good quality high power, high voltage N P N transistors are far m o r e available than P N P transistors, it is desirable to use a power N P N transistor in a high voltage switching regulator. The problem in this case is to provide the base drive for that N P N transistor. A c o m ­ m o n technique used in the present state of the art is a P N P driver connected in a Darlington config­ uration to drive the power N P N transistor. With this technique, an N P N transistor is used to drive the P N P - N P N Darlington pair (see Figure 2). In a high voltage application, this configuration has a serious deficit in that all three transistors m u s t be capable of supporting the m a x i m u m line volt­ age. Such a configuration does not offer the ground isolation required in this application. Typically, where ground isolation is required, the magnetically coupled switching driver is nor­ mally limited by the magnetic reset time of the coupling transformer. It is a simple matter to INVFRTER 1 ^ PUWtK SWITCH SOLAR PANEL MAGNETIC AMPLIFIERS DC FEEDBACK CONTROL CIRCUIT AC FEED­ BACK ISOLATED "RETURN FIGURE 1 . FUNCTIONAL BLOCK DIAGRAM INPUT LOAD 10 k H z FUNDAMENTAL SUBHARMONIC CARRIER TYPE 1 MODULATION INPUT TYPE 2 MODULATION INPUT j—ι ι—I I "L XT J~L _ΓΊ_ n_TL η OUTPUT COMMON F I G U R E 2. BASIC S W I T C H I N G R E G U L A T O R turn off (i. e. , 0 percent duty cycle) the magneti­ cally coupled switching regulator, it is usually impossible to turn on the magnetically coupled switching regulator all the time (i.e. , 100 per­ cent duty cycle). In the series switching regulator, it is highly desirable to have as wide a dynamic range of control as possible. The capability to turn on the regulator completely is important if the regu­ lator is to be subjected to transient loads or if the input voltage to the regulator is allowed to fall to a value very near the output regulated value. B y utilizing s o m e type of modulated ac carrier, a 100 percent dynamic range of drive can be m a g ­ netically coupled to the power transistor in a switching regulator. For example, a carrier m a y be applied to a transformer with a full w a v e recti­ fier, current limiting resistor, and power trans­ istor connected to the secondary (see Figure 3). If this carrier is applied continually the power transistor is driven continually. If the carrier w e r e turned on and off by a duty cycle modulator, the drive to the power transistor would be m o d u ­ lated. The technique shown would utilize a high frequency carrier, which might not be readily available or simply generated. y MODULATOR CARRIER ^ OUTPUT H- F I G U R E 4. S U B H A R M O N I C MODULATION utilizing type 1 modulation, volt second balance is maintained on the center tap drive transformer by applying modulation on alternate half cycles of the subharmonic carrier. Type 1 modulation shown in Figure 4 is expanded about the center of the subharmonic carrier and at all times, the modulated input is applied in the s a m e half cycle of the subharmonic carrier. The advantage to this type of modulation is that the output of the rectifiers that provide drive to the power transis­ tor is constant and contains no switching transients due to the subharmonic carrier except for that special condition w h e n the modulator is requesting 100 percent duty cycle. The type 2 modulator also maintains volt second balance on the drive transformer. In this case, balance is maintained by splitting the modulated time in half and applying half of the modulated w a v e f o r m to either side of the trans­ former during the subharmonic switching interval. In this case, a small switching transient occurs in the output of the rectifiers in the middle of the modulated period. Initially type 1 modulation w a s considered for this switching regulator. H o w e v e r , an investigation into the isolated sensing technique to be used in the regulator disclosed the fact that the subharmonic carrier could also be used as a carrier for the remote sensing if type 2 modula­ tion w e r e utilized. This discussion will be expanded as a part of the sense circuitry descrip­ tion included later. MODULATED OUTPUT F I G U R E 3. H I G H F R E Q U E N C Y C A R R I E R MODULATION For the problem at hand, a better solution seemed to be one of using a first subharmonic of the 10 k H z operating frequency to perform the driving function. The 5 k H z subharmonic carrier is easily generated by using a toggle flip-flop clocked by the 10 k H z fundamental frequency. Modulation utilizing subharmonic carrier m a y be accomplished in two ways (see Figure 4). W h e n The primary concern of utilizing type 2 modulation is that of the switching transient dur^ ing the toggling interval of the subharmonic gen­ erator. B y using high frequency pulse transformer techniques and high speed diodes, it w a s possible to reduce the transient to something under 200 ns. The storage times of power tran­ sistors considered for this application w e r e in excess of 1 μβ and, as a result, change in col­ lector voltage or current w a v e f o r m s could not be observed during the transient caused by the switching of the subharmonic carrier. PESC 74 R E C O R D - 1 0 7 FIGURE 5. SIMPLIFIED DRIVE SCHEMATIC U s e of a subharmonic drive circuit provides a solution to the problems mentioned in that a magnetically isolated switching regulator with a 100 percent dynamic range can be implemented. This method works equally well with a power N P N or P N P transistor and allows that transistor to be fully saturated. Moreover, the power transistor is the only transistor sub­ jected to a high voltage stress. DRIVE CIRCUIT Figure 5 is a simplified schematic of the drive circuit. A square w a v e clock signal is applied to R l and to the toggle input of the flip-flop. Resis­ tor R l and capacitor C l form an integrator that integrates the square w a v e signal into a small voltage r a m p which is applied to one of the inputs of level detector A l . The other input to the level detector is a feedback signal. If this signal is allowed to vary slowly through the range of the r a m p , the level detector forms a pulse width modulated output. This action is shown in wave­ forms 3 and 4 of the master timing diagram, Figure 6. The falling edge of the square w a v e clock is used to toggle the flip-flop m a d e up of transistors Q 5 , Q 6 , and toggle gating circuitry. Transformer T2 is the m a i n base drive transformer for power transistor Q 7 . The 1 0 8 - P E S C 74 R E C O R D CLOCK SUBHARMONIC DRIVE TO DRIVE AND SENSE TRANSFORMERS RAMP LEVEL DETECTOR OUTPUT POWER SWITCH OUTPUT FILTER RIPPLE SENSE INPUT RIPPLE SENSE OUTPUT RIPPLE A1 OUTPUT TO LEVEL DETECTOR FIGURE 6. MASTER TIMING DIAGRAM primary side of transformer T 2 is connected through diodes to the collectors of Q 5 and Q 6 . Q 5 and Q 6 form a discrete toggle binary which is clocked at 10 kHz. The center tap of the primary of T2 is connected to transistors Q 3 and Q 4 . These two transistors are a complementary pair which drive the center tap of transformer T 2 as dictated by the output of the level detector (modulator). The output of transformer T 2 is connected through diodes C R 2 and C R 3 and the current limiting resistor R 7 to the base emitter of the power transistor Q 7 . For any interval of time, with the excep­ tion of the toggling interval, either Q 5 or Q 6 is on. Therefore, during any interval, the center tap of T2 primary m a y be raised to provide base drive to Q 7 . Transistor Q 2 and resistor R 6 drive the complementary pair Q 3 and Q 4 . The transistor Q 2 is driven from the basic duty cycle modulator, Al. T o turn off Q 7 quickly, TI is used as a magnetically timed blocking oscillator that is triggered by the rising edge of the output of A l . Diode C R 1 and resistor R 4 form a turn-on, turn-off network for the blocking oscillator. The output of level detector A l is at a voltage below ground w h e n power transistor Q 7 is on. At that time, diode C R 1 is forward biased and is conduc­ ting current through resistors R 4 and R 5 and into the output of level detector A l . At the time that level detector A l c o m m a n d s power transistor Q 7 off, its output rises very rapidly. This rapid rise in output of A 1 forces clearing current to flow through diode C R 1 . Diode C R 1 is a low speed rectifier and therefore passes clearing current for a significant time. This clearing current flows into the base of transistor Q l , initiating the time interval of the positive feed­ back blocking oscillator. Transformer TI is connected in such a polarity that w h e n the blocking oscillator is on, i. e. , Q l conducting, a negative voltage is applied at output transformer TI. This negative voltage causes a current to flow out of the base of transis­ tor Q 7 , and the negative current (on the order of IA) causes transistor Q7 to turn off very rapidly. Transistor Q l is turned on at approximately the s a m e time that the center tap of transformer T 2 is actively forced to ground. Because of the action of these twc transformers, the base drive to power transistor Q 7 changes from the positive drive of approximately 250 m A to a negative drive of approximately 1 A in approximately 100 ns. The magnetic time constant of the blocking c oscillator is nominally longer than 15 μβ, thereby ensuring that negative current can be removed from the base of Q 7 for a period in excess of its storage time. If the switching regulator is operating at nominal or low duty cycles, the magnetically timed blocking oscillator will time out and switch off. If, however, the input voltage to the switch­ ing regulator is low and the switching regulator is required to operate at long duty cycles, level detector A l m a y switch negative before the block­ ing oscillator has timed out. In this case, transis­ tor Q l will rapidly turn off because of the forward currents through diode C R 1 and resistor R 4 . The blocking oscillator m a y therefore be turned off at any time prior to its normal time out interval. Because of this and the subharmonic carrier nature of the on drive to transistor Q 7 , the switching regulator has an extremely broad dyna­ mic range. It m a y indeed be operated over a 0 percent to 100 percent duty cycle. ISOLATED SENSE CIRCUIT Figure 7 illustrates a m e a n s of transmitting a dc voltage across a winding in an isolated sense circuit. The two transistors are driven by two square waves of the s a m e frequency 180° out of phase. This impresses the input volt­ age across first one half and then the other of the center tapped primary of the transformer T. The ac secondary voltage that results from this action is rectified by the diode bridge and filtered by the R C network. This circuitry is suitable for the passage of dc information, but if the input has an ac component, the R C network limits the band­ width of the signal that m a y be actively transmitted through this circuit. If there is no filtering, a switching transient will always be evident in the output w h e n the transistors switch. This transient normally presents a problem in maintaining the fidelity of the high frequency information. In this application, the output voltage of the line regulator contains the desired ac information. Also a subharmonic carrier w a s available to transmit this information. B y modifying the cir­ cuit shown in Figure 7 to that shown in Figure 8, the desired information is transmitted across transformer T3. Notice that the primary of transformer T 3 is n o w current driven, and it is the center tap of the primary T3 that contains the desired output information. In essence, the sig­ nal flow is reversed through the sensing transformer. The switching transient problem w a s solved by taking advantage of the fact that the occurrence of the switching transient in the time domain is controlled by the excitation frequency of the driving transistors, and it is possible to synchronize the sense excitation to that of the pulse width modulator clock. If phased as shown in the master timing diagram of Figure 6, this INPUT V O L T A G E R F I G U R E 7. V O L T A G E C H O P P E R I S O L A T E D S E N S E C I R C U I T PESC 74 R E C O R D - 1 0 9 will cause the switching transient to occur between pulse width sampling intervals. Using this method, ac information of a bandwidth beyond the excita­ tion frequency can be transmitted. A description of the circuit techniques utilized follows (refer to Figure 8). w o r k for the line regulator. Its loads include a square w a v e inverter that drives several magnetic amplifiers. These constant power loads appear incrementally to be negative impedances. One type of compensation c o m m o n l y used in regulators is achieved with the placement of a dominant pole s o m e w h e r e in the feedback loop, such that unity loop gain is below the resonant frequency of the output filter. If this method is used, then the closed loop output impedance of the regulator is roughly equal to the open loop output impedance for frequencies above unity gain. It should be noted that the following analysis assumes the output of the switching element m a y be timeaveraged and linearized. With this assumption, Laplace transform methods are used and perfor­ m a n c e inferred from the frequency domain. The output impedance of a circuit with voltage feed­ back is indicated in Equation 1 Ζ oc = Zoo 1+T (1) where Zoe is the closed loop output impedance, Zoo is the open loop output impedance, and Τ is the loop gain. T o see the effect of a negative resistance load with this type of compensation, consider the following argument. F I G U R E 8. I S O L A T E D SENSE CIRCUIT The collector of transistor Q 9 is connected to the base of transistor Q 8 and as a result, the emitter of Q9 and the collector of Q 8 form a very low impedance voltage shunting source. The volt­ age on the collector of Q 8 is approximately the voltage at the junction of the voltage divider R 8 and R 9 . The diode bridge is forced to maintain the voltage defined by the junction of the voltage divider R 8 and R 9 , and therefore, the center tap of the primary of transformer T 3 is held at a voltage which is proportional to the voltage at the junction of the resistor divider R 8 and R9 and is therefore proportional to the bus voltage. Capa­ citor C 2 provides high frequency lead compensa­ tion. Although from a stability standpoint it m a k e s no difference w h e r e the loop compensation is placed, the effect of the switching transient caused by the switchover of T3 is reduced by plac­ ing this compensation in front of the sense transformer. A dc isolated wide bandwidth voltage is thus produced at signal level that is proportional to the switching regulator output voltage. Since the subharmonic carrier is generated for the power transistor drive, this s a m e carrier is used to excite the sense transformer. C O M M E N T S O N STABILITY Referring to Figure 9, if this circuit is to oscillate, then a right half plane pole m u s t be present in the driving point impedance seen at the terminals labeled A B. This impedance ( Z ^ g ) is shown in Equation 2 J A B Zoe// R -Zoe · R Zoe - R T o deduce whether a right half plane pole is present, divide top and bottom by Zoe to get Equation 3. 1 + (-Zo-c> 1 + T 110-PESC 74 RECORD (3) f A s shown T is a pseudo loop gain which allows the use of the Nyquist criterion to determine whether the loaded filter will be unstable. If it is assumed that dominant pole compensation is used and that the unity gain frequency of the regulator is well below the resonant frequency of the filter, it m a y be assumed that the output impedance of the regulator is that of the L C filter. Then the closed loop output impedance (Zoe) m a y be simplified as shown in Equation 4 for frequencies where Τ « 1. 1 Ç *V -R " ^ o c During the power subsystem developmental phase for the ion engine, it b e c a m e evident that standard compensation techniques w e r e not to (2) M— Ć AB Β F I G U R E 9. N E G A T I V E R E S I S T A N C E L O A D E D L C F I L T E R „ sL + R , „ Zoo „ L Zoc = — - Zoo = — s LC + s C R + 1 L (4) R L s LC 2 (sL/R + s C + 1) L + R L 1 With this assumption T , the pseudo loop gain, m a y be 1 The approach here w a s to r e m o v e the resonant peaking of Zoe by extending the band­ width of the regulator beyond the resonant fre­ quency of the filter. This solves the oscillation problem by reducing the magnitude of Zoe, and significantly improves the transient response to line and load changes. This type of compensation also tends to m a k e the regulator insensitive to the Q of the output filter. At frequencies where the loop gain is m u c h greater than 1, Zoe is approximately given bv Equation 6. Zoe = -R (s L C T R = + sCR (sL/R T L + T L + 1) ( f 0 P T « l ) 1) Zoo 1+T Zoo Τ (if Τ » 1 ) (6) (5) The poles of Τ include the poles of Z o o since output voltage is fed back. Thus considering an unloaded output filter of the type shown in Figure 9. Τ will contain the transfer function f r o m the source Η · V (which represents the linearized power switch) to the output A B . Zoe m a y be c o m ­ puted for frequencies w h e r e Τ » 1 as shown in Equation 7. L approximated by Equation 5. Figure 10 is a Nyquist plot of this pseudo loop gain. s L + R, Zoe Zoo 1+T Zoo M ~ s LC + sCR L + 1 j ô H(s) . \-r s L C + sCR. + 1 L sL + R l R_ ( S ^ L C+ S C R (SL/R L L + + 1) 1) Z FIGURE 10. NYQUIST PLOT O F L O A D E D FILTER LOOP GAIN Ô It is clear that if the Q of the output filter is sufficiently high, the filter with a negative resis­ tance load will oscillate. Note that the method used here to deduce instability is well suited to experimental verification. That is if the true magnitude and phase of the load can be measured, then this information coupled with design data on Zoc should allow determination of potential instability by plotting a Nyquist plot of Zload/Zoc and checking for clockwise encirclements of the -1 point. With dominant pole compensation in the circuit, the output filter had sufficient Q such that the load induced oscillation near the reso­ nant frequency of the output filter. Considering Equation 2 for Ζ ^ β , it is noted that if the magnitude of the closed loop impedance can be m a d e m u c h less than the magnitude of the load impedance, then Ζ ^ β is approximately Zoc regardless of the load characteristic and the regulator is stable. Another approach to stabilizing the loaded filter would be to directly lower its Q by adding a small series resistor to the output capacitor. This approach can work, but only with increased output ripple and lower efficienc y. o c = H f i T f ° r T > y 1 (8) Equations 7 and 8 show that sufficient feedback beyond the resonant frequency can effectively r e m o v e the resonance f r o m the closed loop output impedance. Using this approach and a simple describing function technique, a suitable feedback function H (s) w a s developed. COMPENSATION CIRCUIT The switching part of the feedback loop w a s linearized in the following m a n n e r . Referring to Figure 5, note that as the feedback input to the level detector m o v e s over the full range of the triangle input, the duty cycle varies f r o m 0 per­ cent to 100 percent causing the average output of the regulator to vary from 0 to V s volts. The gain of the modulator w a s then characterized as G M = V s / V p p where V s is the input voltage to the line regulator and V p p is the peak to peak voltage on the triangle input. Since for simplicity, the size of the triangle w a s fixed and V s varies f r o m 200 to 400 volts, G m then varies by a factor of two. This variance in gain with line voltage m e a n s that the magnitude plot of loop gain could be translated 6 d B for line variations. A s mentioned earlier, stability considera­ tions required that the loop gain cross over 0 d B above the resonant frequency of the output filter. P E S C 74 R E C O R D - 1 1 1 30 F R E Q U E N C Y , HZ F I G U R E 11. L I N E R E G U L A T O R B O D E T o m a k e the describing function approach valid and to keep noise from triggering the level detec­ tor, it w a s decided to have the loop gain cross zero no higher than a factor of 3 below the switch­ ing frequency. Referring to the loop gain plot of Figure 11, stability w a s achieved by placing a zero at 1 k H z to overcome part of the phase shift that the two 400 H z poles of the resonant filter con tribute. T w o additional poles w e r e placed at 20 k H z to attenuate switching noise and provide additional phase shift after crossover to balance the subharmonic drive circuit after the level detector. Referring to Figure 12, the midfrequency gain w a s set by resistors R a and R b on operational amplifier A 2. This w a s chosen to m a k e unity gain crossover occur between 1 k H z and 2 k H z for line variations. Finally, to obtain o p t i m u m dc regulation, the operational amplifier's full open loop gain w a s used at low frequencies by making it an integrator with capacitors C a and Cb. The resistor divider and capacitor C 2 shown in Figure 8 provide the 1 k H z zero and one of the 20 k H z poles. The other 20 k H z pole is derived from R b and C a connected to operational amplifier A 2 . The combination of high frequency poles and zeros provided nearly a constant 60° of phase margin over the range of possible crossover frequencies as shown in Figure 11. These data w e r e taken with a w a v e analyzer. 112-PESC 74 RECORD DIAGRAM REFERENCE FEEDBACK o—AAAr- F I G U R E 12. C O M P E N S A T I O N C I R C U I T R Y The net result of this compensation w a s the transient response shown in Figure 13 and a dc output virtually independent of line voltage or load variation. A n additional wrinkle that w a s added to the actual system w a s to ac couple the high speed feedback from the subharmonic sense circuit and combine this signal with the 15 volt system power which is derived from the regulator through a con­ verter. Thus, the +15 volt supply w a s directly regulated while the wideband sense provided high frequency stability. 30 c m L I N E R E G U L A T O R S T E P L O A D R E S P O N S E authors feel that these solutions m a y be useful in far m o r e general applications. For example, the subharmonic carrier technique m a y be useful in any switching regulator application and in parti­ cular, useful where high voltage isolation is required. E v e n if the control circuitry need not be high voltage isolated, it is convenient to have only one switching transistor subjected to high voltage stresses and the subharmonic carrier drive would s e e m to be an excellent general solu­ tion to this problem. It should be noted that the subharmonic carrier drive technique, w h e n actually implemented, allowed the construction of a lightweight (approximately 1.5 pounds) 500 watt switching regulator which operated at an efficiency of approximately 96 percent at full load and 300 volt input. Further, the isolated sensing cir­ cuitry provided a m e a n s of high frequency output signal feedback that w a s necessary to meet the system stability criteria. Equally important, this paper presents a linearized technique that can be used to obtain a stability criterion for resonant circuits loaded by a negative impedance. CONCLUSIONS Certain simplifying assumptions w e r e m a d e in the analysis to illustrate an example of the technique. The only necessary assumption is that a describing function can adequately char­ acterize the modulator and switch. The tech­ nique is sufficiently general to apply to a n u m b e r of regulated dc-dc type converters with resonant input or output filters which are loaded with negative impedances. In conclusion, this paper describes the techniques used to solve s o m e rather special design problems. Even though these techniques w e r e developed to satisfy a specific need the Hopefully, this paper will be both speci­ fically useful to those attempting to design high voltage converters, and generally useful to those w h o m u s t face the stability problems encountered by operating with negative impedance loads. UPPER T R A C E LOWER TRACE 180 V O U T P U T , 1 V / C M L O A D C U R R E N T S T E P , 0.2 A / C M F I G U R E 13. R E G U L A T O R T R A N S I E N T R E S P O N S E , 10 T O 100 W L O A D P E S C 74 R E C O R D - 1 1 3