i - 35 ? 1998 ixys all rights reserved high performance dual pwm microstepping controller type package temperature range ixms150 psi 24-pin skinny dip -40 c to +85 c the ixms150 is a high performance monolithic 2-channel pwm controller. implemented in cmos, the low power ixms150 precisely controls the current in each of two separate power h-bridge drivers using unique sampling and signal processing techniques. each channel contains an error amplifier, pwm, feedback amplifier, and protec- tion circuitry. protection features include over/excess current shutdown, min/max duty cycle clamp, under voltage lock- out, dead time insertion, and a shutdown input for over-temp or other external fault circuitry. other features include a common oscillator, feedforward circuit for motor supply compensation, and an onchip negative bias generator. the ixms150 has been optimized for microstep control of two phase step motors. due to its high level of accu- racy, the ixms150 will allow a designer to implement a control system with a resolution in excess of 250 microsteps per step, or 50,000 steps per revolution with a 200 step per revolution step motor. the ixms150 greatly improves positioning accuracy and virtually eliminates low speed velocity ripple and resonance effects at a fraction of the cost of a board level microstepping system. other applications which the ixms150 is designed for include control of two single-phase (dc) motors or control of synchronous reluctance motors. the ixms150 is ideal for robotics, printers, plotters, and x-y tables and can facilita- te the construction of very sophisticated positioning control systems while signi- ficantly reducing component cost, board space, design time and systems cost. features l two complete, synchronous pwms l command input range 2.0 v full scale l 0.625 v full scale current feedback signal l 1% gain matching between channels without external trim l 1.6% gain linearity l feedforward to compensate for motor supply variations l only one sense resistor per h-bridge needed l onboard two level current limiting l undervoltage lockout assures proper behavior on power up and power down l enable input for external over temperature or fault circuit input l duty cycles limited for ac coupled gate drive l wide range of built in dead time. l on board negative power supply generator l single +12 v supply operation l 24-pin dip package applications l full, half quarter, or microstepping 2-phase step motor position controller l dual dc servo motor torque controller l solenoid actuator force controller l general 2-channel current- commanded pwm control block diagram of ixms 150 symbol definition max. ratings v dd supply voltage -0.3...15 v operating range 10.8...13.2 v common-mode-range -15...15 v differential input voltage ? 30 v v in input voltage ? -15...15 v v o output voltage -0.3...v dd +0.3 v p d maximum power dissipation 500 mw t a ambient temperature range -40...85 c t stg storage temperature range -55...125 c ? input voltage may not exceed either supply rail by more than 0.3 v at any time. ixys reserves the right to change limits, test conditions and dimensions.
i - 36 ? 1998 ixys all rights reserved ixms 150 symbol definition/condition characteristic values (v dd = 12 v, t a = 25 c unless otherwise specified) min. typ. max. oscillator f osc frequency c o 10 400 khz v a(p-p) amplitude ffwd = open 7 v z out output impedance i out = 400 m a 2.5 m w resistance range r o 15 100 k w capacitance range c o 100 2000 pf feed forward v ffwd feedforward ffwd = open 3.5 v voltage z inff impedance to agnd 25 45 k w analog inputs v fs input fullscale v ina dc 2v v inb z in1 v in to comp 2 dc 20 32 k w impedance z in2 comp 1 to comp 2 dc 12 20 k w impedance sense inputs sense a v sense full scale input sense b dc 0.625 v z ins input impedance dc 100 200 k w protection circuit sense a v ov-1 over current sense b 0.8 0.95 1.0 v voltage t ov-1 reset pulse width 0.5 1 m s v ex-1 excess current voltage 3.45 3.6 3.75 v t ex-1 reset pulse width 300 ns under voltage v uv minimum v dd outdis 7.5 8 8.5 v i ih input high current v ih = 11.5 v 100 m a i il input low current v il = 0.5 v 1.8 ma outputs v oh output high v outa , v outa i oh = -10 ma 8.0 11.2 v voltage v ol output low v outb , v outb i ol = 10 ma 0.8 1.1 v voltage t r rise time c l = 100 pf 35 50 ns t f fall time c l = 100 pf 35 50 ns t dt dead-time c o = 180 pf 200 300 450 ns t min minimum pulse width c p = 30 pf 0.6 0.8 1.5 m s vbb generator v bbmin minimum v bb outdis -1.4 -1.9 v negative bias = v dd v bb negative bias i out = -3 ma -2.1 -2.4 v voltage v reg load regulation f osc 60 mv = 100 khz v oh output high volt. c pump i oh = -10 ma 11.2 v v ol output low volt. i ol = 32 ma 0.8 v supply i dd1 idle current v dd v in = 0 16 26 ma i dd2 operating current f osc 15 45 ma = 100 khz v bypass bypass voltage bypass 5.9 16.1 v z inbp impedance to agnd 9 16 k w dimensions in inch (1" = 25.4 mm) 24-pin skinny dip
i - 37 ? 1998 ixys all rights reserved ixms 150 pin description ixms 150 nomenclature of dual pwm microstepping controller sym. pin description agnd 1 analog ground comp 2 analog compensation 4 (see application notes for 5 recommendations). 20 21 23 vin 3 analog input: the analog 22 input range is 2 v. a low output im pedance voltage source should drive these pins. the input is greater than 20 k w . sense 6 analog sense: each of the 19 phases sense resistors are connected to these pins. input range is + 0.625 v. ffwd 7 ffwd, for motor high voltage compensation: a voltage on this pin sets the oscillator amplitude. input range = 0.9-4 v (see application notes for recommendations). by- 8 filter cap: a capacitor on pass this pin provides filtering to the internal bias network. vout 9 output stage: to drive 10 buffered power mosfet 15 h-bridge. 16 vbb 11 negative bias generator output: for internal use by the ixms 150. dgnd 12 digital ground cpump 13 charge pump capacitor: used by the internal negative bias generator. outdis 14 digital enable input and status output: forcing this pin low causes pins 9, 10, 15, and 16 to go low, disab- ling the h-bridge. when uses as an output, a low state on this pin indicates an over current, excess current, or insufficient +v dd or v bb error condition. r o , c o 17 oscillator frequency and 18 dead-time set: independent adjustment can be made to the oscillator frequency and dead-time (see applications notes). vdd 24 positive supply voltage * pin numbers in parantheses are associated with channel b. ixms 150 ps i (example) ix ixys ms 150 dual pwm controller package type ps plastic skinny dip temperature range i industrial
i - 38 ? 1998 ixys all rights reserved ixms 150 functional description introduction the ixms150 is designed with mono- lithic cmos technology. the ic is primarily intended for use with two- phase step motors in the microstepping mode but may also be used for control of two dc motors, audio amplifiers, or any application requiring two synchro- nized pwms. the ixms150 simulta- neously controls the currents in each of two separate h-bridges. this device utilizes both analog and digital functions. the ic has five fundamental sections: (1) oscillator and feedforward circuitry, (2) analog section for control of the motor currents, (3) a protection network to protect the h-bridges and the motor from abnormal conditions, (4) the digital pwm logic for the control signals, and (5) the power supply section which includes a negative bias generator. oscillator the ixms150 contains an internal oscillator which is controlled by adjusting the values of r o and c o . these two components determine the switching frequency, amount of dead time, and the minimum pulse width at output pins 9, 10, 15 and 16. the minimum and maximum values of r o and c o are given in the electrical characteristics. the oscillator also sets the frequency of the charge pump circuit in the internal negative bias generator (v bb ). at lower frequencies (<40 khz) the value of cpump must be increased to assure proper operation. feedforward compansation in all fixed frequency pwm control systems open loop gain, motor current slew rate, and motor current ripple are proportional to the motor supply voltage. gain variations due to supply voltage changes complicate the design of such systems and restrict their band- width to the minimum worst case condition. for this reason, an advanced adaptive compensation scheme is built- in using a feedforward technique. this feature has been designed such that open loop gain is inversely proportional to the voltage applied to the ffwd pin, normally a fraction of the motor supply. as a result, open loop gain can be made independent of the high voltage supply and system bandwidth can be maximized. analog section the analog section of each channel of the ixms150 consists of a signal processor and an error amplifier. the signal processor is required since the voltage developed across the sense resistor often contains transients asso- ciated with the switching characteristics of the power devices. these transients need to be properly filtered for the system to operate with the desired degree of precision. because of this, the ixms150 uses proprietary analog and digital signal processing techni- ques that sense the true average phase currents. since this requires only one sense resistor per h-bridge it avoids mismatches in charge/discharge currents associated with two sense resistor per h-bridge topologies. the instantaneous difference between the motor current and the control input is integrated via the e/a amp and fed to the pwm comparator to generate the appropriate signals for the h-bridges. external compensation of the input and sense signals is provided for via the comp1, comp2 and comp3 pins. protection circuitry the ic has a two-level over/excess current protection circuit. maximum current is represented as 0.625 v at the sense input. if the sense voltage exceeds 0.9 volts for more than one microsecond, the switching outputs (vout) and outdis will be forced low. this represents a current that is 40 % beyond full scale. if the sense voltage exceeds 3.6 v, these outputs will be forced low immediately. this repre- sents a current that is 500% beyond full scale. the time delay on the lower level of overcurrent avoids erroneous shutdowns as a result of noise spikes that are coupled from the motor?s h- bridges. note that the threshold voltages cited here assume a supply of +12 v. undervoltage lockout a third protection mechanism is the under-voltage lockout. it assures proper behavior on power-up and power-down and avoids high power dissipation in the h-bridge due to insufficient gate voltage. it uses a zener for reference and has a trip point set at 8 v. it will also check to make sure there is sufficient negative bias to insure proper operation. this is typically -1.6 v. outdis will be held low by the uv lockout circuit until v bb and v dd reach these values. output disable feature to enable external over-temperature protection, the output disable pin (outdis) is available on the ixms150. when pulled low this disables the output by forcing all output pins low. the same output disable input pin is also used as a status output. when it is pulled low by the internal circuitry it indicates an error condition such as undervoltage (v dd ), insufficient negative bias voltage (v bb ) or over/excess current. this can be used as a status indicator in smart systems. pwm section the pwm comparator generates two complementary signals based on the output of the error amplifier. dead-time is then added which is adjusted by the selection of the external oscillator capacitor. there is also a minimum duty cycle clamp circuit that allows the use of an ac coupled h-bridge. supply section the main power supply (v dd ) is applied to pin 24. this is typically +12 v. internal bias circuitry presents a v dd /2 reference voltage at pin 8, bypass. a 0.1 m f capacitor should be connected from pin 8 to analog ground for noise immunity. negative bias generator the ixms150 samples both positive and negative voltages at the motor sense feedback resistor. in addition, since errors in the input current around zero are a major contributor to micro- step positioning error, the input control range is bipolar and specified as 2 v full scale. for these reasons it is desi- rable to have both positive and nega- tive power supplies. in order to enable single 12 v supply operation, a negative voltage generator and regulator are built into the ic. this is a charge pump circuit whose frequency is that of the onboard oscillator. it utilizes an external pair of capacitors and diodes to gene- rate a negative bias equal to -v dd /5 or approximately -2.4 v for v dd = 12 v.
i - 39 ? 1998 ixys all rights reserved application information introduction the advantages of step motors are well known. they may be operated in an open loop fashion, the accuracy of which is mostly dependent on the mechanical accuracy of the motor. they move in quantized increments (steps) which lends them easily to digitally controlled motion systems. in addition, their drive signals are square wave in nature and are therefore easily gene- rated with relatively high efficiency due to their on/off characteristics. but step motors are not free of prob- lems. their large pulse drive wave- forms create mechanical forces which excite and aggravate the mechanical resonances in the system. these are load dependent and difficult to control since step motors have very little damping of their own. at resonance a step motor system is likely to lose synchronization and therefore skip or gain a step. being an open loop system, this would imply loss of position infor- mation and would be unacceptable. a common method of solving this problem is to avoid the band of resonance frequencies altogether, but this might put severe limitations on system performance. steppers have 200 steps per revolution or 1.8 degrees per step. the highest resolution commercially available steppers have 400 steps per revolution or 0.9 degrees per step. microstepping mode one way to circumvent the problems associated with step motors while still retaining their open loop advantages is to use them in the microstepping mode. in this mode each of the steps is subdi- vided into smaller steps or ?microsteps". applying currents to both phases of the motor creates a torque phaser which is proportional to the vector sum of both currents. when the phasor completes one ?turn? (360 electrical degrees), the motor moves exactly four full steps or one torque cycle. similarly, when that phasor moves 22.5 electrical degrees the motor will move (22.5/90) ? 100 = 25 % of a full step. thus the position of the motor is determined by the angle of the torque phasor. when used with an appropriate motor a positioning accu- racy of 2 % of a full step can be achie- ved, equaling 0.036 degrees for a 200 full steps per revolution motor. in this manner the motor can be positioned to any arbitrary angle. a common way to control the angle of the torque phasor is by applying to the motor?s phases two periodic waveforms shifted by 90 electrical degrees. let the phase current equations be: i a = i o ? cos q e (1) i b = i o ? sin q e (2) note that q e is the electrical position. the resulting torque generated by the corresponding phases would then be: t a = k 0 ? i a = k 0 ? i 0 ? cos q e (3) t b = k 0 ? i b = k 0 ? i 0 ? sin q e (4) where k 0 is the torque constant of the motor. substituting eqs. (1), (2) into (3), (4) and doing vector summation the resulting total generated torque mea- sured on the motor shaft is given by: t g = k 0 ? i 0 (5) note that in this case we have zero torque ripple. using this technique one can theore- tically achieve infinite resolution with any step motor. since the drive current waveforms are sinusoidal instead of square, the step to step oscillations are eliminated and the associated velocity ripple. this greatly improves perfor- mance at low rotational speeds and helps avoid resonance problems. in an actual application, the extent to which these things are true depends on how the two sinusoidal reference waveforms are generated. seemingly we have lost the quantized motion feature of a stepper when used in this mode. this can be regained by defining the term microsteps per step. each full step is subdivided into micro- steps by applying to the motor?s phases those intermediate current levels for which their vector sum tracks the circle of fig. 2 and divides the full step (90 electrical degrees) into the require number of microsteps. an example of the required phase currents for full step and four microstep per step operation are shown in fig. 1 and 2 respectively. phase current matching requirements assuming microstepping is being used for resolution improvement and not as a resonance avoidance technique, a step motor can be selected knowing the torque needed, its specified step ixms 150 fig. 1 full step drive waveforms accuracy, and the required resolution or the number of microsteps per step. next, one must determine the accuracy required of the phase currents to main- tain the accuracy of the complete system. equations (1) - (4) clearly indicate that errors in the absolute value or phase of the phase currents will impact positioning accuracy. another observation is that by keeping the ratio of the phase currents i a /i b constant, errors in their value will result fig. 2 four microstep per step drive waveforms
i - 40 ? 1998 ixys all rights reserved ixms 150 the h-bridge that must be properly filtered if the system is to operate with the desired degree of precision. this presents a significant engineering challenge that has been solved by ixys?s design team. using proprietary analog and digital signal processing techniques, ixys has developed a control system that measures the true average phase currents. requiring only one sense resistor per h-bridge, this technique avoids errors due to mis- matches in charge/discharge currents associated with using one sense resi- stor on each leg of the h-bridge. this improves system performance as well as minimizing component count. the sense resistor for each h-bridge should be selected based on the required peak motor current: r s = 0.625 v/i mpk (9) the voltage developed across this resistor is then applied to the corres- ponding sense input for each h-bridge. negative bias generator one of today?s cost cutting trends is to minimize the number of power supplies, implying single supply operation for the control section. yet the current feed- back and reference inputs are bipolar signals. level shifting has been used for the reference input in the past, but that can not be easily done for the feedback signal without impacting accuracy or efficiency. in practice one finds that in order to generate true zero voltage having low impedance drive there must be a negative power supply. otherwise there will be a tradeoff sacrificing accuracy for simpler system design. for these reasons the approach selec- ted by ixys was different. taking advantage of our cmos design, we opted to build into the chip a negative bias generator. this does put stringent demands on noise coupling but results in the most flexible system having the highest possible accuracy. the built in charge pump circuit requires two capa- citors and two diodes to be added externally. the recommended compo- nent values for an oscillator frequency of 100 khz are given below. c1 = 0.047 m f c2 = 100 m f d1 = d2 = 1n4148 note: v bb = -(v dd /5) in torque value errors but no positioning errors. the question is, what is the upper bound on the current errors in order to keep the position error within some given angle dq . referring to fig. 3, assume the required currents i a , i b are given by equations (1), (2) respectively such that their vector sum points to position p. let the phase currents vary by a small amount such that their vector sum lies within a circle centered at point p and having the radius i, as indicated in fig. 3. fig. 3 effect of current errors on position if follows that the worst case position error occurs for the cases where the vector sum is tangent to the circle such as point p 1 , at which: tan ( d q ) = d i/l 0 (6) for instance, to keep position error to less than 1% of a full step, the electrical angular error would be: d q = 0.01 ? 90 = 0.9 (7) this is assuming there are 90 electrical degrees for a full step. therefore total current error must be: i/i 0 = tan ( dq ) = 0.016 or 1.6 %) (8) thus the current error must be kept to less than 1.6 % of full scale or peak current at each phase for 1 % maximum position error. this upper bound on error includes all error sources such as zero offset errors and full scale matching errors. another interesting observation is that in the vicinity of a full step (i.e., q e = 0), the phase having the bigger impact on position error is the one carrying the smaller current through it. this has a strong impact on input waveform generation. input waveform generation it has been shown that the two input signals, vin a and vin b , are sinusoidal and 90 out of phase. this may be accomplished by using two look-up fig. 4 simple reference waveform generator tables stored in rom and two dacs per fig. 4. an up/down counter may be used to generate the appropriate address locations for the roms and the data outputs used to control the dacs. the user then need only supply up or down pulses to the counter to control the ixms150 and hence the motor. in higher performance systems a microprocessor may be used in place of the counter and the roms. the micro can perform the look-up function and calculate the appropriate system responses, velocity profiles, etc. necessary for total system operation. an example of this configuration is shown in fig. 5. current sensing considerations most commercially available monolithic pwm controllers monitor and control the peak of the phase current by com- paring the voltage across the sense resistor with a ramp voltage. this approach assumes that the ripple current is fixed in amplitude. results shown later clearly indicate the varia- tion of the ripple current with frequency. but even in fixed frequency systems the ripple current is directly proportional to the motor supply voltage and to the back emf voltage of the motor. ripple current is not insignificant compared to the full scale current and therefore cannot be neglected in a precision system. in addition, there are transients associated with the turn on and turn off characteristics of the power devices in fig. 5 microprocessor based referenced waveform generator
i - 41 ? 1998 ixys all rights reserved use the formula c2 = 100 m f ? 100 khz/f osc for other frequencies. with v dd = 12 v and an oscillator fre- quency of 100 khz, the bias generator should be able to source 3 ma at -2.4 v using these component values. this capability may be used to power other external circuitry as long as there is sufficient remaining negative bias to allow the ixms150 to operate properly. impact of pwm frequency on system operation pwm switching frequency has a pronounced effect on ripple current through the motor windings, the resul- ting eddy current losses in the motor, and system efficiency. as expected, motor current ripple goes down as frequency increases and therefore losses resulting from ripple currents are also reduced. switching frequency also impacts losses in the power stage. these losses are associated with the energy necessary to turn on and off the power mosfets and are proportional to the switching frequency. in addition, the switching frequency has a limiting effect on maximum current loop band- width and therefore system bandwidth and therefore system bandwidth and maximum motor velocity. oscillator the oscillator block diagram is shown in fig. 6. the frequency is set by the values of r o and c o : f osc = 1/r o ? (c o + c p )) (10) note: c p is a 38 pf (typ.) internal parasitic capacitor. ixms 150 v a 1/f o v(t) 2 ? v (pin 7) 7 v (pin 7 open) [ ] v a = 1/f osc = r o ? (c o + c p ) > > > > > > fig. 6a: oscillator block diagram fig. 6b: oscillator waveform diagram feedforward the amplitude of the oscillator wave- form and overall system gain are modu- lated by the voltage applied to the feedforward pin (ffwd). this is nomi- nally 3.5 v which should be divided down from the motor high voltage supply. this will allow system band- width to be maximized by making overall system gain inversely propor- tional to the motor supply voltage. refer to fig. 7 for an example of how feedforward is connected to the motor supply. it is recommended that a filter capacitor be connected from ffwd to agnd to filter noise spikes from the motor supply. its value should be chosen so that the time constant of the capacitor and the parallel combination of r ff1 and r ff2 is such that switching noise will be filtered but not variations in the motor supply such as 120 hz ripple, etc. minimum pulse width the minimum output pulse width can also be modified by adjusting the oscil- lator capacitor c o . the relationship is: t pw(min) = r mp ? (c o + c p )(11) note: r mp is a 3.6 k w (typ.) internal resistor, and c p is a 38 pf (typ.) internal parasitic capacitor. dead time dead time is adjusted via the external oscillator capacitor c o . there is an internal resistor in the dead time circuit as well. the relationship is: t dt = r dt ? (c o + c p ) (12) note: r dt is a 1.4 k w (typ.) internal resistor and c p is a 38 pf (typ.) internal parasitic capacitor. fig. 7 feedforward connection diagram motor slew rate limitations the maximum motor velocity in a microstepping application is determined by the maximum rate of change of the phase currents. once this limit is reached the system is ?slew rate limited,? at which point the peak undistorted phase current times the frequency of the input command is a fixed value. the theoretical limit for the maximum di/dt of the phase currents is determined by the motor supply voltage and the inductance of the motor: di/dt (max) = v hv /l m (13) the limit does not take into account the back emf of the motor, the bandwidth of the current loop driving the motor, or the minimum pulse width. the motor?s back emf will tend to reduce the voltage applied across the motor windings, effectively reducing the maximum slew rate. the bandwidth of the current loop must also be high enough so as not to degrade system performance. non-circulating operating mode the ixms150 is designed to control an h-bridge in the non-circulating mode. the equivalent circuit for an h-bridge is shown in fig. 8. in the non-circulating 1/f osc
i - 42 ? 1998 ixys all rights reserved ixms 150 mode, either sw1 and sw4 are on (v m = v hv ) or sw2 + sw3 are on (v m = - v hv ). by appropriately controlling the duty cycle of sw1//4 vs. sw2/3, the average motor voltage can be controlled such that: v m(avg) = 2 ? v hv (0.5-duty) note: duty is defined as the duty cycle of v outa . the ixms150 can now regulate the motor coil current by commanding the voltage level and polarity required. enhance the mosfets, with the top two transistors (q2, q4) being destroyed due to excessive power dissipation. therefore one has to limit the duty cycle excursions. the solution selected by ixys limits the minimum output pulse-width to 0.5 ms, which translates to a duty cycle range of 5 % to 95 % when operating at 100 khz, or wider at lower frequencies. there is a penalty of slightly limiting the maximum slew rate to (1-2 ? min duty) of the unrestricted case, which translates to 90 % of the ration with a particular motor. the basic elements involved in the current loop are illustrated in fig. 11a. referring to fig. 11b, the loop gain for this system (the product of the forward and feed- back gain terms) can be expressed as: g loop (s) = g e/a (s) ? k pwm ? g m (s) ? g i (s) (14) where g e/a (s) = error amplifier gain k pwm = cascade of pwm and output h- bridge gain fig. 8 simplified h-bridge diagram sw1 sw3 sw2 sw4 d1 d2 vm d3 d4 the power stage: an ac coupled h-bridge fig. 9 shows the power driver selected for this application. two of these are required to drive the two phase step motor. this circuit uses two n-channel and two p-channel power mosfets as opposed to an all n-channel architec- ture. the drawback of using p-channel transistors is that they are larger and therefore more expensive than similarly rated n-channel devices. but the advantages are much simplified drive and level shifting circuitry. this results in a lower component count and therefore higher reliability. it also lends itself easily to hybridization. other advantages of this topology are: a) the high efficiency associated with level shifting by ac coupling since no power is dissipated in the capacitors, and b) the same circuit can be used for motor applications ranging from 12 v to several hundred volts, the only modification being appropriately rated power tran- sistors and coupling capacitors. a limitation of this circuit is that it cannot be used at duty cycle extremes. this would require one input to be continu- ously low while the other is continu- ously high. eventually the coupling capacitors (c1, c2) would charge up to a voltage that would no longer fully fig. 9 ac coupled h-bridge diagram fig. 10a simplified microstepping system unrestricted maximum slew rate for 100 khz operation. loop compensation information when used with the appropriate power stage, each channel of the ixms150 acts as a closed loop transconductance amplifier. as such, it must be properly compensated to guarantee stable ope- g m (s) = cascade of motor winding impedance and h-bridge parasitic resistance g i (s) = current sense resistor and sampling amplifier gain the value of each of these terms can be determined from the laplace transform diagram in fig. 11b:
i - 43 ? 1998 ixys all rights reserved ixms 150 fig. 10b input offset adjust circuit l m = motor inductance r m = motor winding resistance r sw = power switch resistance r s = sense resistor it is very important that the motor induc- tance value used in the analysis is not the value on the manufacturer?s data sheet but rather the value observed in actual operation. the pwm action causes high frequency effects that can change the apparent small signal inductance significantly. these effects are dependent upon voltage as well as current and frequency. it is best to measure the observed current ripple at the motor supply voltage and switching frequency you expect to use and calculate the actual motor inductance using: l m = v hv /((2 ? f osc )(i max -i min )) (19) it is also important to note that both r m and r sw are temperature dependent. the motor winding resistance can increase by as much as 30 % at high temperatures, and if fets are used as power devices, r sw can increase to 2.2 times its value at room temperature. substituting equations 15 through 18 into equation 14 gives the expanded loop gain equation (eq. 20): (1+src) ? 2vhv ? 1 ? 2rs g loop (s) = sr 2 c ? v a ? (sl m +r m +r s +r sw ) which can be written as (eq.21): 4 ? v hv ? r s g loop (s) = ? v a (r m +r s ? r sw ) (1+rc) (sr 2 ? c) [1+sl m /r m +r s +r sw )] therefore the poles and zeros of the system are: pole at dc, with a 0db intercept of: 4v hv r s /[v a r 2 c(r m + r s + r sw )] zero at 1/(r ? c) pole at (r m + r s + r sw ) /l m a simple bode analysis can be per- formed to provide the necessary infor- mation to guarantee the stability of the loop. a stable system will result when the gain crossover occurs at a point where the loop phase shift is less than - 180 degrees. the gain crossover point is defined as the frequency where the magnitude of g loop (s) = 1 (0db). the bode plot will show two figures of merit that give an indication of the behavior of the closed loop system, gain margin and phase margin. gain margin is the amount of loop signal at- tenuation at the point where the loop phase has reached -180 degrees. it is a qualitative measure of how susceptible the loop is to noise outside its band- width. phase margin is the amount of fig. 10c gain adjust circuit g e/a (s) = (1 + src)/(sr 2 c) (15) k pwm = 2 ? v hv /v a (16) g m (s) = 1/(sl m + r m +r sw +r s ) (17) g i (s) = 2 ? r s (ignoring sampling effects) (18) where: r, c = external compensation components r 2 = internal input resistor, typically 20 k w v hv = motor high voltage power supply v a = oscillator amplitude, typically 7 v fig. 11a loop compensation block diagram
i - 44 ? 1998 ixys all rights reserved ixms 150 fig. 12 complete microstepping system q1, q2: irf9530 q3, q4: irf532 d1, d2: mur161oct d3, d4: mur410 u1: 40498 u2: 40508 all diodes are 1n4148 unless otherwise specified fig. 11b simplified laplace transform for stability analysis phase shift left (i.e., 180 - (loop phase)) at the gain crossover. this number gives the most intuitive feeling for how the loop will respond to perturbations and variations in system parameters. theoretically, a system with 1 degree of phase margin is stable. however, a step input to a system with small phase margin will cause an underdamped, ringly response or an oscillation that dies out after a long time. in a step motor, this overshoot and ring in the current waveform is unaccep- table. as the phase margin of a system is increased, the response to a step input slows down and the ringing is de- creased. the response becomes more damped. in a practical system, the minimum acceptable phase margin is about 30 degrees. more than 90 degrees slows the system response with no significant improvement in sta- bility. 60 degrees is usually considered optimal, if no other constraints exist. in a pwm motor drive amplifier, there are several additional constraints that apply. because the levels of voltage and current being switched are so high, synchronous noise appears every- where and can degrade system perfor- mance. it is common to see apparent instabilities that are simply loop ampli- fication of subharmonic switching transient noise. it is important to main- tain at least 60 degrees of phase margin and to maintain as much gain margin as is practical. the pwm comparator delays, power stage gate drive delays, and the sampling tech- nique used to generate the current feedback signal also account for signifi- cant phase delays when the switching frequency is high, or when the excitation approaches the switching frequency. for these reasons it is usually advis- able to design for a calculated 60 to 90 degree phase margin because of the importance of the effects not accounted for in the linearized circuit model.
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