Apparatus and method using waveform shaping for reducing high frequency noise from switching inductive loads

A low-noise switching regulator and a method for driving an inductive load, employing current slew control and voltage slew control, is provided. Open and closed loop embodiments, as well as first and higher order slewing, are also provided.

BACKGROUND OF THE INVENTION 
This invention relates to an apparatus and a method for using waveform 
shaping to reduce high frequency noise from switching (also referred to as 
"driving") inductive loads and, more particularly, using current slew 
control and voltage slew control, where "slew" refers to the slope (or 
rate of change) of a waveform. 
An increasingly important issue in the design of electric products is high 
frequency electromagnetic noise. This noise can reduce product performance 
or cause interference with other products. Tremendous energy and cost are 
spent trying to eliminate the source and reduce the effects of the noise. 
Switching currents and voltages in electric devices such as motors, 
solenoids and switching regulators are sources of noise that are 
omnipresent. New products, such as cellular telephones, require ever lower 
levels of both conducted and radiated electromagnetic noise in order to 
operate properly. There is also increased legislation regarding 
containment of electromagnetic pollution. European emission and 
susceptibility standards are a case in point. 
Sharp transitions in a waveform contain greater high frequency components. 
This can be shown mathematically through Fourier series and transforms. 
For instance, a pure sine wave has a single frequency component and a 
square wave has a large number of high frequency components whose 
amplitude decrease with frequency. Reducing high frequency content means 
reducing the sharpness of the transitions. 
FIG. 1 shows a simple rule of thumb regarding high frequency components. In 
a square wave, the high frequency components decrease in magnitude from 
the fundamental frequency 
##EQU1## 
at a 20 db/decade rate, where "on-time" is the time when the switch 
conducts current. 
A waveform with slewed edges is a waveform with transitions of nearly 
constant slope, i.e., a ramped signal. This means that the first 
derivative of the waveform is controlled. Often, waveforms with slewed 
edges have rounded corners. In a waveform with slewed edges and a constant 
first derivative, the high frequency components roll off at 20 db/decade 
from the fundamental frequency and at 40 db/decade from a frequency equal 
to 
##EQU2## 
where t.sub.slew is the transition time of the slewed edge. 
Radiation from electric devices can usually be considered in terms of the 
dominant electromagnetic field, which is either electric or magnetic. 
Either type of field can introduce noise into circuits. Electric field 
radiation is caused by changes in voltage. Magnetic field radiation is 
caused by changes in current. Countermeasures often involve both reducing 
the source of the radiation as well as shielding receiving circuits. 
Reducing electric field induced noise can be accomplished by slowing 
voltage transitions with elements like capacitors. Reducing coupling 
capacitances can lessen the strength of noise at the receiving end. This 
is done with metal enclosures and metal shielding of components, wires and 
printed circuit board traces. 
Containing magnetic field induced noise is more difficult. Reducing the 
source strength involves slowing down current transitions. Often this is 
done by adding inductive elements which are usually more expensive than 
capacitive elements. Shielding receiving elements from magnetic field 
induced noise requires a special and often expensive mu-metal shield. 
Since magnetic field induced noise can induce current in nearby printed 
circuit board traces, it is often difficult to provide a complete shield. 
Some switching regulator topologies integrate high frequency filter 
elements with power components which can help to reduce the cost. However, 
such topologies still often add specific components to reduce emissions. 
Adding external components necessarily increases system cost so it is 
desirable to minimize their number. Such external components are usually 
added to slow the rate of change in current and/or voltage. This can be 
done either by diverting high frequency components after they are created 
(adding a filter) or by minimizing their creation. Often because the 
currents are large, there is an associated power loss due to the 
filtering. 
Controlling the voltage slew (dv/dt) across an inductor is sometimes done 
by creating a filter. Adding capacitance to the switching node slows the 
voltage transition and absorbs high frequency components. However, because 
of the high currents involved, the capacitor may be physically large and 
can dissipate substantial power, reducing switching efficiency. 
Switching regulators are highly desirable because of their conversion 
efficiency. However this efficiency comes at the expense of creating 
current and voltage waveforms with greater high frequency electromagnetic 
content. This high frequency noise couples to nearby circuitry either 
through conduction or radiative electromagnetic coupling (capacitive and 
inductive). Switching regulator designers are often forced to compromise 
between efficiency, noise and performance. 
In a switching regulator, most electromagnetic interference is generated 
by: 1) abrupt changes in current through the inductor which create high 
frequency magnetic noise and induce changes on nearby lines; 2) changes in 
inductor current which create abrupt voltage changes through equivalent 
series resistance ("ESR") and equivalent series inductance ("ESL") in 
decoupling capacitors; 3) abrupt voltage changes on an output switching 
element which capacitively couple to ground, introducing transient 
currents onto power lines; and 4) turn-off of diodes which produces sharp 
current transients, produces high frequency magnetic noise and also may 
produce high frequency voltage transients through capacitor ESR. 
The interfering noise is introduced into other circuitry through conduction 
in power and ground wires and by capacitive or magnetic radiative coupling 
from "hot" components to other circuitry. Typically, conducted noise is 
more of a problem for the lower frequencies while radiated noise is more 
of a problem for higher frequencies. For a switching regulator, the 
current in the inductor or transformer and the currents in the switching 
elements are usually the most troublesome sources of noise because they 
are the largest currents. Likewise, voltage excursions in switching 
regulator switches are often the greatest source of noise due to the speed 
of transition and connection to the power path. 
In view of the foregoing, it would be desirable to provide an apparatus and 
a method for reducing high frequency noise components caused by switching 
an inductive load, without sacrificing circuit performance or adding 
additional components. 
It would also be desirable to allow more control over the tradeoff between 
harmonic content and conversion efficiency. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide an apparatus and a 
method for reducing high frequency noise components caused by switching an 
inductive load, without sacrificing circuit performance or adding 
additional components. 
It is also an object to allow more control over the tradeoff between 
harmonic content and conversion efficiency. 
These and other objects are accomplished by switching the inductive load 
using a drive voltage supply, the load coupled between a signal node and 
an output node, by slewing the output node voltage and slewing the signal 
node current.

DETAILED DESCRIPTION OF THE INVENTION 
The present invention is an apparatus and a method for reducing noise 
caused by high frequency electric and magnetic noise from switching 
inductive loads. 
The present invention enables a switching regulator controller to be 
modified to reduce electric and magnetic frequency harmonics economically 
while, at the same time, allowing more control over the tradeoff between 
harmonic content and conversion efficiency. Since most of the circuitry 
called for by the invention can be incorporated into an integrated 
controller, overall system costs can also be reduced. 
The harmonics are reduced by controlling the slew rates of both voltage and 
current in the switching regulator, thereby decreasing the need for large 
power handling filter components. This is done by reducing the abrupt 
changes of voltage and current in power components. In one embodiment, the 
output switching element has both voltage and current slewed by means of 
feedback control loops that are integrated into the controller. 
FIG. 2 shows a prior art boost (also referred to as "step-up") switching 
regulator circuit without controller driven by drive voltage V.sub.drive 
applied to drive node 95. Inductor current I.sub.L, ramps up when 
transistor 40 conducts (node 120 near ground). When transistor 40 is 
turned off, the voltage at node 120 rises rapidly as inductor 30 attempts 
to maintain constant current. Diode 60 turns on, and inductor 30 dumps 
current into capacitor 70. The main concern with diode 60 is its current 
transition (radiated magnetic field). Diode 60 turns off when transistor 
40 turns on. The abrupt turn-off of the diode produces a sharp current 
slew (di/dt) into the output. This is sometimes addressed by the use of a 
Schottky diode or by putting a snubber 100 across diode 60. Output voltage 
V.sub.out can be much larger than input voltage V.sub.in. Also shown are 
parasitic capacitances 20 and 50. 
Input common mode noise is defined as voltage or current that occurs in 
phase on both the supply line (V.sub.in) and return line (signal ground), 
i.e. both move the same way with respect to earth ground. Input 
differential mode noise is caused by differences in supply line and return 
line voltage values. Input common mode noise tends to be caused by voltage 
excursions of the switch and parasitic capacitances. Input differential 
mode noise tends to be caused by inductor currents acting on the impedance 
of the input capacitor (i.e, a capacitor placed on the input voltage line 
to filter noise coming from the source supply). Controlling dv/dt helps to 
reduce input common mode noise. Controlling di/dt helps to reduce input 
differential mode noise. 
Switching regulator circuits, such as the one shown in FIG. 2, reduce input 
common mode noise by slewing the output of the switch (i.e., by providing 
the output with a substantially linearly increasing output voltage). As 
shown in FIG. 2, Miller capacitor 90 with capacitance C.sub.miller is 
placed between collector and base of transistor 40 to control the voltage 
slew (dv/dt) when transistor 40 operates in the linear range. Because of 
the Miller effect, the feedback through Miller capacitor 90 causes the 
input capacitance of transistor 40 to increase to C.sub.miller 
.multidot.(G.sub.Q +1), where G.sub.Q is the gain of transistor 40. 
However, Miller capacitor 90 requires access to the input base or gate of 
transistor 40. Depending on the circuit, this may require that the 
capacitance of external Miller capacitor 90 be large. Normally, 
capacitance decreases with voltage for a bipolar transistor. Since Miller 
capacitor 90 is in parallel with the collector to base capacitance of 
transistor 40, it either has to be large enough to dominate the collector 
to base capacitance or change such that the total capacitance remains 
constant Therefore, it may be difficult to easily adjust the voltage slew 
(dv/dt) for fine tuning. Miller capacitor 90 is a feedback element that, 
depending on the load and drive conditions, may produce undesirable 
oscillations. 
One might expect that using Miller capacitor 90 would also ramp (i.e., 
cause to increase in substantially linear fashion) output current I.sub.L. 
However, since, as shown in FIG. 4, output voltage V.sub.out changes at a 
different time than the major change in inductor current I.sub.L1 
(approximately equal to I.sub.load in FIG. 4), Miller capacitor 90 has 
little effect on output current. This is because most of the current does 
not divert to diode 60 until the time the voltage change has occurred. 
Output voltage V.sub.out ramps up, turning on diode 60 which diverts the 
current and then clamping diode 60. 
Another way that noise can be introduced into the output is by capacitive 
coupling from the switching node. Again, slewing this node reduces this 
kind of noise. One way that voltage slew (dv/dt) is controlled (other than 
a Miller cap) is by ramping the input to the driver. An example of voltage 
slew control is shown in Linear Technology Application Note 29. 
The following discussion uses a switching regulator as an example but the 
invention is not limited to a switching regulator, which is but one device 
in which the invention may be embodied. This invention is applicable to 
other inductive load switching situations. Examples include motors (for 
instance, in a disk drive), impact printer printing pins, relays, 
solenoids (such as mechanical actuators and automotive fuel injector 
solenoids) and phased array radar waveguide adjusters. 
Conducted output noise of a switching regulator circuit depends on many 
factors. Circuit topology has a big influence on noise but often a 
predominant effect is the switching of the current onto the output 
capacitor. This current acting through the ESR of the capacitor can create 
sharp voltage steps. Therefore, reducing the sharpness of the current 
transition reduces this problem. 
A common solution to the output noise problem is to add additional 
filtering elements. Again, reducing the source of this output noise allows 
us to eliminate or reduce the need for such filtering elements. 
A switching inductor can introduce noise into a system in several ways. The 
first is by magnetic radiation of the component itself which depends on 
the current in the device. Current can also cause noise problems by acting 
on decoupling components, such as the voltage created in the ESR of a 
decoupling capacitor due to the current in the inductor. Another way is 
large voltage change. An example of a large voltage change would be the 
voltage "flyback" that is created when the current in an inductor changes 
suddenly. Thus, it is desirable to reduce the high frequency content of 
inductor current. As discussed above, high frequency content is controlled 
by current slew. For an inductor, the current slew (di/dt) is proportional 
to the voltage across the inductor, as shown below: 
##EQU3## 
The value of the voltage applied across the inductor is often a result of 
circuit topology. Voltage can be controlled by supply voltages, 
transformer action and clamps (such as zeners or snubbers). So, by 
limiting voltage, topology can control slew to a first order and, 
therefore, the first order high frequency components of an inductor's 
current. 
In a switching regulator, increased conversion efficiency is obtained by 
reducing power losses in the switching element. Current in an inductor 
does not change instantaneously, however voltage can change nearly 
instantaneously. When switching an inductor, one is usually switching 
between a clamp voltage and an on-state voltage. This places an 
approximate square wave voltage across the inductor. 
Switching regulators may be operated in one of two modes, continuous 
inductor current or discontinuous inductor current. In continuous mode, 
the current waveform is almost triangular with current slew controlled by 
voltage. In discontinuous mode, the current waveform is almost 
trapezoidal. The driving voltage is defined as the voltage across an 
inductor when the inductor is on. In either case, current slew is 
controlled by driving voltages. 
A principal concern with switching element 40 is that output voltage slew 
(dv/dt) will couple through parasitic capacitance 50 
(C.sub.Q.sbsb.parasitic) to ground producing input common mode noise. The 
transitions on the switching element are typically abrupt. In fact, in the 
continuous mode of operation, the transitions are almost a step function 
with transition times limited only by device turn-on or turn-off. 
The present invention controls switch dv/dt using a similar Miller 
capacitor that reduces input common mode noise. By integrating capacitive 
feedback into the output stage design, the amount of feedback is easily 
adjustable by the user and not as prone to oscillations. The invention 
also ties voltage slew (dv/dt) and current slew (di/dt) together by 
summing voltage feedback and current feedback at node 540, as shown in 
FIG. 5. 
The embodiments of the present invention shown in FIGS. 3, 5, 6 and 8 
attempt to control slew rates (voltage or current) such that the 
derivative of the changing output (voltage or current) is constant (i.e., 
constant slew causing the output to linearly ramp). 
By controlling the current slew (di/dt) of the switching element, it is 
possible to reduce transients (and thus high frequency content) caused by 
abrupt current change in the switching element that otherwise might couple 
through the power connection to the switching element. 
Controlling the current in the switching element (for example, Q.sub.switch 
above) also controls current in diode 60. As long as other parasitic 
elements are not too large, this is simply a result of Kirchoff's law. 
This implies that we can control the switching element current slew 
(di/dt) and automatically take care of the diode current slew (di/dt). 
In another embodiment, increased reduction of high frequency signal 
components can be obtained by controlling higher order derivatives of the 
signal. For these waveforms, not only is the first derivative finite and 
controlled, but higher order derivatives are finite and controlled, 
thereby eliminating abrupt transitions in the waveforms. One way of doing 
this is by creating differential feedback filters in a dual feedback loop 
method, as shown in FIG. 3, for example. Another way is to generate a 
waveform such as a tanh (hyperbolic tangent) shaped waveform in an open 
loop system, as shown in FIG. 13. 
As shown above with reference to FIG. 2, control of high frequency 
harmonics requires control of output switching element voltage slew 
(dv/dt) and current slew (di/dt). As shown in FIG. 4, when controlling 
output voltage and current during turn-on, switching element current 
I.sub.switch (the current in the collector of switching element 40) 
initially builds until it is nearly equal to the inductor current I.sub.L1 
at which point the output voltage V.sub.out then falls. When diode 60 
conducts, output voltage V.sub.out tracks switching element 40 collector 
voltage and differs only by the de minimis drop across diode 60. During 
turn-off, output voltage V.sub.out increases and then output current 
I.sub.load drops. Many circuits for controlling waveforms do not allow for 
control of all these transitions. The present invention is the first 
circuit to do this. 
The present invention allows for independent control of both output voltage 
and switching element current transitions. This is done by having two 
interlinked feedback paths: one for current and one for voltage. 
The following description is based on a closed loop control system, a slew 
control circuit, as shown in FIG. 3. The present invention is, of course, 
applicable to an open loop control system, whereby a correctly shaped 
waveform is amplified and used to drive the output, as shown in FIG. 13. 
To provide a given output current and voltage in an open loop system, 
knowledge about the load (e.g., the loads impedance characteristics) is 
necessary to design the drive to the output stage. 
As shown in FIG. 3, inductive load 230 is driven by drive voltage 
V.sub.drive applied to drive node 205. Signal node 300 current I.sub.out 
flows through load 230, which is coupled between signal node 300 and 
output node 310. Output node 310 voltage V.sub.out is differentiated by 
differentiating amplifier 290 (gain G.sub.V) to generate a first feedback 
signal which is applied to an input terminal of summer 210 and used to 
control the slew of V.sub.out. Signal node current I.sub.out is 
transformed by resistor 240 to a voltage signal, amplified by sense 
amplifier 250 (gain A.sub.sense), differentiated by differentiating 
amplifier 260 (gain G.sub.c), limited to a magnitude of I.sub.c.sbsb.slew 
by limiter 270, and multiplied by a coefficient I.sub.v.sbsb.slew 
/I.sub.c.sbsb.slew to generate a second feedback signal which is applied 
to an input terminal of summer 210 to control the slew of I.sub.out. 
Currents I.sub.c.sbsb.slew, I.sub.v.sbsb.slew are created by external 
resistors coupled to supply voltage V.sub.in which allows for user 
programmability. These resistors could be put on chip at fixed values or 
programmed electrically. Summer 210 combines the first and second feedback 
signals with drive voltage V.sub.drive, whose magnitude has been limited 
to I.sub.v.sbsb.slew, to drive load 230 through drive amplifier 220 (of 
gain equal to -G.sub.drive). 
FIG. 5 shows a block diagram of a preferred embodiment which comprises two 
feedback loops. Drive voltage V.sub.drive is applied to the positive input 
terminal of transconductance amplifier 400. Transconductance amplifier 400 
has its negative input terminal coupled to V.sub.r and is controlled by 
I.sub.v.sbsb.slew. Transconductance amplifier can also be thought of as a 
voltage controlled current switch that switches between sourcing 
I.sub.v.sbsb.slew and sinking I.sub.v.sbsb.slew. Output buffer amplifier 
450 is coupled between drive node 540 and the base of output switch 460. 
Output switch 460 may be a transistor, as shown in FIG. 5. In FIG. 5, the 
inductive load comprises inductor 480 coupled between V.sub.in and signal 
node 520; diode 490 coupled between signal node 520 and output node 530; 
capacitor 500 coupled between output node 530 and ground; and resistor 510 
coupled between output node 530 and ground. I.sub.c.sbsb.slew and 
I.sub.v.sbsb.slew are currents created by resistors which may be adjusted 
for a given slew rate. 
The first feedback loop of FIG. 5, the voltage slew control loop, comprises 
Miller capacitor 470 which is coupled between signal node 520 and drive 
node 540. 
The second feedback loop of FIG. 5, the current slew control loop, 
comprises resistor 440 coupled between the emitter of transistor 460 at 
node 550 and ground; sense amplifier 430 coupled across resistor 440; 
capacitor 560 coupled between output terminal of sense amplifier 430 and 
current slew control feedback node 570; transconductance amplifier 420 
controlled by I.sub.c.sbsb.slew with negative input terminal coupled to 
current slew control feedback node 570, positive input terminal coupled to 
reference voltage V.sub.r and output terminal coupled to current slew 
control feedback node 570; and transconductance amplifier 410 controlled 
by I.sub.v.sbsb.slew with negative input terminal coupled to current slew 
control feedback node 570, positive input terminal coupled to V.sub.r and 
output terminal coupled to drive node 540. For transconductance amplifier 
420, output current I.sub.x =G.sub.c .multidot.(V.sub.r -V.sub.gc). For 
transconductance amplifier 410, output current I.sub.y =G.sub.cv 
.multidot.(V.sub.r -V.sub.gc). Therefore, I.sub.y =I.sub.x 
.multidot.G.sub.cv /G.sub.c. When transconductance amplifiers 410 and 420 
have limiting currents of I.sub.v.sbsb.slew and I.sub.c.sbsb.sle.spsb.w, 
respectively, then 
##EQU4## 
where A represents an additional gain variable. This loop controls the 
current slew (di/dt) of output transistor 460, which acts as the switching 
element. During output current excursions, voltage V.sub.gc at current 
slew control feedback node 570 is slewed by means of the current outputs 
of G.sub.c and the capacitor C.sub.c. 
Because the two loops share the common drive node, both loops can interact 
with each other, allowing a smooth transition between voltage and current 
slewing. 
The current i.sub.c.sbsb.slew, the capacitor C.sub.c, the sense amplifier 
and sense resistor together control the current slew rate. The current 
i.sub.v.sbsb.slew, and the capacitor C.sub.v control the voltage slew 
rate. Approximate equations are: 
##EQU5## 
One limitation of the circuit of FIG. 5 is the sudden clamping off of the 
output voltage by diode 490. Because of the speed at which this clamping 
off takes place, the current slew feedback loop must quickly take over 
from the voltage slew feedback loop for good control. FIG. 6 shows a 
possible transistor level embodiment of transconductance amplifier 400, 
transconductance amplifier 410, transconductance amplifier 420 and sense 
amplifier 430 of the slew control circuit of FIG. 5 and includes switch 
over circuit 600 to facilitate the change over from current slew feedback 
to voltage slew feedback and to compensate for the overlapping feedback 
loops and device limitations. Device limitations include finite transistor 
bandwidth and finite transistor gain. 
During output turn off, transistor 690 sinks current. The positive voltage 
slew on the output creates a current through capacitors 610 and 760. 
Current from capacitor 610 stops flowing, causing the voltage on the 
collector of transistor 640 to fall from about two diode voltage drops 
above ground toward saturation. This then pulls current through diode 630 
from transistor 660, diverting current from current mirror 680, 690. Thus, 
the output voltage slew diverts current from transistor 690 momentarily, 
preventing further output turnoff and allowing the current feedback loop 
time to respond. 
FIG. 6 also includes capacitor 770 which helps invoke the current loop 
during turn-on of the output driver in order to pull the base of 
transistor 860 high during output driver turn on, thereby giving the 
current control loop time to respond and inductor 970 which helps to 
stabilize the current control loop during turn-off. 
FIG. 7 illustrates representative waveforms corresponding to the circuit of 
FIG. 6 as a function of time. FIG. 7a shows the current in diode 630. FIG. 
7b shows the current in capacitors 760 and 780. FIG. 7c shows the current 
in transconductance amplifier 400. FIG. 7d shows the current in 
transconductance amplifier 410. FIG. 7e shows the voltage at the output of 
transconductance amplifier 420. FIG. 7f shows the voltage at the output of 
sense amplifier 430. FIG. 7g shows voltages V.sub.drive and V.sub.in. FIG. 
7h shows output current and output voltage. 
One skilled in the art will easily recognize that a switched mode power 
supply controller employing output slew control with dual output terminals 
may be provided for use in push-pull applications. In such an embodiment, 
the sense amplifier and G.sub.c amplifier can be common (i.e., both 
outputs can share a single sense amplifier) with separate G.sub.v, 
G.sub.vc amplifiers and drivers. 
A complete switcher is shown in FIG. 8. The complete switcher includes 
driver block 1020. Driver block 1020 may include a voltage regulator, such 
as low-dropout linear regulator 1220 to generate a regulated voltage 
V.sub.reg. The complete switcher may also include decoupling capacitor 
1000 as well as additional circuitry for adjusting voltage and current 
slew, such as resistors 1300 and 1310 connected to nodes R.sub.Vslew and 
R.sub.Cslew (nodes shown in FIG. 9). Further simplification of slew 
control in a switching regulator controller may be obtained by using 
information from output terminal of error amplifier and the feedback pin 
FB. It is desirable to have higher efficiency (faster slews) during 
startup. As the system starts to regulate, slew is increased by action of 
oscillator/logic block 1200, thereby quieting the system. 
FIG. 9 shows a possible transistor level embodiment of transconductance 
amplifier 1040, transconductance amplifier 1050, output buffer amplifier 
1045 (including bias circuit), transconductance amplifier 1060 and sense 
amplifier 1080 of the complete switcher circuit of FIG. 8 and includes 
switch over circuit 1400 to facilitate the change over from current slew 
feedback to voltage slew feedback and to compensate for the overlapping 
feedback loops and device limitations. 
Another embodiment of a slew control circuit is shown in FIG. 10. FIG. 10 
is a single control resistor slew control circuit which corresponds to the 
circuit of FIG. 6. In this embodiment, the voltage slew control is as 
described above with reference to FIG. 6, i.e., via the feedback through 
capacitor 1590. Current sense and amplification is done by transistor 1570 
and associated resistors. Current slew feedback is done by capacitor 1560 
which feeds directly to the common drive node 1640. In this embodiment, 
voltage and current slew rates are adjusted by a single element (capacitor 
1590) and are thus in tandem. 
To provide increased levels of control of the high frequency components of 
inductor current, higher order derivatives of current should be finite and 
well behaved. Since the voltage slew (dv/dt) across an inductor can be 
expressed 
##EQU6## 
it follows that the voltage slew across the inductor can be controlled by 
controlling the second derivative of the current. Therefore, inductor 
current harmonics can be further dampened by softening the corners of the 
current transitions by controlling the second derivative of inductor 
current, as shown in FIG. 11, using second derivative loop 1795 coupled to 
current slew control feedback loop 1797. In effect, second derivative loop 
1795 slews the current slew control feedback signal from current slew 
control feedback loop 1797. This adds an additional 20 db roll-off that is 
of more use at higher frequencies. The second derivative (d.sup.2 
i/dt.sup.2) indicates the rate of change in the first derivative (di/dt), 
and therefore is a good indicator of how sharp the transitions are. A 
voltage slew feedback loop is not required. As an added benefit, 
controlling voltage slew across the inductor reduces parasitic capacitance 
(C.sub.Q.sbsb.parasitic, C.sub.L.sbsb.parasitic) currents which can 
produce additional noise components. Thus, for an inductive load, it is 
desirable not only to control the current slew (di/dt) but also to control 
the second derivative of the current. Controlling the voltage slew (dv/dt) 
controls the second derivative of the current and also helps to reduce 
parasitic component additions to high frequency noise. 
Increased reduction of high frequency signal harmonics can be obtained by 
controlling higher order derivatives of the signal (for example the Mth 
derivative of the output voltage and the Nth derivative of the output 
current), as shown in FIG. 12. The general expressions for the voltage and 
current slew signals are respectively 
##EQU7## 
For these waveforms not only is the first derivative finite and controlled 
but higher order derivatives are finite and controlled, thereby 
eliminating abrupt transitions in the waveforms. One way of doing this is 
by creating different feedback filters in a dual feedback loop method. 
Another way would be to generate a tanh (hyperbolic tangent) shaped 
waveform in an open loop system. 
The embodiments of the present invention described above use output voltage 
and output current derivatives as feedback to control harmonics. However, 
the present invention is not limited to using feedback. It is possible to 
use first and higher order derivatives of output voltage and output 
current in an open loop method whereby a drive signal is amplified and 
applied directly to the load, as shown in FIG. 13. 
Thus, it is seen that an apparatus and a method for using waveform shaping 
to reduce high frequency noise from switching inductive loads is provided. 
One skilled in the art will appreciate that the present invention can be 
practiced by other than the described embodiments, which are presented for 
the purposes of illustration and not of limitation, and the present 
invention is limited only by the claims which follow.