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Component = selection, layout=20 lead to success with Class D audio = amps


By Jun Honda & Jonathan = Adams,=20 International Rectifier


3D""=20
Courtesy of =20 Audio DesignLine =
(01/23/2006 8:18 = AM=20 EST)

=20
A Class D audio amplifier is basically a=20 switching amplifier or PWM amplifier. = There are=20 a number of different classes of = amplifiers. We will take a look at the definitions for = the=20 main classifications as an introduction: =

Class A =96 In a Class A = amplifier, the=20 output devices are continuously = conducting for=20 the entire cycle, or in other words = there is=20 always bias current flowing in the = output=20 devices. This topology has the least = distortion=20 and is the most linear, but at the same = time is=20 the least efficient at about 20%. The = design is=20 typically not complementary with a high = and low=20 side output devices.

Class B =96 = This type=20 of amplifier operates in the opposite = way to=20 Class A amplifiers. The output devices = only=20 conduct for half the sinusoidal cycle = (one=20 conducts in the positive region, and one = conducts in the negative region), or in = other=20 words, if there is no input signal then = there is=20 no current flow in the output devices. = This=20 class of amplifier is obviously more = efficient=20 than Class A, at about 50%, but has some = issue=20 with linearity at the crossover point, = due to=20 the time it takes to turn one device off = and=20 turn the other device on.

Class = AB =96=20 This type of amplifier is a combination = of the above two types, and is currently one = of the=20 most common types of power amplifier in=20 existence. Here both devices are allowed = to=20 conduct at the same time, but just a = small=20 amount near the crossover point. Hence = each device is conducting for more than half = a cycle=20 but less than the whole cycle, so the = inherent=20 non-linearity of Class B designs is = overcome, without the inefficiencies of a Class A = design.=20 Efficiencies for Class AB amplifiers is = about=20 50%.

Class D =96 This class of = amplifier=20 is a switching or PWM amplifier as = mentioned=20 above. This class of amplifier is the = main focus of this application note. In this type = of=20 amplifier, the switches are either fully = on or=20 fully off, significantly reducing the = power=20 losses in the output devices. = Efficiencies of=20 90-95% are possible. The audio signal is = used to=20 modulate a PWM carrier signal which = drives the=20 output devices, with the last stage = being a low=20 pass filter to remove the high frequency = PWM=20 carrier frequency.

Classes A, B = and AB=20 are all what is termed linear = amplifiers. We=20 will discuss the differences between = Linear and=20 Class D amplifiers in the next section. = The=20 block diagram of a linear amplifier is = shown=20 below in figure 1. In a linear amplifier = the=20 signals always remain in the analog = domain, and=20 the output transistors act as linear = regulators=20 to modulate the output voltage. This = results in=20 a voltage drop across the output = devices, which=20 reduces efficiency. Class D amplifiers = take on=20 many different forms, some can have = digital=20 inputs and some can have analog inputs. = Here we=20 will focus on the type which have analog = inputs.=20

=20


=20 Figure 1 above shows the basic block = diagram=20 for a Half Bridge Class D amplifier, = with the=20 waveforms at each stage. This circuit = uses=20 feedback from the output of the = half-bridge to=20 help compensate for variations in the = bus=20 voltages.

So how does a Class D=20 amplifier work? A Class D amplifier = works in=20 very much the same way as a PWM power = supply (we=20 will show the analogy later). Let=92s = start with=20 an assumption that the input signal is a standard audio line level signal. This = audio=20 line level signal is sinusoidal with a = frequency=20 ranging from 20Hz to 20kHz typically. = This signal is compared with a high = frequency=20 triangle or sawtooth waveform to create = the PWM=20 signal as seen in =20 figure 2a below.

=20


This PWM signal is then used to drive = the=20 power stage, creating the amplified = digital=20 signal, and finally a low pass filter is = applied=20 to the signal to filter out the PWM = carrier=20 frequency and retrieve the sinusoidal = audio=20 signal (also seen in figure 2b).=20

Topology Comparison =96 = Linear vs.=20 Class D
In this section we will = discuss=20 the differences between linear (Class A = and=20 Class AB) amplifiers, and Class D = digital power=20 amplifiers. The primary and main = difference=20 between linear and Class D amplifiers is = the=20 efficiency. This is the whole reason for = the=20 invention of Class D amplifiers. The = Linear=20 amplifier is inherently very linear in = terms of=20 its performance, but it is also very = inefficient=20 at about 50% typically for a Class AB = amplifier,=20 whereas a Class D amplifier is more = efficient,=20 with values in the order of 90% in = practical=20 designs. Figure 3 below shows typical = efficiency=20 curves for linear and Class D=20 amplifiers.

=20


Gain =96 With Linear = amplifiers the gain=20 is constant irrespective of bus voltage=20 variations, however with Class D = amplifiers the=20 gain is proportional to the bus voltage. = This=20 means that the power supply rejection = ratio=20 (PSRR) of a Class D amplifier is 0dB, = whereas=20 the PSRR of a linear amplifier is very = good. It=20 is common in Class D amplifiers to use = feedback=20 to compensate for the bus voltage = variations.=20

Energy Flow =96 In linear = amplifiers the energy flow is always = from supply=20 to the load, and in Full bridge Class D=20 amplifiers this is also true. A = half-bridge=20 Class D amplifier however is different, = as the energy flow can be bi-directional, = which leads=20 to the =93Bus pumping=94 phenomena, = which causes the=20 bus capacitors to be charged up by the = energy=20 flow from the load back to the supply. = This=20 occurs mainly at the low audio = frequencies i.e.=20 below 100Hz.

Analogy to a = Synchronous=20 Buck Converter
A simple analogy = can be=20 made between a Class D amplifier and a=20 synchronous buck converter. The = topologies are=20 essentially the same as can be seen = below in =20 figure 4.

=20


The main difference between the two = circuits=20 is that the reference signal for the = synchronous=20 buck converter is a slow changing signal = from=20 the feedback circuit (a fixed voltage), = in the=20 case of the Class D amplifier the = reference=20 signal is an audio signal which is = continuously changing. This means that the duty = cycle is=20 relatively fixed in the synch buck = converter,=20 whereas the duty is continuously = changing in the Class D amplifier with an average duty = of 50%.=20 In the synchronous buck converter the = load=20 current direction is always towards the = load,=20 but in Class D the current flows in both = directions.

The final difference = is in=20 the way the MOSFETs are optimized. The=20 Synchronous buck converter is optimized=20 differently for the high and low side = MOSFETs,=20 with lower RDS(on) for longer duty and = low Qg=20 for short duty. The Class D amplifier = has the=20 same optimization for both of the = MOSFETs, with=20 the same RDS(on) for high and low=20 side.

Power Losses in the=20 MOSFETs
The losses in the power = switches=20 are very different between linear = amplifiers and=20 Class D amplifiers. First lets look at = the=20 losses in a linear Class AB amplifier. = The=20 losses can be defined as:

=20


Where K is the ratio of Vbus to = output=20 voltage. This can then be simplified = down to the=20 following equation for the linear = amplifier Power switch losses:

=20


Note that the power loss is not = related to=20 the output device parameters. Figure 5 = below=20 shows the power loss vs K.

=20


Now lets look at the losses for a = Class D=20 amplifier. The total power loss in the = output=20 devices for a Class D amplifier are = given by:=20

=20


Psw are the switching losses and are = given by=20 the equation:

=20


Pcond are the conduction losses and = are given=20 by the equation:

=20


Pgd are the gate drive losses and are = given=20 by the equation:

=20


As can be seen in a Class D amplifier = the=20 output losses are dependant on the = parameters of=20 the device used, so optimization is = needed to=20 have the most effective device, based on = Qg,=20 RDS(on), COSS, and tf . Figure 6 below = shows the=20 power losses vs K for the Class D=20 amplifier.

=20


Similar to conventional Class AB = amplifiers,=20 Class D amplifiers can be categorized = into two=20 topologies, half-bridge and full-bridge configurations. Each topology has pros = and=20 cons. In brief, a half-bridge is = potentially=20 simpler, while a full-bridge is better = in audio=20 performance. The full-bridge topology = requires=20 two half-bridge amplifiers, and thus, = more=20 components. However, the differential = output structure of the bridge topology = inherently can=20 cancel even the order of harmonic = distortion=20 components and DC offsets, as in Class = AB amplifiers. A fullbridge topology = allows of the=20 use of a better PWM modulation scheme, = such as=20 the three level PWM which essentially = has fewer=20 errors due to quantization.

In = the=20 half-bridge topology, the power supply = might=20 suffer from the energy being pumped back = from=20 the amplifier, resulting in severe bus = voltage=20 fluctuations when the amplifier outputs = low=20 frequency audio signals to the load. = This=20 kickback energy to the power supply is a fundamental characteristic of Class D=20 amplification. Complementary switching = legs in=20 the full-bridge tend to consume energy = from the=20 other side of the leg, so there is no = energy=20 being pumped back towards the power = supply. =20 Table 1 shows the summary of the=20 comparison.

=20


An ideal Class D amplifying stage has = no=20 distortion and no noise generation in = the=20 audible band, along with providing 100%=20 efficiency. However, as shown in =20 Figure 7, practical Class D = amplifiers have=20 imperfections that generate distortions = and=20 noise.

=20


The = imperfections=20 are caused by the distorted switching = waveform=20 being generated by the Class D stage. = The causes=20 are:

1. Nonlinearity in the PWM = signal=20 from modulator to switching stage due to = limited=20 resolution and/or jitter in timing
2. = Timing=20 errors added by the gate drivers, such = as=20 dead-time, ton/toff, and tr/tf
3. = Unwanted=20 characteristics in the switching = devices, such=20 as finite ON resistance, finite = switching speed=20 or body diode characteristics.
4. = Parasitic=20 components that cause ringing on = transient edges=20
5. Power supply voltage fluctuations = due to=20 its finite output impedance and reactive = power=20 flowing through the DC bus
6. = Non-linearity=20 in the output LPF.

In general, = switching=20 timing error in a gate signal is the = primary cause of the nonlinearity. The timing = error due=20 to dead-time in particular has the most=20 significant contribution of nonlinearity = in a Class D stage. A small amount of = deadtime in=20 the tens of nano-seconds can easily = generate=20 more than 1% of THD (Total Harmonic = Distortion). Accurate switching timing is always a = primary=20 concern. Let=92s take a look at how the = dead-time=20 affects nonlinearity. The operation mode = in a Class D output stage can be categorized = into=20 three different regions based on how the = output=20 waveform follows the input timing. In = those three different operation regions, the = output=20 waveform follows different edges in high = side=20 and low side input = signals.

Consider the=20 first operating region where the output = current=20 flows from the Class D stage to the load = when=20 the amount of the current is larger than = the=20 inductor ripple current. At the instant = of high=20 side turn-off and prior to low side = turn-on, the=20 output node is driven to the negative DC = bus.=20 This action is automatically caused by = the=20 commutation current from the = demodulation=20 inductor, regardless of low side turn-on = timing.=20 Therefore the timing in the output = waveform is=20 not influenced by the dead-time inserted = into=20 the turn-on edge of low side, and always = follows=20 the high side input timing. = Consequently, the=20 PWM waveform is shortened only by the = dead-time=20 inserted into the high side gate signal, = resulting in slightly lower voltage gain = as=20 expected from the input duty cycle. A = similar=20 situation happens to the negative = operation=20 region where the output current flows = from the=20 load to the Class D stage. The amount of = the=20 current is larger than the inductor = ripple=20 current. In this case, the timing in the = output=20 waveform is not influenced by the = dead-time inserted into the turn-on edge of the = high=20 side, and always follows the low side = input=20 timing. Consequently, the PWM waveform = is=20 shortened only by the dead-time inserted = into=20 the low side gate signal.

There = is a=20 region between the two operation modes = described=20 earlier where the output timing is = independent=20 of the dead-time. When the output = current is=20 smaller than the inductor ripple = current, the=20 output timing follows the turn-off edge = of each=20 input because, in this region, turnon is = made by=20 ZVS (Zero Voltage Switching) operation. = Hence,=20 there is no distortion in this middle = region. As=20 the output current varies according to = the audio=20 input signal, the Class D stage changes = its operation regions, which each have a = slightly=20 different gain. The output waveform will = be=20 distorted by these three different gain = regions in a cycle of the audio = signal.

=20 Figure 8 shows how significantly = dead time=20 affects THD performance. A 40nS dead = time can=20 create 2% THD. This can be improved to = 0.2% by=20 tightening the dead time down to 15nS. = This=20 punctuates the significance of seamless = high=20 side and low side switching for better=20 linearity.

=20


Audio Performance = Measurement
Audio=20 measuring equipment with an AES17 brick = wall=20 filter, such as the Audio Precision AP2, = are=20 necessary. However a classic audio = analyzer like=20 the HP8903B can be used with appropriate = pre-stage low pass filter is applied. = The=20 important consideration here is that the = output=20 signal of a Class D amplifier still = contains=20 substantial amount of switching = frequency=20 carrier on its waveform, which causes a = wrong=20 reading, and those analyzers might not = be immune=20 enough to the carrier leak from a Class = D=20 amplifier. =20 Figure 9 shows an example of a=20 filter.

=20


Narrow Deadtime Risk
A = narrow=20 dead-time can be very risky in mass = production.=20 Once both high and low side MOSFETs are = turned=20 on simultaneously, the DC bus voltage = will be=20 short circuited by the MOSFETs. A huge = amount of=20 shoot-through current starts to flow, = which will=20 result in device destruction. It should = be=20 noticed that the effective deadtime can = be vary=20 from unit to unit due to variation of = component=20 values and the MOSFET die = temperature.

=20 Figure 10 shows the relationship = between the=20 length of the dead time and the amount = of=20 shoot-through charge. It is extremely = important=20 for a reliable design of a Class D = amplifier to=20 ensure that the dead-time is always = positive and=20 never negative to prevent MOSFETs from = entering=20 the shoot through condition.

=20


Another marked cause of degradation = in Class=20 D amplifiers is bus pumping, which can = be seen=20 when the half bridge topology is = powering a low=20 frequency output to the load. Always = keep in=20 mind that the gain of a Class D = amplifier stage=20 is directly proportional to the bus = voltage. Therefore, bus fluctuation creates = distortion.=20 Since the energy flowing in the Class D=20 switching stage is bi-directional, there = is a=20 period where the Class D amplifier feeds = energy=20 back to the power supply. The majority = of the=20 energy flowing back to the supply is = from the=20 energy stored in the inductor in the = output LPF.=20 Usually, the power supply has no way to = absorb=20 the energy coming back from the load.=20 Consequently the bus voltage is pumped = up, creating bus voltage fluctuations. Bus = pumping=20 does not occur in full bridge topologies = because=20 the energy kicked back to the power = supply from=20 one side of the switching leg will be = consumed=20 in the other side of the switching=20 leg.

EMI in Class D = Amplifiers
EMI (Electro-Magnetic Interference) in = Class D=20 amplifier design is troublesome like in = other=20 switching applications. One of the major = sources=20 of EMI comes from the reverse recovery = charge of=20 the MOSFET body diode flowing from the = top rail=20 to the bottom, similar to the = shoot-through=20 current. During the dead-time inserted = to=20 prevent shoot through current, the = inductor=20 current in the output LPF turns on the = body=20 diode. In the next phase when the other = side of=20 the MOSFET starts to turn on at the end = of the=20 dead-time, the body diode stays in a = conducting=20 state unless the stored minority carrier = is=20 fully discharged. This reverse recovery = current=20 tends to have a =20 sharp spiky shape and leads to = unwanted=20 ringing from stray inductances in PCB = traces and the package. Therefore, PCB layout is = crucial=20 for both ruggedness of the design and = reduction=20 of EMI.

Conclusion
Highly efficient = Class D=20 amplifiers now provide performance = similar to conventional Class AB amplifiers if key = components are carefully selected and = the layout=20 takes into account the subtle, yet = significant impact of parasitic components. Greater = efficiency, increased power density and = better=20 audio performance are driving the = increased use=20 of Class D amplifiers with even more=20 improvements on the horizon. =

=20

 
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background-position: left top; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/main_body_bg.jpg= "); background-attachment: fixed; background-repeat: repeat-x; } .menu_welcome { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(255, 204, 102); text-transform: none; } .menu_white { font: 10px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(255, 255, 255); text-transform: none; text-decoration: none; } .menu_gold { font: 10px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(255, 204, 102); text-transform: none; text-decoration: none; } .tech_online { font: 9px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; } .tol_online { font: 10px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .tol_small { font: 9px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .teardown { font: 9px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 0, 0); text-transform: none; } .date { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 0, 0); text-transform: none; text-decoration: none; } .prod_black { font: 13px/normal Arial, Helvetica, sans-serif; color: rgb(0, 0, 0); = text-transform: none; text-decoration: none; } .eval_black { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(0, 0, 0); = text-transform: none; text-decoration: none; } .submenu_gray { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(152, 153, 155); text-transform: none; text-decoration: none; } .topmenu_gray { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(152, 153, = 155); text-transform: none; text-decoration: none; } .topmenu_black { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(0, 0, 0); = text-transform: none; text-decoration: none; } .black { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 0, 0); text-transform: none; } .cod_black { font: 14px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 0, 0); text-transform: none; } .nano_text { font: 15px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; text-decoration: none; } .gray_text { font: 14px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(143, 143, 143); text-transform: none; } .agilent_gray { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(130, 129, 129); text-transform: none; } .body_text { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 0, 0); text-transform: none; } .qnx_text { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 0, 0); text-transform: none; } .table_text { color: rgb(0, 0, 0); text-transform: none; line-height: normal; = font-family: Arial, Helvetica, sans-serif; font-size: 11px; font-style: = normal; font-weight: normal; } .company_text { color: rgb(0, 0, 0); text-transform: none; line-height: normal; = font-family: Arial, Helvetica, sans-serif; font-size: 11px; font-style: = normal; font-weight: normal; } .table_blue { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .analog_blue { font: 12px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .gold_text { font: 14px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(203, 144, 29); text-transform: none; } .gold_medium { font: 13px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(203, 144, 29); text-transform: none; } .gold_big { font: 16px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(203, 144, 29); text-transform: none; } .agilent_gold { font: 15px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(203, 144, 29); text-transform: none; } .footer_gold_text { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(203, 144, 29); text-transform: none; } .freescale_gold_text { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(203, 144, 29); text-transform: none; } .side_form_text { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; } .side_blue_link { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; text-decoration: none; } .related_companies { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(255, 255, 255); text-transform: none; } .module_white { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(255, 255, 255); text-transform: none; } .side_related_link { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; text-decoration: none; } .side_related_link1 { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; } .middle_blue_link { font: 10px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; text-decoration: none; } .virtua_blue_link { font: 10px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; } .footer_red { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(191, 10, 10); text-transform: none; text-decoration: none; } .audio_red { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(191, 10, 10); text-transform: none; text-decoration: none; } .footer_gray { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(105, 105, = 105); text-transform: none; text-decoration: none; } .red_big { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(191, 10, 10); text-transform: none; text-decoration: none; } .red_medium { font: bolder 16px/normal Arial, Helvetica, sans-serif; color: rgb(191, = 10, 10); text-transform: none; text-decoration: none; } .red_small { font: bolder 10px/normal Arial, Helvetica, sans-serif; color: rgb(191, = 10, 10); text-transform: none; text-decoration: none; } .red_large { font: 16px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(191, 10, 10); text-decoration: none; } .number_blue_link { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; padding-left: 4px; } .number_black { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; = text-transform: none; padding-left: 4px; } .number_blue_link2 { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; padding-left: 5px; } .number_blue_link3 { font: 12px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .more_link { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .number_black2 { font: 12px/normal Verdana, Arial, Helvetica, sans-serif; = text-transform: none; padding-left: 5px; } .lists { color: rgb(0, 51, 153); text-indent: -35px; font-family: Verdana, = Arial, Helvetica, sans-serif; font-size: 11px; text-decoration: none; = margin-bottom: 10px; list-style-type: decimal; list-style-position: = inside; } .agilent_lists { color: rgb(0, 51, 153); font-family: Verdana, Arial, Helvetica, = sans-serif; font-size: 11px; list-style-type: square; = list-style-position: inside; } .agilent_lists_member_company { list-style: inside = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/rel_mem_spot2.gi= f"); color: rgb(0, 51, 153); text-indent: -30px; font-family: Verdana, = Arial, Helvetica, sans-serif; font-size: 11px; } .hood_lists { color: rgb(0, 0, 0); font-family: Verdana, Arial, Helvetica, = sans-serif; font-size: 11px; margin-left: -20px; } .hood_lists1 { color: rgb(0, 0, 0); text-indent: -39px; font-family: Verdana, Arial, = Helvetica, sans-serif; font-size: 11px; list-style-type: disc; = list-style-position: inside; } .vlab_lists { color: rgb(0, 0, 0); text-indent: -39px; font-family: Verdana, Arial, = Helvetica, sans-serif; font-size: 12px; list-style-type: disc; = list-style-position: inside; } .article_lists { color: rgb(0, 0, 0); text-indent: -39px; font-family: Verdana, Arial, = Helvetica, sans-serif; font-size: 11px; margin-bottom: -5px; = list-style-type: disc; list-style-position: inside; } #coll1 { width: 15px; } #coll2 { width: 18px; } #coll3 { width: 170px; } #coll_hood { width: 158px; } #coll_hood2 { width: 426px; } #coll_cod1 { width: 160px; } #coll_cod2 { width: 230px; } #coll_tol1 { width: 412px; } #coll_first { width: 415px; } #coll_tol2 { width: 351px; } #coll_tol_netsem { width: 605px; } #coll_vlab_big { width: 960px; } #coll_netsem { width: 169px; background-color: rgb(243, 247, 250); } #coll_member { width: 170px; } #coll_netsem2 { width: 238px; } #coll4 { width: 19px; } #coll_new { width: 20px; } #coll_new2 { height: 1px; background-color: rgb(255, 255, 255); } #coll_new3 { height: 6px; } #coll_next { width: 22px; } #coll5 { width: 335px; } #coll_tol { width: 351px; } #coll6 { width: 7px; } #coll9 { width: 5px; } #coll_tol4_first { width: 400px; } #coll_height_top { height: 28px; } #coll_height_small { height: 13px; } #coll7 { width: 1px; background-color: rgb(204, 204, 204); } #coll_all { width: 1px; background-color: rgb(141, 167, 192); } #coll8 { background-position: left top; width: 9px; height: 29px; = background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/small_header_bg.= jpg"); background-repeat: repeat-x; } #coll_height1 { height: 1px; background-color: rgb(114, 140, 165); } #coll_height3 { height: 7px; } #coll_height4 { height: 1px; background-color: rgb(204, 204, 204); } #coll_height5 { height: 15px; } #coll_height_big { height: 24px; } .all_bg { background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/submenu/all_bg.j= pg"); background-repeat: repeat-x; } .sub_menu_bg { background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/submenu/main_bg.= jpg"); background-repeat: repeat-x; } .hood_bg { background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/submenu/hood_bg.= jpg"); background-repeat: repeat-x; } .design_bg { height: 20px; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/submenu/design_b= g.jpg"); background-repeat: repeat-x; } .learn_bg { height: 20px; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/submenu/learn_bg= .jpg"); background-repeat: repeat-x; } .content_bg { background-position: left top; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/small_header_bg.= jpg"); background-repeat: repeat-x; } .related_content_bg { background-position: left top; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/small_header_bg.= jpg"); background-repeat: repeat-x; } .popular_content_bg { background-position: left top; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/small_header_bg.= jpg"); background-repeat: repeat-x; } .freescale_bg { background-position: left top; height: 18px; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/freescale_bg.jpg= "); background-repeat: repeat-x; } #head_cell { height: 20px; background-color: rgb(0, 52, 102); } #blue_cell { padding-top: 3px; padding-bottom: 5px; background-color: rgb(241, 246, = 250); } #white_cell { padding-top: 3px; padding-bottom: 5px; background-color: rgb(255, 255, = 255); } #blue_smallcell { background-color: rgb(241, 246, 250); } #white_smallcell { background-color: rgb(255, 255, 255); } #blue_midcell { padding-top: 2px; padding-bottom: 2px; background-color: rgb(241, 246, = 250); } #white_midcell { padding-top: 2px; padding-bottom: 2px; background-color: rgb(255, 255, = 255); } #main_cell { background-color: rgb(243, 247, 250); } #first_cell { width: 20px; } #top_cell { height: 10px; } #middle_cell { height: 3px; } #form_cell { height: 5px; } #bottom_cell { height: 32px; } #line { height: 1px; background-color: rgb(148, 173, 195); } #coll_icon1 { width: 1px; background-color: rgb(127, 153, 176); } #coll_icon_height1 { height: 1px; background-color: rgb(127, 153, 176); } .related_image_bg { background-position: left top; width: 155px; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/related_bg.jpg")= ; background-repeat: repeat-x; } .image_bg { background-position: left top; height: 36px; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/right_image_bg.j= pg"); background-repeat: repeat-x; } #image_table_width { width: 1px; background-color: rgb(0, 0, 0); } #image_table_height { height: 1px; background-color: rgb(0, 0, 0); } #coll_vlab4_first { width: 522px; } #coll_vlab4_second { width: 149px; } #coll_vlab4_third { width: 289px; } #vlab_table_width { width: 1px; background-color: rgb(152, 173, 194); } #vlab_table_height { height: 1px; background-color: rgb(152, 173, 194); } .vlab_brown_text { font: 11px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(204, 166, 121); text-transform: none; } p.bottommargin { margin-bottom: -11px; } p.bottommargin2 { margin-bottom: -12px; } p.bottommargin3 { margin-bottom: -9px; } p.bottommargin4 { margin-bottom: -15px; } p.bottommargin5 { margin-bottom: -14px; } p.bottommargin6 { margin-bottom: -17px; } p.bottommargin7 { margin-bottom: 25px; } p.bottommargin8 { margin-bottom: -5px; } p.bottommargin9 { margin-bottom: 15px; } p.bottommargin10 { margin-bottom: -16px; } .tabberlive .tabbertabhide { display: none; } .tabber { =09 } .tabberlive { margin-top: 1em; } ul.tabbernav { font: bold 10px/normal Verdana, Arial, Helvetica, sans-serif; margin: = 0px; padding: 3px 0px; border-bottom-color: rgb(204, 204, 204); = border-bottom-width: 1px; border-bottom-style: solid; font-size-adjust: = none; font-stretch: normal; } ul.tabbernav li { list-style: none; margin: 0px; display: inline; } ul.tabbernav li a { border-width: 1px 1px medium; border-style: solid solid none; = border-color: rgb(204, 204, 204) rgb(204, 204, 204) currentColor; font: = bold 10px/normal Verdana, Arial, Helvetica, sans-serif; padding: 3px = 2.3em; border-image: none; text-decoration: none; margin-left: 0px; = font-size-adjust: none; font-stretch: normal; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/submenu/learn2_b= g.jpg"); } ul.tabbernav li a:link { color: rgb(101, 103, 102); } ul.tabbernav li a:visited { color: rgb(102, 102, 119); } ul.tabbernav li.tabberactive a { font: bold 10px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(0, 0, 0); border-top-color: rgb(114, 140, 167); border-bottom-color: = rgb(255, 255, 255); border-bottom-width: 1px; border-bottom-style: = solid; font-size-adjust: none; font-stretch: normal; background-image: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/submenu/design2_= bg.jpg"); } ul.tabbernav li.tabberactive a:hover { border-bottom-color: white; border-bottom-width: 1px; = border-bottom-style: solid; } .tabberlive .tabbertab { border-width: 0px 1px 1px; border-style: none solid solid; = border-color: currentColor rgb(204, 204, 204) rgb(204, 204, 204); = padding: 5px; border-image: none; } .tabberlive .tabbertab h2 { display: none; } .tabberlive .tabbertab h3 { display: none; } .tabberlive#tab1 { =09 } .tabberlive#tab2 { =09 } .tabberlive#tab2 .tabbertab { height: 200px; overflow: auto; } #colltol_pref1 { width: 11px; } #colltol_pref_main { width: 978px; } #tol_pref_width1 { width: 1px; background-color: rgb(224, 233, 240); } #tol_pref_height1 { height: 1px; background-color: rgb(224, 233, 240); } #tol_pref_width2 { width: 8px; background-color: rgb(239, 242, 247); } #tol_pref_height2 { height: 8px; background-color: rgb(239, 242, 247); } #tol_form_bg { background-color: rgb(247, 251, 254); } #tol_login_width { width: 3px; background-color: rgb(247, 251, 254); } #tol_login_height { height: 3px; background-color: rgb(247, 251, 254); } #tol_results1 { width: 158px; } #tol_results2 { width: 11px; } #tol_results3 { width: 385px; } #tol_results4 { width: 4px; } #tol_results5 { width: 12px; } #tol_results6 { width: 334px; } #tol_results7 { width: 1px; background-color: rgb(204, 204, 204); } .tol_maroon { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(108, 19, = 25); text-transform: none; } .tol_big_maroon { font: 14px/normal Arial, Helvetica, sans-serif; color: rgb(108, 19, = 25); text-transform: none; } .tol_lists { color: rgb(0, 51, 153); text-indent: -40px; font-family: Arial, = Helvetica, sans-serif; font-size: 11px; text-decoration: none; = margin-bottom: 1px; list-style-type: decimal; list-style-position: = inside; } .tol_search_red { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(191, 10, = 10); text-transform: none; } .john_white { font: 22px/normal Arial, Helvetica, sans-serif; color: rgb(255, 255, = 255); text-transform: none; } .tol_black { font: 12px/normal Arial, Helvetica, sans-serif; color: rgb(0, 0, 0); = text-transform: none; } .tol_blue { font: 12px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .tol_link_blue { font: 13px/normal Arial, Helvetica, sans-serif; color: rgb(0, 51, 153); = text-transform: none; } .register_blue { font: 13px/normal Verdana, Arial, Helvetica, sans-serif; color: rgb(0, = 51, 153); text-transform: none; } .tol_gold { font: 16px/normal Arial, Helvetica, sans-serif; color: rgb(203, 144, = 29); text-transform: none; } .tol_big_blue { font: bolder 16px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(0, 51, 153); text-transform: none; } .tol_gray { font: 10px/normal Verdana, Arial, Helvetica, sans-serif; color: = rgb(102, 102, 102); text-transform: none; } .tol_red { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(191, 10, = 10); text-transform: none; text-decoration: none; } .tol_welcome_red { font: 11px/normal Arial, Helvetica, sans-serif; color: rgb(191, 10, = 10); text-transform: none; } .tol_red_search { font: 14px/normal Arial, Helvetica, sans-serif; color: rgb(191, 10, = 10); text-transform: none; text-decoration: none; } .tol_red_header { font: 13px/normal Arial, Helvetica, sans-serif; color: rgb(191, 10, = 10); text-transform: none; text-decoration: none; } .ee_gray { font: 13px/normal Arial, Helvetica, sans-serif; color: rgb(115, 127, = 141); text-transform: none; text-decoration: none; } .chromestyle { width: 100%; font-weight: bold; } .chromestyle::after { height: 0px; clear: both; display: block; visibility: hidden; content: = "."; } .chromestyle ul { background: = url("http://i.cmpnet.com/v2.automotivedesignline.com/new/menu/menu_bg.jpg= ") repeat-x center; margin: 0px; padding: 4px 0px; border: 1px solid = rgb(190, 190, 190); border-image: none; width: 100%; text-align: left; } .chromestyle ul li { display: inline; } .chromestyle ul li a { margin: 0px; padding: 4px 7px; color: rgb(255, 255, 255); = text-decoration: none; } .dropmenudiv { border-width: 1px 1px 0px; border-style: solid; border-color: rgb(190, = 190, 190); font: 10px/18px Verdana; border-image: none; top: 0px; width: = 150px; margin-top: 7px; visibility: hidden; position: absolute; z-index: = 100; font-size-adjust: none; font-stretch: normal; background-color: = rgb(249, 249, 249); } .dropmenudiv a { padding: 2px 0px; width: auto; color: rgb(140, 140, 140); text-indent: = 3px; font-weight: bold; text-decoration: none; border-bottom-color: = rgb(190, 190, 190); border-bottom-width: 1px; border-bottom-style: = solid; display: block; } * html .dropmenudiv a { width: 100%; } .dropmenudiv a:hover { background-color: rgb(233, 233, 233); } html > body .dropmenudiv { margin-top: 7px; } table.elfixo { table-layout: fixed; } ------=_NextPart_000_0029_01CF15C4.FEB43530 Content-Type: text/css; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/Users/R%26D%201/Documents/Research/Power%20Amplifiers/Class%20D%20Design%20Info/Layout%20Issues_files/newLayout.css div { float: left; } .noFloat { float: none; } div.topMenu { width: 1000px; height: 38px; background-image: = url("../ImagesNew/topMenuBG.gif"); background-repeat: repeat-x; } div.contentTop { background-position: left -38px; width: 1000px; min-height: 20px; = background-image: url("../ImagesNew/topMenuBG.gif"); background-repeat: = repeat-x; } div.contentBottom { width: 1000px; min-height: 20px; } div.w170 { background: fixed no-repeat; width: 170px; min-height: 20px; } div.w335 { background: fixed no-repeat; width: 335px; min-height: 20px; } div.w350 { background: fixed no-repeat; width: 350px; min-height: 20px; } div.w400 { background: fixed no-repeat; width: 400px; min-height: 20px; } div.w415 { background: fixed no-repeat; width: 415px; min-height: 20px; } div.colSpacer { width: 20px; height: 15px; } div.footer { width: 960px; height: 155px; } body { 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Times New Roman, Times, serif; font-size: 10pt; } .topline { font-family: Arial, Times New Roman, Times, serif; font-size: 10pt; = font-weight: bold; margin-bottom: 3px; } ------=_NextPart_000_0029_01CF15C4.FEB43530 Content-Type: text/css; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/Users/R%26D%201/Documents/Research/Power%20Amplifiers/Class%20D%20Design%20Info/Layout%20Issues_files/Main.css .UserOptions { height: 135px; } .LeftNavTable { margin-top: 10pt; margin-bottom: 10pt; } .UserSelect { padding-top: 2pt; padding-bottom: 1pt; } .ContentTable { margin: 10pt 10pt 10pt 0pt; } .MainHeading { color: navy; text-transform: uppercase; font-family: Arial; font-size: = 14pt; font-weight: bold; } .SubHeading { color: navy; font-family: Arial; font-size: 11pt; font-weight: bold; } .DefaultFont { font-family: Arial; font-size: 10pt; } .ProxyFont { color: rgb(102, 102, 102); font-family: Arial; font-size: 9pt; = font-weight: bold; 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Petroleum Engineer
Internal Revenue = Service
San Jose, CA US
3/23/2007 5:26 = PM
Petroleum Engineer
Internal Revenue = Service
San Francisco County, CA US
3/23/2007 3:23 = PM
'); ------=_NextPart_000_0029_01CF15C4.FEB43530 Content-Type: application/octet-stream Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/Users/R%26D%201/Documents/Research/Power%20Amplifiers/Class%20D%20Design%20Info/Layout%20Issues_files/jsct.js document.write('
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