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rev. 0.1 10/10 copyright ? 2010 by silicon laboratories an542 an542 p erformance i mprovements in c lass d a udio a mplifiers u sing si824 x a udio d rivers 1. introduction the si8241/44 audio ga te drivers facilitate high-fidelity, class d amplification while offering many other advantages over competing gate drivers. based on silicon labs' prop rietary cmos isolati on technology, these drivers offer the benefits of: ? precise dead time adjustment for low total harmoni c distortion (thd) and high system efficiency ? individually-isolated driver s to facilitate simpler system topologies and external component flexibility ? high functional integration for small installed size and competitive cost the gate driver ic is a critical system component because it influences both system architecture and system performance. the si8241 audio gate driver is a high-vol tage driver capable of switching at frequencies up to 8 mhz to realize pre- or post-filter control. these devi ces have integrated precision dead time generators for low thd and high efficiency, as well as isolated output driv ers that eliminate the need for input level shifting and facilitate the straightforward im plementation of a two-state, half-bridge class d amplifier. this application note discusses the silicon labs class d re ference design, a stereo, tw o-state, half-bridge class d amplifier that delivers 12 0 w per channel into 8 ? or 150 w into 4 ? . the reference design and demo board is available at www.silabs.com/isolation and uses the si8241 audio gate dr iver driven by a self-oscillating pwm modulator, as shown in figure 1. figure 1. si8241-based class d amplifier block diagram + - + - + - si8241 isodriver pwm 5v -50v comparator error amplifier feedback amplifier vboot +50v vdda voa vddb vob gndb gnd1 vddi dt r dt audio in gnda speaker filter bootstrap
an542 2 rev. 0.1 2. the si8241 audio gate driver every so often, a new ic is introduced that challen ges the current technological hegemony. with features that make these products the perfect driver s for class d amplification, the silicon labs si8241/44 au dio gate drivers represent a new standard for the class d amplifier industry. key features are outlined in the following sections. 2.1. programmable dead time it is well documented that a precise dead time setting is cr itical in class d amplifiers. during dead time, both the high-side and low-side mosfets are off. however, the low-side mosfet body diode continues to conduct current, which manifests itself as output distortion. too short a dead time causes shoot-through current that reduces system efficiency; too long a dead time increa ses thd, negatively impacting audio quality. while competing audio drivers typically have coar se, digital dead-time settings (i.e. 1 of n delay values), the si8241/44 audio gate drivers have a precise linear dead time settin g that programs with a single external resistor. this feature provides the resolution necessary to precisely set dead time for optimal system performance. the audio gate driver dead time equation is shown in equation 1. equation 1. audio gate driver dead time per equation 1, the silicon labs class d amplifier uses a 2 k ? resistor to generate 20 ns of dead time. changing this dead time value to 18 ns only requires changing the rdt to 1.8 k ? (connected from the dead-time pin (dt) input to ground). this setting mechanism allows dead time to be incrementally increased or decreased in nanosecond increments, instead of tens of nanoseconds like competitive products. 2.2. input/output isolation implementing a two-state, class d amplifier can be diffic ult due to input level shifting requirements, and most available class d drivers lack the capabilit y to eliminate level shifti ng. drivers that do elim inate level shifting have other peculiarities making them less-than-ideal for class d operation (example: driver output ground terminal referenced to the ?vbus rail, requiring the input drive sign al to be level-shifted). this is not the case with the si8241 audio gate driver where the isolation (i.e. level sh ift function) is implemented internally and is transparent to the user. the si8241 audio gate driver controlled by ttl input signal levels drives the outputs to vbus, and only a single ttl pwm input signal is re quired to drive a two-state class d amplifier. 2.3. high-voltage outputs the si8241 is capable of switching very high voltages (up to a 1,500 vdc peak driver-to-driver differential voltage is possible) allowing a 750 vbus. for practical class d amplifier designs, a voltage of 100 vdc can deliver an astounding 600 w of audio power into 8 ? . 2.4. output current drive class d amplifier switching mosfets shoul d not be "slammed" on and off by excessively high current gate drivers. with its 0.5 a peak current outputs, the si8241 audio gate driver hits the sweet spot for class d operation up to 400 w. power levels beyond 400 w typically require larger mosfets and, consequently, more gate drive. for applications of this type, the SI8244 (4a) audio gate dr iver provides the required added gate drive, where rise and fall times can be adjusted with a series gate resistor. 2.5. high-frequency operation one of the best attributes of the si8241 audio gate driver is its 8 mhz maximum switching frequency, making it the fastest driver on the market for class d operation. the silicon labs class d reference design operates at approximately 500 khz, and operating the amplifier be tween 500 khz and 1 mhz dramatically reduces the high- frequency artifacts, resulting in a remarkably clean audio waveform. dt 10r dt where dead time (dt) is in ns and r dt is in k ? =
an542 rev. 0.1 3 3. gate drive structure figure 2 illustrates the simplicity of the si8241 driving a two-state, half-bri dge class d amplifier. the boot supply tied to d1 must be 12 v higher than the ?50 v reference (?38 v) so that the mosfets each have a 12 v drive signal. figure 2. si8241 audio gate driver gate drive circuit 4. filter inductor selection in early class d amplifiers, the most common type of inductor used was a toroid of type 2 iron material manufactured by micrometals (figure 3). this wa s because type 2 material has a very low magnetic permeability ( in equation 2), slightly higher than an air core inductor, whic h has a linear bh curve and will not saturate. equation 2. magnetic permeability however, when an iron core inductor operates further up on the bh curv e, its permeability decreases with the falling slope of the bh curve and approaches zero as the core saturates. when this happens, there are no more iron particles to align within the core, and the inductance approaches zero. recently, a number of manufacturers developed inductors specifically for class d amp lification, such as sagami elec. co., whose inductors are used in the silicon labs class d reference design. the inductance value of these devices does not decrease with current as happens in most inductors. instead, it remains relatively flat over the range of interest and is a good choice for class d amplifier applications. figure 3. micrometal inductor bh plot si8241 isodriver -38v pwm nc vddi gndi disable dt nc vddi vdda voa gnda nc nc vddb vob gndb -50v +50v c1 c3 pwm +5v c2 shdn_hi r3 c4 d1 r1 r2 -38v speaker ? b h --- - =
an542 4 rev. 0.1 5. reference design board architecture the silicon labs class d reference de sign architecture uses a phase-shif t, self-oscillating mo dulation approach capable of achieving a far grea ter signal-to-noise ratio than that of a clock-driven am plifier. this self-oscillating implementation eliminates th e circuitry necessary to gener ate the triangle waveform (s ee "8. self oscillation" on page 6 for details). to keep the circuit as simple as possible, a two-state, half- bridge is implemented and demonstrates the benefits of usin g the si8241 audio gate driver. 5.1. control theory basics looking at the equation derivation in the frequency domai n, figure 4 shows input signal r(s), which is the laplace transform of the time domain regulation input signal r( t). c(s) is the laplace transform of the time-domain- controlled output signal c(t), where s = j ? . figure 4. first order control loop model equation 3. equation 4. substituting c(s) from equati on 4 into equation 1, and solving for e(s)/r(s) yields: equation 5. similarly, substituting e(s) from equation 4 into equation 3 and solving for c(s)/r(s) yields: equation 6. examining these equations within the cont ext of a class d control loop, g(s) is the forward transfer function; h(s) is the feedback transfer function, and e(s) is the error si gnal (i.e., the difference between the input and output). + g(s) h(s) ? - e(s) c(s) r(s) es ?? rs ?? c(s)h(s) ? = cs ?? e(s)g(s) = e(s) r(s) ---------- - 1 1 g(s)h(s) + -------------------------------- = c(s) r(s) ----------- g(s) 1 g(s)h(s) + -------------------------------- =
an542 rev. 0.1 5 6. closed loop transfer function the closed loop transfer function is de fined as the ratio of the controlled variable to the input variable. the controlled variables are the speaker terminals, and the in put variable is the mp3 player input, the cd input, or some other input source connected to the amplifier. ther efore, the equation for the closed-loop transfer function is given by equation 7. equation 7. closed loop transfer function the closed loop gain describes how th e output responds over the audio bandwidth to the input regulation signal. it is understood that the output should have a specific clos ed loop gain with respect to the input regulation signal, and that gain should be as flat as possible over the audio bandwidth. the inductor between the controlled variable and the speaker terminals plays a crucial role in the perform ance of the amplifier as prev iously discussed. the closed loop gain of the silicon labs class d reference design is impl emented such that appro ximately 1 vpp input will yield full output power into an 8 ? load. 7. open loop transfer function the open-loop transfer function is obtained by breaking the loop at some arbitrary point and traversing the entire loop back to the same point. when h(s) = 1, the open loop and the forward transfer functions are identical. therefore, the open loop transfer function is given by equation 8. equation 8. the open loop transfer function determines whether the lo op is stable, as well as dete rmining what the overall open loop gain of the amplifier will be over the audio bandwidth. the higher the open loop gain, the lower the error signal and, therefore, the more ea sily the control loop can keep the out put following the input command. some early class d amplifier designs used an integrator for the error amplifier. this produced high gain at low frequencies but low gain at high frequencies due to the pole produced by the integrator. this caused the thd to increase dramatically above 5 khz, destroying the high-frequency resp onse of the amplifier. a be tter solution is to keep the open loop gain constant and as high as possible throughou t the audio bandwidth. this should yield a constant thd response, and, in deed, it does, as will be shown in the perfor mance curves in "13. performance" on page 8. care should be taken in designing the open loop response of the amplifier. the three key elements are the bandwidth, phase margin, and gain margin. in designing a class d amplifier, the target is to have 45 of phase margin with a bandwidth of approximately half the switching frequency. the control loop cannot compensate for the lc filter response since the filter is outside of the loop. th e entire lc filter is designed as a bessel function with a load resistance of 6 ? . therefore, the filter is slightly underdamped at 8 ? and slightly overdamped at 4 ? . this can be seen by placing a 100 mvpp square wave into the in put and looking at the output response with an 8 ? load and a 4 ? load. closed_loop_transfer_function g(s) 1 g(s)h(s) + -------------------------------- = open_loop_transfer_function g(s)h(s) =
an542 6 rev. 0.1 8. self oscillation the amplifier is self-oscillati ng, enabling its signal-t o-noise ratio to far exceed that of a clock driven system. the main mechanism for this is the delta-sigma effect of sh ifting in-band noise to a much higher out-of-band frequency. the amplifier is a basic, phase-shift type, which has significant advantage s over an amplifier running as a hysteretic oscillator. there is a pole in the forward path g(s) and a pole in the feedback path h(s). the 180 phase shift, coupled with the transport delay, yields an oscillation frequency of nearly 500 khz. the transport delay is given by equation 9, where ?t? is the del ay of the comparator plus the si8241. equation 9. taking into consideration the delay tolerances of the co mparator and si8241 driver, the total delay can range from 90 ns to 140 ns. the frequency of oscillation occurs at the point when t he open loop transfer function phase response times the transport delay is equal to ?180 . equation 10. the frequency of oscillation is set by capacitors in each audio channel where reducing capacitance value increases oscillation frequency. tight tolerance capacitors are used to k eep the channel frequencie s as close to each other as possible. 9. drive voltage the upper and lower gate driv e voltages can be gene rated by a linear regulator (the regulator used in the silicon labs class d reference design is a high-voltage regulator able to withstand a 125 v input). when referenced to the negative supply, the regulator generates a low-side mosfet drive voltage of ?38 v (i.e., 12 v of gate drive with respect to the source). likewise, the bootstrap capacitor charges to 12 v when the phase lead swings to the negative rail. the only downside to using a linear regulator is the power dissipation, whic h is directly-proportional to the frequency of the switching amplifier and the bus voltag e. alternatively, a small, high-frequency switching regulator may be used to reduce the power dissipation of the mosfet gate drive supply, but this can add unwanted system noise. t delay e tj ? ? = f osc occurs when: arg(g(s)h(s) e ts ? )180 ? ? =
an542 rev. 0.1 7 10. overcurrent protection the silicon labs class d reference desi gn has an overcu rrent protection circuit co nsisting of a low-power comparator floating off the upper and lower bus voltages. the upper rail circuit is shown in figure 5 and is duplicated on the lower rail. it monitors the current flowing through the 0.005 ? resistor (rsense) (zener diode d1 and resistor r5 supply power to the co mparator and the silicon labs si8410 digital isolator). the si8410 performs the necessary leve l shifting to interface to the shutdown circuitry. the circuit is set to trip at roughly a 20 a fault, usually caused by a short-circuit across the speaker terminals or a large overdrive signal at the audio inputs. note that the upper and lower overcurrent circuits are ord together through a pair of diodes and sent to the reset control circ uit. the normally low si8410 a1 input is driven high upon detection of an overcurrent condition and asserts the shutdown signal, forcing the reset controller to assert a reset signal, momentarily halting amplifier operation. the reset control circuit attempts restart after one second, and, if the fault is still pres ent, again cycles reset in "hiccup" mode with a frequency of one second. this process continues until the fault is removed. figure 5. overcurrent protection circuit 11. undervoltage protection the undervoltage protection comparator monitors the posi tive bus voltage and releases the undervoltage lockout when the voltage is above 37 v, and the amplifier star ts-up after a one-second delay. note that the red led remains lit when the amplifier is in shutdown mode and turns off when the amplifier is enabled. 12. other features a protection circuit jumper option is in cluded that allows the amplifier to be manually shut down. this jumper can be replaced with a switch or other control circuit, allo wing the amplifier to be muted. the one-second undervoltage lockout delay allows the opamps and comparator to settle before the shutdown circuit is released, thereby preventing speaker pops. there are also individual jumper op tions on each channel that allow the user to enable or disable each channel independently to aid in system performance evaluation. + - c1 r2 r4 r3 si8410 digital isolator r5 r1 rsense gnd2 gnd2 gnd1 a1 vdd1 vdd1 to high side mosfet vdd2 b1 5v shutdown d1 50v
an542 8 rev. 0.1 13. performance the silicon labs class d re ference design b oard was tested for thd + n, snr, dfd and ifd with an audio precision analyzer. power efficiency was also measured using conventional lab equipment. the following graphs show the results of this testing. for more performance data, please visit www.silabs.com/isolation . figure 6 shows a 1 khz sine wave input signal swept over the entire pow er range of the amplifier fr om 1 w to 120 w. note the maximum thd+n is 0.06%, occurring at 1 w. figure 6. 1 khz sweep across amplifier power range figure 7 shows an snr measurement amplifier of approxim ately 92 db. an equivalent clock-driven amplifier would likely produce an snr in the range of 70 to 80 db. figure 7. snr measurement
an542 rev. 0.1 9 figure 8 shows a dynamic range measurement, while figure 9 shows the difference frequency distortion (dfd) plot. dfd is a technique for measuring intermodulation di stortion (imd); note that the two tones at 18 khz and 19 khz cause a difference frequency of 1 khz. the sideb ands generated are located at 17 khz and 20 khz and, ideally, should be as low as possible (i md levels are about ?80 db in this plot ). figure 10 is identical to figure 9, but with the dfd ratio in percent (%) instead of db. figure 11 shows amplifier efficiency. figure 8. dynamic range measurement figure 9. imd plot (db)
an542 10 rev. 0.1 figure 10. imd plot (%) figure 11. amplifier efficiency from zero to full load ? amplifier efficiency 0 10 20 30 40 50 60 70 80 90 100 1 5 10 20 30 40 50 60 70 80 90 100 110 120 output power (watts) efficiency ( % si8241 amplifier
an542 rev. 0.1 11 14. summary class d amplification offers advantages far above traditio nal analog amplifiers, including lower total harmonic distortion (thd), smaller size, higher power efficiency, an d lower cost. the gate driver ic can impact both system architecture and performance. silicon labs si824x audio gate drivers offer benefits not available in co mpetitive driver solu tions. these benefits include high resolution dead time setting for the lowest poss ible thd and best efficiency, no input signal level shift circuits to complicate design and increa se component count, and isolated outpu t drivers for easy two-state switcher implementation. 15. references ? simple self-oscillating class d amplifier with full ou tput filter control - putzeys, aes convention paper, 2005 may 28 ? introduction to control systems de sign, eveleigh - mcgraw-hill, 1972
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