Dimensioning audio power amplifier designs
At the outset some parameters will be known; output power, load impedance, maximum supply voltage, bandwidth, input level and impedance, for example. Given practical constraints, a compromise is usually required between a maximum output load and current-handling considerations.
Output signal swing is found by
To obtain the maximum supply voltage, add the dropout voltage (Vod, say 5V) to the peak output swing (Vo pk) when supplied by a current peak of Io pk. Regulation can add 15% and, under no-load conditions, the supply line can rise by 10%, thus
Normally the gain is set somewhere between 20 and 200 and can be derived by
Some favour high gain settings. However, these do not make the amplifier more powerful or improve dynamic performance, quite the opposite in fact (gain bandwidth product) and can render a circuit more prone to instabilities. These can be evidenced from the 'extra' ceramic capacitors and resistors that can be found added to a production PCB. A useful estimate can be derived from the supply voltage dividing this by about 3 (for line-level inputs), eg; with a supply of ±30V, set a gain of 20 and with a supply of ±70V, set a gain of 46.
Much of the travel on an average volume control is redundant, most domestic amplifiers giving a sufficient volume at about '2', with objectionable distortion, either of amplifiers or speakers, occuring long before the end stop. If the gain of the power amplifier is reduced to suit and set below clipping at all normal preamp settings of the programme material at the maximum volume setting, bandwidth will be increased. The amplifier will then be better able to tackle nonlinearities. At the same time the input referred noise floor will be reduced and the signal to noise ratio will improve.
Many preamps will supply signals far in excess of line levels, some at 10 or even 20V. Accommodating and even using this will further reduce contributory noise levels from power amps.
We'll assume that an agreed load of eight ohms can safely handle 40Wrms, and a flat response of 20Hz to 20kHz (±0.25dB) is required. Input level should be 1V max into 100k, and the amplifier is non-inverting.
40Wrms into 8R = Vo pk of 25.3V and Io pk of 3.16A, therefore the supply required is ±30.3V @ 3.16A. Adding regulation and other rises gives ±38.3V for a maximum.
The gain (Av) minimum is 18, so 21 is chosen giving a sensitivity of 894mV. If Rf is normally 10k to 100k, and in this case is 100k then Ri = Rf/(Av-1) = 100k/(21-1) = 5k, or 5k1. Personal preference would set this to 1k or less.
Bandwidth is defined by poles, say the -3dB frequency, for example. Five times from a pole gives 0.17dB which is better than 0.25dB. fL then = 20Hz/5 = 4Hz and fH = 20kHz x 5 = 100kHz. Solving Ci for a reactance, using 1/(2 x pi x frequency x resistance), = Ri @ 4Hz gives 7.8µF, or 10µF. If Rhf = 1k, then Chf = 1.59nF, or 1.5nF @ 100kHz.
Omission of Ci and the use of DC offsetting or a servo will remove modulations, especially with large LF signal swings, caused by the time it takes this capacitor to charge and discharge. Limitations of electrolytics, used in this position, both at LF and HF can become apparent. High frequency performance can be improved by paralleling a good quality HF capacitor across an electrolytic, if used. This capacitor can be irreparably stressed if exposed to an output short to a supply rail, say in the event of a shorted output device. Back-to-back zeners (eg 3V6) tying the inputs to ground will protect these areas.
A capacitor can be added in parallel with Rf, limiting the upper bandwidth to prevent spurious oscillations or unwanted HF excursions. If Rf = 100k, to give a -3dB drop at 100kHz, 15.9pF would suit. Rate caps like these at four times the total supply voltage. Alternatively, put one across the two inputs (see Instabilities).
Most commercial and professional designs will offer -3dB responses better than 10Hz-50kHz, whilst specialist PAs can offer a flat response from DC-1MHz. An impressive bandwidth can be indicative of a high standard of engineering but in a practical sense may have no real, or perceptible, value. For example, a fast transient response, whilst desirable, may be curtailed by any input filtering. Rin can be any reasonable high value, 47-100k being the norm.
Experience favours the use of AC input coupling thus blocking any harmful DC that may arise in the signal path and/or reducing unnecessary power consumption by either the amplifier or load that may affect performance at higher frequencies. Preference sets the roll-off at the same or higher frequency than that set by the feedback. Ground both sides of a coupling capacitor with resistors of 100k, or less.
Maximum power dissipation can be determined by formula 1 below where Vcc is the total supply voltage.
Personal preference has erred to overrating an output stage's safe operating voltage. For example, if a design can run at ±55V, no significant subjective difference will normally be noticed if the supply is run at ±40V, the mechanical handling capacity of the load usually imposing limitations long before the rated electrical handling is exceeded. No real benefit may accrue by trying to stretch a design to potentially deliver 150W, which will probably be never used, when a comfortable 75-100W maximum, or less, is all that will be likely to be required. If a conflict arises between marginal voltage and VA ratings in a given transformer type, opt for a lower output voltage. A mains transformer of the same rating, but lower output voltage, will provide better regulation and will also reduce the stress on the output stage increasing safe power handling capability and, thus, longevity. This is particularly true of sealed modules, where the failure of even the most insignificant internal component renders an expensive lump of hardware useless.
'Unstable' loads, like ESLs, whose operation may not be understood, can be destroyed by amplifiers exceeding 15W. The important point with these is not the drive power, but the amp's ability to withstand short-circuits. The same can be said about isobariks.
Parts condensed from National's LM3876 datasheet, June 1993, recommended, with additions.
Power Supplies | Protection | Distortion | Layouts and Heat-sinking | Setting up an audio amplifier
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