How do you do a very simple but high-efficiency audio output circuit on a microcontroller?
The simplest possible approach is to connect a speaker between a GPIO pin and a power rail, then generate a signal on the GPIO pin. Digital outputs are quite low impedance when generating either a 1 or a 0, so very little power is wasted in the pin driver in the microcontroller.
This has wonderful linearity, but it has a few different problems: power, DC waste, impedance matching, and high-frequency noise.
Power: the GPIO pin is typically capable of sinking or sourcing 5–50 mA, sometimes at 5 V but often at only 3.3 volts. 50 mA at 5 V is 0.25 W, which is not going to be very loud unless it’s in an earphone.
DC waste: the average value of the GPIO pin when it’s emitting a signal that’s symmetric around some zero value is going to be 2.5 V or 1.7 V, half the supply voltage. This DC component of the signal is going to draw current through the speaker coil without producing any sound. Worse, it will typically see a lower resistance than the speaker’s nominal impedance.
Impedance matching: when you have a source with an internal impedance driving a load, the maximum power applied to the load is when the load’s impedance equals the source impedance. If the load’s impedance is too low, most of the voltage is dropped in the source impedance, and the voltage that actually reaches the load is too low. If the load’s impedance is too high, all the voltage reaches the load, but only a fraction of the source’s current-delivery capacity comes into play. To be concrete, driving 20 mA (ac!) through a garden-variety 8Ω dynamic speaker is only going to give you 160 mV (ac) across it, rather than the 3.3V or 5V your microcontroller can theoretically deliver.
High-frequency noise: GPIO pin voltage transitions are fairly sharp and so potentially have a lot of power in the ultrasound part of the spectrum. For directly driving a speaker, this may not be a problem, but under some circumstances the high-frequency signal can result in excessive heat dissipation in the speaker as well, especially once you solve the above power delilvery problems.
So I was thinking about these ideas:
First, how about just driving the speaker through an audio transformer? This ensures no dc reaches the speaker, allows the microcontroller to see an effectively higher speaker impedance (by the square of the turns ratio) and the waste of driving dc through the transformer’s winding is potentially smaller than the waste of driving it through the hair-fine speaker winding. Transformers may even reduce the transmission of high-frequency noise, though probably not in a very well controlled way.
Second, how about using a transistor switch as an amplifier? An N-channel MOSFET or NPN transistor to ground would work, as would a PNP BJT to a positive voltage supply. The MOSFET case can work with extremely high efficiency! A 2N7002 can switch 200 mA at up to 60 V with only 5Ω of on-resistance; in theory that would be up to 12 W of output, at which point it would be dissipating 1 W, requiring the TO-92 package for heatsinking rather than the SOT23-3L.
To solve the high-frequency noise problem, though, we need analog filtering — and we need it after the transistor switch, because if we do it before, we lose the efficiency that brought us here in the first place. If we use mostly LC filtering, rather than RC, maybe we can get high efficiency.
More elaborately:
Put a speaker in series with a capacitor to ground to block DC and stuff below, say, 20 Hz; this way the power dissipated by the speaker is almost all in the right frequency band to be turned into sound, even if the speaker’s best-case efficiency is low, like 5% or so. Put another, much smaller capacitor in parallel with the speaker-capacitor combination in order to attenuate high frequencies, like above 20kHz or so. Put an inductor in series with the capacitor-speaker-capacitor combination in order to attenuate high frequencies further and prevent short-circuit currents. Put a Schottky clamping diode in parallel with the inductor-capacitor-speaker-capacitor combination, from ground up to the inductor’s “input”, to prevent inductive voltage spikes to large negative voltages. Drive the diode-inductor junction with a MOSFET to the positive voltage power supply — either a GPIO output from the microcontroller itself (which perhaps avoids the necessity for the Schottky diode), a logic-level-input P-MOSFET with its gate hooked up to the GPIO, a regular power P-MOSFET with its gate driven by a logic-level-input MOSFET or by a BJT, or maybe even a bootstrapped N-MOSFET.
Basically this is a buck converter driving a speaker through a DC-blocking capacitor.
So far so good, but there’s one missing piece still: when there’s a signal, the input has a positive DC level relative to ground, and there’s no DC path to ground for it. So stick an additional humongous inductor in parallel with the original capacitor-speaker-capacitor combination in order to provide a non-dissipative DC path.
It might be more convenient to turn the whole passive-and-diode output part of the circuit upside down, hooking it up to the positive power supply rather than ground, so we can use an N-channel MOSFET to drive its input by shorting it to ground intermittently, rather than any of the annoying options for CMOS high-side switching.
Some rough numbers. Suppose the speaker is a standard 8Ω half-watt dynamic speaker. To make the whole mess feasible, let’s use a 10:1 audio transformer to drive it; that way 1VAC 125mA on the output works out to 10V 12.5mA on the input, an impedance of 800 Ω instead of 8 Ω. The DC-blocking capacitor then shouldn’t have too much more than 1kΩ of impedance at 20Hz (1/ωC < 1kΩ) which gives us 8μF, a blessedly quite feasible value. The parallel capacitor to short out stuff above 20kHz also shouldn’t have too much more than 4kΩ of impedance, but at 20kHz, so 8nF is adequate. The impedance of the whole capacitor-transformer-capacitor thing is going to be in the neighborhod of 2–3kΩ, so we want the input inductor to be in the neighborhood of that when we hit 20kHz; this requires a relatively large inductor of around 16mH in series. However, the much worse problem is that our parallel inductor to ground — the one that’s supposed to drain off our DC voltage so we can keep running the circuit — is supposed to have an impedance in the neighborhood of 2–3kΩ for frequencies of 20Hz. And that would require a humongous monster 16 HENRY inductor.
So, what’s the problem here? I think that maybe I’ve made the load impedance too high, requiring high-impedance capacitors (which are cheap) and high-impedance inductors (which aren’t). Maybe I don’t really need the transformer; then both the capacitors and inductors could be 100× lower impedance. That means the capacitors would need to be 800μF (annoying but fairly commonplace) and 800nF (totally normal), while the inductors would need to be 160μH (totally normal) and 160mH (also annoying but not exotic).
With ideal components, all the energy here would be dissipated either by the diode or the speaker. In practice, the inductors in particular will have significant parasitic resistance, depending on how much copper you’re willing to lavish on them. One 150μH inductor I have a datasheet for here, the toroidal SMD PM2110-151K-RC from Bourns, has 0.049Ω of DC resistance; another, Bourns’s “dual-winding SRF0703-151M” (really a transformer), has 0.986Ω. So the losses should be manageable.
Simulation shows reasonable results with these values and 100kHz PWM, though there’s some serious harmonic distortion on the “negative-polarity” side of the wave at high amplitudes (presumably from the diode), and there’s about 6 dB attenuation already at 8 kHz, and significant bleedthrough with a 40kHz PWM carrier. Probably a more judicious choice of component values would yield a sharper cutoff at a more appropriate frequency. It also seems to have rather large currents through the diode at times, not to mention the other passive components.
In Falstad’s circuit format:
$ 1 1.0E-7 10.20027730826997 50 5.0 43
r 928 336 928 384 0 8.0
c 928 384 928 464 0 7.999999999999999E-4 0.060217163598211165
w 928 304 992 304 0
l 992 304 992 464 0 0.16 1.0273205335302287
w 928 304 864 304 0
c 864 304 864 464 0 8.000000000000001E-7 0.10880129845424946
l 864 464 768 464 0 1.6E-4 1.0359085688452483
d 768 464 768 304 1 0.305904783
w 864 304 768 304 0
w 928 304 928 336 0
w 864 464 928 464 0
w 928 464 992 464 0
R 768 304 768 256 0 0 40.0 5.0 0.0 0.0 0.5
f 688 480 768 480 0 1.5
g 768 496 768 544 0
a 592 480 688 480 1 15.0 0.0 1000000.0
R 592 496 544 496 0 4 100000.0 5.0 0.0 0.0 0.5
170 592 464 544 448 3 20.0 40000.0 2.0 0.2
o 0 64 0 35 0.15625 0.025 0 -1
o 13 16 0 35 10.0 1.6 1 -1
o 17 64 0 35 2.5 9.765625E-5 2 -1
I was thinking that maybe I could use an electrolytic capacitor for the series capacitor for the speaker, since one end of it is periodically almost shorted to ground, but now I realize that won’t actually work; the capacitor-speaker combination is in parallel with an inductor, which means its average voltage over time must be zero. (Otherwise the current through the inductor is growing without limit!) On the minus side, this means that you can’t use an electrolytic capacitor. On the plus side, it means that by the same token, you don’t need any capacitor, because the parallel inductor itself guarantees a zero DC component to the signal as seen by the speaker. And that, in turn, means that we don’t really need such a large inductor; its impedance above 20Hz only needs to be large compared to 8Ω, not 20–30 Ω. (160mH at 20Hz gives us an impedance of 2πfL = 20.1 Ω.)
Fuck inductors, though. We probably can’t get by with just capacitors because any just-capacitor circuit of this sort is going to have a massive shoot-through current when it first turns on, and your MOSFET is maybe going to explode. But what if the only inductor in the system is a little choke that’s there to stop that from happening? Maybe with a diode or capacitor in parallel with it to keep it from generating massive voltage spikes that blow up the transistor when we turn it off.
But then maybe we can use a capacitor in series with the speaker to high-pass filter the signal (at 20 Hz or so) and another in parallel with either the speaker or the capacitor-speaker combination to low-pass filter it (at 20 kHz or so). Maybe we’d like the time constant of the high-pass-filtering capacitor to be around 50 ms, and the low-pass filtering cap to be around 20 μs. Now we really do want to use a transformer, say 10:1, making the effective speaker impedance 800 Ω, so our high-pass-filtering cap in series with the transformer can be 68 μF (and either electrolytic or MLCC ceramic), while the high-pass filter in parallel with that can be 22 nF.
Let’s say 100kHz PWM with a 50%-max duty cycle is our working assumption, and we’re feeding the whole shebang from five volts. So the transistor is on for up to 5 microseconds, then off for at least 5 microseconds. And let’s say we don’t want more than, say, 200 mA going through the MOSFET, because it’s a 2N7002 or something. How big should the choke be?
We want the current to ramp up to 200 mA in 5 microseconds when the choke sees all 5 volts, since that’s probably the worst case. That’s 125 μH. Let’s use a capacitor in parallel with it to keep its voltage spikes limited without wasting any energy or introducing any nonlinearity; if we want the combination to resonate at 1MHz, we want the capacitor’s reactance to exactly cancel the inductor’s reactance at that frequency: 2πfL = 785 ohms = 1/(2πfC), giving 202 pF (and indeed 1 MHz ≈ (125 mH 200 pF)^-½). This does reintroduce the startup short-circuit path we were hoping to get away from, but now it ends 4000 times faster. However, in simulation, this only limits the inductive voltage spike to 140 V, which is still too high. So we probably need some kind of more aggressive damping. A 4.7nF capacitor instead, in series with a 100Ω resistor, keeps the spike down to -23 V.
An interesting thing is that whatever the ringdown network for the choke is, whatever losses it has are mostly switching losses, i.e., they happen after each pulse, so using more pulses means more losses there. So to the extent that your normal filtering is adequate to keep your PWM or whatever out of your audio, you can lower the PWM frequency to reduce the ringdown losses.
If you wanted to keep the voltage spike down to 5 volts at 200 mA, you could use a 21.5Ω resistor in series with a regular silicon 700mV diode. Except that of course the resistor's voltage drop will fall as the current does, so it’s more of an exponential decay than a linear one, and so it doesn’t come close to stopping the choke current before the transistor turns back on. But maybe that’s actually what we want? In simulation, it does keep the voltage spike to 4.6 volts.
Hmm, I just realized that maybe the body diode in the 2N7002 would have a similar effect. Maybe it points the wrong way, though.
Also I think the whole idea of capacitors on all the paths from power to ground is a dumb idea. Sooner or later all those capacitors are going to be charged up to 5V and then no more current will flow.