Audio Details

tl;dr:

The PPU is a bunch of state machines, and the APU is a bunch of counters.

Each of the four “conceptual” channels is composed of a “generation” circuit (designated “channel” in the above diagram), and a DAC. The digital value produced by the generator, which ranges between $0 and $F (0 and 15), is linearly translated by the DAC into an analog¹ value between -1 and 1 (the unit is arbitrary).

The four analog channel outputs are then fed into the mixer², which selectively adds them (depending on NR51) into two analog outputs (Left and Right). Thus, the analog range of those outputs is 4× that of each channel, -4 to 4.

Then, both of these two get their respective volume scaled, once from NR50, and once from the volume knob (if the console has one). Note that the former step never mutes a non-silent input, but the latter can.

Each of the two analog outputs then goes through a high-pass filter (HPF). For short, a HPF constantly tries to “pull” the signal towards analog 0 (neutral); the reason for that is explained further below.

PCM registers

These two registers, only present in the Game Boy Color and later models, allow reading the output of the generation circuits directly; this is very useful for testing “internal” APU behavior. These registers are not documented in any known Nintendo manual.

FF76 — PCM12 (CGB Mode only): Digital outputs 1 & 2 [read-only]

The low nibble is a copy of sound channel 1’s digital output, the high nibble a copy of sound channel 2’s.

FF77 — PCM34 (CGB Mode only): Digital outputs 3 & 4 [read-only]

Same, but with channels 3 and 4.

Finer technical explanation

DIV-APU

A “DIV-APU” counter is increased every time DIV’s bit 4 (5 in double-speed mode) goes from 1 to 0, therefore at a frequency of 512 Hz (regardless of whether double-speed is active). Thus, the counter can be made to increase faster by writing to DIV while its relevant bit is set (which clears DIV, and triggers the falling edge).

The following events occur every N DIV-APU ticks:

Mixer

A high-pass filter (HPF) removes constant biases over time. The HPFs therefore remove the DC offset created by inactive channels with an enabled DAC, and off-center waveforms.

The HPF is more aggressive on GBA than on GBC, which itself is more aggressive than on DMG. (The more “aggressive” a HPF, the faster it pulls the signal towards “analog 0”; this tends to also distort waveforms.)

DACs

Channel x’s DAC is enabled if and only if [NRx2] & $F8 != 0; the exception is CH3, whose DAC is directly controlled by bit 7 of NR30 instead. Note that the envelope functionality changes the volume, but not the value stored in NRx2, and thus doesn’t disable the DACs.

If a DAC is enabled, the digital range $0 to $F is linearly translated to the analog range -1 to 1, in arbitrary units. Importantly, the slope is negative: “digital 0” maps to “analog 1”, not “analog -1”.

If a DAC is disabled, it fades to an analog value of 0, which corresponds to “digital 7.5”. The nature of this fade is not entirely deterministic and varies between models.

NR52’s low 4 bits report whether the channels are turned on, not their DACs.

Channels

A channel is activated by a write to NRx4’s MSB, unless its DAC is off, which forces it to be disabled as well. The opposite is not true, however: a disabled channel outputs 0, which an enabled DAC will dutifully convert into “analog 1”.

A channel can be deactivated in one of the following ways:

• Turning off its DAC
• Its length timer expiring
• (CH1 only) Frequency sweep overflowing the frequency

Pulse channels (CH1, CH2)

Each pulse channel has an internal “duty step” counter, which is used to index into the selected waveform (each background stripe corresponds to one “duty step”)⁴. The “duty step” increments at the channel’s sample rate, which is 8 times the channel’s frequency).

The “duty step” counter cannot be reset, except by turning the APU off, which sets both back to 0. Retriggering a pulse channel causes its “duty step timer” to reset, thus retriggering a pulse channel often enough will cause its “duty step” to never advance.

When first starting up a pulse channel, it will always output a (digital) zero.

Wave channel (CH3)

CH3 has an internal “sample index” counter. The “sample index” increments at the channel’s sample rate, which is 32 times the channel’s frequency Each time it increments, the corresponding “sample” (nibble) is read from wave RAM. (This means that sample #0 is skipped when first starting up CH3.)

CH3 does not emit samples directly, but stores every sample read into a buffer, and emits that continuously; (re)triggering the channel does not clear nor refresh this buffer, so the last sample ever read will be emitted again. This buffer is cleared when turning the APU on, so CH3 will emit a “digital 0” when first powered on.

CH3 output level control does not, in fact, alter the output level. It shifts the digital value CH3 is outputting, not the analog value. This only matters when changing the setting mid-playback: the digital values being shifted bias them towards 0, which biases the analog output towards “1”; the HPF will smooth this over time, but not instantly.

Noise channel (CH4)

CH4 revolves around a LFSR, pictured above. The LFSR has 16 bits: 15 bits for its current state and 1 bit to temporarily store the next bit to shift in.

When CH4 is ticked (at the frequency specified via NR43):

1. The result of $\overline{{\mathrm{LFSR}}_0\odot {\mathrm{LFSR}}_1}$ (1 if bit 0 and bit 1 are identical, 0 otherwise) is written to bit 15.
2. If “short mode” was selected in NR43, then bit 15 is copied to bit 7 as well.
3. Finally, the entire LFSR is shifted right, and bit 0 selects between 0 and the chosen volume.

The LFSR is set to 0 when (re)triggering the channel.

Game Boy Advance audio

The APU was reworked pretty heavily for the GBA, which introduces some slightly different behavior:

• Instead of mixing being done by analog circuitry, it’s instead done digitally; then, sound is converted to an analog signal and an offset is added (see SOUNDBIAS in GBATEK for more details).
• This also means that the GBA APU has no DACs. Instead, they are emulated digitally such that a disabled “DAC” behaves like an enabled DAC receiving 0 as its input.
• Additionally, CH3’s DAC has its output inverted. In particular, this causes the channel to emit a loud spike when disabled; therefore, it’s a good idea to “disconnect” the channel using NR51 before accessing wave RAM.

None of the additional features (more wave RAM, digital FIFOs, etc.) are available to CGB programs.