APU Pulse

Each of the two NES APU pulse (square) wave channels generate a pulse wave with variable duty.

Each pulse channel contains the following:

• envelope generator
• sweep unit
• timer
• 8-step sequencer
• length counter

                     Sweep -----> Timer
                       |            |
                       |            |
                       |            v 
                       |        Sequencer   Length Counter
                       |            |             |
                       |            |             |
                       v            v             v
    Envelope -------> Gate -----> Gate -------> Gate --->(to mixer)

Note: the addresses below are write-only!

Address	Bitfield	Description
$4000	DDlc.vvvv	Pulse 1 Duty cycle, length counter halt, constant volume/envelope flag, and volume/envelope divider period
$4004	DDlc.vvvv	Pulse 2 Duty cycle, length counter halt, constant volume/envelope flag, and volume/envelope divider period
Side effects		The duty cycle is changed (see table below), but the sequencer's current position isn't affected.
$4001	EPPP.NSSS	See APU Sweep
$4005	EPPP.NSSS	See APU Sweep
$4002	LLLL.LLLL	Pulse 1 timer Low 8 bits
$4006	LLLL.LLLL	Pulse 2 timer Low 8 bits
$4003	llll.lHHH	Pulse 1 length counter load and timer High 3 bits
$4007	llll.lHHH	Pulse 2 length counter load and timer High 3 bits
Side effects		The sequencer is immediately restarted at the first value of the current sequence. The envelope is also restarted. The period divider is not reset.[1]

Duty Cycle Sequences

Duty	Output waveform
0	0 1 0 0 0 0 0 0 (12.5%)
1	0 1 1 0 0 0 0 0 (25%)
2	0 1 1 1 1 0 0 0 (50%)
3	1 0 0 1 1 1 1 1 (25% negated)

Notice that a few Famiclone units have swapped APU duty cycles, as 12.5 [0], 50 [1], 25 [2] and 25 negated [3] instead.

Sequencer behavior

The sequencer is clocked by an 11-bit timer. Given the timer value t = HHHLLLLLLLL formed by timer high and timer low, this timer is updated every APU cycle (i.e., every second CPU cycle), and counts t, t-1, ..., 0, t, t-1, ..., clocking the waveform generator when it goes from 0 to t. Since the period of the timer is t+1 APU cycles and the sequencer has 8 steps, the period of the waveform is 8*(t+1) APU cycles, or equivalently 16*(t+1) CPU cycles.

Hence

• f_pulse = f_CPU/(16*(t+1)) (where f_CPU is 1.789773 MHz for NTSC, 1.662607 MHz for PAL, and 1.773448 MHz for Dendy)
• t = f_CPU/(16*f_pulse) - 1

Note: A period of t < 8, either set explicitly or via a sweep period update, silences the corresponding pulse channel. The highest frequency a pulse channel can output is hence about 12.4 kHz for NTSC. (TODO: PAL behavior?)

Pulse channel output to mixer

The mixer receives the current envelope volume (lower 4 bits from $4000/$4004) except when

• The sequencer output is zero, or
• overflow from the sweep unit's adder is silencing the channel, or
• the length counter is zero, or
• the timer has a value less than eight (t<8, noted above).

If any of the above are true, then the pulse channel sends zero (silence) to the mixer.

Pulse channel 1 vs Pulse channel 2 behavior

The behavior of the two pulse channels differs only in the effect of the negate mode of their sweep units.

Implementation details

The reason for the odd output from the sequencer is that the counter is initialized to zero but counts downward rather than upward. Thus it reads the sequence lookup table in the order 0, 7, 6, 5, 4, 3, 2, 1.

Duty	Sequence lookup table	Output waveform
0	0 0 0 0 0 0 0 1	0 1 0 0 0 0 0 0 (12.5%)
1	0 0 0 0 0 0 1 1	0 1 1 0 0 0 0 0 (25%)
2	0 0 0 0 1 1 1 1	0 1 1 1 1 0 0 0 (50%)
3	1 1 1 1 1 1 0 0	1 0 0 1 1 1 1 1 (25% negated)