Reference Manual

USB Protocol

The data connection to a PDQ stack is a single, full speed USB, parallel FIFO with byte granularity. On the host this appears as a “character device” or “serial port”. Windows users may need to install the FTDI device drivers available at the FTDI web site and enable “Virtual COM port (VCP) emulation” so the device becomes available as a COM port. Under Linux the drivers are usually already shipped with the distribution and immediately available. Device permissions have to be handled as usual through group membership and udev rules. The USB bus topology or the device serial number can be used to uniquely identify and access a given PDQ stack. The serial number is stored in the FTDI FT245R USB FIFO chip and can be set as described in the old PDQ documentation. The byte order is little-endian (least significant byte first).

Control Messages

The communication to the device is one-way, write-only. Synchronization has to be achieved by properly sequencing the setting of digital lines with control commands, control commands, and memory writes on the USB bus.

Control commands apply to all channels on all boards in a stack.

Control commands on the USB bus are single bytes prefixed by the 0xa5 escape sequence (0xa5 0xYY). If the byte 0xa5 is to be part of the (non-control) data stream it has to be escaped by 0xa5 itself.

Name Command Description
RESET 0x00 Reset the FPGA registers. Does not reset memories. Does not reload the bitstream. Does not reset the USB interface.
TRIGGER 0x02 Soft trigger. Logical OR with the external trigger control line to form the trigger signal to the spline.
ARM 0x04 Enable triggering. Disarming also aborts parsing of a frame and forces the parser to the frame jump table. A currently active line will finish execution.
DCM 0x06 Set the clock speed. Enabling chooses the Digital Clock Manager which doubles the clock and thus operates all FPGA logic and the DACs at 100 MHz. Disabling chooses a 50 MHz sampling and logic clock. The PDQ logic is inherently agnostic to the value of the sample clock. Scaling of coefficients and duration values must be performed on the host.
START 0x08 Enable starting new frames (enables leaving the frame jump table).

The LSB of the command byte then determines whether the command is a “disable” or an “enable” command.

Examples:

  • 0xa5 0x02 is TRIGGER enable,
  • 0xa5 0x03 is TRIGGER disable,
  • 0xa5 0xa5 is a single 0xa5 in the non-control data stream.

Memory writes

The non-control data stream is interpreted as 16 bit values (two bytes little-endian). The stream consists purely of writes of data to memory locations on individual channels. One channel/one memory can be written to at any given time. A memory write has the format (each row is one word of 16 bits):

channel
start_addr
end_addr
data[0]
data[1]
...
data[length-1]

The channel number is a function of the board number (selected on the dial switch on each PDQ board) and the DAC number (0, 1, 2): channel = (board_addr << 4) | dac_number. The length of the data written is length = end_addr - start_addr + 1.

Warning

  • No length check or address verification is performed.
  • Overflowing writes wrap.
  • Non-existent or invalid combinations of board address and/or channel number are silently ignored or wrapped.
  • If the write format is not adhered to, synchronization is lost and behavior is undefined.
  • A valid RESET sequence will restore synchronization. To reliably reset under all circumstances, ensure that the reset sequence 0xa5 0x00 is not preceded by an (un-escaped) escape character.

Control commands can be inserted at any point in the non-control data stream.

Examples:

  • 0x0072 0x0001 0x0003 0x0005 0x0007 0x0008 writes the three words 0x0005 0x0007 0x0008 to the memory address 0x0001 of DAC channel 2 (the last of three) on board 7 (counting from 0).
  • 0xa5 0x06 0x0000 0x00a5a5 0x00a5a5 0xa5a5a5a5 0xa5 0x02 0xa5 0x04 0xa5 0x08 enables the clock doubler (100 MHz) on all channels, then writes the single word 0xa5a5 to address 0x00a5 (note the escaping and the endianess) of channel 0 of board 0, enables soft trigger on all channels, arms all channels, and finally starts all channels.

Memory Layout

The three DAC channels on each board have 8192, 8192, 4096 words (16 bit each) capacity (16 KiB, 16 KiB, 8 KiB). Overflowing writes wrap around. The memory is interpreted as consisting of a table of frame start addresses with 8 entries, followed by data. The layout allows partitioning the waveform memory arbitrarily among the frames of a channel. The data for frame i is expected to start at memory[memory[i]].

The memory is interpreted as follows (each row is one word of 16 bits):

Address Data
0 frame[0].addr
1 frame[1].addr
... ...
frame[0].addr frame[0].data[0]
frame[0].addr + 1 frame[0].data[1]
... ...
frame[0].addr + N frame[0].data[N]
... ...
frame[1].addr frame[1].data[0]
frame[1].addr + 1 frame[1].data[1]
... ...
frame[1].addr + L frame[1].data[L]
... ...

Warning

  • The memory layout is not enforced or verified.
  • If violated, the behavior is undefined.
  • Jumping to undefined addresses leads to undefined behavior.
  • Jumping to frame numbers that have invalid addresses written into their address location leads to undefined behavior.

Note

This layout can be exploited to rapidly swap frame data between multiple different waveforms (without having to re-upload any data) by only updating the corresponding frame address(es).

Line Format

The frame data consists of a concatenation of lines. Each line has the following format (a row being a word of 16 bits):

header
duration
data[0]
...
data[length - 2]

Warning

  • If reading and parsing the next line (including potentially jumping into and out of the frame address table) takes longer than the duration of the current line, the pipeline is stalled and the evolution of the splines is paused until the next line becomes available.
  • duration must be positive.

Spline Data

The interpretation of the sequence of up to 14 data words contained in each line depends on the typ of spline interpolator targeted by header.typ.

The data is always zero-padded to 14 words.

The assignment of the spline coefficients to the data words is as follows:

typ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0 a0 a1 a2 a3  
1 b0 b1 b2 b3 c0 c1 c2

If the length of a line is shorter than 14 words, the remaining coefficients (or parts of coefficients) are set to zero.

The coefficients can be interpreted as two’s complement signed integers or as unsigned integers depending depending on preference and convenience. The word order is the same as the byte order of the USB protocol: little-endian (least significant word first).

The scaling of the coefficients is as follows:

  • a0 is in units of full_scale/(1 << 16).
  • a1 is in units of full_scale/(1 << (32 + shift))/clock_period.
  • a2 is in units of full_scale/(1 << (48 + 2*shift))/clock_period**2.
  • a3 is in units of full_scale/(1 << (48 + 3*shift))/clock_period**3.
  • b0 is in units of full_scale*cordic_gain/(1 << 16).
  • b1 is in units of full_scale*cordic_gain/(1 << (32 + shift))/clock_period.
  • b2 is in units of full_scale*cordic_gain/(1 << (48 + 2*shift))/clock_period**2.
  • b3 is in units of full_scale*cordic_gain/(1 << (48 + 3*shift))/clock_period**3.
  • c0 is in units of 2*pi/(1 << 16).
  • c1 is in units of 2*pi/(1 << 32)/clock_period.
  • c2 is in units of 2*pi/(1 << (48 + shift))/clock_period**2.
  • full_scale is 20 V.
  • The step size full_scale/(1 << 16) is 305 µV.
  • clock_period is 10 ns or 20 ns depending on the DCM setting.
  • shift is header.shift.
  • 2*pi is one full phase turn.
  • cordic_gain is 1.64676 (see gateware.cordic).

Note

With the default analog frontend, this means: a0 == 0 corresponds to close to 0 V output, a0 == 0x7fff corresponds to close to 10V output, and a0 == 0x8000 corresponds to close to -10 V output.

Note

There is no correction for DAC or amplifier offsets, reference errors, or DAC scale errors.

Note

Latencies of the CORDIC path, the DC spline path, and the AUX path are not matched. The CORDIC path (both the amplitude and the phase spline) has about 19 clock cycles more latency than the DC spline path. This can be exploited to align the DC spline knot start and the CORDIC output change. DC spline path and AUX path differe by the DAC latency.

Warning

  • There is no clipping or saturation.
  • When accumulators overflow, they wrap.
  • That’s desired for the phase accumulator but will lead to jumps in the DC spline and CORDIC amplitude.
  • When the CORDIC amplitude b0 reaches an absolute value of (1 << 15)/cordic_gain, the CORDIC output becomes undefined.
  • When the sum of the CORDIC output amplitude and the DC spline overflows, the output wraps.

Note

All splines (except the DDS phase) continue evolving even when a line of a different typ is being executed. All splines (except the DDS phase) stop evolving when the current line has reached its duration and no next line has been read yet or the machinery is waiting for TRIGGER, ARM, or START.

Note

The phase input to the CORDIC the sum of the phase offset c0 and the accumulated phase due to c1 and c2. The phase accumulator always accumulates at full clock speed, not at the clock speed reduced by shift != 0. It also never stops or pauses. This is in intentional contrast to the amplitude, DC spline, and frequency evolution that takes place at the reduced clock speed if shift != 0 and may be paused.

Wavesynth Format

To describe a complete PDQ stack program, the Wavesynth format has been defined.

  • program is a sequence of frames.

  • frame is a concatentation of segments. Its index in the program determines its frame number.

  • segment is a sequence is lines. The first line should be triggered to establish synchronization with external hardware.

  • line is a dictionary containing the following fields:

    • duration: Integer duration in spline evolution steps, in units of dac_divider*clock_period.
    • dac_divider == 2**header.shift
    • trigger: Whether to wait for trigger assertion to execute this line.
    • channel_data: Sequence of spline, one for each channel.
  • spline is a dictionary containing as key a single spline to be set: either bias or dds and as its value a dictionary of spline_data. spline has exactly one key.

  • spline_data is a dictionary that may contain the following keys:

    • amplitude: The uncompensated polynomial spline amplitude coefficients. Units are Volts and increasing powers of 1/(dac_divider*clock_period) respectively.
    • phase: Phase/Frequency spline coefficients. Only valid if the key for spline_data was dds. Units are [turns, turns/clock_period, turns/clock_period**2/dac_divider].
    • clear: header.clear.
    • silence: header.silence.

Note

  • amplitude and phase spline coefficients can be truncated. Lower order splines are then executed.

Example Wavesynth Program

The following example wavesynth program configures a PDQ stack with a single board, three DAC channels.

It configures a single frame (the first and only) consisting of a single triggered segment with three lines. The total frame duration is 80 cycles. The following waveforms are emitted on the three channels:

  • A quadratic smooth pulse in bias amplitude from 0 to 0.8 V and back to zero.
  • A cubic smooth step from 1 V to 0.5 V, followed by 40 cycles of constant 0.5 V and then another cubic step down to 0 V.
  • A sequence of amplitude shaped pulses with varying phase, frequency, and chirp.
wavesynth_program = [
    [
        {
            "trigger": True,
            "duration": 20,
            "channel_data": [
                {"bias": {"amplitude": [0, 0, 2e-3]}},
                {"bias": {"amplitude": [1, 0, -7.5e-3, 7.5e-4]}},
                {"dds": {
                    "amplitude": [0, 0, 4e-3, 0],
                    "phase": [.25, .025],
                }},
            ],
        },
        {
            "duration": 40,
            "channel_data": [
                {"bias": {"amplitude": [.4, .04, -2e-3]}},
                {"bias": {
                    "amplitude": [.5],
                    "silence": True,
                }},
                {"dds": {
                    "amplitude": [.8, .08, -4e-3, 0],
                    "phase": [.25, .025, .02/40],
                    "clear": True,
                }},
            ],
        },
        {
            "duration": 20,
            "channel_data": [
                {"bias": {"amplitude": [.4, -.04, 2e-3]}},
                {"bias": {"amplitude": [.5, 0, -7.5e-3, 7.5e-4]}},
                {"dds": {
                    "amplitude": [.8, -.08, 4e-3, 0],
                    "phase": [-.25],
                }},
            ],
        },
    ]
]

The following figure compares the output of the three channels as simulated by the artiq.wavesynth.compute_samples.Synthesizer test tool with the output from a full simulation of the PDQ gateware including the host side code, control commands, memory writing, memory parsing, triggering and spline evaluation.

_images/pdq_wavesynth_test.png

PDQ and Synthesizer outputs for wavesynth test program.

The abcissa is the time in clock cycles, the ordinate is the output voltage of the channel.

The plot consists of six curves, three colored ones from the gateware simulation of the board and three black ones from the Synthesizer verification tool. The colored curves should be masked by the black curves up to integer rounding errors.

The source of this unittest is part of ARTIQ at artiq.test.test_pdq.TestPdq.test_run_plot.