Using airhdl to Design a PN Sequence Checker for Analog Devices ADCs

Analog Devices Analog-to-Digital Converters like the 14-bit AD9645 feature built-in pseudo-random sequence generators, which are invaluable when it comes to checking that the ADC samples can be transmitted error-free to a receiving device, such as an FPGA, over a high-speed link. When bringing up a board featuring such an ADC-to-FPGA link, you want the ADC to output a known pattern so that you can check that the FPGA is indeed receiving the expected data.

For initial smoke tests, a fixed or a checkerboard pattern is fine, but in order to thoroughly check that your data transmission is working error-free, you will want to use more “difficult” test patterns like the PN9 and PN23 ones. Those are industry-standard sequences, which can easily be generated (and checked) using circuits called linear-feedback shift registers (LFSRs). In case you’re not familiar with them, LFSRs are just a chains of registers, with a few strategically placed XOR-type feedback taps.

The difference between the PN9 and the PN23 patterns is the sequence length. The PN9 sequence repeats every 2^9 – 1 = 511 cycles, whereas the PN23 sequence repeats every 2^23 – 1 = 8388607 cycles. This makes the PN23 sequence more suited for higher data rates, as the bit patterns repeat less often than with the PN9 sequence. Also, the PN23 will have longer sequences of contiguous zeros and ones than the PN9 sequence, which is of importance for AC-coupled links. In general, the PN23 sequence is considered more difficult than the PN9 sequence.

To bring up a board like the one shown below, with an AD9645 outputting samples over an LVDS link and an FPGA receiving them, I like to have the test pattern checker(s) built directly into the FPGA. In this article, I’ll show you how to implement such a test pattern checker using the LFSR components generated by the web-based airhdl code generator. We’ll be looking at the PN9 checker, but once you understand how it’s done, you’ll find it very easy to design your own checker for PN23 or other sequences.

Built-in test pattern checkers are great for board bring-ups.

First let’s look at the AD9645 datasheet to find out how to PN9 sequence (also called the PN sequence short) is defined:

PN sequence short description (source: AD9645 datasheet)

The description above is only part of the information we need to fully define the PN9 sequence. The missing part is the generator polynomial, which is given in another part of the datasheet as X^9 +X^5 +1. This is very mathematical way of describing a 9-bit shift-register with XOR feedback taps at bit positions 9 and 5 (using 1-based bit indexing).

The datasheet also gives the first words of the PN9 and PN23 sequences, which is super valuable information because it will allow us to easily check that we’re indeed generating the correct sequence:

The first words of the AD9645 PN sequences (source: AD9645 datasheet)

To create a PN9 checker, we’ll be generating the expected PN9 sequence internally in the FPGA and checking that the words we receive from the FPGA actually match the expected ones. Of course, we’ll need to somehow synchronize the internally-generated sequence with the received one. For that, we’ll just wait until the initial value shown in the table above (0x1FE0) is received and then we’ll let our internal sequence generator update on every received word.

The first step is to head over to After you have logged in, select the LFSRs entry in the left sidebar to show the Linear-Feedback Shift Registers view, and click the round “+” action button to bring up the New LFSR dialog:

The airhdl New LFSR dialog

By setting the length to 9 bits and the feedback type to xor, airhdl will generate the following LFSR circuit. Note that based on the configured length of the LFSR (9 bits), airhdl automatically computes the correct positions of the feedback taps (5 and 9):

The generated 9-bit LFSR circuit

If you’re curious about the sequence of numbers that the circuit shown above generates, you can download the corresponding Python model and run it like this:

% python

The output above shows the first 16 states of this 9-bit LFSR (as we have said above, the sequence repeats every 2^9 – 1 = 511 cycles). This is not exactly the sequence that the AD9645 will output when placed in the PN9 test mode though, as the AD9645 is a 14-bit ADC and the PN9 circuit has a 9-bit word length. The AD9645 datasheet explains how to construct the 14-bit words from the LFSR output:

Source: AD9645 datasheet

Using the airhdl-generated Python model for our PN9 LFSR, let’s look at the first 14 output words in binary form (we can use the -r bin option for that):

% python -r bin 14

As explained above, we can construct the first 14-bit word of the PN9 sequence by concatenating the MSBs of the LFSR’s first 14 output words: 11_1111_1110_0000. In order to match the two’s complement sequence that is indicated in the datasheet, we also need to invert the MSB, which gives us 01_1111_1110_0000 = 0x1FE0. This nicely matches the initial value of the PN sequence short from the table above!

Of course, there is always the risk that this is pure coincidence and a bit of paranoia is always a good thing for a developer; so let’s compute one more output word. This time we’ll ask our Python model to output the first 28 LFSR output words, and take the MSBs of the last 14 words:

% python -r bin 28  

The corresponding output word, again obtained by concatenating the MSBs of the 9-bit LFSR states equals 11_1101_1111_0001. Inverting the MSB and converting the word to hexadecimal gives 0x1DF1, which matches the second output sample of the PN sequence short in the table above. At this point, the result being a pure coincidence is quite unlikely and we’ll assume that our algorithm works fine.

We now have a clear understanding of the algorithm for generating the 14-bit PN9 sequence. The next step is to design the corresponding checker circuit, using a hardware description language such as VHDL. As a starting point, we can download the VHDL package for our pn9 LFSR from the website. This package contains all the constants and a function we need to get us started:

The VHDL LFSR package generated by

In particular, the next_pn9_lfsr function allows us to compute the next LFSR state, given the current one.

The principle of operation for our checker is as follows:

  1. Receive the first 14-bit ADC output word, let’s call it adc_output[n].
  2. Using the next_pn9_lfsr function, compute the next expected ADC output word; let’s call it adc_expected[n+1].
  3. Wait for the next ADC output word, adc_output[n+1], and compare it to adc_expected[n+1]. If both values match, declare the test pattern checker synchronized and proceed with step 2. If there is a mismatch, the pattern checker is not synchronized and re-start at step 1.

The checker has two states: SYNC and TRACK. In the SYNC state, the checker waits until the PN9 initial value, which is given in the datasheet as 0x1FE0, appears on the data input. When that happens, the checker jumps into the TRACK state where it checks that every subsequent input word matches the next expected word from the PN9 sequence. As long as this is the case, the checker is considered synchronized and this is reflected by the pn9_ok output port being asserted high. If at any time an input word doesn’t match the next expected word, the checker immediately de-asserts its pn9_ok and jumps back into the SYNC state.

When doing hardware tests, you can connect the pn9_ok signal to a debug port of your FPGA design for easy monitoring using an oscilloscope. That way you can just trigger on falling edges of the pn9_ok signal to catch any bit errors, even transient ones.

The VHDL code for the PN9 checker, including a VUnit testbench, is available on the airhdl GitHub. We hope you’ll find this useful!

New Generator: Linear-Feedback Shift Registers

Building on our vision to offer a comprehensive, web-based code generator for FPGA and ASIC developers, we are thrilled to announce the initial rollout of our Linear-Feedback Shift Register (LFSR) generator.

LFSRs are a class of pseudo-random number generators that can be implemented very efficiently in FPGA or ASIC technologies. As you can see in the figure below, a 7-bit LFSR is just a chain of 7 register stages with two XNOR feedback taps at positions 6 and 7. When initialized to zero, and provided with a clock signal, this marvelous little circuit will almost magically cycle through every possible state (except one) of the 7-bit word in a defined sequence that repeats itself every 127 cycles.

The micro-architecture of a 7-bit linear-feedback shift register

LFSRs have a single invalid state which—like a beetle stuck on its back—they cannot exit on their own. For XNOR feedback types LFSRs, the invalid state is all ones. Fortunately, the invalid word is not part of the LFSR’s natural sequence whose length is thus 2N-1 instead of 2N, N being the LFSR length in bits.

In digital electronics, LFSRs are often used to generate Pseudorandom Binary Sequences (PRBS) for testing serial or parallel communication links. PRBS-7 and PRBS-31 are two common kinds of Pseudorandom Binary Sequences, which can be generated respectively with 7-bit and 31-bit LFSRs. In the case of a serial communication link, the bit sequence is obtained from the MSB of the shift register (e.g. Q7 in the diagram above).

Implementing LFSRs in hardware is no rocket science. Still, since it’s not something that developers do every day, it can easily take an hour or two until the proper feedback taps and feedback type have been figured out and the circuit is finally working in simulation and in synthesis.

Using the new LFSR generator in airhdl, you can now design an LFSR in minutes and immediately download the VHDL or SystemVerilog implementation.

The new LFSR view in

For your convenience, airhdl also provides C and Python models of the LFSR so that you can easily display the sequence of numbers that the LFSR will cycle through. This can be super convenient when it comes to comparing numbers recorded with a logic analyzer with the expected sequence.

By default, the Python model outputs the first 16 words of the LFSR sequence in hexadecimal format:

$ python .\

Using the optional count argument, you can tell the script how many output words to generate:

$ python .\ 4

The -i option allows you to start the sequence on an arbitrary initial value:

$ python .\ -i 0x3F 8

This way you can easily convince yourself that it’s a very bad idea to initialize the LFSR to all ones (that’s the beetle stuck on its back):

$ python .\ -i 0x7F 8

We hope you’ll find the new LFSR generator useful and as always, make sure to let us know what you think!

Update (30-AUG-2023): Philip Abbey has generic VHDL implementation of LFSRs, which is described on his blog: Swapping Synchronous and LFSR Counters

How to Import 100 Registers from a Text File to airhdl

One of our users recently asked how he could import a list of 100 registers into airhdl without having to create every single register by hand in the user interface. He had the names of the registers available in a text file, one name per line:



Subscribers to the airhdl Professional CL plan can import register maps into airhdl by uploading a JSON file whose structure is described in the documentation.

To help import the user’s registers into airhdl, we have created a small Python script that transforms the user’s text file into an airhdl register map JSON object. The script, which is called, is available on our GitHub page. It can be used as follows:

python registers.txt map_name

Where registers.txt is the path to the text file containing the register names and map_name is the name of the register map to be created. The script generates an output file called out.json in the current working directory, which looks like this:

  "jsonVersion": 2,
  "registerMap": {
    "name": "my_map",
    "description": "",
    "width": 32,
    "baseAddress": 0,
    "addrWidthBits": 32,
    "revision": 1,
    "generateRecordPorts": false,
    "registers": [
        "type": "Register",
        "name": "REG_0",
        "description": "",
        "access": "READ_WRITE",
        "addressOffset": 0,
        "size": 32,
        "fields": [
            "name": "value",
            "description": "",
            "bitWidth": 32,
            "bitOffset": 0,
            "reset": 0,
            "selfClear": false

The last step is to upload the generated out.json file to the airhdl web application using the Upload button in the Register Maps view:

This creates a new register map with the name that we have specified when executing the script (in this example, my_map):

The out.json file can also be used as an input to the airhdl command line generator, which can generate all the airhdl output products (VHDL and SystemVerilog RTL code, testbenches, C header and documentation) locally on the user’s machine:

java -jar airhdl-cl.jar out.json

As we have seen, all it takes is a few lines of Python code to turn a text file into an airhdl register map JSON object that can be either uploaded to the airhdl web application to create a new register map, or used locally as an input to the airhdl command line generator.

Shiny and New: the SPI to AXI4-Lite Bridge

Following a user request, we have created an open-source SPI to AXI4-Lite bridge which allows you to access register banks generated by from any microcontroller over a Serial Peripheral Interface (SPI).

SPI to AXI4-Lite Bridge

The bridge is available in both VHDL and SystemVerilog versions, and comes as a single, self-contained file with no additional dependencies. It supports all four combinations of SPI clock phases and polarities, also known as SPI modes.

The source-code repository includes a VHDL testbench that was developed using the Open-Source VHDL Verification Methodology (OSVVM). The simulation requires a VHDL-2008 capable simulator such as Aldec Riviera-Pro.

We are releasing the SPI to AXI4-Lite bridge under a permissive Apache License 2.0, which allows you to use it in commercial applications.

Please feel free to try it out and let us know what you think!