3 August 2021

use PuTTY as Arduino monitor for LFSR circuits

Given the lack of really interesting signals on air, at least these days or no luck in hunting, I am playing with the semi-hardware (1) implementation of pseudo-random sequence generators: a way to spend these hot afternoons combining electronics and signal analysis. Waiting for the delivery of the 74xx595 chips, necessary for the 188-110A sequence generator, I wanted to implement a version of the LFSR (Linear Feedback Shift Register) described by the polynomial x^4+x+1 and verify - even if there was no need - its binary sequence. 

So, why a post title about PuTTY? I needed to save the bit stream produced by the circuit for its subsequent graphical representation but unfortunately the Arduino' console (embedded in its development environment) does not allow the content to be saved unless you stop the process and use the copy & paste method, a workaround not always effective in case of output that cause scrolling screen: using PuTTy is just what you need. "Putty" is a free SSH and telnet client for Windows and if it's not yet part of your resources you can quickly download and install it from its site [1]. After launched, select the right serial port number and speed as indicated by Arduino then on the session tab select the printable output and the path of the output file (figure 1): that's all, power-on your circuit and connect Putty, you do not have to run the Arduino environment to get a monitor.

Fig. 1 - configuring PuTTY for use as Arduino' monitor

Fig. 2 - PuTTY at work

Back to the LFSR circuit (four D-type Flip Flop and one XOR gate), its logic is quite simple and does not require much explanation even if I'm not really an artist in wiring the bredboards (figs. 3,4). Just notice that I use the Arduino MEGA 2560 so if you do not use such board you will have to change the input/output pins 6 (preset/clear), 8 (clock), 10 (Q1), 11 (Q2), 12 (Q3), 13 (Q4) by editing the sketch [2] according to your choices. Mind you that the clocking speed is exaggeratedly low to allow both the set of  the initial state of the registers (see below) and an easier reading of the monitor.

Fig. 3

Fig. 4

As said, the LFSR is described by the primitive polynomial x^4+x+1, i.e. its sequence is termed as m-sequence (maximum-length sequence) and has a length T = 2^n -1, where n is the number of the used registers (also termed as "stages"); in this case the LFSR employes four registers thus produces a 15-bit length sequence that repeats itself over time. Storing the "state" of each register (outputs Q1, Q2, Q3, Q4) we get 4 × 15 = 60-bit length pattern (figure 6).
Notice that the 0000 state is never crossed since in that state the sequence simply does not start, the registers are as stuck in that state; therefore, the 0000 state is never used as initial state (or "seed") of the LFSR. To start the state' cycles and set the seed to 1000, you will need to keep pin2 HIGH just for a clock positive transition, ie simply wire pin 2 - the data input of the first register - to the +5 V line of the bredboard, clock pulses are monitored by the LED in figure 4. 

Obviously, the same sequence will be obtained by simulating the LFSR using an Octave script (LFSRv2.m) [3] or the Logic Simulator App [4] [5] or the LFSR Testbench too [6]: you have many tools at your disposal.

Fig. 5 - LFSR states output logged by PuTTY and states output produced by Octave script

Fig. 6 - the 60-bit patterns generated by the four states of the LFSR

The sequences in figures 5-6 are obtained implementing the "many-to-one" feedback structure but you could also implement its "one-to-many" counterpart (2): in which case the sequence of the states will be slightly different (!) though the initial states are the same (figure 7).

Fig. 7 - many-to-one and one-to-many feedback structures for x^4+x+1 LFSR

«A way to spend these hot afternoons combining electronics and signal analysis» I said... yep, but the beach is much more better! 

(1) semi-hardware since some features such as the clock are software implemented 

(2) in "one-to-many" configuration there is never more than one level of combinational logic in the feedback path, irrespective of the number of taps being employed in the traditional "many-to-one" configuration (increasing the levels of logic in the combinational feedback path can negatively impact the maximum clocking frequency).

[1] https://www.putty.org
[2] https://disk.yandex.com/d/U4rXrZ7JWWgAGQ
[3] LFSRv2.m Octave script https://disk.yandex.com/d/jOX64f8u19jYFw
[4] Logic Simulator project https://disk.yandex.com/d/UcLU_1eAwtubXA
[5] Logic Simulator Apk https://logic-circuit-simulator-pro.it.aptoide.com/app
[6] https://disk.yandex.com/d/hMe696WAWjth8Q

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