Pseudorandom-binary-sequence (PRBS), or pseudonoise (PN), generators find a broad range of applications in digital-data transmission (Reference 1). These circuits often comprise simple shift registers with feedback that can serve as test sources for serial-data links. As their name implies, the output sequence is not truly random and in fact repeats after 2N–1 bits, where N denotes the shift register's length. Polynomial notation, in which the polynomial order corresponds to the shift register's length and, thus, the PRBS' period provides a convenient method of describing the sequence. Communications-equipment tests use certain standard polynomials. For example, x7+x6+1 yields a PRBS period of 127 bits, x23+x18+1 yields a period of more than 8 million bits, and x31+x28+1 yields a period that's 256 times longer. A PRBS with a longer period generally produces a greater variety of data patterns that more thoroughly check the transmission system's performance. A simple shift register with feedback from an intermediate stage can generate a PRBS. The flip-flops constituting the register must run at a speed equal to the transmission speed, which may pose a problem if you want to build a long-period PRBS generator that runs at a gigahertz clock rate. A high-speed serialiser such as Texas Instruments' TLK2201B, which runs at data rates as high as 1.6Gbit/s, offers one potential solution to the problem. However, instead of accepting a PRBS in its natural fully serial format, the serialiser accepts only 10bit portions at a time.

EDNAOL 2016JUN14 AN 02Fig1Figure 1: This circuit implements a 10bit parallel-output PRBS generator defined by the polynomial equation x311x2811. To reduce clutter, the schematic shows only one of 10 exclusive-OR gates that generates the register's feedback signals. A common clock source (not shown) drives all 31 flip-flops' clock inputs.

The circuit in figure 1 illustrates a 31st-order, parallel-PRBS generator that delivers 10bit output segments and can easily adapt to other PRBS orders and output widths. To design the circuit, begin by drawing a diagram with 31 flip-flops arranged in rows containing nominally 10 flip-flops. In this instance, the design comprises four rows, with only one flip-flop in Row 1. Figure 1 shows the timing relationships among the flip-flops and the numbering convention. The resulting structure forms a parallel shift register, with the fourth row fed directly from the third row, the third fed from the second, and so on. Flip-flops 10 through 2 in Row 2 and flip-flop 1 in Row 1 receive their inputs from the feedback path. This arrangement ensures that flip-flops in consecutive rows always deliver their outputs 10 time instants apart, and the generator's clock thus runs at one-tenth the speed of an equivalent serial-shift-register PRBS implementation. To determine the feedback signals, derive the equation that describes a standard—that is, serial—PRBS generator's output, which, for a polynomial of x31+x28+1, yields: y(n)=y(n–31) xor y(n–28). Using that equation, you can derive the equations that describe feedback signals fdbk1 through fdbk10. That is, fdbk1: y (n+9)=y(n–22) xor y(n–19), fdbk2: y(n+8)=y(n–23) xor y(n–20), ... fdbk10: y(n)=y(n–31) xor y(n–28). For example, feedback signal fdbk1 derives from the output of a two-input exclusive-OR gate driven by the outputs of flip-flops 22 and 19.

EDNAOL 2016JUN14 AN 02Fig2* Figure 2: A pseudorandom sequence produces this eye diagram as measured at the output of a TLK2201B serialiser that an FPGA-sequence generator drives.*

Listing 1 contains the VHDL code that implements the circuit of figure 1 in either a CPLD or an FPGA device. Lines 15 through 18 define the parallel-shift register, and lines 21 through 23 define the feedback circuit's construction. The circuit in this Design Idea fits into an XC3S50 Spartan 3 device from Xilinx, runs at a 150MHz clock rate, and drives a Texas Instruments TLK2201B serialiser at 150MHz through a 10bit interface. Xilinx's ISE 7.1i software compiled the circuit's VHDL files. Figure 2 displays an eye diagram for the serialiser's output and confirms the circuit's operation at 1.5Gbit/s. The compilation software predicts that the circuit should run at clock rates exceeding 300MHz, but the TLK2201B limits operation to 150MHz.
Reference
Miller, Andy, and Mike Gulotta, "PN generators using the SRL macro," Application Note APP211, Xilinx Inc, June 15, 2004.
This article is a Design Idea selected for re-publication by the editors. It was first published on March 29, 2007 in EDN.com.