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Lab Project (JOP792)

PRBS Generator Module (using PSpice)

INSTRUCTORS

Prof. Vinod Chandra

Prof. V.K. Jain

Submitted by:

J. Sirisha (2014JOP2496) Saheli Nargis (2014JOP2495)

Vishwaraj Esham (2014JOP2895)

Ajay Singh (2014JOP2558)

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Contents 1. Introduction[2]:...........................................................................................................................3

2. LFSR (Linear Feedback Shift Register)[1]: ..........................................................................................3

2.1 Feedback Action: .......................................................................................................................4

2.2 Tapping Action: .........................................................................................................................5

3. Theoretical Overview of 4 bit feedback ............................................................................................5

4. Simulation and Results:- ..................................................................................................................8

5. Application ................................................................................................................................... 11

6. Results: ........................................................................................................................................ 11

7. Further Extension:......................................................................................................................... 11

8.Conclusion:.................................................................................................................................... 13

9. References: .................................................................................................................................. 14

LIST OF FIGURES:

Figure 1:PRBS Generation Using 4 Bit Linear Feedback Shift Register (LFSR) using XOR gate[1]. ...............4

Figure 2:Circuit diagram for generating desired sequence using parallel to serial conversion ................ 12

Figure 3:Duty cycle corresponding to different bit pattern using desired sequence generator(using

parallel to serial convertor) ............................................................................................................... 13

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1. Introduction[2]:

In digital work a binary sequence, with a known pattern of ‘1’ and ‘0’, is common. It is more

common to measure bit error rates (BER) than signal to-noise ratio (SNR), and this is simplified

by the fact that known binary sequences are easy to generate and reproduce. A common

sequence is the pseudo random binary sequence. The output from a pseudo random binary

sequence generator is a bit stream of binary pulses; i.e., a sequence of 1`s (HI) or 0`s (LO), of a

known and reproducible pattern. The bit rate, or number of bits per second, is determined by

the frequency of an external clock, which is used to drive the generator. For each clock period a

single bit is emitted from the generator; either at the ‘1’ or ‘0’ level, and of a width equal to the

clock period. For this reason the external clock is referred to as a bit clock. For a long sequence

the 1`s and 0`s are distributed in a (pseudo) random manner. The sequence pattern repeats

after a defined number of clock periods. In a typical generator the length of the sequence is (2n-

1) clock periods, where n is an integer.

2. LFSR (Linear Feedback Shift Register)[1]:

A PRBS bit stream can be generated by using a linear feedback shift register (LFSR). Figure 1

illustrates an example of a 4-bit LFSR and its shifting data pattern. When the shift register is

filled up with a seed pattern of all 1’s here, the table in the right hand side depicts how the

register contents change and put out a series of PRBS. Right after the final bit, it returns to the

top of the bit stream. There are 15 bits of pseudo random bit stream generated. An L-bit LFSR

generates 2L -1 bits of PRBS. With carefully looking at the bit pattern in the shift register, you

can see there are all 4-bit combinations appeared except all 0’s. If you feed the pattern of

“0000”, the shift register would be stuck and it generates only 0’s infinitely. A seed pattern

must not be all 0’s. So one of the 15 4-bit patterns can be accepted as a seed.

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Figure 1:PRBS Generation Using 4 Bit Linear Feedback Shift Register (LFSR) using XOR gate[1].

2.1 Feedback Action:

In an LFSR, the bits contained in selected positions in the shift register are combined in some

sort of function and the result is fed back into the register's input bit. By definition, the selected

bit values are collected before the register is clocked and the result of the feedback function is

inserted into the shift register during the shift, filling the position that is emptied as a result of

the shift. Feedback around an LFSR's shift register comes from a selection of points (taps) in the

register chain and constitutes XNORing these taps to provide tap(s) back into the register.

Register bits that do not need an input tap, operate as a standard shift register. It is this

feedback that causes the register to loop through repetitive sequences of pseudo-random

value. The choice of taps determines how many values there are in a given sequence before the

sequence repeats. The implemented LFSR uses a one-to-many structure, rather than a many-to-

one structure, since this structure always has the shortest clock-to-clock delay path. The

feedback is done so as to make the system more stable and free from errors. Specific taps are

taken from the tapping points and then by using the XNOR operation on them they are

feedback into the registers. 22 The bit positions selected for use in the feedback function are

called "taps". The list of the taps is known as the "tap sequence". By convention, the output bit

of an LFSR that is n bits long is the nth bit; the input bit of an LFSR is bit 1

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2.2 Tapping Action:

An LFSR is one of a class of devices known as state machines. The contents of the register, the

bits tapped for the feedback function, and the output of the feedback function together

describe the state of the LFSR. With each shift, the LFSR moves to a new state. (There is one

exception to this -when the contents of the register are all ones, the LFSR will never change

state.) For any given state, there can be only one succeeding state. The reverse is also true: any

given state can have only one preceding state. For the rest of this discussion, only the contents

of the register will be used to describe the state of the LFSR. A state space of an LFSR is the list

of all the states the LFSR can be in for a particular tap sequence and a particular starting value.

Any tap sequence will yield at least two state spaces for an LFSR. (One of these spaces will be

the one that contains only one state -- the all zero one.) Tap sequences that yield only two state

spaces are referred to as maximal length tap sequences. The state of an LFSR that is n bits long

can be any one of 2^n different values. The largest state space possible for such an LFSR will be

2^n - 1 (all possible values minus the zero state). Because each state can have only once

succeeding state, an LFSR with a maximal length tap sequence will pass through every non-zero

state once and only once before repeating a state. One corollary to this behaviour is the out put

bit stream. The period of an LFSR is defined as the length of the stream before it repeats. The

period, like the state space, is tied to the tap sequence and the starting value. As a matter of

fact, the period is equal to the size of the state space. The longest period possible corresponds

to the largest possible state space, which is produced by a maximal length tap sequence.

(Hence "maximal length")

The PRBS signal generated as above will have the following characteristics:-

1. The length of the sequence generated by it, m = 2N-1 , where N = number of bits (i. e., Flip-

flops) of the shift register,

2. After every m number of binary bits, the sequence will be repeating itself.

3. Theoretical Overview of 4 bit feedback

The theoretical calculations of XNOR operation are given below in tables. Bit 1, Bit 2, Bit 3 and

Bit 4 corresponding to bits of shift register. Tap is used for giving feedback. The output is taken

from Bit 1. Initially we have considered 0000 so that XNOR can be proceed further.

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Bit 4 Bit 3 Bit 2 (Tap) Bit 1(Tap )

Bit 4 Bit 3(Tap ) Bit 2 Bit 1(Tap )

0 0 0 0

0 0 0 0

1 0 0 0

1 0 0 0

1 1 0 0

1 1 0 0

1 1 1 0

0 1 1 0

0 1 1 1

0 0 1 1

1 0 1 1

0 0 0 1

1 1 0 1

0 0 0 0

0 1 1 0

1 0 0 0

0 0 1 1

1 1 0 0

1 0 0 1

0 1 1 0

0 1 0 0

0 0 1 1

1 0 1 0

0 0 0 1

0 1 0 1

0 0 0 0

0 0 1 0

1 0 0 0

0 0 0 1

1 1 0 0

Bit 4(Tap ) Bit 3 Bit 2 Bit 1(Tap )

Bit 4 Bit 3(Tap ) Bit 2(Tap ) Bit 1

0 0 0 0

0 0 0 0

1 0 0 0

1 0 0 0

0 1 0 0

1 1 0 0

1 0 1 0

0 1 1 0

0 1 0 1

1 0 1 1

0 0 1 0

0 1 0 1

1 0 0 1

0 0 1 0

1 1 0 0

0 0 0 1

0 1 1 0

1 0 0 0

1 0 1 1

1 1 0 0

1 1 0 1

0 1 1 0

1 1 1 0

1 0 1 1

0 1 1 1

0 1 0 1

0 0 1 1

0 0 1 0

0 0 0 1

0 0 0 1

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Bit 4(Tap ) Bit 3 Bit 2(Tap ) Bit 1

Bit 4(Tap ) Bit 3(Tap ) Bit 2 Bit 1

0 0 0 0

0 0 0 0

1 0 0 0

1 0 0 0

0 1 0 0

0 1 0 0

1 0 1 0

0 0 1 0

1 1 0 1

1 0 0 1

0 1 1 0

0 1 0 0

0 0 1 1

0 0 1 0

0 0 0 1

1 0 0 1

1 0 0 0

0 1 0 0

0 1 0 0

0 0 1 0

1 0 1 0

1 0 0 1

1 1 0 1

0 1 0 0

0 1 1 0

0 0 1 0

0 0 1 1

1 0 0 1

0 0 0 1

0 1 0 0

Table 1.XNORing for different feedback from four bit shift register

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4. Simulation and Results:-

Feedback from Bit 1 and Bit 2:-

Feedback from Bit 1 and Bit 3:

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Feedback from Bit 1 and Bit 4:

Feedback from Bit 2 and Bit 3:

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Feedback from Bit 2 and Bit 4:

Feedback from Bit 3 and Bit 4:

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5. Application

The area of PRBS application is wide, for example, during design and testing of pseudorandom

position encoders, then for testing of measurement transducer, AD converters testing , in the

field of communication ,measurement of frequency response ,navigation systems, scrambling,

cryptographic applications, etc. Other example applications are found in surface

characterization and 3D scene modeling, and in audio applications to measure the properties of

loudspeakers.

6. Results:

The bit sequence output corresponding to the feedback is shown in table2.The output bit

pattern from the CRO is shown below in figure 3.

S.No. Feedback Output sequence

1 24 000010110000101

2 14 000010100110111

3 23 000011010001101

4 12 000011101100101

5 13 000011000011000

6 34 000010010010010

Table 2. Output Sequence corresponding to different feedback

7. Further Extension:

Known Sequence Generator: The prototype can also be extended to generate any of the

desired sequence of length of 8 bit, by extending the circuit . The circuit includes 8 single-way

micro switches and a parallel to serial convertor. Parallel to serial conversion can be done by

using IC 74165. The Circuit diagram is shown below. The Designed circuit/prototype canbe

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used for frequency division. The system can also be used to get a pulse with duty cycle of 1/8,

2/8, 3/8, 4/8, 5/8, 6/8 and 7/8.

Figure 2:Circuit diagram for generating desired sequence using parallel to serial conversion

Frequency division can be done by choosing an appropriate bit pattern. Below in table

frequency division is shown corresponding to some of the bits patterns, where the state ot the

switch “open”is represented by 0 and “closed” state by 1 .

S.No. State of switches/Bit pattern Output Frequency

1 10101010 f/2

2 11110000 f/4

Table 3. Frequency division and corresponding bit pattern for parallel to serial conversion ci rcuit,

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Figure 3:Duty cycle corresponding to different bit pattern using desired sequence generator(using parallel to serial convertor)

8. Conclusion:

The code for implementing the required PRBS is realized by writing PSPICE program. In the

program the logic implemented is very simple. A 8-bit PRBS is realized by shifting the input

through the D-flip flops and feed backing the outputs of some registers known as taps again

into the first register after passing them through a XNOR gate. The process of rea lizing LFSR is

carried out by first using Shift feedback resistor IC. The 4 bit shift register is used for the

same.The different output combinations of the shift resistor are then faded to the XNOR in

order to realise the output bit sequence. Tapings are taken from 1st, 2nd, 3rd and 4th Shift

registers so that the maximum length sequence of binary digits is produced. Initially when the

reset is kept at zero the outputs of each of the registers is uninitialized and hence the output is

uninitialized as well. However as soon as the reset is made high the output of all the registers

start coming out. A dead lock condition arises in the case when the initial input into the first

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register as output of the XNOR gate are all 0’s.Under this condition the output of a ll the register

of the PRBS Generator remains as 1 at all instants of time. Therefore it is necessary that the

initial input to the PRBS Generator be equal to 0, the output of the XNOR gate. Maximum

randomness in the sequence was realised when the feedback was given from 1st and 2nd.shift

registers.The code for implementing the above circuit was written and hence the simulation

results were generated and tested.

9. References:

[1] http://www.cs.miami.edu/~burt/learning/Csc609.022/random_numbers.html

[2] Tew, A. I. (2000). Digital Sequences, Correlation and Linear Systems, University of

York.Horowitz, P. & Hill, W. (1989).The Art of Electronics, Cambridge University Press , 2nd

edition.

[3] www.electronics.stackexchange.com.