CONCEPT OF PSEUDO-RING SELF-TEST OF THE RAM.
This paper presents the concept of pseudo-ring self-test (p-test) of the random access memory (RAM) The distinctive particularity of p-testing is that RAM truly is self-tested.. The process of emulation can be controlled and analytically described. This allows adapting optimally the p-test parameters in order to obtain the maximal value of fault coverage. The elaborated methodical and software tools help to reach this aim.
Keywords: Embedded system RAM Pseudo-Ring Self-Test
RAM truly came about in 1966 when Robert Dennard from
IBM's research center came up with the basic idea for
Dynamic Random Access Memory (commonly referred to as DRAM or mostly RAM). Dennard had gone home for the day and shortly later was somehow inspired by the basic idea for making DRAM. This turned out to be the most important advances in computer technology. This was just the beginning. It wasn't until the 1970s that Intel released the first RAM chip called the 1103 .
Random access memory (RAM) is the best known form of computer memory. RAM is considered "random access" because you can access any memory cell directly if you
know the row and column that intersect at that cell.
The opposite of RAM is serial access memory (SAM). SAM stores data as a series of memory cells that can only be accessed sequentially (like a cassette tape). If the data is not in the current location each memory cell is checked until the needed data is found. SAM works very well for memory buffers where the data is normally stored in the order in which it will be used (a good example is the texture buffer memory on a video card). RAM data on the other hand can be accessed in any order.
Similar to a microprocessor a memory chip is an integrated
circuit(IC) made of millions of transistors and capacitors. In the most common form of computer memory dynamic random access memory (DRAM) a transistor and a capacitor are paired to create a memory cell which represents a single bit of data. The capacitor holds the bit of information -- a 0 or a 1 (see How Bits and Bytes Work for
information on bits). The transistor acts as a switch that lets the control circuitry on the memory chip read the capacitor or change its state.
It is easy to see that the samples (1) are pseudorandom sequences generated by trivial Linear Feedback Shift Register (LFSR) described by the polynomial p(x) =
Example 1. In figure 1 is presented the process of generation of the first sequence a in (1).
But the pioneer and fundamental works in the random
testing RAM should be considered to be the papers Scheme of random testing RAM contains the reference memory the memory under test and the comparator (Figure 1). Considering scheme shown in the figure 2 RAM test quality i.e. fault coverage is estimated by the length of random testing. As it is remarked in  the test length is a function of the fault number of cells the detection uncertainty the initial state an the pattern probabilities. All calculus are applicable for the truly random test but not for pseudorandom testing where tests are generated repeatable starting by an initial seed.
In the same time the test results from pseudorandom tests are not well suited for Built-In Self-Test (BIST) . For
implementation of the BIST RAM in [6 7] preference is given to the deterministic test technique based on the March algorithm. A typical RAM BIST architecture is shown in figure 2. Controller and pattern generator can be configured to execute the deterministic or the
pseudorandom testing .
March algorithm is designed to cover a predefined set of faults. But a new RAM fault needs a novel test algorithm and so BIST module must be configured or/and reprogrammed for it.
Another test approach been really a self-test scheme was proposed recently [9 10]. This test technique called pseudo-ring (or p-) testing is based on emulation of the linear automaton in particular LFSR by memory itself. In this case no pattern generator is needed. The test quality is estimated at the end of p-test iteration. There is more degree of freedom to control the test procedure than in the deterministic or in the random testing. And such control is not so expensive.
The paper is organized as follows: section 2 introduces in
the p-testing RAM; section 3 describes the hardware and software tools; section 4 considers some concluding remarks.
Notion of pseudo-ring comes from the ring-like testing of digital circuits . In the ring-like testing circuit is
reconfigured so that it is transformed to a linear (or nonlinear) automaton i.e. LFSR. Test procedure is quite
simple: automaton is clocked during a period of time T equal to: T= 2m 1
wherem is the number of register stages.
After this period the final state Fin of register is compared
with expected one. In particular the expected state is equal to initial Init state. Then the comparison is made as:
The level of confidence of the test quality is estimated by the detection uncertainty.
Memory at the top-level of abstraction can be interpreted as a long register with random access to its stages. Of course there is no reason to reconfigure so long register" to the structure of a linear automaton. We go in another way.
The idea of pseudo-ring RAM testing is to use a set of memory's cells as the register stages. Second after each clock of time are shifted not the data in the register (see figure 1) but the virtual register itself. The only what is needed is to help supplementary to push from outside this virtual automaton in the memory address space. Complete transition of the virtual LFSR across all addresses of the memory is called the p-test iteration or simple p-iteration. -test iteration consists of: initialization of virtual automaton pushing this automaton in the space of memory array unloading the automaton final state and analysis of the results.
Go/no go p-iteration is evaluated as in the ring-like testing: comparing at the end of p-iteration the final and expected states of the virtual automaton i.e. register.
Consider the Example 2. Let the LFSR and its initial state is
the same as it is shown in figure 1. Conventionally suppose
that the memory size array is equal to 4; the cell size is
equal to 1. Let the addressing mode is counted up. -test iteration starts with loading the virtual register by an initial seed. Let the first two memory cells (with address 0 and 1) play the role of the stages of virtual register. Load these stages by the initial seed less than 1; 1greater than (Figure 4 a).
In accordance with structure of polynomial p(x) are performed (on corresponding cells) the read and modulo operations. Continue this operations until the final state will
be reached. If don't take into account the peculiarity of
performing the read-write operations then it can be accepted thatN+m conditional clocks of time were carried out to move the virtual automaton in the memory cells
address space. Since N"m then the complexity of p- iteration is of order:
O(p-iteration) = N.
In the above example was presented the main idea of the mechanism" (algorithm) of the p-iteration which is a constitutive part of the p-testing RAM. Generally p-test procedure consists in the execution of the controlled p-test iterations finalized by analyzing of the results i.e. the automaton states. In fact there are three controlling parameters (degree of freedom):
automaton structure defined by polynomial p(x);
initial seed in the p-iteration;
Addressing mode or trajectory of automaton.
Tell some words about each of these parameters. As a rule linear automaton follows the structure of an irreducible polynomial p(x) of degree m= deg p(x). Since p-iteration must be performed at least T clocks of time then:
whereN is the memory array size.
In dependence of the seed value at the beginning of each p- iteration can be distinguished two types of the p-test scheme: via-register and self-memory. In the self-type
scheme the final state of the previous p-iteration is the initial state of the next p-iteration. In this case p-test procedure is executed non-stop. In the via-scheme hardware and time overhead are needed to reload the virtual automaton in the each p-iteration.
There are three basic addressing modes for p-test executions: count up count down and random. Need to outline that in some works (for example ) is remarked that use of different initial conditions such as address order or background changing can increase the test quality of the March algorithm.
Another remarkable property of the p-testing that must be denoted is the invariability of the testing scheme. It means that the same p-test scheme can be applied (without essential modifications) as for bit-oriented so for the word- oriented memories and as for single-port so for multi-port memories. In this context it should be use a specific method of calculation of such parameter as the test length. Since in dependence of the memory type the p-testing scheme can has different variants of its implementation then it is reasonable to evaluate the p-test length by number of states that the virtual automaton has gone in the predefined period of p-test time. Let k be the number of p-iteration. Considering estimation (4) the p-test length L is of order:
L= O(kN). (6)
Finally in spite of the word random" in the notion pseudo-random" the behavior of the (virtual) automaton is just very deterministic and predictable. -test approach has a fundamental mathematical support namely the theory of linear automaton.
3. HARDWARE AND SOFTWARE TOOLS
Memory manufactured as a circuit unit or as an embedded block is almost ready automaton i.e. contains almost all
components necessary to implement the p-test procedure. Test-engineer should only to select the single scheme of p- testing from the proposed one then to specify the control parameters to simulate the RAM under test for the selected faults and to analyze the obtained results.
3.1. Hardware tools
In accordance with the p-test technique hardware overhead must carry out the modular operation and to push virtual automaton in the address space of memory array. Consider further an example which is the instructive and illustrative from the practical point of view.
Example 3. Let as it was in examples 1 and 2 p(x)=1+x+x2
m=2. Memory array size is multiple with m. Other control parameters are: trajectory counting up and self-testing; initial seed a degeneration (zero) state. Memory is a
standard static RAM circuit. Then it is enough to use an
Up/Down counter to generate the address of the selected cells. Two flip-flops FF and a XOR gate will be used to save the read data and to calculate the sum modulo 2 of these data.
In accordance with random (see figure 2) and deterministic testing RAM must be initialized before. In the p-testing scheme the signature analyzer is used as for initialization of
RAM so for processing" the output data. The resulted scheme for analyzed example is shown in figure 5 (make comparison with figures 2 and 3).
-test starts with initialization of RAM by patterns generated by signature analyzer SA (output of multiplexor MUX is switch on input 0). In this iteration of initialization counter CT will up from low to high address value. Further are executed non-stop three p-iterations where counter follows the states: 0(rd)1(rd)1(wr);
1(rd)2(rd)3(wr) etc. rd and wr are read and write operations. In each such iteration different backgrounds will be generated. From figure 4 is resulted that backgrounds are: 1101 1011 and 0110. On the end of iteration corresponding virtual automaton final state is expected. The expected final states and the signature analyzer states are values for p-test quality estimation.
3.2. Software tools
Test-engineer can elaborate and debug a p-test procedure by Development and Simulation Tools Environment (DSTE).
In this paper the concept hardware and software tools of
the RAM pseudo-ring (p-) self-test are presented. Test engineer has 3 degree of freedom to control the p-test procedure. Elaborated software tools allow to debug p-test algorithms simulate faulty memory and evaluate the p-test quality.
Results of the trivial p-testing fault coverage are presented.
13 single and 15 two-cell functional faults of static RAM
were simulated in this trivial test experiment. Length of p- test is equal to 4N where N is the size of memory array and for its implementation is needed an up-down counter two flip-flops and a XOR gate. Other practical p-test schemes are not more complex than the trivial one.
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