Pipelining approach
- 1. Pipelining Approach D.Gopinath AP/ECE Ramco Institute of technology Academic year (2019-20 Even)
- 2. Pipelining An approach to optimize sequential circuits Pipelining is a popular design technique used to accelerate the operation of the datapaths in digital processors. The idea is easily explained with the example of Figure a shown below.
- 3. Pipelining: An approach to optimize sequential circuits The goal of the circuit is to compute log(|a - b|), where both a and b represent streams of numbers, that is, the computation must be performed on a large set of input values. The minimal clock period Tmin necessary to ensure correct evaluation is given as: where tc-q and tsu are the propagation delay and the set-up time of the register, respectively.
- 4. We assume that the registers are edge-triggered D registers. The term tpd,logic stands for the worst-case delay path through the combinational network, which consists of the adder, absolute value, and logarithm functions. Assume that each logic module has an equal propagation delay. We note that each logic module is active for only 1/3 of the clock period (if the delay of the register is ignored). For example, the adder unit is active during the first third of the period and remains idle—this is, it does no useful computation— during the other 2/3 of the period.
- 5. Pipelining is a technique to improve the resource utilization, and increase the functional throughput. Assume that we introduce registers between the logic blocks, as shown in above Figure b. This causes the computation for one set of input data to spread over a number of clock periods, as shown in below Table. The result for the data set (a1, b1) only appears at the output after three clock-periods. At that time, the circuit has already performed parts of the computations for the next data sets, (a2, b2) and (a3,b3). The computation is performed in an assembly-line fashion, hence the name pipeline.
- 6. Pipelining: An approach to optimize sequential circuits This effectively reduces the value of the minimum allowable clock period:
- 7. Latch- vs. Register-Based Pipelines Pipelined circuits can be constructed using level- sensitive latches instead of edge-triggered registers. Consider the pipelined circuit of below Figure. The pipeline system is implemented based on pass- transistor-based positive and negative latches instead of edge triggered registers.
- 8. A latch-based system gives significantly more flexibility in implementing a pipelined system, and often offers higher performance. When the clocks CLK and 𝐶𝐿𝐾 are non- overlapping, correct pipeline operation is obtained. Input data is sampled on C1 at the negative edge of CLK and the computation of logic block F starts; the result of the logic block F is stored on C2 on the falling edge of 𝐶𝐿𝐾, and the computation of logic block G starts. The non-overlapping of the clocks ensures correct operation. The value stored on C2 at the end of the CLK low phase is the result of passing the previous input (stored on the falling edge of CLK on C1) through the logic function F.
- 9. When overlap exists between CLK and 𝐶𝐿𝐾, the next input is already being applied to F, and its effect might propagate to C2 before 𝐶𝐿𝐾 goes low In other words, a race develops between the previous input and the current one. Which value wins depends upon the logic function F, the overlap time, and the value of the inputs
- 10. NORA-CMOS—A Logic Style for Pipelined Structures The latch-based pipeline circuit can also be implemented using C2MOS latches, as shown in below Figure.
- 11. The operation is similar to the one discussed above. This topology has one additional, important property: A C2MOS-based pipelined circuit is race-free as long as all the logic functions F (implemented using static logic) between the latches are non- inverting. NORA-CMOS—A Logic Style for Pipelined Structures
- 12. The reasoning for the above argument is similar to the argument made in the construction of a C2MOS register. During a (0-0) overlap between CLK and 𝐶𝐿𝐾, all C2MOS latches, simplify to pure pull-up networks (see in C2MOS register Figure). The only way a signal can race from stage to stage under this condition is when the logic function F is inverting, as illustrated in below Figure, where F is replaced by a single, static CMOS inverter.
- 13. NORA-CMOS—A Logic Style for Pipelined Structures Based on this concept, a logic circuit style called NORA-CMOS was conceived. It combines C2MOS pipeline registers and NORA dynamic logic function blocks. Each module consists of a block of combinational logic that can be a mixture of static and dynamic logic, followed by a C2MOS latch. Logic and latch are clocked in such a way that both are simultaneously in either evaluation, or hold (precharge) mode. A block that is in evaluation during CLK = 1 is called a CLK-module, while the inverse is called a 𝐶𝐿𝐾-module.
- 15. Design Rules In order to ensure correct operation, two important rules should always be followed: The dynamic-logic rule: Inputs to a dynamic CLKn (CLKp) block are only allowed to make a single 0 to 1 (1 to 0) transition during the evaluation period. The C2MOS rule: In order to avoid races, the number of static inversions between C2MOS latches should be even.
- 16. Consider the situation pictured in below Figure a. During precharge (CLK = 0), the output register of the module has to be in hold mode, isolating the output node from the internal events in the module. Assume now that a (0-0) overlap occurs. Node A gets precharged to VDD, while the latch simplifies to a pull-up network (Figure b). It can be observed that under those circumstances the output node charges to VDD, and the stored value is erased! This malfunctioning is caused by the fact that the number of static inversions between the last dynamic node in the module and the latch is odd, which creates an active path between the precharged node and the output. This translates into the following rule: The number of static inversions between the last dynamic block in a logic function and the C2MOS latch should be even. This and similar considerations lead to a reformulated C2MOS rule
- 18. Revised C2MOS Rule The number of static inversions between C2MOS latches should be even (in the absence of dynamic nodes); if dynamic nodes are present, the number of static inverters between a latch and a dynamic gate in the logic block should be even. The number of static inversions between the last dynamic gate in a logic block and the latch should be even as well.
- 19. Non-Bistable Sequential Circuits Other regenerative circuits can be catalogued as astable and monostable. The astable circuit act as oscillators and can, for instance, be used for on-chip clock generation. The monostable circuit serve as pulse generators, also called one-shot circuits. Another interesting regenerative circuit is the Schmitt trigger. This component has the useful property of showing hysteresis in its dc characteristics—its switching threshold is variable and depends upon the direction of the transition (low-to-high or high-to-low).
- 20. The Schmitt Trigger A Schmitt trigger is a device with two important properties: It responds to a slowly changing input waveform with a fast transition time at the output. The voltage-transfer characteristic of the device displays different switching thresholds for positive- and negative-going input signals.
- 21. This is demonstrated in below Figure, where a typical voltage-transfer characteristic of the Schmitt trigger is shown (and its schematics symbol). The switching thresholds for the low-to-high and high to low transitions are called VM+ and VM-, respectively. The hysteresis voltage is defined as the difference between the two.
- 22. One of the main uses of the Schmitt trigger is to turn a noisy or slowly varying input signal into a clean digital output signal. This is illustrated in below Figure.
- 23. CMOS Implementation of Schmitt trigger The idea behind this circuit is that the switching threshold of a CMOS inverter is determined by the (kn/kp) ratio between the NMOS and PMOS transistors. Increasing the ratio results in a reduction of the threshold, while decreasing it results in an increase in VM.
- 24. Suppose that Vin is initially equal to 0, so that Vout = 0 as well. The feedback loop biases the PMOS transistor M4 in the conductive mode while M3 is off. The input signal effectively connects to an inverter consisting of two PMOS transistors in parallel (M2 and M4) as a pull-up network, and a single NMOS transistor (M1) in the pull-down chain. This modifies the effective transistor ratio of the inverter to kM1/(kM2+kM4), which moves the switching threshold upwards. Similar behavior
- 25. Monostable Sequential Circuits A monostable element is a circuit that generates a pulse of a predetermined width every time the quiescent circuit is triggered by a pulse or transition event. It is called monostable because it has only one stable state (the quiescent one). A trigger event, which is either a signal transition or a pulse, causes the circuit to go temporarily into another quasi-stable state. This means that it eventually returns to its original state after a time period determined by the circuit parameters. This circuit, also called a one-shot, is useful in generating pulses of a known length. This functionality is required in a wide range of applications. We have already seen the use of a one-shot in the construction of glitch registers.
- 26. Astable Circuits An astable circuit has no stable states. The output oscillates back and forth between two quasi-stable states with a period determined by the circuit topology and parameters (delay, power supply, etc.). One of the main applications of oscillators is the on-chip generation of clock signals. The ring oscillator is a simple, example of an astable circuit. It consists of an odd number of inverters connected in a circular chain. Due to the odd number of inversions, no stable operation point exists, and the circuit oscillates with a period equal to 2xtpxN, with N the number of inverters in the chain and tp the propagation delay of each inverter.
- 27. Ring oscillator The ring oscillator composed of cascaded inverters produces a waveform with a fixed oscillating frequency determined by the delay of an inverter in the CMOS process. In many applications, it is necessary to control the frequency of the oscillator. An example of such a circuit is the voltage-controlled oscillator (VCO), whose oscillation frequency is a function of a control voltage. The standard ring oscillator can be modified into a VCO by replacing the standard inverter with a current- starved inverter as shown in below Figure. The mechanism for controlling the delay of each inverter is to limit the current available to discharge the load capacitance of the gate.
- 28. In this modified inverter circuit, the maximal discharge current of the inverter is limited by adding an extra series device. Note that the low-to-high transition on the inverter can also be controlled by adding a PMOS device in series with M2.
- 29. The added NMOS transistor M3, is controlled by an analog control voltage Vcntl, which determines the available discharge current. Lowering Vcntl reduces the discharge current and, hence, increases tpHL. The ability to alter the propagation delay per stage allows us to control the frequency of the ring structure.
- 30. TEXT BOOKS: Neil H.E. Weste, David Money Harris “CMOS VLSI Design: A Circuits and Systems Perspective”, 4th Edition, Pearson, 2017 (UNIT I,II,V). Jan M. Rabaey, Anantha Chandrakasan, Borivoje. Nikolic, “Digital Integrated Circuits:A Design perspective”, Second Edition , Pearson , 2016.(UNIT III,IV) REFERENCES M.J. Smith, “Application Specific Integrated Circuits”, Addisson Wesley, 1997. Sung-Mo kang, Yusuf leblebici, Chulwoo Kim “CMOS Digital Integrated Circuits:Analysis & Design”,4th edition McGraw Hill Education,2013. Wayne Wolf, “Modern VLSI Design: System On Chip”, Pearson Education, 2007. R.Jacob Baker, Harry W.LI, David E.Boyee, “CMOS Circuit Design, Layout and Simulation”, Prentice Hall of India 2005.
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