![176 Computer Science & Information Technology (CS & IT)
dissipation requires larger heat sinks hence increased area and cost, and therefore highlight the
need and importance of low power circuits.
Adiabatic Logic is based on adiabatic switching principle. The term ‘adiabatic’ refers to a process
in which there is no heat exchange with the environment [8-10]. The adiabatic switching
technique can achieve very low power dissipation, but at the expense of circuit complexity.
Adiabatic logic offers a way to reuse the energy stored in the load capacitors rather than the
traditional way of discharging the load capacitors to the ground and wasting this energy [1].
2. ADIABATIC LOGIC TYPES
Adiabatic families can be mainly classified as either Partially Adiabatic or Fully Adiabatic [2]. In
Partially Adiabatic circuits, some charge is allowed to be transferred to the ground, while in Fully
Adiabatic Circuits, all the charge on the load capacitance is recovered by the power supply.
Efficient Charge Recovery Logic (ECRL) and Positive Feedback Adiabatic Logic (PFAL) are
partially adiabatic techniques. ECRL is based around a pair of cross-coupled PMOS transistors.
Their source terminals are connected to the power-clock, and the gate of each one is connected to
the drain of the other. These nodes form the complementary output signals. The function is
evaluated by a series of pull-down NMOS devices [3]. The basic structure of ECRL circuits is
shown in figure 1. The core of the PFAL circuits is a latch made by the two PMOS and two
NMOS, that avoid a logic level degradation on the output nodes “out” and “/out”. The two n-
trees realize the logic functions. This logic family also generates both positive and negative
outputs. Figure 2 shows the PFAL basic structure.
Fig 1: Basic structure of ECRL [3] Fig 2: Basic structure of PFAL [4]
3. CIRCUIT IMPLEMENTATION
A 1-bit full adder is a basic cell in digital computing systems. If it has three 1-bit inputs (A, B,
and C) and two 1-bit outputs (sum and carry), then the relations between the inputs and the
outputs can be expressed as:](https://image.slidesharecdn.com/csit3418-130816060232-phpapp02/85/SEMI-ADIABATIC-ECRL-AND-PFAL-FULL-ADDER-2-320.jpg)
![Computer Science & Information Technology (CS & IT) 177
sum = Aഥሺ BഥC + BCഥሻ + Aሺ BഥCത + BCሻ
carry = AB + BC + CA
Tanner ECAD tool [8] is used for implementing the ECRL and PFAL semi adiabatic, dual rail
full adder circuit and results obtained from the two are compared. 1.25 micron and 0.18 micron
technologies are used. Tanner suit components S-edit is used for schematic entry, TSpice for
simulation and W-Edit for waveform analysis.
The logic function blocks (F) shown in the basic structures of ECRL and PFAL can be
implemented using the above equations of sum and carry. Similarly, /F logic function block can
be implemented by finding out the complement of sum and carry equations and then simplifying
them. The equations for /F logic function block will be as follows:
sumതതതതതത = Aሺ BCത + BഥCሻ + Aഥሺ BC + BഥCതሻ
ܿܽݕݎݎതതതതതതതത = ሺܣ̅ + ܤതሻ. ሺܤത + ܥ̅ ሻ. ሺܥ̅ + ܣ̅ሻ
Figure 3 to figure 6 show the circuit implementations of the sum and carry using ECRL and
PFAL techniques.
Fig 3: Circuit of Sum in an Adder using ECRL
Fig 4: Circuit of Carry in an Adder using ECRL](https://image.slidesharecdn.com/csit3418-130816060232-phpapp02/85/SEMI-ADIABATIC-ECRL-AND-PFAL-FULL-ADDER-3-320.jpg)
![184 Computer Science & Information Technology (CS & IT)
5. CONCLUSION
Authors have implemented the full adder circuit using semi adiabatic, dual rail, ECRL and PFAL
techniques with 1.25 micron and 0.18 micron technology. Through the implementation, authors
have compared the two techniques with respect to the transistor count, maximum operating
frequency, power dissipation and output level quality. The transistor count for carry and sum are
14, 22 and 16, 24 respectively for ECRL and PFAL. It is found that for 1.25 micron technology
ECRL based carry circuit dissipates least power of 2.860176 µW at 25 MHz, max power of
18.17460 µW at 100 MHz and maximum Cload derived is 7 fF with 8.464489 µW at 50 MHz.
The PFAL based carry circuit dissipates least power of 38.52858 µW at 20 MHz, max power of
51.52832 µW at 100MHz and maximum Cload derived is 20 fF with 40.61746 µW at 50 MHz .
ECRL based sum circuit dissipates least power of 4.932597 µW at 25 MHz, max power of
53.1588 µW at 100 MHz and maximum Cload derived is 30 fF with 29.6655 µW at 50 MHz. The
PFAL based sum circuit dissipates least power of 7.052026 µW at 25 MHz, max power of
53.33038 µW at 100 MHz and maximum Cload derived is 20 fF with 24.11132 µW at 50 MHz.
For 0.180 micron technology – ECRL based carry circuit dissipates 59.2158 µW at fmax of 200
MHz and maximum Cload derived is 20 fF with 88.63479 µW at 200MHz. PFAL based carry
circuit dissipates 583.6617 µW at 20 MHz. ECRL based sum circuit dissipates 24.37457 µW at
fmax of 200 MHz and maximum Cload derived is 10 fF with 38.95504 µW at 200MHz. PFAL
based sum circuit dissipates 1555.033 µW at 20 MHz. The output levels for PFAL are better and
stabilize quickly as compared to the ECRL based full adder circuit.
REFERENCES
[1] Rama Tulasi, G., Venugopal, K., Vijayabaskar, B., SuryaPrakash, R.: Design & Analysis of full
adders using adiabatic logic. In: International Journal of Engineering Research & Technology
(IJERT), vol. 1, Issue 5, July 2012.
[2] Indermauer, T., Horowitz, M.: Evaluation of Charge Recovery Circuits and Adiabatic Switching for
Low Power Design. In: Technical Digest IEEE Symposium Low Power Electronics, San Diego, pp.
102-103, October 2002.
[3] http://dspace.thapar.edu, Sanjay Kumar “Design Of Low Power Cmos Cell Structures Based On
Adiabatic Switching Principle”.
[4] Fischer, J., Amirante, E.,Bargagli-Stoffi, A., Schmitt-Landsiedel, D.: Improving the positive feedback
adiabatic logic family. In: Advances in Radio Science(2004), pp. 221-225
[5] Atul Kumar Maurya, Gagnesh Kumar: Energy Efficient Adiabatic Logic for Low Power VLSI
Applications. In: International Conference on Communication Systems and Network Technologies
2011.
[6] Y. Sunil Gavaskar Reddy, V.V.G.S. Rajendra Prasad. In: Power Comparison Of CMOS and
Adiabatic Full Adder Circuits.
[7] http://www.tannereda.com/ poduct 21 dec 2012
[8] Adiabatic Process http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html date 21 Dec 2012
[9] Adiabatic Process, http://www.britannica.com/ EBchecked/topic/5898/adiabatic-process date 21 dec
2012
[10] The Adiabatic Principle http://academic. brooklyn.cuny.edu/education/jlemke/webs/time/mca-
adiabatic.htm date 21 dec 2012](https://image.slidesharecdn.com/csit3418-130816060232-phpapp02/85/SEMI-ADIABATIC-ECRL-AND-PFAL-FULL-ADDER-10-320.jpg)
SEMI ADIABATIC ECRL AND PFAL FULL ADDER
- 1. Sundarapandian et al. (Eds) : ACITY, AIAA, CNSA, DPPR, NeCoM, WeST, DMS, P2PTM, VLSI - 2013 pp. 175–184, 2013. © CS & IT-CSCP 2013 DOI : 10.5121/csit.2013.3418 SEMI ADIABATIC ECRL AND PFAL FULL ADDER Subhanshi Agarwal and Manoj Sharma Electronics and Communication Engineering Department Bharati Vidyapeeth’s College of Engineering New Delhi, India ABSTRACT Market demands have compelled the VLSI industry stake holders to integrate more and more number of functionalities and which is also being well supported by the advances in fabrication techniques. This has challenged the circuit designers to design the power ware circuits and in the process many experts are using concept from other engineering areas to resolve the power equations more optimally. Adiabatic Logic is one such technique used to reduce the power dissipation of the circuit utilizing the principle from thermo dynamic of zero entropy exchange with environment. Authors have used adiabatic principle and implemented full adder circuit with ECRL and PFAL techniques. Transistor count for carry and sum are 14, 22 and 16, 24 respectively for ECRL and PFAL. The maximum frequency, maximum load driving capability are analyzed for 1.25 micron and 0.18 micron technology. It is found that for 1.25 micron technology ECRL based carry circuit dissipates least power of 2.860176 µW at 25 MHz, max power of 18.17460 µW at 100 MHz and maximum Cload derived is 7 fF with 8.464489 µW at 50 MHz. The PFAL based carry circuit dissipates least power of 38.52858 µW at 20 MHz, max power of 51.52832 µW at 100MHz and maximum Cload derived is 20 fF with 40.61746 µW at 50 MHz. ECRL based sum circuit dissipates least power of 4.932597 µW at 25 MHz, max power of 53.1588 µW at 100 MHz and maximum Cload derived is 30 fF with 29.6655 µW at 50 MHz. The PFAL based sum circuit dissipates least power of 7.052026 µW at 25 MHz, max power of 53.33038 µW at 100 MHz and maximum Cload derived is 20 fF with 24.11132 µW at 50 MHz. For 0.180 micron technology – ECRL based carry circuit dissipates 59.2158 µW at fmax of 200MHz and maximum Cload derived is 20 fF with 88.63479 µW at 200MHz. PFAL based carry circuit dissipates 583.6617 µW at 20 MHz. ECRL based sum circuit dissipates 24.37457 µW at fmax of 200 MHz and maximum Cload derived is 10 fF with 38.95504 µW at 200MHz. PFAL based sum circuit dissipates 1555.033 µW at 20 MHz. KEYWORDS ECRL, PFAL, Full Adder, Adiabatic circuit 1. INTRODUCTION Low power circuits aim at providing best output and utilizing minimum possible power. Need for low power VLSI circuits is increasing day by day due to remarkable success and growth of the class of personal computing devices and wireless communications systems which demand high- speed computation and complex functionality with low power consumption. Large power
- 2. 176 Computer Science & Information Technology (CS & IT) dissipation requires larger heat sinks hence increased area and cost, and therefore highlight the need and importance of low power circuits. Adiabatic Logic is based on adiabatic switching principle. The term ‘adiabatic’ refers to a process in which there is no heat exchange with the environment [8-10]. The adiabatic switching technique can achieve very low power dissipation, but at the expense of circuit complexity. Adiabatic logic offers a way to reuse the energy stored in the load capacitors rather than the traditional way of discharging the load capacitors to the ground and wasting this energy [1]. 2. ADIABATIC LOGIC TYPES Adiabatic families can be mainly classified as either Partially Adiabatic or Fully Adiabatic [2]. In Partially Adiabatic circuits, some charge is allowed to be transferred to the ground, while in Fully Adiabatic Circuits, all the charge on the load capacitance is recovered by the power supply. Efficient Charge Recovery Logic (ECRL) and Positive Feedback Adiabatic Logic (PFAL) are partially adiabatic techniques. ECRL is based around a pair of cross-coupled PMOS transistors. Their source terminals are connected to the power-clock, and the gate of each one is connected to the drain of the other. These nodes form the complementary output signals. The function is evaluated by a series of pull-down NMOS devices [3]. The basic structure of ECRL circuits is shown in figure 1. The core of the PFAL circuits is a latch made by the two PMOS and two NMOS, that avoid a logic level degradation on the output nodes “out” and “/out”. The two n- trees realize the logic functions. This logic family also generates both positive and negative outputs. Figure 2 shows the PFAL basic structure. Fig 1: Basic structure of ECRL [3] Fig 2: Basic structure of PFAL [4] 3. CIRCUIT IMPLEMENTATION A 1-bit full adder is a basic cell in digital computing systems. If it has three 1-bit inputs (A, B, and C) and two 1-bit outputs (sum and carry), then the relations between the inputs and the outputs can be expressed as:
- 3. Computer Science & Information Technology (CS & IT) 177 sum = Aഥሺ BഥC + BCഥሻ + Aሺ BഥCത + BCሻ carry = AB + BC + CA Tanner ECAD tool [8] is used for implementing the ECRL and PFAL semi adiabatic, dual rail full adder circuit and results obtained from the two are compared. 1.25 micron and 0.18 micron technologies are used. Tanner suit components S-edit is used for schematic entry, TSpice for simulation and W-Edit for waveform analysis. The logic function blocks (F) shown in the basic structures of ECRL and PFAL can be implemented using the above equations of sum and carry. Similarly, /F logic function block can be implemented by finding out the complement of sum and carry equations and then simplifying them. The equations for /F logic function block will be as follows: sumതതതതതത = Aሺ BCത + BഥCሻ + Aഥሺ BC + BഥCതሻ ܿܽݕݎݎതതതതതതതത = ሺܣ̅ + ܤതሻ. ሺܤത + ܥ̅ ሻ. ሺܥ̅ + ܣ̅ሻ Figure 3 to figure 6 show the circuit implementations of the sum and carry using ECRL and PFAL techniques. Fig 3: Circuit of Sum in an Adder using ECRL Fig 4: Circuit of Carry in an Adder using ECRL
- 4. 178 Computer Science & Information Technology (CS & IT) Fig 5: Circuit of Sum in an Adder using PFAL Fig 6: Circuit of Carry in an Adder using PFAL 4. RESULTS The two circuits are verified with different set of test vectors covering several input combinations for different set of frequencies and load capacitances. The simulation waveforms are shown in figure 7 to figure 10. The results pertaining to minimum voltage, average power, maximum frequency and maximum load are tabulated in table1 to table 7. The results are graphically analyzed and shown in figure 11 to figure 17.
- 5. Computer Science & Information Technology (CS & IT) 179 Fig 7: Waveform for Sum in an Adder using ECRL Fig 8: Waveform for Carry in an Adder using ECRL Fig 9: Waveform for Sum in an Adder using PFAL
- 6. 180 Computer Science & Information Technology (CS & IT) Fig 10: Waveform for Carry in an Adder using PFAL
- 7. Computer Science & Information Technology (CS & IT) Fig 11: Comparison between 0 100 200 300 400 500 600 NUMBER OF TRANSISTORS 14 16 Transistor Count, Maximum Frequency and Average Power for carry using 0.18micron technology Computer Science & Information Technology (CS & IT) Fig 11: Comparison between carry-ECRL and PFAL for 0.18 micron technology MAXIMUM FREQUENCY(MHz) AVERAGE POWER(µW) 200 59.2158 20 583.6617 Transistor Count, Maximum Frequency and Average Power for carry using 0.18micron technology 181 ECRL and PFAL for 0.18 micron technology ECRL PFAL
- 8. 182 Computer Science & Information Technology (CS & IT) Fig 12: Comparison between sum Fig 13: Transistor Count, Maximum Load Capacitance and Average Power at f=200MHz ECRL sum and carry for 0.18 micron technology Fig 14: Average Power and Frequency for Sum ECRL and PFAL for 1.25 micron technology 0 500 1000 1500 2000 NUMBER OF TRANSISTORS 22 24 Transistor Count, Maximum Frequency and Average Power for Sum(0.18 micron technology) 0 20 40 60 80 100 NUMBER OF TRANSISTORS 14 22 Transistor Count, Maximum Load Capacitance and Average Power at f=200MHz(0.18 Computer Science & Information Technology (CS & IT) Fig 12: Comparison between sum-ECRL and PFAL for 0.18 micron technology Fig 13: Transistor Count, Maximum Load Capacitance and Average Power at f=200MHz ECRL sum and carry for 0.18 micron technology Fig 14: Average Power and Frequency for Sum ECRL and PFAL for 1.25 micron technology MAXIMUM FREQUENCY(MHz) AVERAGE POWER(µW) 200 24.3745720 1555.033 Transistor Count, Maximum Frequency and Average Power for Sum(0.18 micron technology) MAXIMUM LOAD CAPACITANCE(fF) AVERAGE POWER(µW) 20 88.63479 10 38.95504 Transistor Count, Maximum Load Capacitance and Average Power at f=200MHz(0.18 micron technology) ECRL(CARRY) ECRL(SUM) ECRL and PFAL for 0.18 micron technology Fig 13: Transistor Count, Maximum Load Capacitance and Average Power at f=200MHz ECRL Fig 14: Average Power and Frequency for Sum ECRL and PFAL for 1.25 micron technology Transistor Count, Maximum Frequency and Average Power for Sum(0.18 micron technology) ECRL PFAL ECRL(CARRY) ECRL(SUM)
- 9. Computer Science & Information Technology (CS & IT) Fig 15: ECRL and PFAL Carry Circuit at f=50MHz using 1.25 micron technology Fig 16: ECRL and PFAL Sum Circuit at f=50MHz using 1.25 micron technology Fig 17: ECRL and PFAL 0 10 20 30 40 50 NUMBER OF TRANSISTORS 14 16 For Carry Circuit at f=50MHz using 1.25 micron technology 0 50 22 24 Analysis for SUM at f=50MHz using 1.25 micron technology 0 10 20 30 40 50 60 25 AVERAGEPOWER(µW) Average Power versus Frequency for Carry Computer Science & Information Technology (CS & IT) Fig 15: ECRL and PFAL Carry Circuit at f=50MHz using 1.25 micron technology Fig 16: ECRL and PFAL Sum Circuit at f=50MHz using 1.25 micron technology Fig 17: ECRL and PFAL Carry Circuit Power vs frequency MAXIMUM LOAD CAPACITANCE(fF) AVERAGE POWER(µW) 7 8.464489 20 40.61746 For Carry Circuit at f=50MHz using 1.25 micron technology 30 29.6655 20 24.11132 Analysis for SUM at f=50MHz using 1.25 micron technology 50 100 FREQUENCY(MHz) Average Power versus Frequency for Carry 183 Fig 15: ECRL and PFAL Carry Circuit at f=50MHz using 1.25 micron technology Fig 16: ECRL and PFAL Sum Circuit at f=50MHz using 1.25 micron technology ECRL PFAL ECRL PFAL ECRL PFAL
- 10. 184 Computer Science & Information Technology (CS & IT) 5. CONCLUSION Authors have implemented the full adder circuit using semi adiabatic, dual rail, ECRL and PFAL techniques with 1.25 micron and 0.18 micron technology. Through the implementation, authors have compared the two techniques with respect to the transistor count, maximum operating frequency, power dissipation and output level quality. The transistor count for carry and sum are 14, 22 and 16, 24 respectively for ECRL and PFAL. It is found that for 1.25 micron technology ECRL based carry circuit dissipates least power of 2.860176 µW at 25 MHz, max power of 18.17460 µW at 100 MHz and maximum Cload derived is 7 fF with 8.464489 µW at 50 MHz. The PFAL based carry circuit dissipates least power of 38.52858 µW at 20 MHz, max power of 51.52832 µW at 100MHz and maximum Cload derived is 20 fF with 40.61746 µW at 50 MHz . ECRL based sum circuit dissipates least power of 4.932597 µW at 25 MHz, max power of 53.1588 µW at 100 MHz and maximum Cload derived is 30 fF with 29.6655 µW at 50 MHz. The PFAL based sum circuit dissipates least power of 7.052026 µW at 25 MHz, max power of 53.33038 µW at 100 MHz and maximum Cload derived is 20 fF with 24.11132 µW at 50 MHz. For 0.180 micron technology – ECRL based carry circuit dissipates 59.2158 µW at fmax of 200 MHz and maximum Cload derived is 20 fF with 88.63479 µW at 200MHz. PFAL based carry circuit dissipates 583.6617 µW at 20 MHz. ECRL based sum circuit dissipates 24.37457 µW at fmax of 200 MHz and maximum Cload derived is 10 fF with 38.95504 µW at 200MHz. PFAL based sum circuit dissipates 1555.033 µW at 20 MHz. The output levels for PFAL are better and stabilize quickly as compared to the ECRL based full adder circuit. REFERENCES [1] Rama Tulasi, G., Venugopal, K., Vijayabaskar, B., SuryaPrakash, R.: Design & Analysis of full adders using adiabatic logic. In: International Journal of Engineering Research & Technology (IJERT), vol. 1, Issue 5, July 2012. [2] Indermauer, T., Horowitz, M.: Evaluation of Charge Recovery Circuits and Adiabatic Switching for Low Power Design. In: Technical Digest IEEE Symposium Low Power Electronics, San Diego, pp. 102-103, October 2002. [3] http://dspace.thapar.edu, Sanjay Kumar “Design Of Low Power Cmos Cell Structures Based On Adiabatic Switching Principle”. [4] Fischer, J., Amirante, E.,Bargagli-Stoffi, A., Schmitt-Landsiedel, D.: Improving the positive feedback adiabatic logic family. In: Advances in Radio Science(2004), pp. 221-225 [5] Atul Kumar Maurya, Gagnesh Kumar: Energy Efficient Adiabatic Logic for Low Power VLSI Applications. In: International Conference on Communication Systems and Network Technologies 2011. [6] Y. Sunil Gavaskar Reddy, V.V.G.S. Rajendra Prasad. In: Power Comparison Of CMOS and Adiabatic Full Adder Circuits. [7] http://www.tannereda.com/ poduct 21 dec 2012 [8] Adiabatic Process http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html date 21 Dec 2012 [9] Adiabatic Process, http://www.britannica.com/ EBchecked/topic/5898/adiabatic-process date 21 dec 2012 [10] The Adiabatic Principle http://academic. brooklyn.cuny.edu/education/jlemke/webs/time/mca- adiabatic.htm date 21 dec 2012