A Presentation on

Cascadable Adiabatic Logic Circuits

for Low-Power applications

By

Divya Yashwanth

What is an adiabatic circuit ?Adiabatic circuits are low power circuits which use "reversible logic" to conserve energy. The term comes from the fact that an adiabatic process is one in which the total heat or energy in the system remains constant. Most research has focused on building adiabatic logic out of CMOS. However, current CMOS technology, though fairly energy efficient compared to similar technologies, dissipate energy as heat, mostly when switching. Adiabatic circuits attempt to conserve charge by following two key rules:Never turn on a transistor when there is a voltage potential between the source and drain. Never turn off a transistor when current is flowing through it.

Adiabatic Logic circuits from CMOS CMOS transistors dissipate power when they switch. The main part of this dissipation is due to the need to charge and discharge the gate capacitance C through a component that has some resistivity R. The energy dissipated when charging of the gate is

where T is the time it takes the gate to charge or discharge. In non-reversible circuits, the charging time T is proportional to RC. Reversible logic uses the fact that a single clock cycle is much longer then RC and thus attempts to spread the charging of the gate over the whole cycle and thus reduces the energy dissipated.

2CVTRCE

In order to extend the charging time of the gate never turn on a transistor that has a potential difference between source and drain, and furthermore, once the transistor is turned on, energy flows through it in a gradual and controlled manner.

The second rule that adiabatic circuits must follow is never to turn off a transistor when there is current flowing through it because transistors are not perfect switches going from on to off instantly. Instead, it gradually changes from on to off when the gate voltage changes. Furthermore, the change is proportional to the speed at which the gate voltage changes. During this time, the voltage drop across the transistor greatly increases yet the resistance is not high enough to bring power dissipation to zero.

GFCAL inverter GFCAL means glitch free and cascadable adiabatic logic circuits.

This circuit consists of one P-channel MOSFET and a diode in parallel with one N-channel MOSFET and a diode, which in turn are connected in series with the loadcapacitance C.The supply voltage VDD is a slowly varying triangular

voltage.The P-channel MOSFET (T1) and diode (D1) provide a charging path, and the N-channel MOSFET (T2) and diode (D2) provide a discharging path for the load current.

Operation of the circuit

When the input is ‘0’ (logic ‘0’), T11 is on and T2 is off. Path T11, D1 allows the current flow from the supply and the capacitor becomes charged close to the peak value of VDD, producing logic ‘1’. The diode D11 does not allow discharge into the supply when VDD is less than the output voltage.

When the input is logic‘1’, T22 is on and T11 is off. The path D2, T2 starts conducting. The diode, D2 prevents charging of the capacitor since it is reverse biased when VDD >VC and allows only discharging of the capacitor or pumping of energy back into the supply when VDD < VC. Thus, the capacitor voltage is brought down to a low value when the input is high irrespective of the previous output. Hence, the output is the complement of the input.

The output voltage level is almost independent of the time at which the input voltage is applied with respect to the supply voltage as long as it is applied at a time before VDD reaches the peak value.

Features

Typical input and output waveforms

Energy dissipation in the inverter during charging

When the P-channel MOSFET is on, and as VDD increases from 0 to Vo, the load capacitor is charged through the diode in the charging path.

The voltage reaches a peak value Vo in a time period T and its value VDD(t) at any time ‘t’ is when 0 ≤t ≤T when T ≤t ≤2TThe voltage VDD (t) reaches a value VB in a period Tth, when the diode starts conducting. Let Rch be the total resistance in the charging path. The voltage VC across the load capacitor ‘C’ for t> Tth, is

Assuming that Tth > CRch, Energy Ech dissipated over the period 0 – T in the diode and the transistor is

]TT)(t[1V(t)V

tTV(t)V

ODD

ODD

CC

chBO Vdt

dVCRVtTV

)VV)(1VT

VCC(RVEO

BB

OchOch

Energy dissipation in the inverter during dischargingWhen the N-channel MOSFET is on, the P-channel MOSFET

is off, charging of the capacitor is prevented at the load and the capacitor discharges through the diode in the discharge path till t1, that is, till VC is higher than the supply by at least VB, during the period when VDD increases from 0 to Vo. The capacitor then stops discharging at t1 and again continues discharging from 2T–t1 until VC = VB. Let Rdis be the total resistance in the discharging path. Assuming CRdis < t1, the energy Edc dissipated during discharging is the sum of energy dissipated during 0 to t1 and (2T–t1 ) to 2T which can be shown to be

where

C2B2

BCVBCRTV2C-)RC2

TV(2tE Bdis

Odis2

O2

1dc

TVCRVVB O

disBCO

The total energy ED, dissipated during one cycle of charging and discharging is given by

C2BBCVBCRT

V2C)RCTV(2t)V

V)(1VTVCC(RVEEE

2Bdis

Odis2

2

2O1

O

BB

OchOdcchD

Where t1 is given by

}TCRV

)TCR(VVV

Cln{RtdisO

disOBCOdis1

Equation (1)

From equation (1)the energy dissipated decreases as T increases. T indicates the rate at which the supply voltage varies and, hence, the energy dissipated decreases with slowly varying the supply voltages. The power dissipation generally changes with parameters like VO, the value of the capacitance, the equivalent series resistance because of the diode and the MOSFET.

Simulation of the inverter

Simulated using Virtuoso Spectre circuit simulator of Cadence EDA tools.Models used for the simulation are BSIM3V3 model parameters.Length of the transistor=180nm, width of the transistor = 720nm.Load capacitance=30fF.Supply waveform is triangular with frequency=25MHz and peak supply voltage=1.8V.Input signal is square wave with frequency=25MHz.The input logic ‘0’ value is 0.45 V and input logic ‘1’ value is 1.4 V.The output logic values have been found to be 0.45and 1.4 V corresponding to logic ‘0’ and logic ‘1’,

Name of the circuit

Energy dissipatedSimulation results

Theoretical values

Adiabatic inverter

4.04×10-14 4.38×10-14

CMOS inverter 9.12×10-14 9.72×10-14

Comparison of theoretical and simulated values of energy dissipation for adiabatic inverter with CMOS inverter for input data ‘01’ at 25–MHZ

From the table, for both the cases, it is clear that in adiabatic inverter, the energy dissipation is only about 50% of that in the CMOS inverter.

* The threshold voltage is 0.6 V for the N-channel MOSFET and -0.5 V for the P-channel MOSFET.* The peak value of voltage between gate and source (VGS) of the P-channel MOSFET is

VGS =0.45 -1.8= -1.35V * When the input is logic ‘1’, the output does not go through charging of the capacitor. This feature enables this circuit to be used to drive the circuits, which follow without malfunctioning. These aspects have been verified by connecting two, three and four inverters in tandem. * A single power supply for all the inverters is used.

Cascadability

Effect of variation of frequency* The simulation is carried out by varying the input frequencyand supply frequency simultaneously (keeping the input andsupply frequencies equal) from 2.5 to 250 MHZ with allother circuit parameters remaining the same.

The energy dissipated decreases marginally with increase in frequency.

The output logic levels up to frequencies of 25 MHz are 1.4 Vcorresponding to logic ‘1’ and 0.45 V corresponding to logic ‘0’.At frequencies higher than 25 MHz, the energy dissipated decreases gradually and the logic values vary from 1.4 to 1.35 V for logic ‘1’ and 0.45 to 0.47 V for logic ‘0’ at 250 MHzAt frequencies of 2.50 GHz, the logic ‘1’ tends to a value of 0.8 V and logic ‘0’ of –0.6 V. This is because the time period of the supply waveform is small compared with the time constant of charging and discharging, and the capacitor is unable to charge and discharge to the required levels.The frequency of operation is increased by increasing the width of the transistors, which results in a decrease of the charging and discharging time constants but large W/L ratio results in higher power dissipation in both the CMOS and GFCAL circuits.

Energy dissipation during one cycle of charging and discharging, rise and fall times in GFCAL inverter at different values of supply frequency with constant input frequency of 5MHz

Supply frequency(MHz)

Energy dissipation

Rise time (ns)

Fall time (ns)

Sum of rise time and fall times(ns)

5 3.417×10-14

46 4 50

10 3.44×10-14 24 3 2725 4.047×10-

149 7 16

50 4.30×10-14 6 3 9100 5.24×10-14 5 3 8250 6.17×10-14 4 2 6From these results it is observed that the rise and fall times are reduced at higher values of the supply frequency but with a marginal increase of energy dissipation.

Energy dissipated during 12 cycles of charging and discharging when the supply voltage is a sine, clamped to a zero reference level and a trapezium waveform of 25MHz with the same circuit parameters. The input and the supply frequencies are synchronised.Supply waveform

Energy dissipation, J

Output voltage levels, VLogic “1” Logic“0

”

Triangular 4.85×10-13 1.40 0.45Trapezium 5.00×10-13 1.5 0.45Sine 5.34×10-13 1.44 0.40Energy dissipated by a trapezium waveform is more than the triangular waveform. It is because the capacitor is allowed to charge to a higher value of voltage corresponding to logic ‘1’ since the duration of the peak value of supply voltage is longer compared with that of the triangular wave form.

In the case of the sine wave, the energy dissipation is more than that in the above cases because of the fast voltage rise near the zero crossing. Therefore triangular waveform is more suitable for less energy dissipation.

The circuit consists of two P channel MOSFETS (T5, T6) in parallel and a diode (D3) in series. The second branch consists of two N-channel MOSFETS (T7, T8) in series with a diode (D4).The two parallel branches are connected in series with the load capacitance C

GFCAL NAND GATE

The supply voltage for the proposed gates is VDD, which is a slowly varying triangular voltage

GFCAL NOR GATEThis circuit consists of two branches in parallel. The first branch consists of two P-channel MOSFETS (T1, T2) and a diode (D1) in series. The second branch consists of two N-channel MOSFETS (T3, T4) in parallel, connected in series with a diode (D2). The two parallel branches are connected in series with the load capacitance CThe circuits of CMOS NAND and NOR gates are

simulated with identical transistors and load capacitance. The supply voltage for these circuits is 1.8 V.

Comparison of simulated values of energy dissipation for the GFCAL NOR and NAND gates corresponding to input strings A =101010101010101010101010 and B = ‘101010101010101010101010’ for one cycle of charging and discharging at 25MHz.

Name of the circuit

Energy dissipated, J

Proposed GFCAL CMOSNAND gate 4.88×10-14 1.15×10-13

NOR gate 4.94×10-14 1.180×10-13

From the table, for both the cases, it is clear that in adiabatic gates, the energy dissipation is only about 50% of that in the CMOS gates.

GFCAL adder circuitsGFCAL half adder

It consists of one XOR gate and one AND gate. The XOR gate is realised using two NOR gates and one AND gate. The AND gate is realised by connecting the output of a NAND gate as input to the inverter. The OR gate is realised by connecting the output of a NOR gate as input to the inverter. The load capacitance for the gate in the last stage, which has to drive the next stage, is 30 fF and for all the other gates, the value of the load capacitance is 10 fF (including the input capacitance of the next stage). The supply for all the circuits is a triangular waveform

GFCAL XOR gate circuit

If the inputs are A = 01010101 and B = ‘00110011’. The outputs namely the SUM and CARRY are obtained as strings ‘01100110’ and ‘00010001’, respectively. Using the half adder as the block, a full adder is designed which consists of two half adders and an OR gate.

GFCAL Full Adder

SUM and CARRY output waveforms for the input strings ofA = ‘101010’ and B = ‘101010’ and input carry = ‘101010’are shown.

GFCAL 4 bit Ripple Carry Adder

It consists of four full adders and the carry output is given as the carry input to the following adder.The functionality of the circuit is guaranteed by maintaining the supply frequency higher than the frequency of the input data.

Energy dissipation for the proposed GFCAL adder circuits and CMOS circuits at input frequency of 25 MHZ and supply frequency of 250MHzName of the circuit

Energy dissipation, J

Logic “1”

Logic “0”

GFCAL half adder 2.82×10-13 1.4 0.45GFCAL full adder 7.35×10-13 1.4 0.45GFCAL 4 bit adder

3.32×10-12 1.4 0.45

CMOS half adder 6.21×10-13 1.78 0CMOS full adder 1.67×10-12 1.78 0CMOS 4 bit adder 6.68×10-12 1.78 0

From the table, the energy dissipation in the GFCAL adder circuits is about 50% of that of a CMOS adder circuits. The logic “0” in GFCAL can be reduced further by using a Schottkey diode

GFCAL JK Flip-flop

The JK flip-flop circuit consists of four GFCAL NAND gates. The inputs are J and K along with the clock signal and Q and are the outputs where is the complement of Q. The supply voltage is VDD, which is a slowly varying triangular voltage

Q

Q

Simulation results of GFCAL JK flip-flop

When the clock is enabled, the output changes according to the inputs, that is, outputs Q = ‘1’ and = ‘0’ when J = ‘1’ and K = ‘0’. Similarly, Q = ‘0’ and =‘1’ when J = ‘0’ and K = ‘1’. Further, the outputs Q and are latched to their corresponding values when the clock input is disabled.

Q

Q

Q

Energy dissipation for the proposed GFCAL JK Flip-flop and CMOS circuits at input frequency of 25 MHZ and supply frequency of 250MHz

Name of the circuit

Energy dissipation, J

Logic “1”

Logic “0”

GFCAL JK Flip-flop

1.28×10-13 1.4 0.45

CMOS JK Flip-flop

2.87×10-13 1.78 0

From the table, the energy dissipation in the GFCAL JK Flip-flop is about 50% of that of a CMOS JK Flip flop circuits.

Comparison of proposed GFCAL family with other adiabatic logic families

Given the length and width of a transistor are 180 nm and 720 nm, respectively, and the value of load capacitance is 30 fF. The input frequency is same as the supply frequency (25 MHZ).A 2N-2N2D inverter uses four transistors and two-diodes. The capacitor has to be charged first before evaluating the outputs, which may cause unwanted switching activities at the output nodes. A 2N-2P inverter uses four-transistors and a 2N-2N2P inverter uses six-transistors. A PAL inverter uses four-transistors but requires two complementary sinusoidal power clocks in cascaded circuits.

* A CAL inverter contains eight-transistors and needs a single clock and two additional timing control clocks for correct operation.* A True single phase energy recovery logic (TSEL) inverter contains six-transistors and needs a single clock, but it has discharge /charge and evaluation phases, which may cause unnecessary switching activities at nodes in hierarchical circuits.* A Quasi-static energy recovery logic (QSERL) inverter contains four transistors and needs a single clock, but a threshold voltage drop at MOSFETS used as diodes will occur and also the capacitance effect exists at higher frequencies. * An ADL inverter contains one-transistor and one diode along with a load capacitor and needs a four-phase clock in cascaded circuits. Since the capacitor has to be pre-charged, unwanted switching activity may occur at the output nodes.

Type of inverter Energy dissipation, J

CMOS 9.12×10-14

GFCAL 4.04×10-14

ADL 3.41×10-14

2N-2N2D 6.64×10-14

QSERL 5.11×10-14

2N-2P 5.21×10-14

2N-2N2P 5.26×10-14

CAL 5.19×10-14

The energy dissipated by different inverters at an input frequency of 25 MHz and a supply frequency of 25 MHz during one cycle of charging and discharging of the load capacitor

Type of inverter Energy dissipated, JCMOS 9.15×10-14

GFCAL 3.84×10-14

ADL 3.64×10-14

2N-2ND 6.51×10-14

The energy dissipated by different inverters at an input frequency of 125 MHz and a supply frequency of 125 MHz during one cycle of charging and discharging of the load capacitor

CONCLUSIONS1. In Cascadable adiabatic circuits the energy saved is more than 50% compared with that of conventional CMOS circuits. 2.This circuit can be used in building hierarchical circuits as the input and output logic levels are the same, just like in the case of conventional digital circuits, and there are no glitches. 3.All the circuits can be operated with a single power supply and there is no need of a complementary input. It has been shown that GFCAL circuits can work well up to 250 MHZ using 0.18 μm with a reasonable W/L ratio of the transistors. 4. The number of transistors in CMOS and adiabatic circuit are the same, except that one diode per branch is extra in adiabatic circuit. Thus, the circuits can be easily cascaded.

5. Power saving in these circuits is because of (i) The supply voltage is a slowly varying voltage, which results in energy saving during charging and discharging. (ii) The energy stored in the load capacitor is pumped back into the supply to realise a transition from logic ‘1’ to logic ‘0’.(iii) There is no short circuit current from the supply to the ground at any time during the transition of logic ‘1’ to logic ‘0’ or logic ‘0’ to logic ‘1’ unlike in the CMOS circuits.(iv) The diode in the discharge path of the gate prevents the flow of current spikes from the input data into the load capacitor.

REFERENCES1. Cascadable adiabatic logic circuits for low-power applications N.S.S. Reddy, M. Satyam, K.L. Kishore, IET Circuits, Devices and Systems November 2008, Volume 2, No.6, Pages 518-526.2. Adiabatic Logic by Benjamin Gojman, August 8, 2004http://www.cs.caltech.edu/cbsss/finalreport/nanoscale_ind_gojman.pdf

3. ‘Second-order adiabatic computation with 2N-2P and 2N- 2N-2P logic circuits’ by Kramer A, Denker J.S., Flower B, Moroney J, Proc. Intern. Symposium on Low Power Design, 1995, pp.191–196