Title: A Presentation on Cascadable Adiabatic Logic Circuits for Low-Power applications By Divya Yashwanth
1 A Presentation on Cascadable
Adiabatic Logic Circuits for Low-Power
applications By Divya Yashwanth
2What 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.
3 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.
4In 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.
5GFCAL 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 load - capacitance 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.
6Operation of the circuit When the input is 0
(logic 0), T1 is on and T2 is off. Path T1, 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 D1 does
not allow discharge into the supply when VDD is
less than the output voltage. When the input is
logic1, T2 is on and T1 is off. The path D2,
T2 starts conducting. The diode, D2 prevents
charging of the capacitor since it is reverse
biased when VDD gtVC and allows only discharging
of the capacitor or pumping of energy back into
the supply when VDD lt 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.
7The 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.
Typical input and output waveforms
Features
8Energy 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.
9The 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
2T The 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
tgt Tth, is Assuming that Tth gt CRch, Energy
Ech dissipated over the period 0 T in the
diode and the transistor is
10Energy dissipation in the inverter during
discharging When 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 2Tt1 until VC VB.
Let Rdis be the total resistance in the
discharging path. Assuming CRdis lt t1, the energy
Edc dissipated during discharging is the sum of
energy dissipated during 0 to t1 and (2Tt1 ) to
2T which can be shown to be where
11The total energy ED, dissipated during one cycle
of charging and discharging is given by
Where t1 is given by
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.
12Simulation 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 transistor180nm, width of the
transistor 720nm. - Load capacitance30fF.
- Supply waveform is triangular with
frequency25MHz and peak supply voltage1.8V. - Input signal is square wave with frequency25MHz.
- 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
0.45 - and 1.4 V corresponding to logic 0 and logic
1,
13Comparison of theoretical and simulated values of
energy dissipation for adiabatic inverter with
CMOS inverter for input data 01 at 25MHZ
Name of the circuit Energy dissipated Energy dissipated
Name of the circuit Simulation results Theoretical values
Adiabatic inverter 4.0410-14 4.3810-14
CMOS inverter 9.1210-14 9.7210-14
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.
14 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
15Effect 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.
16- The output logic levels up to frequencies of 25
MHz are 1.4 V - corresponding 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 MHz - At 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.
17Energy 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 3.41710-14 46 4 50
10 3.4410-14 24 3 27
25 4.04710-14 9 7 16
50 4.3010-14 6 3 9
100 5.2410-14 5 3 8
250 6.1710-14 4 2 6
From 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.
18Energy 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, V Output voltage levels, V
Supply waveform Energy dissipation, J Logic 1 Logic0
Triangular 4.8510-13 1.40 0.45
Trapezium 5.0010-13 1.5 0.45
Sine 5.3410-13 1.44 0.40
- Energy 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.
19In 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.
20The 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
21GFCAL NOR GATE
- This 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 C
- The 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.
22Comparison 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 Energy dissipated, J
Proposed GFCAL CMOS
NAND gate 4.8810-14 1.1510-13
NOR gate 4.9410-14 1.18010-13
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.
23GFCAL adder circuits
GFCAL 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
24GFCAL 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.
25GFCAL Full Adder
SUM and CARRY output waveforms for the input
strings of A 101010 and B 101010 and
input carry 101010 are shown.
26GFCAL 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.
27Energy dissipation for the proposed GFCAL adder
circuits 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 half adder 2.8210-13 1.4 0.45
GFCAL full adder 7.3510-13 1.4 0.45
GFCAL 4 bit adder 3.3210-12 1.4 0.45
CMOS half adder 6.2110-13 1.78 0
CMOS full adder 1.6710-12 1.78 0
CMOS 4 bit adder 6.6810-12 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
28GFCAL 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
29Simulation 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.
30Energy 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 1.2810-13 1.4 0.45
CMOS JK Flip-flop 2.8710-13 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.
31Comparison 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.
32 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.
33The 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 dissipation, J
CMOS 9.1210-14
GFCAL 4.0410-14
ADL 3.4110-14
2N-2N2D 6.6410-14
QSERL 5.1110-14
2N-2P 5.2110-14
2N-2N2P 5.2610-14
CAL 5.1910-14
34The 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
Type of inverter Energy dissipated, J
CMOS 9.1510-14
GFCAL 3.8410-14
ADL 3.6410-14
2N-2ND 6.5110-14
35CONCLUSIONS1. 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.
365. 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.
37 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/n
anoscale_ind_gojman.pdf3. 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.191196