A Presentation on Cascadable Adiabatic Logic Circuits for Low-Power applications By Divya Yashwanth.
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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:
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.
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 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.
Operation of the circuit 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. 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 logic‘1’, 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 >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.
Typical input and output waveforms 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 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.
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 ≤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
t> Tth, is
Assuming that Tth > CRch, Energy Ech dissipated over the period
0 – T in the diode and the transistor is
Energy dissipation in the inverter during discharging its value V 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 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
Where t1 is given by
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.
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.
* dissipation for adiabatic inverter with CMOS inverter for input data ‘01’ at 25–MHZThe 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.
Effect of variation of frequency dissipation for adiabatic inverter with CMOS inverter for input data ‘01’ at 25–MHZ* 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.
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
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.
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.
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 (T 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. 5, 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
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.
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 circuits GFCAL NOR and NAND gates corresponding to input strings
GFCAL half adder
GFCAL XOR gate circuit GFCAL NOR and NAND gates corresponding to input strings
GFCAL Full Adder GFCAL NOR and NAND gates corresponding to input strings
SUM and CARRY output waveforms for the input strings of
A = ‘101010’ and B = ‘101010’ and input carry = ‘101010’
GFCAL 4 bit Ripple Carry Adder GFCAL NOR and NAND gates corresponding to input strings
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 CMOS circuits at input frequency of 25 MHZ and supply frequency of 250MHz
Simulation results of GFCAL JK flip-flop CMOS circuits at input frequency of 25 MHZ and supply frequency of 250MHz
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
* 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.
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
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
CONCLUSIONS frequency of 125 MHz and a supply frequency of 125 MHz during one cycle of charging and discharging of the load capacitor1. 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 frequency of 125 MHz and a supply frequency of 125 MHz during one cycle of charging and discharging of the load capacitor(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.
REFERENCES frequency of 125 MHz and a supply frequency of 125 MHz during one cycle of charging and discharging of the load capacitor1. 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.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.191–196