26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 1 A NEW LEVEL RESTORATION CIRCUIT FOR MULTI-VALUED LOGIC Avni MORGÜL and Turgay TEMEL Boğaziçi University.

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Presentation transcript:

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 1 A NEW LEVEL RESTORATION CIRCUIT FOR MULTI-VALUED LOGIC Avni MORGÜL and Turgay TEMEL Boğaziçi University Electrical&Electronics Engineering Department Istanbul, TURKEY Presented By: Avni Morgül

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 2 MVL: Multi-Valued Logic fills the gap between digital&analog More than two logic level (r>2) Logic functions may be implemented –Using less number of transistor (smaller chip area) –Using less number of interconnections –Faster Disadvantages: –Static power dissipation –Lower noise margin

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 3 Comparison of MVL & Binary FA MVL- radix-8 adder: (12 trans.) 87µm×24µm 3-bit binary-adder: (84 trans.) 160µm×85µm

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 4 Definitions m: Number of variables r : radix. Number of discrete values f(x 1, x 2,..., x m ) : Multi Valued Logic function : each x j takes values from the MVL set R={0,1,..., r-1} In the current mode implementation each logic level is represented by a current level I j = j  I b, A logic level l corresponds to an interval of cont. variable, y y  l : {y|(j-0.5)I b  y < (j+0.5)I b } (j+0.5)I b (j-0.5)I b y  jI b discrete output jI b l continuous input The base current I b =10  A is selected for this work

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 5 Definitions max(x,y) = x  y = x + y max complement of x min(x,y) = x  y = x y min truncated difference k-valued literal

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 6 Definitions (cont.) max(x,y) = x + (y  x) min(x,y) = x – (x  y) = x  (x  y) r’=r-0.5 upper threshold Clockwise cyclic lower threshold

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 7 Implementation By using current-mode CMOS circuit i. The basic circuit Elements znzn N z1z :k x n-type current mirror Multiplying and re-directing a current x 1:k z1z1 znzn MdMd MmMm zn zn xkx N z1 z1 P the symbol the circuit

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 8 Inverter r- 1 1:1 z x MdMd MmMm r- 1 x 0 Slope = -1 z 1:1 r- 1 x N

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 9 Implementation ii. The Secondary Blocks z 1:k x y N Truncated Difference y x 1:k z M d MmMm y 0 Slope=k x z x y=x y= the definition the symbolthe circuit

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 10 min(x,y) gate z x y y Slope = 1 y N2 N3 x N1 z N4 y xin vddmin vssmin innext yin 35.5µm×19µm IC Layout y 1:1 x N N z x y y P y N

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 11 max(x,y) gate 0 xy y z Slope=1 y x N1 N5 N3 N4 VDD P1 P2 z z x y 1:1 N N P z N2 vddmax vssmax yin xin outmax innext 29µm×19µm IC Layout

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 12 The new feedback type Threshold circuit upper threshold, th u : z u z u (a,b,c) th u+ b a c a c  I b z u (a,b,c) c N4 a b N1 N2 N3 lower threshold, th l : z l (a,b,c) th l+ b a c z l (a,b,c) c N4 b a N1 N2 N3 a c  I b z l

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 13 Level Restoration The maximum number of identical structures that can be cascaded, without loosing a predefined input logic level at the output, is limited. Maximum radix of a given MVL function implementation depends on logic level degradations of basic gates such as min and max gates,  min,  max. The allowable logic level degradation or a standard deviation for each m -input gate can be determined by

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 14 Level Restoration It is necessary to restore the deviated levels after a certain number of cascaded gates Process (W/L) n ; (W/L) p %σ  z/z z=min(x,y) %σ  z/z z=max(x,y) 1.75/1; 5.5/ /1.5; 8/

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 15 Statistical Analysis Simulation results of deviation of the output current from the nominal value, for k cascaded stages max(x,y),  A x,  A y= 30  A k =1 k =4 k =8

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 16 Switched current type Restorer A/D converter Binary Decoder IbIb 2Ib2Ib logrI b x <x><x> current switches Voltage mode circuits

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 17 Problems of Switched Current Restorers Voltage mode A/D converters and Binary decoders required Spikes are generated by the switches Switching transistor sizes becomes too large for radixes higher than 3 Operation frequency is limited by voltage mode circuits

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 18 The new restoration circuit We propose a novel generalized restoration algorithm for current-mode MVL designs. The new algorithm eliminates current-to- voltage mode conversions used by other circuits and the restored level is obtained directly.

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 19 The new restoration circuit (cont.) The new circuit is based on the new threshold circuit. The restored level current can be established by cascading stages for i =1 through log 2 r, and summing up individual restored level currents.

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 20 The new restoration circuit (cont.) The following quantities are used to obtain the intermediate restored levels:

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 21 The new restoration circuit (cont.) The total restored level current can be established by cascading stages for i =1 through [log 2 r], and summing up individual restored level currents.

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 22 8-Level Restorer Circuit x 3.5I b 4I b 1.5I b 2Ib2Ib 0.5I b IbIb x x1x1 x1x1 x2x2 P-Type Mirror (1:1) Restored output Input Threshold circuit MSLS

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 23 Simulations Simulation results of two restoration circuits Switched current type restorerFull current-mode new restorer

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 24 Performance of the circuit Delay : 2.75ns Power dissipation: 0.25mW

26 May 2004 A. Morgül – ISCAS’2004, Vancouver, Canada 25 CONCLUSION In MVL circuits, it is necessary to restore the current level to nominal values, after a certain number of cascaded stages. –Restoration circuits may be realized with Voltage mode, transmission gate type, current switches, or The new current mode threshold circuits The new full current mode restorers show superiour performance in terms of circuit simplicity and transient behaviour. The transistor sizes vs number of necessary restoration circuits should be optimized in a large circuit.