Research Article  Open Access
New RTDBased General Threshold Gate Topologies and Application to ThreeInput XOR Logic Gates
Abstract
This paper presents two new general threshold gate (GTG) structures which are based on the monostablebistable element (MOBILE) as their main part. These new GTGs eliminate an RTD from the structure compared to old structures and lead to less elements count and better performance in terms of power consumption, maximum frequency, and powerdelay product (PDP). In the paper also two new single gate threeinput XOR logic gates based on the old GTGs and two ones based on the new GTGs are presented and simulated in HSPICE simulator.
1. Introduction
One of the most promising nanoscale devices expected to augment CMOS technology in future is the resonanttunneling diode (RTD) that is the most mature technology of quantum nanoelectronics [1]. RTDs are very fast nonlinear circuit elements which exhibit a negative differential resistance (NDR) region in their currentvoltage characteristics, because of these features it uses in different applications [2, 3]. The most important topologies, among all RTD based topologies, are those that use the monostablebistable logic element (MOBILE) as their main part. The MOBILE consists of two RTDs connected in series, driven by a switching bias voltage [1].
Threshold gate (TG) topology [1], multithreshold threshold gate (MTTG) topology [4], and more recently generalized threshold gate (GTG) topology [5โ7] are three wellknown topologies for implementing logic functions that are based on MOBILE.
Implementing threeinput XOR function in a single gate structure by old MOBILE topologies, such as TG and MTTG, were not practical [4] and the presented threeinput XOR gate in TG and MTTG topologies utilized cascading of two twoinput XOR gates. Fewer element counts and operating in only one clock cycle are the advantages of single gate structures.
In this letter for the first time, to the best of authorโs knowledge, two modified versions for general threshold gate (GTG) topology, which is the newest member of MOBILE based topologies, are presented in order to implement logic functions. Then we introduce two threeinput XOR gates in single gate structure based on generic GTG and two other ones based on our new modified versions of GTG.
2. New GTG Structures and New XOR Gates
The new designs are based on GTG topology. The inputoutput relationship for a generic GTG is shown in (1) called general threshold function:
where is the threshold, are positive weights, are negative weights, is the output, and are the boolean inputs. In this paper, following [6, 7], we utilize only and values for RTD weights and and values for the thresholds. Three different structures for GTG were introduced in 2005 and 2008 [5โ7]. The work in [7] named these structures as GTG1, GTG2, and GTG3. The GTG1 is an extension of TG topology in which, according to the above equation, f and g functions incorporate only AND boolean function [3]. In the GTG2, f and g functions may contains AND and/or OR boolean functions [6]. In the GTG3 structure f function is equal to zero and g function implements the main boolean function with AND, OR, and NOT functions [7]. In other words, in GTG3 structure, there is not any input branch in parallel with load RTD and the driver RTD has a parallel branch that implements the complement function. In this letter we introduce two new GTG structures that are the modifications for GTG2 and GTG3 and therefore we call them GTG4 and GTG5, respectively. In the modified structures we focus on the weights, such that some weights are chosen to be infinity (see (1)). In other words, some RTDs are eliminated from the structure because RTDs with infinity area are actually equal to short circuits. In this letter we have also introduced two threeinput XOR gates based on GTG2 and GTG3 and two others based on GTG4 and GTG5.
2.1. Designing ThreeInput XOR Gates Based on GTG2 and GTG3
Equation (2) shows the boolean function for a threeinput XOR gate. Equation (3) shows the implementation of (2) by general threshold function based on GTG2. In the relations, and are the boolean OR and AND functions, respectively, and the sign and sign are arithmetic subtraction and addition functions, respectively. The sign is the sign function which is equal to 1 if its arguments are greater than or equal to zero and is equal to 0 if its arguments are negative:
Figure 1(a) depicts the proposed threeinput XOR gate based on GTG2. The NDR0 implements the positive terms: , NDR1 implements the negative term: , and is used for adjusting the threshold value. For achieving XOR function the threshold value is equal to 1.
(a)
(b)
Equation (4) shows our general threshold function for threeinput XOR gate based on GTG3 and Figure 1(b) shows its implementation:
In Figure 1(b) the complement of the XOR function is implemented in NDR1 and is for adjusting the threshold value. For achieving XOR function the threshold value is equal to .
2.2. Designing ThreeInput XOR Gates Based on GTG4 and GTG5
As stated before, eliminating RTD(s) from GTGbased circuits would present new structures that we call them GTG4 and GTG5 which correspond to the modified GTG2 and GTG3, respectively (Figure 1). In this section, two new threeinput XOR gates are presented. Considering (3) we realized that the coefficient of the term in (3) can be adjusted toward infinity without changing the output value. Note the brief explanation as follows.
Selecting any higher value for the coefficient of this term does not change the result of the mentioned function and this coefficient is the only one that has this feature. Hence, if the inputs adjust to (111), the output would be equal to 1. Meanwhile, in the implemented circuit the drive RTD should be switched [1]. While all the inputs are equal to 1, all the transistors are on; therefore the prerequisite for switching the drive RTD when all the inputs are equal to 1 is the correctness of the following relation (see Figure 1(a)) [1]:
That is the coefficient for the boolean terms in (1) and also it adjusts the threshold value, is a constant value and corresponds to the RTD fabrication technology (in the simulations is adjusted to 1โm^{2}). By increasing the toward the infinity (2) will remain correct; hence, the dotted RTD in the Figure 1(a) can be eliminated.
This method is repeated for (3) and the dotted RTD in the Figure 1(b) is removed resulting another implementation of threeinput XOR gate.
For the MOBILEbased circuits the RTD areas should be adjusted to appropriate values for correct operation; moreover, the transistors width may be tuned for better performance [4โ7]. In these designs, before and after removing the RTDs in both presented circuits, the transistors widths have been tuned in order to obtain better performance and fortunately; after eliminating RTDs, the modified transistors widths were less than before resulting another benefit from. In Figure 1 the transistors widths after modification are shown in parenthesis.
3. Simulation and Comparisons
Figure 2 shows the simulation results for four proposed XOR logic circuits. The simulations are done in HSPICE simulator. In all simulations LOCOM model for RTDs is used [4โ7] and a 130โnm HSPICE transistor model is used to model transistors. For correct evaluation each output is loaded with four MOBILE inverters. The comparison between four proposed circuits in terms of device counts, maximum frequency, and powerdelay product is shown in Table 1. In addition, we have simulated a different threeinput XOR logic gate that consists of two cascaded twoinput XOR gate based on GTG3 that has been introduced before [7] for comparison. The used twoinput GTG3 XOR gate [7] was the best previously introduced gate, in terms of maximum frequency and PDP, and so the results that shown in Table 1 for maximum frequency and PDP are normalized based on results of this gate (the first row in the table).

(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
The table shows that GTG4 and GTG5 designs have better performance in comparison with GTG2 and GTG3 in all aspects especially in PDP and all new designs have better performance in terms of device count.
4. Conclusion
In this paper we have introduced two modified structures for general threshold gate topology based on MOBILE. These two new structures eliminate RTDs and lead to lower power consumption, better speed, and PDP. Then we proposed two threeinput XOR logic gates based on old GTG topologies and two based on new GTG topologies. Our designs also were compared with a different threeinput XOR logic gate that consists of two cascaded, previously introduced, twoinput XOR gates. The HSPICE simulation results showed that the threeinput XOR based on GTG5 is the best one according to maximum frequency and PDP and that one that is based on GTG4 is the best in terms of device count.
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Copyright
Copyright © 2010 S. M. Mirhoseini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.