# A New Design of Double Edge Triggered Flip-flops*

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2 (c) FIGURE Positive and negative level-sensitive latches; SET flip-flop; (c) ET flip-flop data throughput or doubles the data throughput while preserving the power dissipation. II. LOGIC STRUCTURE OF A ET FLIP-FLOP Latch is the basic unit for composing a flip-flop. The levels of a clock,, are used to drive the latch to either the storage state or the input state. If we use, and to express the input signal, present state and next state of a latch, the state equations for positive and negative levelsensitive latch can be expressed as: ' = + () ' = + (2) Equation () describes a latch which passes the input data when = and stores it when =. Inversely, equation (2) describes a complementary latch, which receives input data at = and stores it at =. The corresponding logic structures can be realized with a, as shown in Fig.. If two complementary latches are connected in series, one will be in the storage state while the other will be in the input state and hence a non-transparent edge triggered flip-flop is formed. Taking the latches in Fig., they can compose a well known master-slave flip-flop as shown in Fig.. [8] When =, its master latch passes input data and its slave latch is in the storage state. When =, its master latch is in the storage state and its slave latch passes and outputs the signal stored by the master latch. Therefore, this flip-flop changes its state at the clock s falling edge and keeps its state unchanged at the clock s rising edge. The above discussion shows that the master latch does not receive the input data when =. Obviously, if the input data has to be received at both clock levels, these two complementary latches should be connected in parallel rather than in series. Then we obtain a side-by-side flip-flop as shown in Fig. (c). Since the flip-flop is required to be non transparent from input to output, the output terminal should always be connected to the latch which is in the storage state. Therefore, the framed by the dotted line is needed. Because the flip-flop s state can change at both falling and rising edges of the clock, it is named ouble-edge- Triggered Flip-Flop and is denoted by the legend shown in Fig. (c). III. A NEW ESIGN OF CMOS ET FLIP-FLOP The can be realized with two CMOS transmission gates, therefore, the logic structure in Fig.(c) can be easily used to design the CMOS ET flip-flop as shown in Fig.2. [7] Note that two inverters are inserted in the feedback path to restore the level in two latches. Besides, all three s are simply composed of a pair of MOS transistors to reduce the number of transistors. We propose a new circuit design of CMOS ET flip-flop shown in Fig.2(c). It has the same number of transistors as a traditional CMOS SET flip-flop as given in [8]. At the same data rate we simulated both of these flip-flops using SPICE and a µ technology, while taking an inverter as the load. Their transient analysis waveforms are shown in Fig.3. Results confirm that the CMOS ET flip-flop can keep the same data rate while working at half the frequency which leads to a 2x reduction in power dissipation. We use the power meter [9] to measure and compare the power dissipation of two types of flip-flops (including the power dissipation of the clock buffers) for an input sequence. Results show that the ET flip-flop can reduce power dissipation by half ( 62%). Reference [7] points out that a random input sequence of n bits causes (n + )/2 expected changes in each latch of the SET flip-flop, but only (n/2 + )/2 expected changes in each latch of the ET flip-flop. With our input sequence, there are five changes ( ) in each latch of both SET and ET flip-flops. This means that the chosen sequence is rather conservative in estimating the power reduction with ET flip-flop. A detailed comparison between the two kinds of flip-flops is given in Table, which

3 TABLE COMPARISON OF SET FLIP-FLOP AN ET FLIP-FLOP SET flip-flop ET flip-flop average delay time.72 ns.57 ns maximum data rate 55 Mbits/s 9 Mbits/s TABLE 2 REPORTE RESULTS OF VARIOUS STATIC CMOS ET FLIP-FLOPS (data taken from relevant references) _ design number of transistors maximum data rate average delay time power reduction Ref. [4] 28 Mbits/s 3 ns ---- Ref. [6] 2 5 Mbits/s Ref. [7] 8 25 Mbits/s % Fig. 2(c) 2 9 Mbits/s.57 ns 62 % TABLE 3 RESULTS WITH THE SAME SIMULATION CONITION design number of transistors maximum data rate average delay time power reduction in Ref. [4] 28 5 Mbits/s.54 ns 22 % in Ref. [7] 8 55 Mbits/s.6 ns 52 % Fig. 2(c) 2 9 Mbits/s.57 ns 62 % _ Fig Mbits/s.63 ns 66 % _ (c) FIGURE 2 The design of CMOS ET flip-flop in Ref.[7] A modified design of CMOS ET flip-flop (c) The new design of CMOS ET flip-flop. demonstrate the higher quality of the ET flip-flop. In this table the delay time is defined as the clock-to- delay, that is the delay from the active clock input to the new value of the output. [8] Since the new value is stored in the master latch in the SET flip-flop and passed through the slave latch to the output after the triggering clock transition comes, the average delay time is a little bit longer than that of the ET flip-flop. If we feed back the output of the load inverter to the input of ET flip-flop, we can observe the maximum frequency of the flip-flop. [5,7] The maximum clock frequency for ET flip-flop is measured to be 45MHz, however, its maximum data rate is doubled that as shown in Table. A comparison of our simulation result with those reported in Refs.[4,6,7] are listed in Table 2. The table shows that our design has a simpler structure, lower delay time and higher maximum date rate. We should point out that the technology used in Refs. [4],[6],[7] are 2µ,.5µ, and 2µ, respectively. Besides, all s used in Ref. [7] are simply composed of two pass-transistors so it has the smallest transistor count. For a fair comparison we use the same SPICE simulator and µ technology to simulate all presented circuits. Results are given in Table 3, where the design in Ref.[6] has been omitted since it requires transistor sizing in the new technology which we wanted to avoid. Besides, we also simulated a modified ET flip-flop in Fig.2, which uses transmission gates to replace all pass transistors in Fig.2. Under the same input sequence, the energy dissipation diagrams (including both flip-flop itself and the buffers on the clock tree) in Fig.4 shows that a ET flip-flop consumes significantly lower energy dissipation compared to a conventional SET flip-flop.

4 (SET) (SET) (ET) (ET) Time (ns) FIGURE 3 Transient analysis waveforms Energy dissipation (pj) SET ET FIGURE 5 Connection of two ET flip-flops in series Equivalent structure with SET flip-flops. Time (ns) FIGURE 4 Energy dissipation diagram IV. ET EVICES BASE ON TRAITIONAL SET FLIP-FLOP ynamic ET flip-flops have also been investigated [5-6] based on the fact that the ET flip-flops can be connected in series to form a shift register. Figure 5 shows two ET flip-flops connected in series, which form a 2-bit shift register. The resulting logic function is the same as the function of the logic structure shown in Fig.5. We notice that the latter structure is simply composed of two traditional SET flip-flops with opposite edge-triggering mechanisms connected in parallel and output-switched by a. This example hints that the traditional SET flip-flop can also be used to form a 2-bit register which is double-edge-triggered. The reason we can use two levels of the clock in Fig.(c) is FIGURE 6. 2n-bit serial-in/serial-out shift register SET design ET design using SET flip-flops. that the latches are arranged in parallel and receive the input data alternately. Thus, if these latches are replaced by traditional SET flip-flops with complementary clocks, the resulting structure is a double-edge-triggered 2-bit shift register. This is especially important when designing a 2n-bit serial-in/serial-out shift register as shown next. Suppose 2n=6, a traditional shift register can be realized by using sixteen SET flip-flops cascaded in series, as shown in Fig.6. Sixteen clock periods are needed for it to store or output 6-bit data in series. uring this time each of the sixteen flip-flops receives 32 clock transitions. A dual-

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