# ECE124 Digital Circuits and Systems Page 1

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1 ECE124 Digital Circuits and Systems Page 1

2 Chip level timing Have discussed some issues related to timing analysis. Talked briefly about longest combinational path for a combinational circuit. Talked briefly about timing with flip-flops; i.e., Data input must be stable before active clock edge (setup time). Data input must be stable after active clock edge (hold time). Data output doesn t change immediately after the active clock edge (clock-tooutput time). When we build an entire circuit (one with both flip-flops and combinational logic), there are other important timing concepts to understand. ECE124 Digital Circuits and Systems Page 2

3 Cycle times (1) Consider flip-flop outputs being used to generate flip-flop inputs: Tco Tdata Tsu clk combinatorial D Q D Q logic (and delay) Tclk1 Tclk2 It takes time for signals to arrive where they need to be ECE124 Digital Circuits and Systems Page 3

4 Cycle times (2) Sequence of events in transfer of data between flip-flops : Takes time for active clock edge to arrive at first FF (Tclk1). Once active clock edge arrives, takes time for output of first FF to change (+Tco). Takes time for output of first FF to cause changes in the input value to the second FF due to combinatorial logic between FF (+Tdata). Input at second FF must be present prior to active clock edge at second FF (Tsu). Takes time for clock to arrive at second FF (Tclk2). Must be some limit of how fast we can clock the circuit (i.e., the frequency of clock signal): Data output from first FF must get to data input of second FF prior to the next active clock edge. ECE124 Digital Circuits and Systems Page 4

5 Cycle times (3) For the data output of the first FF to get to the data input of the second FF in sufficient time, the following must be true: The minimum period (maximum frequency) of the circuit is: ECE124 Digital Circuits and Systems Page 5

6 Cycle times (4) Tco Tdata Tsu clk combinatorial D Q D Q logic (and delay) Tclk1 Tclk2 The equation for Tcycle tells us a minimum clock period (or maximum frequency) at which our circuit can operate without violating the setup time at the second FF input. ECE124 Digital Circuits and Systems Page 6

7 Cycle times (5) Tclk1 Tco Tdata Tsu CLK FF1 CLK FF2 CLK FF1 Q FF2 D Tclk1 Tcycle ECE124 Digital Circuits and Systems Page 7

8 Clock skew If we look at our equation for maximum frequency: Circuit frequency <= 1/Tcycle The term (Tclk1 Tclk2) that measures the difference in time between the arrival of the active clock edge at the two flip-flops. This difference is called clock skew and it can be positive or negative. In general, clock skew is a big hassle, and we would like to avoid it if possible. ECE124 Digital Circuits and Systems Page 8

9 Inverted clocks (1) Sometimes we might have flip-flops clocked on different edges of the clock; some flipflops trigger on the rising edge and others on the falling edge. This can limit the maximum frequency of the circuit too since we have less time to get data to where it needs to be! Tco Tdata Tsu clk combinatorial D Q D Q logic (and delay) Tclk1 Tclk2 Rising edge Falling edge ECE124 Digital Circuits and Systems Page 9

10 Inverted clocks (2) Tclk1 Tco Tdata Tsu CLK FF1 CLK FF2 CLK FF1 Q FF2 D Tclk1 Tcycle Since the second FF is triggered on the falling edge, either Tdata must be short enough, or the cycle time for the clock needs to be lengthened (lower frequency) to allow the data to get to the second FF. ECE124 Digital Circuits and Systems Page 10

11 Tclk1 Tco Tdata Tsu CLK FF1 CLK FF2 CLK FF1 Q FF2 D Tclk1 Tcycle ECE124 Digital Circuits and Systems Page 11

12 Duty cycles Sometimes the clock signal is not symmetric; It has a non-uniform duty cycle. If we use both rising and falling edge triggering, this can also affect the clock frequency. 2/3 high (66% duty cycle) CLK 1/3 low ECE124 Digital Circuits and Systems Page 12

13 Setup and hold times at the pins of a chip (1) Say we have a circuit implemented inside of an integrated circuit (IC) chip. The circuit and IC now looks like a black-box. Timing at the pins of the chip are now important. Suppose you have a data present at at input pin on the IC. The signal might go through some logic inside the IC prior to reaching a flipflop input inside of the IC. The flip-flop inside of the IC is clocked by another clock signal applied at another pin of the IC. ECE124 Digital Circuits and Systems Page 13

14 Setup and hold times at the pins of a chip (2) There is a setup and hold time at the flip-flop inside of the IC and a relationship between the FF-D input and the FF-CLK input. Therefore, there must be a relationship between the data input and the clock input at the chip pins. data Tdata Tsu combinatorial logic (and delay) Tsu/Th D Q clk pins at IC boundary Tclk logic inside IC flip-flop inside IC ECE124 Digital Circuits and Systems Page 14

15 Setup and hold times at the pins of a chip (3) Let: cf - time when active clock edge arrives at FF CLK INPUT. cc - time when active clock edge arrives at CLK PIN. df - time when data input at FF D INPUT makes a transition. dc - time when data input at DATA PIN makes a transition. Let: Tsu - the setup time of the FF D input w.r.t. the FF CLK input. Th - the hold time of the FF D input w.r.t. the FF CLK input. Let: Tsetup - the setup time of the DATA PIN input w.r.t. the CLK PIN. Thold - the hold time of the DATA PIN input w.r.t. the CLK PIN. ECE124 Digital Circuits and Systems Page 15

16 Setup and hold times at the pins of a chip (4) The following must be true at the flip-flop: df not in [cf-tsu,cf+th] otherwise the flipflop might not work correctly (data must be stable around the active clock edge). Two inequalities: df not in [cf-tsu,cf+th] implies: df not in [cf-tsu,cf+th] implies: df < cf Tsu dc+tdata = df cc + Tclk = cf dc+tdata < cc+tclk-tsu but: and: so: and: df > cf + Th dc+tdata = df cc + Tclk = cf dc+tdata > cc+tclk+th but: and: so: and: dc < cc (Tsu-Tclk+Tdata). df can occur here Recall: cf - time when active clock edge arrives at FF CLK INPUT. cc - time when active clock edge arrives at CLK PIN. df - time when data input at FF D INPUT makes a transition. dc - time when data input at DATA PIN dc+tdata makes a transition. dc > cc + (Th+Tclk-Tdata). cc cf-tsu Tsu cf cc+tclk ECE124 Digital Circuits and Systems Page 16

17 Setup and hold times at the pins of a chip (5) We find a relationship between the data input and clock input at the IC PINS due to the relationship at the FF inputs inside the chip: dc < cc (Tsu-Tclk+Tdata). dc > cc + (Th+Tclk-Tdata). So, we have the relationship: dc not in [cc-tsetup,cc+thold] There are setup and hold times at the IC inputs. When we use an IC, we must pay attention to these times to make sure that the IC will work correctly. ECE124 Digital Circuits and Systems Page 17

18 Setup and hold times at the pins of a chip (6) data Tdata Tsu combinatorial logic (and delay) Tsu/Th D Q clk Tseup Thold Tsu Th pins at IC boundary Tclk logic inside IC flip-flop inside IC Tclk CLK FF CLK FF D DATA Tdata Tdata ECE124 Digital Circuits and Systems Page 18

19 Setup and hold times at the pins of a chip (7) When active clock edge arrives at a FF CLK input, the FF Q output changes after Tco. Consider that the FF Q output drives OUTPUT PIN of IC. Output will not appear for an amount of time called CLOCK-TO-OUTPUT TIME. Tdata clk D Tco Q combinatorial logic (and delay) data Tclk pins at IC boundary flip-flop inside IC logic inside IC Tclock_to_output = Tclk + Tco + Tdata ECE124 Digital Circuits and Systems Page 19

20 Setup and hold times at the pins of a chip (8) Tdata clk D Tco Q combinatorial logic (and delay) data Tclk Tco Tdata Tclk pins at IC boundary flip-flop inside IC logic inside IC CLK FF CLK FF D FF Q DATA ECE124 Digital Circuits and Systems Page 20

21 Implementing logic gates in CMOS Logic gates are implemented via transistors. One popular technology for implementing transistors is Complementary Metal Oxide Semiconductor (CMOS) technology. Transistors effectively implement switches. There are two types of Metal Oxide Semiconductor Field Effect Transistors (MOSFETs), namely the n-channel (NMOS) and p- channel (PMOS) transistor. CMOS uses both NMOS and CMOS transistors to implement logic gates in a complementary way. ECE124 Digital Circuits and Systems Page 21

22 Voltages and logic levels Logic levels are represented with voltages. The logic level 0 is represented by the lowest voltage (GND) The logic level 1 is represented by the highest voltage (VDD) Transistors are used as switches to open or close and connect wires to either VDD or GND. ECE124 Digital Circuits and Systems Page 22

23 NMOS transistor Simplified NMOS transistor has 3 terminals: 1) the Gate (G); 2) the Source (S) and 3) the Drain (D). The source is at a lower voltage; The drain is at a higher voltage. When a high voltage is applied to G (w.r.t. to S) and V GS is above some threshold voltage V T the switch closes and D is connected to S (current flows from D to S). This pulls down the voltage at D to the voltage at S. When the voltage between G and S is less than some threshold voltage V T the switch opens and D is disconnected from S (no current flows from D to S). ECE124 Digital Circuits and Systems Page 23

24 PMOS transistor Simplified PMOS transistor has 3 terminals: 1) the Gate (G); 2) the Source (S) and 3) the Drain (D). The source is at a higher voltage; The drain is at a lower voltage. When a low voltage is applied to G (w.r.t. to S) and V SG is above some threshold voltage V T the switch closes and S is connected to D (current flows from S to D). This pulls up the voltage at D to the voltage at S. When the voltage between S and G is less than some threshold voltage V T the switch opens and S is disconnected from D (no current flows from S to D). ECE124 Digital Circuits and Systems Page 24

25 CMOS structure CMOS combines NMOS and PMOS transistors in a structure which consists of a Pull-Up Network (PUN) and a Pull-Down Network (PDN) to implement logic functions. PUN and PDN are duals of each other. g A current path (connection) from V DD to V F means V F is high (f is logic 1) A current path (connection) from V F to GND means V F is low (f is logic 0).!f AND corresponds to transistors in series OR corresponds to transistors in parallel ECE124 Digital Circuits and Systems Page 25

26 CMOS inverter When V X is high (logic 1): 1) NMOS is closed; 2) PMOS is open;3) current flows from V F to GND V F is GND (logic 0). When V X is low (logic 0): 1) NMOS is open; 2) PMOS is closed;3) current flows from V DD to V F V F is V DD (logic 1). ECE124 Digital Circuits and Systems Page 26

27 CMOS NAND!x +!y 4 transistors!(xy) ECE124 Digital Circuits and Systems Page 27

28 CMOS NOR!x!y!(x+y) 4 transistors ECE124 Digital Circuits and Systems Page 28

29 CMOS AND Uses a CMOS NAND followed by a CMOS inverter 6 transistors ECE124 Digital Circuits and Systems Page 29

30 What s this? A B C V0o ut Vdd Vdd Vdd Vdd Vdd Gnd Gnd Gnd ECE124 Digital Circuits and Systems Page 30

31 Transmission gates When S is high (!S is low), both NMOS and PMOS are closed f = x. When S is low (!S is high), both NMOS and PMOS are open f is disconnected from x (high impedence). ECE124 Digital Circuits and Systems Page 31

32 XOR (using transmission gates) 8 transistors ECE124 Digital Circuits and Systems Page 32

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