ECE124 Digital Circuits and Systems Page 1

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-to-output time).

 When we build an entire circuit (one with both flip-flops and combinational logic), there are other important timing concepts to understand.

Cycle times (1)

 Consider flip-flop outputs being used to generate flip-flop inputs:

D Q combinatorial D Q

logic (and delay) clk

Tco Tdata Tsu

Tclk1

Tclk2

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.

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:

Cycle times (4)

D Q combinatorial D Q

logic (and delay) clk

Tco Tdata Tsu

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.

Cycle times (5)

Clock skew

 If we look at our equation for maximum frequency:

 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. Circuit frequency <= 1/Tcycle

Inverted clocks (1)

 Sometimes we might have flops clocked on different edges of the clock; some flip-flops 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!

D Q combinatorial D Q

logic (and delay) clk

Tco Tdata Tsu

Tclk1

Tclk2

Falling edge Rising edge

Inverted clocks (2)

 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.

CLK FF1 CLK FF2 CLK FF1 Q FF2 D Tclk1 Tco Tdata Tclk1 Tcycle Tsu

CLK FF1 CLK FF2 CLK FF1 Q FF2 D Tclk1 Tco Tdata Tclk1 Tcycle Tsu

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.

CLK

2/3 high (66% duty cycle) 1/3 low

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 flip-flop 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.

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.

D Q combinatorial

logic (and delay)

Tsu/Th Tdata Tclk clk data pins at IC

boundary logicinside IC flip-flopinside IC Tsu

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.

Setup and hold times at the pins of a chip (4)

 The following must be true at the flop: df not in [cf-Tsu,cf+th] otherwise the flip-flop might not work correctly (data must be stable around the active clock edge).

 Two inequalities:

 df not in [cf-Tsu,cf+Th] implies:

 df < cf – Tsu but:

 dc+Tdata = df and:

 cc + Tclk = cf so:

 dc+Tdata < cc+Tclk-Tsu and:

 dc < cc – (Tsu-Tclk+Tdata).

 df not in [cf-Tsu,cf+Th] implies:

 df > cf + Th but:  dc+Tdata = df and:  cc + Tclk = cf so:  dc+Tdata > cc+Tclk+Th and:  dc > cc + (Th+Tclk-Tdata). 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 makes a transition.

cc cf

df can occur here

dc+Tdata

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.

Setup and hold times at the pins of a chip (6)

Tsu/Th Tdata Tclk clk data pins at IC

boundary logicinside IC flip-flopinside IC Tsu

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.

D Q combinatorial

logic (and delay) Tco

Tdata

Tclk clk

pins at IC

boundary flip-flopinside IC logicinside IC

data

Setup and hold times at the pins of a chip (8)

D Q combinatorial

logic (and delay) Tco

Tdata

Tclk clk

pins at IC

boundary flip-flopinside IC logicinside IC

data CLK FF CLK FF D FF Q Tclk Tco Tdata DATA

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.

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.

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).

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

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.

 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).

 “AND” corresponds to transistors in series…

 “OR” corresponds to transistors in parallel…

!f g

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).

CMOS NAND

!(xy) !x + !y

CMOS NOR

!(x+y) !x!y

CMOS AND

 Uses a CMOS NAND followed by a CMOS inverter

What’s this?

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).

XOR (using transmission gates)