1. Digital Design: Principles and Practices
Chapter 3
Digital Circuits

2. 3.1 Logic Signals and Gates

3. Digital Circuits We live in an analog world, not a digital one.
Values of voltage, current, temperature, time and speed are all continuous (analog).
Digital circuits:
are easier to design (than analog circuits)
provide higher noise immunity (than analog circuits)
Digital logic
Two possible numbers (or logic values): 0 and 1
A logic value (0 or 1) is often called a binary digit or bit.

4. Physical States Representing Bits in Different Technologies

5. Logic Signals
When discussing electronic logic circuits (such as CMOS and TTL), digital designers often use the words “LOW” and “HIGH” in place of “0” and “1”.
LOW: A signal in the range of algebraically lower voltages, which is interpreted as a logic 0.
HIGH: A signal in the range of algebraically higher voltages, which is interpreted as a logic 1.

6. Representation of a Logic Circuit

7. Logic Circuits
Combinational circuit: A logic circuit whose outputs depend only on its current inputs.
Truth table
Sequential circuit: A circuit with memory, whose outputs depend on the current input and the sequence of past inputs.
State table

8. Truth Table
Table 3-2 is the truth table for a logic circuit with three inputs X, Y and Z and a single output F.
This truth table lists all eight possible combinations of values of X, Y, and Z and the circuit’s output value F for each combination.

9. AND gate, OR gate, NOT gate

10. AND gate, OR gate, NOT gate
AND gate: produces a 1 output if and only if all of its inputs are 1.
OR gate: produces a 1 if and only if one or more of its inputs are 1.
NOT gate (inverter): produces an output value that is the opposite of its input value.
The symbols and truth tables for AND and OR may be extended to gates with any number of inputs.

11. NAND gate, NOR gate

12. NAND gate, NOR gate
NAND gate: produces the opposite of an AND gate’s output, a 0 if and only if all of its inputs are 1.
NOR gate: produces the opposite of an OR gate’s output, a 0 if and only if one or more of its inputs are 1.
The symbols and truth tables for NAND and NOR may be extended to gates with any number of inputs.

13. Logic Circuit

14. Timing Diagram

15. 3.2 Logic Families

16. Logic Families
A logic family is a collection of different integrated-circuit chips that have similar input, output, and internal circuit characteristics, but that perform different logic functions.
Chips from the same family can be interconnected to perform any desired logic function.
Chips from different families may not be compatible; they may use different power-supply voltages or may use different input and output conditions to represent logic values.

17. Logic Families Transistor-Transistor Logic (TTL)
Bipolar Junction Transistor (BJT)
Metal-Oxide Semiconductor Field-Effect Transistor (MOSFET)
Complementary MOS (CMOS)
NMOS and PMOS
CMOS circuits now account for the vast majority of the worldwide integrated-circuit market.

18. 3.3 CMOS Logic

19. CMOS Logic Levels

20. MOS Transistors
A MOS transistor can be modeled as a 3-terminal device that acts like a voltage-controlled resistance.
As suggested by Figure 3-7, an input voltage applied to one terminal controls the resistance between the remaining two terminals.
In digital logic application, a MOS transistor is operated so its resistance is always either very high (and the transistor is “off”) or very low (and the transistor is “on”).

21. MOS Transistors Two type of MOS Transistors: n-channel MOS (NMOS)
3 terminals: gate, source, and drain
The drain is normally at a higher voltage than the source.
Vgs is normally zero or positive
Vgs = 0  Rds is very high ( > 1MΩ)
Increase Vgs  Rds decreases
p-channel MOS (PMOS)
The source is normally at a higher voltage than the drain.
Vgs is normally zero or negative
Decrease Vgs  Rds decreases

22. NMOS Transistor

23. PMOS Transistor

24. nMOS & pMOS Symbols
nMOS Symbols
pMOS Symbols

25. nMOS Transistor
Layout
nMOS Symbols

26. MOS Transistors
The gate of a MOS transistor has very high impedance (resistance).
Almost no current flows from the gate to source, or from the gate to drain.
Leakage current
Gate capacitance
NMOS and PMOS transistors are used together in a complementary way to form CMOS logic.

27. Basic CMOS Inverter Circuit

28. Basic CMOS Inverter Circuit

29. Basic CMOS Inverter Circuit

30. CMOS NAND Gate

31. CMOS NAND Gate

32. CMOS NOR Gate

33. NAND vs. NOR -- Performance
CMOS NAND and NOR gates do not have identical electrical performance.
For a given silicon area, an n-channel transistor has lower “on” resistance than a p-channel transistor.
Therefore, when transistors are put in series, k n-channel transistors have lower “on” resistance than do k p-channel ones.
As a result, a k-input NAND gate is generally faster than and preferred over a k-input NOR gate.

34. 3-Input NAND Gate

35. Fan-In
The number of inputs that a gate can have in a particular logic family is called the logic family’s fan-in.
In principle, you could design a CMOS NAND or NOR gate with a very large number of inputs. In practice, however, the additive “on” resistance of series transistors limits the fan-in of CMOS gates, typically to 4 for NOR gates and 6 for NAND gates.
Gates with a large number of inputs can be made faster and smaller by cascading gates with fewer inputs. (See Figure 3- 17)

36. 8-Input NAND Gate

37. CMOS Non-inverting Buffer

38. AND Gate

39. AND-OR-INVERT (AOI) Gate

40. AND-OR-INVERT (AOI) Gate

41. OR-AND-INVERT (OAI) Gate

42. OR-AND-INVERT (OAI) Gate

43. AOI and OAI
The speed and other electrical characteristics of a CMOS AOI or OAI gate are quite comparable to those of a single CMOS NAND or NOR gate.
As a result, these gates (AOI and OAI) are very appealing because they can perform two levels of logic with just one level of delay.
CMOS VLSI devices often use these gates internally, since many HDL synthesis tools can automatically convert AND/OR logic into AOI gates when appropriate.

44. 3.4 Electrical Behavior of CMOS Circuits

45. Electrical Behavior of CMOS Circuits
Static behaviors
a circuit’s input and output signals are not changing
Dynamic behaviors
a circuit’s input and output signals are changing

46. Electrical Behavior of CMOS Circuits - Topics
Logic voltage levels
DC noise margins
Fanout
Speed
Power consumption
Noise
Electrostatic discharge
Open-drain outputs
Three-state outputs

48. Fig. 1-2. Pin diagrams for a few 7400-series SSI integrated circuits
7400-series Pin Diagrams
Fig Pin diagrams for a few 7400-series SSI integrated circuits

50. 74HC vs. 54HC The 74HC00 is the commercial part.
The 54HC00 is the military version.
HC: High-speed CMOS

51. 3.5 CMOS Static Electrical Behavior

52. CMOS Static Behavior
Static behavior = DC behavior = Steady-State behavior
Example: CMOS Inverter
Figure 3-10(b) only considers “0” and “1” (or “LOW” and “HIGH”)
Figure 3-25 depicts the inverter’s electrical behavior
LOW: VIN < 2.4V (OK?)
HIGH: VIN > 2.6V (OK?)
The transition in the middle of the curve may become more or less steep, and it may shift to the left or the right.
Specifications (or “specs”) for LOW and HIGH voltages are usually more conservative. (See Figure 3-26)

53. Basic CMOS Inverter Circuit

54. Input-Output Transfer Characteristic of a CMOS Inverter

55. Logic Levels & Noise Margins

56. Noise Margins
How much noise can a gate input see before it does not recognize the input?

57. Logic Levels & Noise Margins
VOHmin: The minimum output voltage produced in the HIGH state.
VIHmin: The minimum input voltage guaranteed to be recognized as a HIGH.
VILmax: The maximum input voltage guaranteed to be recognized as a LOW.
VOLmax: The maximum output voltage produced in the LOW state.

59. Logic Levels & Noise Margins Table 3-3
The input voltages are determined mainly by switching thresholds of the two transistors, while the output voltages are determined mainly by the “on” resistance of the transistors.
Two values for VOHmin and VOLmax
Depending on whether the output current (IOH or IOL) is large or small

60. Typical CMOS Levels VOHmin: VCC – 0.1 V VIHmin: 70% of VCC
VILmax: 30% of VCC
VOLmax: ground + 0.1V
In Table 3-3, VOHmin = 4.4 V
Worst case VCC = 5.0 – 10% = 4.5 V
4.5 V – 0.1 V = 4.4 V

61. DC Noise Margin Table 3-3 VOHmin : 4.4 V VIHmin : 3.15 V
VILmax : V
VOLmax : 0.1 V
The LOW-state DC noise margin = VIL – VOL = 1.25 V
The HIGH-state DC noise margin = VOH – VIH = 1.25 V

63. Current
IIH: The maximum current that flows into the input in the HIGH state.
IIL: The maximum current that flows into the input in the LOW state.
The input current shown in Table 3-3 for the ’HC00 is only ±1 μA. Thus, it takes very little power to maintain a CMOS input in one state or the other. This is in sharp contrast to older bipolar logic circuits like TTL and ECL, whose inputs may consume significant current (and power) in one or both states.

65. VDD, VCC, VSS VDD = VCC VSS Power (Logic ‘1’ or HIGH)
CMOS: the drain terminal of NMOS (inverter)
TTL: the collector terminal of BJT
VSS
Ground (Logic ‘0’ or LOW)
CMOS: the source terminal of NMOS

66. A CMOS Inverter with a Resistive Load

67. A CMOS Inverter with a Resistive Load (Input = HIGH)

68. A CMOS Inverter with a Resistive Load (Input = LOW)

69. IOLmax & IOHmax
IOLmax : The maximum current that the output can sink in the LOW state while still maintaining an output voltage no greater than VOLmax.
IOHmax : The maximum current that the output can source in the HIGH state while still maintaining an output voltage no less than VOHmin.

70. IOLmax & IOHmax

72. Output Loading Specs
Most CMOS devices have two sets of loading specifications:
CMOS loads : consume very little current
TTL loads : consume significant current
Table 3-4 summarizes Table 3-3 for output loading specs.

73. Output Loading Specs
By convention, the current flow measured at a device terminal is positive if positive current flows into the device; in the HIGH state, current flows out of the output terminal.
As Table 3-4 shows, with CMOS loads, the CMOS gate’s output voltage is maintained within 0.1 V of the power-supply rail.
As Table 3-4 shows, with TTL loads, the output voltage may degrade quite a bit.

74. Estimation of Rp(on) and Rn(on)
The actual “on” resistances of CMOS output transistors are usually not published. However, we can estimate those “on” resistances using the following equations:
The CMOS transistors in Table 3-4, Rp(on) = 165 Ω and Rn(on) = 82.5 Ω. Note that VDD = 4.5 V for this calculation.

75. Estimation of Sink & Source Current

76. Circuit Behavior with Non-ideal Inputs
So far, we have assumed that the HIGH and LOW inputs to a CMOS circuit are ideal voltages, very close to the power supply rails.
However, the behavior of a real CMOS inverter circuit depends on the input voltage as well as on the characteristics of the load.
If the input voltage is not close to the power-supply rail, then the “on” transistor may not be fully “on” and its resistance may increase.
Likewise, the “off” transistor may not be fully “off” and its resistance may be quite a bit less than one megohm.
These two effects combine to move the output voltage away from the power-supply rail.

77. CMOS Inverter with Non-ideal Input Voltages
Iwasted = 1.72 mA
Pwasted = 8.62 mW

78. CMOS Inverter with Load and Non-ideal Input Voltage

79. CMOS Inverter with Load and Non-ideal Input Voltage

80. Fanout
The fanout of a logic gate is the number of inputs that the gate can drive without exceeding its worst-case loading specifications.
The fanout depends not only on the characteristics of the output, but also on the inputs that it is driving.
Fanout must be examined for both possible output states, HIGH and LOW.

81. Fanout In Table 3-4, LOW-state fanout = 20 HIGH-state fanout = 20
IOLmaxC = 20 μA (for an HC-series CMOS gate driving CMOS inputs)
IImax = ±1 μA
HIGH-state fanout = 20
IOHmaxC = –20 μA (for an HC-series CMOS gate driving CMOS inputs)
Note that the HIGH-state and LOW-state fanouts of a gate are not necessarily equal.
In general, the overall fanout of a gate is the minimum of its HIGH- state and LOW-state fanout (20 in the foregoing example).

82. Effects of Loading
Loading an output beyond its rated fanout has several effects:
In the LOW state, the output voltage may increase beyond VOLmax.
In the HIGH state, the output voltage may fall below VOHmin.
Propagation delay to the output may increase beyond specifications.
Output rise and fall times may increase beyond their specifications.
The operating temperature of the device may increase, thereby reducing the reliability of the device and eventually causing device failure.

83. Unused Inputs
Sometimes not all of the inputs of a logic gate are used.
Unused CMOS inputs should never be left unconnected (or floating).
In high-speed circuit design, (b) or (c) are preferred over (a).
It is possible to tie unused inputs directly to power rails.

84. How to Destroy a CMOS Device
You can destroy a CMOS device by simply walking across a carpet and then touch an input pin with your finger. (1000+ V)
CMOS devices are subject to damage from electrostatic discharge (ESD).
In the case of a CMOS input, the dielectric is the insulation between an input transistor’s gate and its source and drain. ESD may damage this insulation, causing a short circuit between the device’s input and its output.

85. nMOS & pMOS Symbols
nMOS Symbols
pMOS Symbols

86. nMOS Transistor
Layout
nMOS Symbols

87. 3.6 CMOS Dynamic Electrical Behavior