A.2.1 MOS Transistor Switches and Boolean Values

The basic elements of digital circuits are switches, i.e., devices which can either conduct a current or not depending on some controlling voltage or current. Voltage levels (HIGH and LOW level voltage, usually equal to the supply voltage and 0V respectively) and conductivities (corresponding to the ON and OFF state of switches) are used to represent the boolean values 1 and .

In CMOS digital circuits switches are realized as MOSFETs, which conduct a current from drain to source controlled by the gate-source voltage. The conductivities of the switches in a circuit, in turn, determine the circuit's internal and output voltages. Fig. A.4 shows the two types of transistors used as switches, the n-channel and the p-channel MOSFET. A HIGH level voltage applied to the gate of an NMOS transistor turns it on, i.e., the inversion channel connects source and drain - the switch is closed. A LOW level voltage, on the other hand, turns the transistor off - the switch is open. For the PMOS transistor the conditions are reversed owing to its reverse polarity: the transistor is turned on by a LOW voltage and turned off by a HIGH voltage (mind the polarities in Fig. A.4).

Figure A.4: MOSFETs used as switches

[NMOS switch]

[PMOS switch]

Current conductivity is determined by the drain current flowing through the transistor with a drain-source voltage of $\ensuremath{V_{\mathit{DS}}}\xspace = \ensuremath{V_{\mathit{DD}}}\xspace$, where is the supply voltage of the circuit. When the gate-source voltage is $\ensuremath{V_{\mathit{GS}}}\xspace = \ensuremath{V_{\mathit{DD}}}\xspace$ the device conducts the on-state current , and with $\ensuremath{V_{\mathit{GS}}}\xspace = \rm0V$ the current is the off-state current . The transition between on and off state is characterized by some threshold voltage : $\ensuremath{V_{\mathit{GS}}}\xspace = \ensuremath{V_{\mathit{T}}}\xspace$. Ideally, should be zero. In this case CMOS circuits like the inverter shown in Fig. A.5 would function independently of the transistors' channel widths. Therefore, such CMOS circuits are also called ratioless, which is a big advantage as it allows designs with all-minimum-size transistors. In reality, however, the transition between on and off state is smooth and the off-state current is limited by $\ensuremath{I_{\mathit{off}}}\xspace > \ensuremath{I_{\mathit{on}}}\xspace e^{-\ensuremath{V_{\mathit{DD}}}\xspace /\ensuremath{U_{\mathit{T}}}\xspace }$ (cf. Section A.1). This has to be kept in mind when considering low-voltage circuits or dynamic logic (see Section A.2.3.2).