### Inverter and Noise in Digital Circuits

Inverter – Voltage Transfer Characteristic
Voltage Transfer Characteristic (VTC) for logic inverters have been standardized.
VTC is the graph between Vout and VIN. On vertical axis, VOH and VOL correspond to output high and
output low voltage levels respectively. On the horizontal axis, VIL is input low voltage and VIH is the input high voltage.

Inverter – Voltage Transfer Characteristic
As the input voltage is increased from 0V, VIL is the maximum input voltage that provides a high output voltage (logical 1 output).
VIH is the minimum input voltage that provides a low output voltage (logical 0 output). VOH, VOL, VIL and VIH are referred to as the critical voltages of the VTC.
VOH > VIH
VOL < VIL

Midpoint Voltage:
Sometimes referred as Threshold voltage  (Vth).
The voltage at which Vout = VIN on VTC is referred as Midpoint voltage. Midpoint voltage can be found graphically by superimposing (the unity slope) Vout = VIN and finding its intersection with the VTC

Logic Swing and Transition Width
Logic Swing
The magnitude of voltage difference between the output high and low voltage levels.
VLS = VOH – VOL

Transition Width
The amount of voltage change that is required of the input voltage to cause a change in the output voltage from the high to the low level (and vice versa).
VTW = VIH - VIL

Noise in Digital Circuits
Noise
Variations in the steady-state voltage levels of digital circuits (i.e. Logical 1 and logical 0 states) are undesirable and cause logic errors. This variation is termed as Noise.

Noise Margins
Voltage Noise Margin represents the safety margin for the high and low voltage levels. Noise voltages must have magnitudes less than the voltage noise margins.
VNMH = VOH – VIH
VNML = VIL - VOL

Noise Sensitivities
The effects of input variations are quantified in terms of the noise sensitivities.
The high noise sensitivity is defined as the difference between input and midpoint voltage for VIN  at VOH.
The low noise sensitivity is defined as the difference between input and midpoint voltage for VIN at VOL.
VNSH = VOH – VM
VNSL = VM - VOL

Noise Immunities
The ability of a gate to reject noise. The high and low noise immunities are defined as the quotient of the noise sensitivities and the logic swing.
VNIH = VNSH / VLS
VNIL = VNSL / VLS

FAN-IN and FAN-OUT
A general logic gate has multiple inputs and multiple outputs.
By multiple outputs we mean the output of a given gate is connected to (driving) the inputs of several load gates.
FAN-IN: the number of inputs of a gate.
FAN-OUT: the number of outputs of a gate.
Maximum FAN-OUT depends on the input and output current of a driving gate.
The maximum fan-out possible during the driving gate’s logical 1 output state is
Nhigh = IOUT (high)/ I’IN (high)
The maximum fan-out possible during the driving gate’s logical 0 output state is
Nlow = IOUT (low)/ I’IN (low)