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Propagation Delay for Low to High Output Transition CMOS Formula

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Time for low to high transition of output refers to the duration taken by a signal at the output terminal of a device or circuit to transition from a low voltage level to a high voltage level. Check FAQs

ζ PLH = (\frac{C load}{K p \cdot (V DD - | V T,p |)}) \cdot ((\frac{2 \cdot | V T,p |}{V DD - | V T,p |}) + \ln ((4 \cdot \frac{V DD - | V T,p |}{V DD}) - 1))

ζ_PLH - Time for Low to High Transition of Output?C_load - Inverter CMOS Load Capacitance?K_p - Transconductance of PMOS?V_DD - Supply Voltage?V_T,p - Threshold Voltage of PMOS with Body Bias?

Propagation Delay for Low to High Output Transition CMOS Example

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Here is how the Propagation Delay for Low to High Output Transition CMOS equation looks like with Values.

Here is how the Propagation Delay for Low to High Output Transition CMOS equation looks like with Units.

Here is how the Propagation Delay for Low to High Output Transition CMOS equation looks like.

0.0068 = (\frac{0.93}{80 \cdot (3.3 - | -0.9 |)}) \cdot ((\frac{2 \cdot | -0.9 |}{3.3 - | -0.9 |}) + \ln ((4 \cdot \frac{3.3 - | -0.9 |}{3.3}) - 1))

0.0068ns = (\frac{0.93fF}{80µA/V² \cdot (3.3V - | -0.9V |)}) \cdot ((\frac{2 \cdot | -0.9V |}{3.3V - | -0.9V |}) + \ln ((4 \cdot \frac{3.3V - | -0.9V |}{3.3V}) - 1))

0.0068 = (\frac{0.93}{80 \cdot (3.3 - | -0.9 |)}) \cdot ((\frac{2 \cdot | -0.9 |}{3.3 - | -0.9 |}) + \ln ((4 \cdot \frac{3.3 - | -0.9 |}{3.3}) - 1))

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Propagation Delay for Low to High Output Transition CMOS Solution

Follow our step by step solution on how to calculate Propagation Delay for Low to High Output Transition CMOS?

FIRST Step Consider the formula

ζ PLH = (\frac{C load}{K p \cdot (V DD - | V T,p |)}) \cdot ((\frac{2 \cdot | V T,p |}{V DD - | V T,p |}) + \ln ((4 \cdot \frac{V DD - | V T,p |}{V DD}) - 1))

Next Step Substitute values of Variables

∴

ζ PLH = (\frac{0.93fF}{80µA/V² \cdot (3.3V - | -0.9V |)}) \cdot ((\frac{2 \cdot | -0.9V |}{3.3V - | -0.9V |}) + \ln ((4 \cdot \frac{3.3V - | -0.9V |}{3.3V}) - 1))

Next Step Convert Units

∴

ζ PLH = (\frac{9.3E-16F}{8E-5A/V² \cdot (3.3V - | -0.9V |)}) \cdot ((\frac{2 \cdot | -0.9V |}{3.3V - | -0.9V |}) + \ln ((4 \cdot \frac{3.3V - | -0.9V |}{3.3V}) - 1))

Next Step Prepare to Evaluate

∴

ζ PLH = (\frac{9.3E-16}{8E-5 \cdot (3.3 - | -0.9 |)}) \cdot ((\frac{2 \cdot | -0.9 |}{3.3 - | -0.9 |}) + \ln ((4 \cdot \frac{3.3 - | -0.9 |}{3.3}) - 1))

Next Step Evaluate

∴

ζ PLH = 6.76491283010572E-12s

Next Step Convert to Output's Unit

∴

ζ PLH = 0.00676491283010572ns

LAST Step Rounding Answer

∴

ζ PLH = 0.0068ns

Propagation Delay for Low to High Output Transition CMOS Formula Elements

Variables

Functions

Time for Low to High Transition of Output

Time for low to high transition of output refers to the duration taken by a signal at the output terminal of a device or circuit to transition from a low voltage level to a high voltage level.

Symbol: ζ_PLH

Measurement: TimeUnit: ns

Note: Value should be greater than 0.

Formulas to find Time for Low to High Transition of Output

Inverter CMOS Load Capacitance

Inverter CMOS Load Capacitance is the capacitance driven by a CMOS inverter's output, including wiring, input capacitances of connected gates, and parasitic capacitances.

Symbol: C_load

Measurement: CapacitanceUnit: fF

Note: Value should be greater than 0.

Formulas to find Inverter CMOS Load Capacitance

Transconductance of PMOS

Transconductance of PMOS refers to the ratio of the change in the output drain current to the change in the input gate-source voltage when the drain-source voltage is constant.

Symbol: K_p

Measurement: Transconductance ParameterUnit: µA/V²

Note: Value should be greater than 0.

Formulas to find Transconductance of PMOS

Supply Voltage

Supply voltage refers to the voltage level provided by a power source to an electrical circuit or device, serving as the potential difference for current flow and operation.

Symbol: V_DD

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Supply Voltage

Threshold Voltage of PMOS with Body Bias

Threshold Voltage of PMOS with Body Bias is defined as the value of minimum required gate voltage for PMOS when substrate is not at ground potential.

Symbol: V_T,p

Measurement: Electric PotentialUnit: V

Note: Value should be between -5 to 5.

Formulas to find Threshold Voltage of PMOS with Body Bias

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

abs

The absolute value of a number is its distance from zero on the number line. It's always a positive value, as it represents the magnitude of a number without considering its direction.

Syntax: abs(Number)

Other formulas in CMOS Inverters category

Go Noise Margin for High Signal CMOS

N MH = V OH - V IH

Go Maximum Input Voltage for Symmetric CMOS

V IL(sym) = \frac{3 \cdot V DD + 2 \cdot V T0,n}{8}

Go Threshold Voltage CMOS

V th = \frac{V T0,n + \sqrt{\frac{1}{K r}} \cdot (V DD + (V T0,p))}{1 + \sqrt{\frac{1}{K r}}}

Go Maximum Input Voltage CMOS

V IL = \frac{2 \cdot V output + (V T0,p) - V DD + K r \cdot V T0,n}{1 + K r}

How to Evaluate Propagation Delay for Low to High Output Transition CMOS?

Propagation Delay for Low to High Output Transition CMOS evaluator uses Time for Low to High Transition of Output = (Inverter CMOS Load Capacitance/(Transconductance of PMOS*(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias))))*(((2*abs(Threshold Voltage of PMOS with Body Bias))/(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias)))+ln((4*(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias))/Supply Voltage)-1)) to evaluate the Time for Low to High Transition of Output, Propagation Delay for Low to High Output Transition CMOS refers to the time taken for a signal at the output terminal of a CMOS device to transition from a low voltage level to a high voltage level. This delay includes various factors such as gate delays and interconnect delays within the CMOS circuit. Time for Low to High Transition of Output is denoted by ζ_PLH symbol.

How to evaluate Propagation Delay for Low to High Output Transition CMOS using this online evaluator? To use this online evaluator for Propagation Delay for Low to High Output Transition CMOS, enter Inverter CMOS Load Capacitance (C_load), Transconductance of PMOS (K_p), Supply Voltage (V_DD) & Threshold Voltage of PMOS with Body Bias (V_T,p) and hit the calculate button.

FAQs on Propagation Delay for Low to High Output Transition CMOS

What is the formula to find Propagation Delay for Low to High Output Transition CMOS?

The formula of Propagation Delay for Low to High Output Transition CMOS is expressed as Time for Low to High Transition of Output = (Inverter CMOS Load Capacitance/(Transconductance of PMOS*(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias))))*(((2*abs(Threshold Voltage of PMOS with Body Bias))/(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias)))+ln((4*(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias))/Supply Voltage)-1)). Here is an example- 6.2E+6 = (9.3E-16/(8E-05*(3.3-abs((-0.9)))))*(((2*abs((-0.9)))/(3.3-abs((-0.9))))+ln((4*(3.3-abs((-0.9)))/3.3)-1)).

How to calculate Propagation Delay for Low to High Output Transition CMOS?

With Inverter CMOS Load Capacitance (C_load), Transconductance of PMOS (K_p), Supply Voltage (V_DD) & Threshold Voltage of PMOS with Body Bias (V_T,p) we can find Propagation Delay for Low to High Output Transition CMOS using the formula - Time for Low to High Transition of Output = (Inverter CMOS Load Capacitance/(Transconductance of PMOS*(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias))))*(((2*abs(Threshold Voltage of PMOS with Body Bias))/(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias)))+ln((4*(Supply Voltage-abs(Threshold Voltage of PMOS with Body Bias))/Supply Voltage)-1)). This formula also uses Natural Logarithm Function, Absolute function(s).

Can the Propagation Delay for Low to High Output Transition CMOS be negative?

No, the Propagation Delay for Low to High Output Transition CMOS, measured in Time cannot be negative.

Which unit is used to measure Propagation Delay for Low to High Output Transition CMOS?

Propagation Delay for Low to High Output Transition CMOS is usually measured using the Nanosecond[ns] for Time. Second[ns], Millisecond[ns], Microsecond[ns] are the few other units in which Propagation Delay for Low to High Output Transition CMOS can be measured.

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Propagation Delay for Low to High Output Transition CMOS Formula

Propagation Delay for Low to High Output Transition CMOS Example

Propagation Delay for Low to High Output Transition CMOS Solution

Propagation Delay for Low to High Output Transition CMOS Formula Elements

Other formulas in CMOS Inverters category

How to Evaluate Propagation Delay for Low to High Output Transition CMOS?

FAQs on Propagation Delay for Low to High Output Transition CMOS

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