Propagation Delay for Low to High Output Transition CMOS Calculator

✖Inverter CMOS Load Capacitance is the capacitance driven by a CMOS inverter's output, including wiring, input capacitances of connected gates, and parasitic capacitances.ⓘ Inverter CMOS Load Capacitance [C_load]			+10% -10%
✖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.ⓘ Transconductance of PMOS [K_p]			+10% -10%
✖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.ⓘ Supply Voltage [V_DD]			+10% -10%
✖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.ⓘ Threshold Voltage of PMOS with Body Bias [V_T,p]			+10% -10%

✖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.ⓘ Propagation Delay for Low to High Output Transition CMOS [ζ_PLH]

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Formula

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Propagation Delay for Low to High Output Transition CMOS

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))

Example

0.006765 ns = (\frac{0.93 fF}{80 µA/V² \cdot (3.3 V - | -0.9 V |)}) \cdot ((\frac{2 \cdot | -0.9 V |}{3.3 V - | -0.9 V |}) + \ln ((4 \cdot \frac{3.3 V - | -0.9 V |}{3.3 V}) - 1))

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Propagation Delay for Low to High Output Transition CMOS Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
ζ_PLH = (C_load/(K_p*(V_DD-abs(V_T,p))))*(((2*abs(V_T,p))/(V_DD-abs(V_T,p)))+ln((4*(V_DD-abs(V_T,p))/V_DD)-1))
This formula uses 2 Functions, 5 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., 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., abs(Number)

Variables Used

Time for Low to High Transition of Output - (Measured in Second) - 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.
Inverter CMOS Load Capacitance - (Measured in Farad) - Inverter CMOS Load Capacitance is the capacitance driven by a CMOS inverter's output, including wiring, input capacitances of connected gates, and parasitic capacitances.
Transconductance of PMOS - (Measured in Ampere per Square Volt) - 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.
Supply Voltage - (Measured in Volt) - 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.
Threshold Voltage of PMOS with Body Bias - (Measured in Volt) - 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.

STEP 1: Convert Input(s) to Base Unit

Inverter CMOS Load Capacitance: 0.93 Femtofarad --> 9.3E-16 Farad (Check conversion here)
Transconductance of PMOS: 80 Microampere per Square Volt --> 8E-05 Ampere per Square Volt (Check conversion here)
Supply Voltage: 3.3 Volt --> 3.3 Volt No Conversion Required
Threshold Voltage of PMOS with Body Bias: -0.9 Volt --> -0.9 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ_PLH = (C_load/(K_p*(V_DD-abs(V_T,p))))*(((2*abs(V_T,p))/(V_DD-abs(V_T,p)))+ln((4*(V_DD-abs(V_T,p))/V_DD)-1)) --> (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))

Evaluating ... ...

ζ_PLH = 6.76491283010572E-12

STEP 3: Convert Result to Output's Unit

6.76491283010572E-12 Second -->0.00676491283010572 Nanosecond (Check conversion here)

FINAL ANSWER

0.00676491283010572 ≈ 0.006765 Nanosecond <-- Time for Low to High Transition of Output

(Calculation completed in 00.004 seconds)

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< CMOS Inverters Calculators

Threshold Voltage CMOS

Go Threshold Voltage = (Threshold Voltage of NMOS Without Body Bias+sqrt(1/Transconductance Ratio)*(Supply Voltage+(Threshold Voltage of PMOS Without Body Bias)))/(1+sqrt(1/Transconductance Ratio))

Maximum Input Voltage CMOS

Go Maximum Input Voltage CMOS = (2*Output Voltage for Max Input+(Threshold Voltage of PMOS Without Body Bias)-Supply Voltage+Transconductance Ratio*Threshold Voltage of NMOS Without Body Bias)/(1+Transconductance Ratio)

Maximum Input Voltage for Symmetric CMOS

Go Maximum Input Voltage Symmetric CMOS = (3*Supply Voltage+2*Threshold Voltage of NMOS Without Body Bias)/8

Noise Margin for High Signal CMOS

Go Noise Margin for High Signal = Maximum Output Voltage-Minimum Input Voltage

Propagation Delay for Low to High Output Transition CMOS Formula

What are the conditions for balanced propagation delay?

For T_PHL =T_PLH in a CMOS inverter are:-
V_T,n = |V_T,p| (Threshold voltage of NMOS & PMOS should be equal),
K_n = K_p (Transconductance of NMOS & PMOS should be equal).

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

Propagation Delay for Low to High Output Transition CMOS calculator 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 calculate 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 calculate Propagation Delay for Low to High Output Transition CMOS using this online calculator? To use this online calculator 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. Here is how the Propagation Delay for Low to High Output Transition CMOS calculation can be explained with given input values -> 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)).

FAQ

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

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 and is represented as ζ_PLH = (C_load/(K_p*(V_DD-abs(V_T,p))))*(((2*abs(V_T,p))/(V_DD-abs(V_T,p)))+ln((4*(V_DD-abs(V_T,p))/V_DD)-1)) or 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)). Inverter CMOS Load Capacitance is the capacitance driven by a CMOS inverter's output, including wiring, input capacitances of connected gates, and parasitic capacitances, 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, 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 & 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.

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

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 is calculated using 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 calculate Propagation Delay for Low to High Output Transition CMOS, you need 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). With our tool, you need to enter the respective value for Inverter CMOS Load Capacitance, Transconductance of PMOS, Supply Voltage & Threshold Voltage of PMOS with Body Bias and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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