Propagation Delay for Low to High Output Transition CMOS Calculator

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✖Load Capacitance of Inverter CMOS is defined as combined capacitances into an equivalent lumped linear capacitance.ⓘ Load Capacitance [C_load]			+10% -10%
✖Transconductance of PMOS in CMOS is defined as the multiplication of mobility of electrons, width to length ratio of PMOS and oxide capacitance.ⓘ Transconductance of PMOS [K_p]			+10% -10%
✖Supply Voltage of CMOS is defined as the supply voltage given to the source terminal of the PMOS.ⓘ 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 is defined as the time required for the output voltage to rise from VOL to the V50% level.ⓘ Propagation Delay for Low to High Output Transition CMOS [ζ_PLH]

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Propagation Delay for Low to High Output Transition CMOS

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))`

Example

`"0.006183ns"=("0.85fF"/("80µA/V²"*("3.3V"-abs("-0.9V"))))*(((2*abs("-0.9V"))/("3.3V"-abs("-0.9V")))+ln((4*("3.3V"-abs("-0.9V"))/"3.3V")-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 = (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 is defined as the time required for the output voltage to rise from VOL to the V50% level.
Load Capacitance - (Measured in Farad) - Load Capacitance of Inverter CMOS is defined as combined capacitances into an equivalent lumped linear capacitance.
Transconductance of PMOS - (Measured in Ampere per Square Volt) - Transconductance of PMOS in CMOS is defined as the multiplication of mobility of electrons, width to length ratio of PMOS and oxide capacitance.
Supply Voltage - (Measured in Volt) - Supply Voltage of CMOS is defined as the supply voltage given to the source terminal of the PMOS.
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

Load Capacitance: 0.85 Femtofarad --> 8.5E-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)) --> (8.5E-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 = 6.18298484472028E-12

STEP 3: Convert Result to Output's Unit

6.18298484472028E-12 Second -->0.00618298484472028 Nanosecond (Check conversion here)

FINAL ANSWER

0.00618298484472028 ≈ 0.006183 Nanosecond <-- Time for Low to High Transition of Output

(Calculation completed in 00.020 seconds)

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< 17 CMOS Inverters Calculators

Propagation Delay for Low to High Output Transition CMOS

Go Time for Low to High Transition of Output = (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))

Propagation Delay for High to Low Output Transition CMOS

Go Time for High to Low Transition of Output = (Load Capacitance/(Transconductance of NMOS*(Supply Voltage-Threshold Voltage of NMOS with Body Bias)))*((2*Threshold Voltage of NMOS with Body Bias/(Supply Voltage-Threshold Voltage of NMOS with Body Bias))+ln((4*(Supply Voltage-Threshold Voltage of NMOS with Body Bias)/Supply Voltage)-1))

Resistive Load Minimum Output Voltage CMOS

Go Resistive Load Minimum Output Voltage = Supply Voltage-Zero Bias Threshold Voltage+(1/(Transconductance of NMOS*Load Resistance))-sqrt((Supply Voltage-Zero Bias Threshold Voltage+(1/(Transconductance of NMOS*Load Resistance)))^2-(2*Supply Voltage/(Transconductance of NMOS*Load Resistance)))

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)

Resistive Load Minimum Input Voltage CMOS

Go Resistive Load Minimum Input Voltage = Zero Bias Threshold Voltage+sqrt((8*Supply Voltage)/(3*Transconductance of NMOS*Load Resistance))-(1/(Transconductance of NMOS*Load Resistance))

Minimum Input Voltage CMOS

Go Minimum Input Voltage = (Supply Voltage+(Threshold Voltage of PMOS Without Body Bias)+Transconductance Ratio*(2*Output Voltage+Threshold Voltage of NMOS Without Body Bias))/(1+Transconductance Ratio)

Load Capacitance of Cascaded Inverter CMOS

Go Load Capacitance = Gate Drain Capacitance of PMOS+Gate Drain Capacitance of NMOS+Drain Bulk Capacitance of PMOS+Drain Bulk Capacitance of NMOS+Internal Capacitance+Gate Capacitance

Energy Delivered by Power Supply

Go Energy Delivered by Power Supply = int(Supply Voltage*Instantaneous Drain Current*x,x,0,Charging Interval of Capacitor)

Resistive Load Maximum Input Voltage CMOS

Go Resistive Load Maximum Input Voltage CMOS = Zero Bias Threshold Voltage+(1/(Transconductance of NMOS*Load Resistance))

Average Propagation Delay CMOS

Go Average Propagation Delay = (Time for High to Low Transition of Output+Time for Low to High Transition of Output)/2

Average Power Dissipation CMOS

Go Average Power Dissipation = Load Capacitance*(Supply Voltage)^2*Frequency

Maximum Input Voltage for Symmetric CMOS

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

Minimum Input Voltage for Symmetric CMOS

Go Minimum Input Voltage = (5*Supply Voltage-2*Threshold Voltage of NMOS Without Body Bias)/8

Oscillation Period Ring Oscillator CMOS

Go Oscillation Period = 2*Number of Stages Ring Oscillator*Average Propagation Delay

Noise Margin for High Signal CMOS

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

Transconductance Ratio CMOS

Go Transconductance Ratio = Transconductance of NMOS/Transconductance of PMOS

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 = (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, The Propagation Delay for Low to High Output Transition CMOS formula is defined as the time required for the output voltage to rise from V_OL to the V_50% level. 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 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 = (8.5E-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?

The Propagation Delay for Low to High Output Transition CMOS formula is defined as the time required for the output voltage to rise from V_OL to the V_50% level 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 = (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)). Load Capacitance of Inverter CMOS is defined as combined capacitances into an equivalent lumped linear capacitance, Transconductance of PMOS in CMOS is defined as the multiplication of mobility of electrons, width to length ratio of PMOS and oxide capacitance, Supply Voltage of CMOS is defined as the supply voltage given to the source terminal of the PMOS & 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?

The Propagation Delay for Low to High Output Transition CMOS formula is defined as the time required for the output voltage to rise from V_OL to the V_50% level is calculated using Time for Low to High Transition of Output = (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 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 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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