## Propagation Delay for High to Low Output Transition CMOS Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time for High to Low Transition of Output = (Inverter CMOS 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))
This formula uses 1 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)
Variables Used
Time for High to Low Transition of Output - (Measured in Second) - Time for high to low transition of output refers to the duration taken by a signal at the output terminal of a device or circuit to transition from a high voltage level to a low 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 NMOS - (Measured in Ampere per Square Volt) - Transconductance of NMOS 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 NMOS with Body Bias - (Measured in Volt) - Threshold voltage of NMOS with body bias refers to the minimum input voltage required to switch an NMOS transistor when an additional bias voltage is applied to the substrate (body).
STEP 1: Convert Input(s) to Base Unit
Transconductance of NMOS: 200 Microampere per Square Volt --> 0.0002 Ampere per Square Volt (Check conversion ​here)
Supply Voltage: 3.3 Volt --> 3.3 Volt No Conversion Required
Threshold Voltage of NMOS with Body Bias: 0.8 Volt --> 0.8 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Evaluating ... ...
ζPHL = 2.50762420773954E-12
STEP 3: Convert Result to Output's Unit
2.50762420773954E-12 Second -->0.00250762420773954 Nanosecond (Check conversion ​here)
0.00250762420773954 0.002508 Nanosecond <-- Time for High to Low Transition of Output
(Calculation completed in 00.004 seconds)
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Created by Priyanka Patel
Lalbhai Dalpatbhai College of engineering (LDCE), Ahmedabad
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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 High to Low Output Transition CMOS Formula

Time for High to Low Transition of Output = (Inverter CMOS 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))

## Which assumption is used for this formula?

The input voltage waveform is usually assumed to be an ideal step pulse with zero rise and fall times.

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

Propagation Delay for High to Low Output Transition CMOS calculator uses Time for High to Low Transition of Output = (Inverter CMOS 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)) to calculate the Time for High to Low Transition of Output, Propagation Delay for High to Low Output Transition CMOS refers to the time taken for a signal at the output terminal of a CMOS device to transition from a high voltage level to a low voltage level. It includes delays caused by logic gates, interconnects, and parasitic capacitances. Time for High to Low Transition of Output is denoted by ζPHL symbol.

How to calculate Propagation Delay for High to Low Output Transition CMOS using this online calculator? To use this online calculator for Propagation Delay for High to Low Output Transition CMOS, enter Inverter CMOS Load Capacitance (Cload), Transconductance of NMOS (Kn), Supply Voltage (VDD) & Threshold Voltage of NMOS with Body Bias (VT,n) and hit the calculate button. Here is how the Propagation Delay for High to Low Output Transition CMOS calculation can be explained with given input values -> 2.3E+6 = (9.3E-16/(0.0002*(3.3-0.8)))*((2*0.8/(3.3-0.8))+ln((4*(3.3-0.8)/3.3)-1)).

### FAQ

What is Propagation Delay for High to Low Output Transition CMOS?
Propagation Delay for High to Low Output Transition CMOS refers to the time taken for a signal at the output terminal of a CMOS device to transition from a high voltage level to a low voltage level. It includes delays caused by logic gates, interconnects, and parasitic capacitances and is represented as ζPHL = (Cload/(Kn*(VDD-VT,n)))*((2*VT,n/(VDD-VT,n))+ln((4*(VDD-VT,n)/VDD)-1)) or Time for High to Low Transition of Output = (Inverter CMOS 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)). 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 NMOS 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 NMOS with body bias refers to the minimum input voltage required to switch an NMOS transistor when an additional bias voltage is applied to the substrate (body).
How to calculate Propagation Delay for High to Low Output Transition CMOS?
Propagation Delay for High to Low Output Transition CMOS refers to the time taken for a signal at the output terminal of a CMOS device to transition from a high voltage level to a low voltage level. It includes delays caused by logic gates, interconnects, and parasitic capacitances is calculated using Time for High to Low Transition of Output = (Inverter CMOS 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)). To calculate Propagation Delay for High to Low Output Transition CMOS, you need Inverter CMOS Load Capacitance (Cload), Transconductance of NMOS (Kn), Supply Voltage (VDD) & Threshold Voltage of NMOS with Body Bias (VT,n). With our tool, you need to enter the respective value for Inverter CMOS Load Capacitance, Transconductance of NMOS, Supply Voltage & Threshold Voltage of NMOS 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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