Propagation Delay for High to Low Output Transition CMOS Calculator

Formula Used:

\[ \zeta_{PHL} = \frac{C_{load}}{K_n \cdot (V_{DD} - V_{T,n})} \cdot \left( \frac{2 \cdot V_{T,n}}{V_{DD} - V_{T,n}} + \ln\left( \frac{4 \cdot (V_{DD} - V_{T,n})}{V_{DD}} - 1 \right) \right) \]

Inverter CMOS Load Capacitance (C_load):

Transconductance of NMOS (K_n):

A/V²

Supply Voltage (V_DD):

Threshold Voltage of NMOS with Body Bias (V_T,n):

Time for High to Low Transition of Output (ζ_PHL):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Propagation Delay for High to Low Output Transition?

The Propagation Delay for High to Low Output Transition (ζ_PHL) is the time taken for a CMOS inverter's output to transition from a high voltage level to a low voltage level. This parameter is crucial in digital circuit design as it affects the maximum operating frequency and timing characteristics of the circuit.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \zeta_{PHL} = \frac{C_{load}}{K_n \cdot (V_{DD} - V_{T,n})} \cdot \left( \frac{2 \cdot V_{T,n}}{V_{DD} - V_{T,n}} + \ln\left( \frac{4 \cdot (V_{DD} - V_{T,n})}{V_{DD}} - 1 \right) \right) \]

Where:

\( C_{load} \) — Inverter CMOS Load Capacitance (F)
\( K_n \) — Transconductance of NMOS (A/V²)
\( V_{DD} \) — Supply Voltage (V)
\( V_{T,n} \) — Threshold Voltage of NMOS with Body Bias (V)

Explanation: The formula calculates the propagation delay by considering the capacitive load, transistor characteristics, and supply voltage to determine the transition time from high to low output.

3. Importance of Propagation Delay Calculation

Details: Accurate propagation delay calculation is essential for designing high-speed digital circuits, ensuring proper timing synchronization, and optimizing circuit performance for specific applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (Farads for capacitance, Amperes per square Volt for transconductance, and Volts for voltages). Ensure that V_DD > V_T,n for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect propagation delay in CMOS circuits?
A: Propagation delay is influenced by load capacitance, transistor sizing, supply voltage, threshold voltage, and temperature.

Q2: How does body bias affect threshold voltage?
A: Body bias changes the threshold voltage by modifying the substrate potential, which affects the depletion region and carrier concentration.

Q3: Why is natural logarithm (ln) used in the formula?
A: The natural logarithm accounts for the exponential relationship between voltage and time during the discharge phase of the capacitive load.

Q4: What are typical values for propagation delay in CMOS circuits?
A: Propagation delays typically range from picoseconds to nanoseconds, depending on technology node, load conditions, and circuit design.

Q5: How can propagation delay be minimized in circuit design?
A: Propagation delay can be reduced by minimizing load capacitance, increasing transistor sizes, optimizing supply voltage, and using advanced process technologies.