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Birsa Institute of Technology (BIT), Sindri
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## Effective time-constant of the MOS cascode amplifier Solution

STEP 0: Pre-Calculation Summary
Formula Used
time_constant = (Signal Resistance*(Capacitance gate to source+Capacitance gate to drain*(1+(Transconductance*drain resistance))))+drain resistance*(Capacitance gate to drain+Drain-body Capacitance+Capacitance gate to source)+(1/Load resistance+1/Output resistance)*(Capacitance+Capacitance gate to drain)
T = (Rs*(Cgs+Cgd*(1+(gm*rd))))+rd*(Cgd+Cdb+Cgs)+(1/Rl+1/Ro)*(C+Cgd)
This formula uses 9 Variables
Variables Used
Signal Resistance- Signal Resistance is the resistance which is fed with the signal voltage source vs to an Amplifier
Capacitance gate to source - Capacitance gate to source is capacitance (Measured in Farad)
Capacitance gate to drain - Capacitance gate to drain is capacitance (Measured in Farad)
Transconductance - Transconductance is the ratio of the change in current at the output terminal to the change in the voltage at the input terminal of an active device. (Measured in Ampere per Volt)
drain resistance - drain resistance is the ratio of change in drain to source voltage to corresponding change in drain current for a constant gate to source voltage. (Measured in Ohm)
Drain-body capacitance - Drain-body capacitance is the capacitance for the drain diffusion. (Measured in Farad)
Load resistance - Load resistance is the resistance value of load given for the network (Measured in Kilohm)
Output resistance - Output resistance is the value of resistance of the network (Measured in Ohm)
Capacitance - Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential. (Measured in Farad)
STEP 1: Convert Input(s) to Base Unit
Signal Resistance: 1 --> No Conversion Required
Capacitance gate to source: 2 Farad --> 2 Farad No Conversion Required
Capacitance gate to drain: 3 Farad --> 3 Farad No Conversion Required
Transconductance: 8 Ampere per Volt --> 8 Siemens (Check conversion here)
drain resistance: 10 Ohm --> 10 Ohm No Conversion Required
Drain-body capacitance: 20 Farad --> 20 Farad No Conversion Required
Load resistance: 1 Kilohm --> 1000 Ohm (Check conversion here)
Output resistance: 200 Ohm --> 200 Ohm No Conversion Required
Capacitance: 3 Farad --> 3 Farad No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = (Rs*(Cgs+Cgd*(1+(gm*rd))))+rd*(Cgd+Cdb+Cgs)+(1/Rl+1/Ro)*(C+Cgd) --> (1*(2+3*(1+(8*10))))+10*(3+20+2)+(1/1000+1/200)*(3+3)
Evaluating ... ...
T = 495.036
STEP 3: Convert Result to Output's Unit
495.036 --> No Conversion Required
FINAL ANSWER
495.036 <-- Time constant
(Calculation completed in 00.016 seconds)

## < 10+ High-Frequency Response of the MOS Cascode Amplifier Calculators

Effective time-constant of the cascode amplifier
effective_high_frequency_time_constant = (Capacitance gate to source*Signal Resistance)+Capacitance gate to drain*((1+(Transconductance*drain resistance)*Signal Resistance)+drain resistance)+(Drain-body Capacitance+Capacitance gate to source)*drain resistance+(Capacitance+Capacitance gate to drain)*(1/Load resistance+1/Output resistance) Go
Effective time-constant of the MOS cascode amplifier
time_constant = (Signal Resistance*(Capacitance gate to source+Capacitance gate to drain*(1+(Transconductance*drain resistance))))+drain resistance*(Capacitance gate to drain+Drain-body Capacitance+Capacitance gate to source)+(1/Load resistance+1/Output resistance)*(Capacitance+Capacitance gate to drain) Go
Output resistance of the cascode amplifier
resistance_output = Resistance of Secondary winding in primary+Resistance of Primary winding in Secondary+(Transconductance*Resistance of Secondary winding in primary)*Resistance of Primary winding in Secondary Go
3-dB frequency in design insight and trade-off
3_db_frequency = 1/((2*pi)*(Capacitance+Capacitance gate to drain)*(1/Load resistance+1/Output resistance)) Go
Gate to drain resistance in the cascode amplifier
resistance_gate_to_drain = (1+(Transconductance*drain resistance))*Signal Resistance+drain resistance Go
Effective time-constant in design insight and trade-off
time_constant = (Capacitance+Capacitance gate to drain)*(1/Load resistance+1/Output resistance) Go
Unity gain frequency of the MOS cascode amplifier
unity_gain_frequency = Transconductance/((2*pi)*(Capacitance+Capacitance gate to drain)) Go
Signal current in the base
signal_current_in_the_base = (MOSFET Transconductance/Common emitter current gain)*Small Signal Go
Drain resistance in the cascode amplifier
drain_resistance = 1/Finite input resistance+1/Input resistance Go
3-dB frequency of the cascode amplifier
3_db_frequency = 1/(2*pi*Time constant) Go

### Effective time-constant of the MOS cascode amplifier Formula

time_constant = (Signal Resistance*(Capacitance gate to source+Capacitance gate to drain*(1+(Transconductance*drain resistance))))+drain resistance*(Capacitance gate to drain+Drain-body Capacitance+Capacitance gate to source)+(1/Load resistance+1/Output resistance)*(Capacitance+Capacitance gate to drain)
T = (Rs*(Cgs+Cgd*(1+(gm*rd))))+rd*(Cgd+Cdb+Cgs)+(1/Rl+1/Ro)*(C+Cgd)

## What is the difference between Cascade and cascode amplifier?

In a cascade amplifier, the transistors are arranged like a chain that is the output of the first transistor is connected as input for the second transistor. While in a cascode amplifier, the transistor is placed one above the other.

## How to Calculate Effective time-constant of the MOS cascode amplifier?

Effective time-constant of the MOS cascode amplifier calculator uses time_constant = (Signal Resistance*(Capacitance gate to source+Capacitance gate to drain*(1+(Transconductance*drain resistance))))+drain resistance*(Capacitance gate to drain+Drain-body Capacitance+Capacitance gate to source)+(1/Load resistance+1/Output resistance)*(Capacitance+Capacitance gate to drain) to calculate the Time constant, The Effective time-constant of the MOS cascode amplifier formula is defined as usually denoted by the Greek letter τ (tau), which is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system. Time constant and is denoted by T symbol.

How to calculate Effective time-constant of the MOS cascode amplifier using this online calculator? To use this online calculator for Effective time-constant of the MOS cascode amplifier, enter Signal Resistance (Rs), Capacitance gate to source (Cgs), Capacitance gate to drain (Cgd), Transconductance (gm), drain resistance (rd), Drain-body capacitance (Cdb), Load resistance (Rl), Output resistance (Ro) and Capacitance (C) and hit the calculate button. Here is how the Effective time-constant of the MOS cascode amplifier calculation can be explained with given input values -> 495.036 = (1*(2+3*(1+(8*10))))+10*(3+20+2)+(1/1000+1/200)*(3+3).

### FAQ

What is Effective time-constant of the MOS cascode amplifier?
The Effective time-constant of the MOS cascode amplifier formula is defined as usually denoted by the Greek letter τ (tau), which is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system and is represented as T = (Rs*(Cgs+Cgd*(1+(gm*rd))))+rd*(Cgd+Cdb+Cgs)+(1/Rl+1/Ro)*(C+Cgd) or time_constant = (Signal Resistance*(Capacitance gate to source+Capacitance gate to drain*(1+(Transconductance*drain resistance))))+drain resistance*(Capacitance gate to drain+Drain-body Capacitance+Capacitance gate to source)+(1/Load resistance+1/Output resistance)*(Capacitance+Capacitance gate to drain). Signal Resistance is the resistance which is fed with the signal voltage source vs to an Amplifier, Capacitance gate to source is capacitance, Capacitance gate to drain is capacitance, Transconductance is the ratio of the change in current at the output terminal to the change in the voltage at the input terminal of an active device, drain resistance is the ratio of change in drain to source voltage to corresponding change in drain current for a constant gate to source voltage, Drain-body capacitance is the capacitance for the drain diffusion, Load resistance is the resistance value of load given for the network, Output resistance is the value of resistance of the network and Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential.
How to calculate Effective time-constant of the MOS cascode amplifier?
The Effective time-constant of the MOS cascode amplifier formula is defined as usually denoted by the Greek letter τ (tau), which is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system is calculated using time_constant = (Signal Resistance*(Capacitance gate to source+Capacitance gate to drain*(1+(Transconductance*drain resistance))))+drain resistance*(Capacitance gate to drain+Drain-body Capacitance+Capacitance gate to source)+(1/Load resistance+1/Output resistance)*(Capacitance+Capacitance gate to drain). To calculate Effective time-constant of the MOS cascode amplifier, you need Signal Resistance (Rs), Capacitance gate to source (Cgs), Capacitance gate to drain (Cgd), Transconductance (gm), drain resistance (rd), Drain-body capacitance (Cdb), Load resistance (Rl), Output resistance (Ro) and Capacitance (C). With our tool, you need to enter the respective value for Signal Resistance, Capacitance gate to source, Capacitance gate to drain, Transconductance, drain resistance, Drain-body capacitance, Load resistance, Output resistance and Capacitance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Time constant?
In this formula, Time constant uses Signal Resistance, Capacitance gate to source, Capacitance gate to drain, Transconductance, drain resistance, Drain-body capacitance, Load resistance, Output resistance and Capacitance. We can use 10 other way(s) to calculate the same, which is/are as follows -
• resistance_gate_to_drain = (1+(Transconductance*drain resistance))*Signal Resistance+drain resistance
• drain_resistance = 1/Finite input resistance+1/Input resistance
• resistance_output = Resistance of Secondary winding in primary+Resistance of Primary winding in Secondary+(Transconductance*Resistance of Secondary winding in primary)*Resistance of Primary winding in Secondary
• effective_high_frequency_time_constant = (Capacitance gate to source*Signal Resistance)+Capacitance gate to drain*((1+(Transconductance*drain resistance)*Signal Resistance)+drain resistance)+(Drain-body Capacitance+Capacitance gate to source)*drain resistance+(Capacitance+Capacitance gate to drain)*(1/Load resistance+1/Output resistance)
• 3_db_frequency = 1/(2*pi*Time constant)
• time_constant = (Signal Resistance*(Capacitance gate to source+Capacitance gate to drain*(1+(Transconductance*drain resistance))))+drain resistance*(Capacitance gate to drain+Drain-body Capacitance+Capacitance gate to source)+(1/Load resistance+1/Output resistance)*(Capacitance+Capacitance gate to drain)
• time_constant = (Capacitance+Capacitance gate to drain)*(1/Load resistance+1/Output resistance)
• 3_db_frequency = 1/((2*pi)*(Capacitance+Capacitance gate to drain)*(1/Load resistance+1/Output resistance))
• unity_gain_frequency = Transconductance/((2*pi)*(Capacitance+Capacitance gate to drain))
• signal_current_in_the_base = (MOSFET Transconductance/Common emitter current gain)*Small Signal
Where is the Effective time-constant of the MOS cascode amplifier calculator used?
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