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Effective time-constant of the cascode amplifier Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
𝜏H = (Cgs*Rs)+Cgd*((1+(gm*rd)*Rs)+rd)+(Cdb+Cgs)*rd+(C+Cgd)*(1/Rl+1/Ro)
This formula uses 9 Variables
Variables Used
Capacitance gate to source - Capacitance gate to source is capacitance (Measured in Farad)
Signal Resistance- Signal Resistance is the resistance which is fed with the signal voltage source vs to an Amplifier
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)
Capacitance - Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential. (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)
STEP 1: Convert Input(s) to Base Unit
Capacitance gate to source: 2 Farad --> 2 Farad No Conversion Required
Signal Resistance: 1 --> 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
Capacitance: 3 Farad --> 3 Farad No Conversion Required
Load resistance: 1 Kilohm --> 1000 Ohm (Check conversion here)
Output resistance: 200 Ohm --> 200 Ohm No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝜏H = (Cgs*Rs)+Cgd*((1+(gm*rd)*Rs)+rd)+(Cdb+Cgs)*rd+(C+Cgd)*(1/Rl+1/Ro) --> (2*1)+3*((1+(8*10)*1)+10)+(20+2)*10+(3+3)*(1/1000+1/200)
Evaluating ... ...
𝜏H = 495.036
STEP 3: Convert Result to Output's Unit
495.036 Second --> No Conversion Required
FINAL ANSWER
495.036 Second <-- Effective high-frequency time constant
(Calculation completed in 00.019 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 cascode amplifier Formula

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)
𝜏H = (Cgs*Rs)+Cgd*((1+(gm*rd)*Rs)+rd)+(Cdb+Cgs)*rd+(C+Cgd)*(1/Rl+1/Ro)

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 cascode amplifier?

Effective time-constant of the cascode amplifier calculator uses 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) to calculate the Effective high-frequency time constant, The Effective time-constant of the cascode amplifier formula of the man-machine system is proposed as a suitable adaptive variable since it is based upon definable properties of the machine and the operator and has been shown to be related to task difficulty. Effective high-frequency time constant and is denoted by 𝜏H symbol.

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

FAQ

What is Effective time-constant of the cascode amplifier?
The Effective time-constant of the cascode amplifier formula of the man-machine system is proposed as a suitable adaptive variable since it is based upon definable properties of the machine and the operator and has been shown to be related to task difficulty and is represented as 𝜏H = (Cgs*Rs)+Cgd*((1+(gm*rd)*Rs)+rd)+(Cdb+Cgs)*rd+(C+Cgd)*(1/Rl+1/Ro) or 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). Capacitance gate to source is capacitance, Signal Resistance is the resistance which is fed with the signal voltage source vs to an Amplifier, 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, Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential, Load resistance is the resistance value of load given for the network and Output resistance is the value of resistance of the network.
How to calculate Effective time-constant of the cascode amplifier?
The Effective time-constant of the cascode amplifier formula of the man-machine system is proposed as a suitable adaptive variable since it is based upon definable properties of the machine and the operator and has been shown to be related to task difficulty is calculated using 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). To calculate Effective time-constant of the cascode amplifier, you need Capacitance gate to source (Cgs), Signal Resistance (Rs), Capacitance gate to drain (Cgd), Transconductance (gm), drain resistance (rd), Drain-body capacitance (Cdb), Capacitance (C), Load resistance (Rl) and Output resistance (Ro). With our tool, you need to enter the respective value for Capacitance gate to source, Signal Resistance, Capacitance gate to drain, Transconductance, drain resistance, Drain-body capacitance, Capacitance, Load resistance and Output resistance 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 Effective high-frequency time constant?
In this formula, Effective high-frequency time constant uses Capacitance gate to source, Signal Resistance, Capacitance gate to drain, Transconductance, drain resistance, Drain-body capacitance, Capacitance, Load resistance and Output resistance. 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 cascode amplifier calculator used?
Among many, Effective time-constant of the cascode amplifier calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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