Small-Signal Input Resistance between Base and Emitter using Transconductance Calculator

✖Common emitter current gain is influenced by 2 factors: width of base region W, and relative dopings of base region and emitter region. Its range varies from 50-200.ⓘ Common Emitter Current Gain [β]			+10% -10%
✖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.ⓘ Transconductance [G_m]			+10% -10%

✖Signal Resistance is the resistance which is fed with the signal voltage source vs to an Amplifier.ⓘ Small-Signal Input Resistance between Base and Emitter using Transconductance [R_s]

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Small-Signal Input Resistance between Base and Emitter using Transconductance

Formula

`"R"_{"s"} = "β"/"G"_{"m"}`

Example

`"37.7907kΩ"="65"/"1.72mS"`

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Small-Signal Input Resistance between Base and Emitter using Transconductance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Signal Resistance = Common Emitter Current Gain/Transconductance
R_s = β/G_m
This formula uses 3 Variables

Variables Used

Signal Resistance - (Measured in Ohm) - Signal Resistance is the resistance which is fed with the signal voltage source vs to an Amplifier.
Common Emitter Current Gain - Common emitter current gain is influenced by 2 factors: width of base region W, and relative dopings of base region and emitter region. Its range varies from 50-200.
Transconductance - (Measured in Siemens) - 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.

STEP 1: Convert Input(s) to Base Unit

Common Emitter Current Gain: 65 --> No Conversion Required
Transconductance: 1.72 Millisiemens --> 0.00172 Siemens (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_s = β/G_m --> 65/0.00172

Evaluating ... ...

R_s = 37790.6976744186

STEP 3: Convert Result to Output's Unit

37790.6976744186 Ohm -->37.7906976744186 Kilohm (Check conversion here)

FINAL ANSWER

37.7906976744186 ≈ 37.7907 Kilohm <-- Signal Resistance

(Calculation completed in 00.020 seconds)

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Birsa Institute of Technology (BIT), Sindri

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Small-Signal Input Resistance between Base and Emitter using Transconductance

Go Signal Resistance = Common Emitter Current Gain/Transconductance

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Go Emitter Resistance = Threshold Voltage/Emitter Current

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Go Emitter Resistance = Threshold Voltage/Emitter Current

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Small-Signal Input Resistance between Base and Emitter using Base Current

Go Signal Resistance = Threshold Voltage/Base Current

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Go Output Resistance = Device Parameter/Drain Current

Output Resistance of Simple Current BJT

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Small-Signal Input Resistance given Emitter Current

Go Small Signal = Signal Current*Emitter Resistance

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Go Emitter Resistance = Small Signal/Signal Current

Input Resistance of BJT

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Small-Signal Input Resistance between Base and Emitter

Go Signal Resistance = Input Voltage/Base Current

Small-Signal Input Resistance between Base and Emitter using Transconductance Formula

Signal Resistance = Common Emitter Current Gain/Transconductance
R_s = β/G_m

Why input resistance of a transistor is low?

While using a transistor, the emitter-base junction is always forward biased and the collector-base junction is always reverse-biased. Due to it, a small change in emitter current. This means that a small signal voltage variation at the input of the transistor produces a large emitter current variation. This showed that the input resistance of a transistor is low. Since the collector is reverse-biased, it collects all the charge carriers which diffuse into it, through the base. Due to it, a very large change in collector voltage shows only a small change in the collector current. This shows that the output resistance of the transistor is high.

How to Calculate Small-Signal Input Resistance between Base and Emitter using Transconductance?

Small-Signal Input Resistance between Base and Emitter using Transconductance calculator uses Signal Resistance = Common Emitter Current Gain/Transconductance to calculate the Signal Resistance, The Small-Signal Input Resistance between Base and Emitter using Transconductance suggests that for a small signal, the transistor behaves as a voltage-controlled current source. The input port of the controlled current source is between base and emitter and the output port is in between collector and emitter. Signal Resistance is denoted by R_s symbol.

How to calculate Small-Signal Input Resistance between Base and Emitter using Transconductance using this online calculator? To use this online calculator for Small-Signal Input Resistance between Base and Emitter using Transconductance, enter Common Emitter Current Gain (β) & Transconductance (G_m) and hit the calculate button. Here is how the Small-Signal Input Resistance between Base and Emitter using Transconductance calculation can be explained with given input values -> 0.037791 = 65/0.00172.

FAQ

What is Small-Signal Input Resistance between Base and Emitter using Transconductance?

The Small-Signal Input Resistance between Base and Emitter using Transconductance suggests that for a small signal, the transistor behaves as a voltage-controlled current source. The input port of the controlled current source is between base and emitter and the output port is in between collector and emitter and is represented as R_s = β/G_m or Signal Resistance = Common Emitter Current Gain/Transconductance. Common emitter current gain is influenced by 2 factors: width of base region W, and relative dopings of base region and emitter region. Its range varies from 50-200 & 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.

How to calculate Small-Signal Input Resistance between Base and Emitter using Transconductance?

The Small-Signal Input Resistance between Base and Emitter using Transconductance suggests that for a small signal, the transistor behaves as a voltage-controlled current source. The input port of the controlled current source is between base and emitter and the output port is in between collector and emitter is calculated using Signal Resistance = Common Emitter Current Gain/Transconductance. To calculate Small-Signal Input Resistance between Base and Emitter using Transconductance, you need Common Emitter Current Gain (β) & Transconductance (G_m). With our tool, you need to enter the respective value for Common Emitter Current Gain & Transconductance 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 Signal Resistance?

In this formula, Signal Resistance uses Common Emitter Current Gain & Transconductance. We can use 2 other way(s) to calculate the same, which is/are as follows -

Signal Resistance = Input Voltage/Base Current
Signal Resistance = Threshold Voltage/Base Current

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