Learn how to calculate the gain of a bipolar junction transistor (BJT) using different methods and formulas. Discover the basic concept and the small-signal model of a BJT.

For Example: If a BJT has a β of 100 and is used in a common emitter configuration with a collector resistor of 1kΩ and an emitter resistor of 100Ω, the voltage gain can be calculated using the following formula: Av ≈ -Rc / Re = -1000 / 100 = -10 The negative sign indicates a phase inversion between the input and output signals.

Last updated on Oct 6, 2024

How do you calculate the gain of a bipolar junction transistor?

Bipolar junction transistors (BJTs) are widely used in electronic engineering for amplifying, switching, and generating signals. One of the key parameters that characterizes the performance of a BJT is its gain, which measures how much the output current changes in response to the input current. In this article, you will learn how to calculate the gain of a BJT using different methods and formulas.

1 Basic concept

A BJT has three terminals: the base, the collector, and the emitter. The base current (Ib) controls the collector current (Ic), which flows from the collector to the emitter. The ratio of Ic to Ib is called the current gain, or beta (β). Beta is usually given by the manufacturer of the transistor, but it can also be measured experimentally or calculated from other parameters. The typical range of beta values for BJTs is from 20 to 500.

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Raghavendra Anjanappa

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The gain of a BJT can be calculated in different ways, depending on current gain, voltage gain or power gain. Current Gain (β) The current gain of a BJT is the ratio of the collector current (Ic) to the base current (Ib). β = Ic / Ib β can range from a few tens to a few hundreds Voltage Gain (Av) The voltage gain of a BJT is the ratio of the output voltage (Vo) to the input voltage (Vi). Av = Vo / Vi The voltage gain of a BJT depends on its configuration (common emitter, common collector, common base), the values of the resistors in the circuit & the transistor's β. Power Gain (Ap) The power gain of a BJT is the ratio of the output power (Po) to the input power (Pi) Ap = Po / Pi Relationship to current & voltage gain Ap = Av * β

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Gary M. Moore

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It's a bad question , sorry. You get the device gain from the data sheet. You calculate stage gain by dividing collector resistor by the emitter resistor.

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2 Small-signal model

Another way to calculate the gain of a BJT is to use a small-signal model, which simplifies the analysis of the transistor by assuming that the input and output signals are small enough to not affect the operating point of the device. A small-signal model consists of linear elements, such as resistors, capacitors, and controlled sources, that represent the behavior of the transistor around its operating point. The gain of a BJT in a small-signal model is equal to the ratio of the output voltage (Vout) to the input voltage (Vin).

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3 Common-emitter configuration

One of the most common configurations for a BJT amplifier is the common-emitter configuration, where the emitter is connected to the ground and the input signal is applied to the base. The output signal is taken from the collector, which is connected to a load resistor (RL). The gain of a common-emitter amplifier depends on the values of RL, the emitter resistor (RE), and beta. The formula for the gain is: Gain = -βRL / (RE + (β + 1)RE) The negative sign indicates that the output signal is inverted with respect to the input signal.

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4 Common-base configuration

Another configuration for a BJT amplifier is the common-base configuration, where the base is connected to the ground and the input signal is applied to the emitter. The output signal is taken from the collector, which is connected to a load resistor (RL). The gain of a common-base amplifier depends on the values of RL, the emitter resistor (RE), and the emitter efficiency (α), which is related to beta by the formula: α = β / (β + 1) The formula for the gain is: Gain = αRL / RE The output signal is in phase with the input signal.

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Krishna Sagar Rayudu

Technical Architect | Systems Analyst | Senior Technical Consultant | specialised in frontend development | frontend lead | UI and Frontend Architect AWS Certified Solutions Architect | Impactful outcomes
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CB Configuration is commonly used as an intermediate stage in multi stage amplifiers to provide voltage gain and to match impedance between stages. This is because It's low input impedance complements the high output impedance of the CE stage for efficiency.

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5 Common-collector configuration

The third configuration for a BJT amplifier is the common-collector configuration, where the collector is connected to the power supply and the input signal is applied to the base. The output signal is taken from the emitter, which is connected to a load resistor (RL). The gain of a common-collector amplifier depends on the values of RL, the emitter resistor (RE), and beta. The formula for the gain is: Gain = (β + 1)RL / (RE + (β + 1)RL) The output signal is in phase with the input signal and has a lower voltage but a higher current than the input signal.

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Krishna Sagar Rayudu

Technical Architect | Systems Analyst | Senior Technical Consultant | specialised in frontend development | frontend lead | UI and Frontend Architect AWS Certified Solutions Architect | Impactful outcomes
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CC configuration is commonly used as the output stage in an amplifier because of it's low output impedance, and substantial current gain. As devices like loud speaker will have low impedance and draws more current.

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6 Factors affecting gain

The gain of a BJT amplifier is not a constant value, but it can vary depending on several factors, such as the temperature, the frequency, and the biasing of the transistor. Some of these factors can cause the gain to change nonlinearly, which can result in distortion or instability of the output signal. Therefore, it is important to design and test the amplifier circuit carefully to ensure that it operates within the desired range of gain and performance.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Raghavendra Anjanappa

27K Followers | LinkedIn Top Voice | Ex-Manager Micron | Signal & Power Integrity | IC Package Design | High Speed Design | EMI-EMC| EDA | Thermal Analysis | Semiconductor Manufacturing & Assembly | Consultant |
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For Example: If a BJT has a β of 100 and is used in a common emitter configuration with a collector resistor of 1kΩ and an emitter resistor of 100Ω, the voltage gain can be calculated using the following formula: Av ≈ -Rc / Re = -1000 / 100 = -10 The negative sign indicates a phase inversion between the input and output signals.

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Swastik K.
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There are a lot of assumptions taken into account while deriving and reaching to these formulae. While the assumptions seem reasonable theoretically, the actual test results may vary considerably. Alternatively, one can try to avoid these assumptions and can reach a more accurate solution. This would become too tedious analytically. Hence, a numerical modelling approach, using tools such as MATLAB/Octave can prove to be more effective. A non linear numerical model of a BJT(without much assumptions) would give much more accurate results, provided the inherent values are tested and accurate. Looking forward to expert perspectives on my perspective😀

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Syamkumar A

10x LinkedIn Top Voice | QC Engineer | PV Design Engineer | Solar Design Expert | Electrical Design Engineer | MBA (Operations) | B. Tech (Electrical & Electronics)
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Calculating the gain of a bipolar junction transistor (BJT) requires an understanding of its operational characteristics and the circuit configuration. The small-signal voltage gain can be assessed by evaluating the output voltage change relative to the input voltage change. Operating the BJT in the active region is essential for reliable amplification; deviations into saturation or cutoff can significantly reduce gain. It's important to consider external factors like temperature variations, as these can impact the transistor's performance and lead to fluctuations in gain.

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How do you calculate the gain of a bipolar junction transistor?

1

2

3

4

5

6

7

1 Basic concept

2 Small-signal model

3 Common-emitter configuration

4 Common-base configuration

5 Common-collector configuration

6 Factors affecting gain

7 Here’s what else to consider

Electronic Engineering

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How do you calculate the gain of a bipolar junction transistor?

1

2

3

4

5

6

7

1 Basic concept

2 Small-signal model

3 Common-emitter configuration

4 Common-base configuration

5 Common-collector configuration

6 Factors affecting gain

7 Here’s what else to consider

Electronic Engineering

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