Name: bjt amplifier gain and input resistance
Uploaded: 2025-05-22T09:06:20.000Z
Duration: 1 min 21 s
Channel: JoVE

Consider a BJT&#160; transistor amplifier circuit operating in its active region to provide linear amplification.
The total instantaneous base-emitter voltage, which combines the DC voltage and the input signal, results in an instantaneous collector current.
The exponential term involving the base-emitter voltage is simplified using the small-signal approximation, where the input signal is significantly less than the thermal voltage.
So, the collector current comprises two components: the DC bias current and the signal component.
The ratio of the signal component to the varying base-emitter voltage is known as the BJT transconductance.
Here, the transconductance of the BJT is directly proportional to the DC bias current, which is determined by the slope of the tangent relative to the characteristic curve at the bias point.
So, the voltage gain equals the negative product of the transconductance and the load resistance. The negative sign indicates a 180 degrees phase shift between the amplified and input signals.
When examining the emitter, the small-signal base-emitter resistance is determined by dividing the thermal voltage by the respective DC bias current.

small-signal analysis of bjt amplifiers

Small signal analysis is a fundamental approach used in electronics to understand how a Bipolar Junction Transistor (BJT) amplifier processes signals. In the active region, the BJT is designed for linear amplification. The transistor's behavior under these conditions is governed by its instantaneous base-emitter voltage VBE, a sum of the DC bias VBE, and a small AC signal VBE, resulting in the collector current iC. Here, the collector current has a DC component and an AC component.
<img alt="Transistor circuit equations; V_BE and i_C formulas; semiconductor analysis; electronic design." src="/files/ftp_upload/15731/15731_Equation_1.svg" style="text-align: center; height: 72px;" data-altupdatedat="1754904545000" data-alt="Transistor equations, V_BE and i_C; formulas for AC analysis, amplification, circuit design.">
Here, VT is the thermal voltage.
When the AC input signal VBE is significantly smaller than VT, a small signal approximation can be used to get the expression for the AC component of the collector current. The AC component of the collector current is the ratio of the product of the DC component of the collector with time-varying input voltage to the thermal voltage.
<img alt="BJT transistor equation, static equilibrium, formula representation, educational diagram." src="/files/ftp_upload/15731/15731_Equation_2.svg" style="text-align: center; height: 54px;" data-altupdatedat="1754904545000" data-alt="Transistor current equation, iC(AC)=iC(DC)(VBE(AC)/VT), electrical engineering formula.">
The ratio of the AC component of the collector current to the input signal is known as transconductance. The voltage gain of the BJT is a function of the transconductance of the BJT and the load resistance.
<img alt="Transistor gain equations; gm=ic(ac)/vbe(ac), Av=-gmRc; circuit analysis." src="/files/ftp_upload/15731/15731_Equation_3.svg" style="text-align: center; height: 88px;" data-altupdatedat="1754904545000" data-alt="Transistor amplifier equation, gain formula; symbols for gm, iC, VBE, AV, RC; electrical analysis">
Here, the negative sign signifies a 180-degree phase shift between input and output signals.
At the base of the BJT, the small-signal base-emitter resistance rπ is crucial for input impedance considerations and is determined by:
<img alt="Transistor resistance formula \(r_{\pi} = \frac{V_T}{i_{B(DC)}}\) equation for electronic analysis." src="/files/ftp_upload/15731/15731_Equation_4.svg" style="text-align: center; height: 60px;" data-altupdatedat="1754904545000" data-alt="Transistor biasing equation, \( r_{\pi} = \frac{V_T}{i_{B(DC)}} \), used in electronic circuits.">
This resistance impacts the transistor's response to input signals and is inversely proportional to the DC bias current.
Through small signal analysis, the detailed performance of BJT amplifiers with small input variations can be precisely characterized and utilized in electronic circuit design.

Small-Signal Analysis of BJT Amplifiers

Small signal analysis is a fundamental approach used in electronics to understand how a Bipolar Junction Transistor (BJT) amplifier processes signals. In ...

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bjt amplifier gain and input resistance

BJT amplifier gain and input resistance can be analyzed with a small-signal model. In the active region, a bipolar junction transistor is used for linear amplification. Its base-emitter voltage includes a DC bias and a small AC signal. That input produces a collector current with both DC and AC parts.

When the AC input signal is much smaller than the thermal voltage VT, the small-signal approximation applies. This makes it possible to find the AC collector current from the DC collector current and the changing input voltage. The ratio of AC collector current to input signal is called transconductance. It shows how strongly the transistor converts a small voltage change into a current change.

The voltage gain of a BJT amplifier depends on the transconductance and the load resistance. The negative sign in the gain expression means the output is 180 degrees out of phase with the input. Another important small-signal feature is the base-emitter resistance rπ. This resistance matters for input impedance, and it is inversely proportional to the DC bias current. Small-signal analysis helps describe how BJT amplifiers respond to small input changes in circuit design.

BJT Amplifier Gain and Input Resistance

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BJT amplifier gain and input resistance can be analyzed with a small-signal model. In the active region, a bipolar junction transistor is used for linear amplification. Its base-emitter voltage includes a DC bias and a small AC signal. That input produces a collector current with both DC and AC parts. When the AC input signal is much smaller than the thermal voltage VT, the small-signal approximation applies. This makes it possible to find the AC collector current from the DC collector current...

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key terms and concepts

Explore how small-signal analysis links BJT transconductance, voltage gain, phase shift, and input resistance for amplifier circuits in grades 9–12.

BJT Amplifier Gain and Input Resistance | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

BJT Amplifier Gain and Input Resistance

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