ECircuits-Lec21-2026 (self-study: BJT part 2)

Overview

The lecture maps BJT circuit analysis onto familiar MOSFET techniques, deriving key small-signal quantities and showing how to analyze common-emitter and emitter-follower stages. It gives practical formulas—such as g_m = I_C/V_T, r_π = β/g_m, and r_e ≈ 1/g_m—then works through a bias-and-gain example and explains why BJTs remain useful in high-frequency circuits.

Key takeaways

At room temperature, BJT transconductance is g_m = I_C/25 mV, so a collector current of 2.3 mA yields about 92 mS.
The BJT small-signal base resistance is r_π = β/g_m, while the emitter resistance is approximately 1/g_m; these replace the MOSFET's nearly infinite DC gate resistance in input analysis.
Emitter degeneration increases the base input resistance to r_π + (1+β)R_E and reduces effective transconductance to approximately g_m/(1+g_mR_E).
For β = 100, α = β/(1+β) ≈ 0.99, explaining why collector current is nearly equal to emitter current.
A 3 V base supply through 100 kΩ, with V_BE = 0.7 V and β = 100, produces I_B = 23 μA and I_C = 2.3 mA; with a 3 kΩ collector resistor and 10 V supply, V_CE is 3.1 V.
BJT and MOSFET amplifier configurations share analysis patterns, but BJTs are especially relevant to high-frequency design because their device structure and gain characteristics can suit millimeter-wave applications.

Chapters

0:00 Course Wrap-Up, Divide-and-Conquer Analysis, and Final Exam Guidance

Electronic-circuit analysis relies on breaking large systems into smaller diode, MOSFET, and BJT stages.
The final exam is scheduled for December 10 at 10:00 a.m.; homework sets 4–9 are highlighted as important preparation.
The lecture frames circuit fundamentals as building blocks for more complex industry designs.

3:15 Mapping BJT Terminals and Symbols to MOSFETs

The base corresponds functionally to the MOSFET gate, the emitter to the source, and the collector to the drain.
BJT symbols place an arrow on the emitter; its direction indicates conventional emitter-current direction.
The lecture compares NPN with n-channel MOSFETs and PNP with p-channel devices.

5:30 BJT Exponential Current, Early Voltage, and Active-Region Conditions

The collector current follows an exponential dependence on base-emitter voltage: I_C ≈ I_S e^(V_BE/V_T), with an Early-effect correction.
The BJT Early voltage V_A is the extrapolated output-characteristic intercept, with λ = 1/V_A.
Because V_BE changes by only roughly 100–200 mV across large current ranges, circuit analysis often approximates the forward-biased junction drop as about 0.7 V.
For the lecture's practical active-region check, V_CE should remain above roughly 0.1–0.2 V.

10:00 BJT Transconductance, Output Resistance, and Intrinsic Gain

Small-signal transconductance is g_m = ∂I_C/∂V_BE = I_C/V_T; at room temperature V_T is about 25 mV.
The Early-effect output resistance is r_o = V_A/I_C, analogous to MOSFET r_o = 1/(λI_D).
BJT intrinsic gain is g_m r_o = V_A/V_T, connecting the Early voltage directly to voltage-gain capability.

14:08 Base Current, β, and Common-Emitter/Common-Base Gain

Unlike the insulated MOSFET gate, a BJT base draws current; the approximation is I_B = I_C/β.
Common-emitter current gain is β = I_C/I_B, while common-base gain is α = I_C/I_E.
The gains are related by α = β/(1+β) and β = α/(1−α); for β = 100, α is about 0.99.
Common-emitter and common-base configurations parallel the MOSFET common-source and common-gate arrangements.

19:54 Deriving BJT Small-Signal Input and Emitter Resistances

The base-emitter small-signal resistance is r_π = β/g_m, representing the finite input resistance absent at an ideal MOSFET gate.
The resistance looking into the emitter is r_e = α/g_m, commonly approximated as 1/g_m because α is close to 1.
The derivation applies a test voltage at the emitter and relates its current to the base-emitter small-signal model.

28:33 Common-Emitter Emitter Degeneration and Effective Transconductance

With a physical emitter resistor R_E, the base input resistance is r_in = r_π + (1+β)R_E.
Since r_π ≈ βr_e, the emitter resistance appears amplified by approximately β when viewed from the base.
Emitter degeneration reduces effective transconductance to approximately g_m/(1+g_mR_E), analogous to MOSFET source degeneration.

36:04 Emitter-Follower Gain and Output Resistance

The emitter follower is the BJT counterpart of the MOSFET source follower, with the collector at AC ground and output at the emitter.
Its voltage gain is approximately g_mR_eq/(1+g_mR_eq), typically near unity.
Looking into the emitter gives approximately 1/g_m; a more complete estimate includes base resistance as 1/g_m + R_B/β.

41:02 Worked BJT Bias Point and Small-Signal Gain Example

With a 3 V base supply, 100 kΩ base resistor, β = 100, and V_BE = 0.7 V, the example finds I_B = 23 μA and I_C = 2.3 mA.
A 3 kΩ collector resistor drops 6.9 V from a 10 V supply, leaving V_CE = 3.1 V and keeping the transistor in forward-active operation.
The operating current gives g_m ≈ 92 mS and r_π ≈ 1.09 kΩ; voltage gain includes input division across 100 kΩ and r_π, followed by the collector-stage gain.

47:00 BJT Applications, High-Frequency Advantages, and Course Close

The lecture says BJT questions are excluded from the final exam but recommends BJT preparation for analog-design interviews at Texas Instruments and Analog Devices.
BJTs lack the MOSFET gate-insulator capacitor but still have parasitic capacitances, so high-frequency behavior remains a design consideration.
The lecture identifies high gain and high-frequency performance as reasons BJTs are used in millimeter-wave, 5G, and 6G circuit applications.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, WISE Lab - UF ECE.