Transistor emitter-current notation: match symbols to meanings in small-signal analysis. List I (Quantity) A. Total instantaneous value of emitter current B. Quiescent (DC) value of emitter current C. Instantaneous value of the AC component of emitter current D. RMS value of the AC component of emitter current List II (Symbol) IE iE Ie ie

Difficulty: Easy

Correct Answer: A-2, B-1, C-4, D-3

Explanation:


Introduction / Context:
Small-signal transistor notation separates total, DC (quiescent), and AC components. Getting the symbols right is crucial when moving between bias calculations and incremental (signal) analysis for BJTs or FETs.



Given Data / Assumptions:

  • Total instantaneous emitter current is the sum of DC and AC components.
  • Uppercase letters typically represent DC quantities; lowercase letters denote instantaneous AC variables; mixed case often denotes RMS values.
  • Standard notation uses iE(t) = IE + ie(t), with Ie commonly reserved for an RMS value of the AC component.


Concept / Approach:

We match by convention: iE is the instantaneous total, IE is the quiescent DC level, ie is the instantaneous small-signal component, and Ie is the RMS of that AC component. This removes ambiguity when writing KCL/KVL and computing gains or impedances.



Step-by-Step Solution:

Total instantaneous → iE ⇒ A-2.Quiescent DC → IE ⇒ B-1.Instantaneous AC component → ie ⇒ C-4.RMS of AC component → Ie ⇒ D-3.


Verification / Alternative check:

Write iE(t) = IE + ie(t). If ie(t) is sinusoidal, its RMS is Ie = Îe / √2. This matches the symbol mapping and standard textbook usage in hybrid-π and h-parameter analyses.



Why Other Options Are Wrong:

  • Mapping IE to instantaneous AC contradicts the uppercase DC convention.
  • Using iE for RMS conflates time-varying instantaneous quantities with averaged measures.
  • Assigning Ie to total instantaneous loses the AC/DC separation needed for linearization.


Common Pitfalls:

Switching between uppercase/lowercase when moving from the “incremental” model back to bias calculations. Keep a clear legend in your solution to avoid misinterpreting gains or impedance formulas.



Final Answer:

A-2, B-1, C-4, D-3

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