core Estimated learning time: 10 hCommon in syllabi

Included in at least one reviewed higher-education syllabus.

S4-1.3 Multistage & High-Frequency Amplifiers

You can analyse cascaded stages, the Darlington pair, and use the hybrid-pi model for high-frequency behaviour including short-circuit current gain.

One stage rarely gives enough gain, so this topic is about what happens when stages are cascaded: gains multiply, but frequency limits compound, and the bandwidth shrinks as the chain grows. It also introduces the hybrid-pi model, which exists because h-parameters stop telling the truth at high frequency once the transistor's internal capacitances matter. The common confusion is expecting two identical stages to give twice the performance; they give the gain product and a narrower bandwidth, and understanding that trade is the point of the unit.

Work through these

  • Coupling schemes: RC, transformer, direct

    How one amplifier stage hands its signal to the next: through a capacitor, through a transformer, or directly. Each choice decides what range of frequencies survives the handover, and direct coupling is the one that passes DC and therefore drifts.

  • Analysis of CE-CE, CE-CB and CC-CC Darlington pair

    Real amplifiers are chains, and this covers the standard chains: two common-emitter stages, a common-emitter feeding a common-base, and the Darlington pair that multiplies current gain. The Darlington is worth recognising on sight, since it appears everywhere.

  • Multi-stage frequency effects

    Cascading stages multiplies the gains but narrows the bandwidth, so a two-stage amplifier is never twice as good as one stage. Understanding why the frequency limits compound is the whole reason this unit exists.

  • Hybrid-pi CE transistor model: conductances and capacitances

    The hybrid-pi model replaces h-parameters once frequency gets high enough that the transistor's internal capacitances matter. It is not a competing theory but a more honest picture of the same device.

  • CE short-circuit current gain (f_T)

    The transition frequency is where a transistor's current gain falls to one, which is the point at which it has stopped amplifying in any useful sense. It appears on every datasheet and sets the ceiling for anything you design with that part.

    Falstad Circuit Simulator · Reference
  • Lab: simulate a two-stage RC-coupled amplifier and observe bandwidth vs single stage

    Simulate a two-stage RC-coupled amplifier and watch the bandwidth shrink against the single-stage version. Seeing the trade rather than reading it is what makes the earlier arithmetic stick.

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Links last checked 29 Aug 2026.

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