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Amplifier fundamentals

Introduction

This chapter discusses the fundamentals of amplifiers and how we talk about and analyze them. These concepts apply to all amplifiers regardless of how they are constructed internally.

What makes this way of thinking about amplifiers so powerful is that we can separate how the the amplifier is used in a larger system from how it is constructed internally. At any given time, a person is only concerned about one of these aspects and can therefore effectively not care about the other.

Pre-requisites

We start with amplifiers which behave the same at all frequencies. This means that we are ignoring capacitors, inductors, and any frequency-dependence of devices such as transistors.

[LEC] has a well-written tour of this material in Chapters 1 through 10 of Lessons in Electric Circuits: Volume 1 - Direct Current.

Most important to how we view amplifiers are the wonderful concept-tools of Thévenin (mostly) and Norton (some) equivalent circuits. You can find more discussion and worked examples at [CL-book]'s section Thevenin Equivalent and Norton Equivalent Circuits.

Any and all of linear circuit theory is necessary for analyzing amplifiers, especially including:

  • Components

    • Ideal independent and dependent sources: VCVS, VCCS, CCVS, CCCS.

    • Resistors, capacitors, inductors.

  • Techniques for analysis

    • Nodal analysis

    • Thevenin / Norton equivalent circuits

    • Apparent resistance

  • AC circuits with complex-valued impedances using the Laplace transform

lower UPPER signal notation

There are several ways to view a circuit besides trying to find the circuit equations directly in the time domain. This is especially terrible difficult when there are semiconductors or other non-linear devices in the circuit besides R, L, C, and sources. To help deal with the complexity, we view circuits from two major perspectives: DC and AC.

Study Symbol capitalization for circuit quantities for a bit and notice how every current or voltage can be espressed using the “lowerUPPER” notation on the first and last line of the table.

Table 1. Symbol capitalization for circuit quantities
Capitalization Example Meaning

lowerUPPER

\$v_{BE}(t)\$

total quantity, as measured by an oscilloscope with DC coupling

UPPERUPPER

\$V_{BE}\$

DC value (average)

lowerlower

\$v_{be}(t)\$

signal quantity, changes

UPPERlower

\$V_{be}\$

complex-valued phasor, a function of frequency

lowerUPPER = UPPERUPPER + lowerlower

\$v_{BE} = V_{BE} + v_{be}\$

total signal is average + changes

AC equivalent circuits

  • Set all DC independent sources to zero.

    • V-sources → short-circuit

    • I-sources → open-circuit

  • Redraw the circuit.

Small-signal equivalent circuits

  • Find the AC equivalent circuit.

  • Decide which inductors and capacitors function as BFCs or BFLs.

  • Keeping in mind your frequencies of interest, decide to whether to keep or simplify additional inductors and capacitors.

  • Replace each transistor with its small-signal model.

  • Re-draw the circuit.

I first learned of the Big Fat Capacitor and Big Fat L (inductor) from Chapter 15 of Thomas Lee’s The Design of CMOS Radio-Frequency Circuits, 2nd ed. (affiliate link)

A BFC is a capacitor whose value has no effect on the frequency response of the circuit by behaving as a short-circuit at all frequencies of interest, while still blocking DC current flow. Similarly, a BFL behaves like an open-circuit at all frequencies of interest, while maintaining a path through it for constant DC current.

These are only for simplifying a discussion or analysis. When you simulate or build a circuit containing a BFC or BFL, you will need to choose an appropriate value. (Watch out for self-resonance and other issues in physical parts!)