Design Build Measure package 3

1. Introduction

Goals

  • Match the small-signal mid-frequency gain of a common-emitter amplifier between hand analysis, simulation, and measurements of physical instance.

  • Review what the idea of a transfer function or amplifier gain means and how the same concept manifests in the circuit analysis, simulator, and laboratory contexts.

Objectives

  • Generate a symbolic expression for the amplifier’s small-signal voltage gain.

  • Compute the expected small-signal voltage gain using the DC bias conditions and component values of the selected CE amplifier.

  • Simulate the amplifier to find its DC bias point.

  • Simulate the frequency response of the amplifier’s voltage gain with an AC frequency sweep of appropriate range and resolution.

  • Simulate the time-domain response of the amplifier to an input signal at an appropriate frequency and amplitude to match the display expected on an oscilloscope in the laboratory.

  • Build the amplifier and confirm that the DC operating point and frequency response match the hand and simulator’s analyses.

2. Elements

Select one of the three “circuits in play” listed in day13.

Apply the Lab 3 Simplifications for small-signal analysis to reduce the analysis complexity from that of a complete circuit to only the behavior of interest at mid-range frequencies (about 1—​10 kHz range).

  • Solve for the DC circuit solution with symbolic circuit analysis. Then substitute numbers for VBE, β, and component values to find the expected node voltages and collector current IC.

  • Find the amplifier’s AC equivalent circuit and then the small-signal equivalent circuit. Find the voltage gain \(v_{\mathit{out}} / v_{\mathit{in}}\), keeping all terms symbolic.

  • Substitute for the actual part values and operating condition and compute the expected voltage gain.

  • Simulate the circuit using LTspice or CircuitLab to find the DC solution.

  • Use your simulator of choice to find the small-signal voltage gain.

  • Build the circuit and make the same measurements.

All three methods of analysis {hand, sim, build} must match for your report! Matching is all values are ≤10% of each other.

\[\mathrm{error} = \left(\dfrac{X_{\mathrm{actual}}}{X_{\mathrm{expected}}} - 1\right) \cdot 100%\]

3. Report

Assemble a report that contains descriptions, information, and relevant materials. A reader should be convinced that you achieved the stated objectives and goals.

You could organize your report by theme (DC, gain, transient) or by method (hand, sim, build) as you feel is best. Don’t forget to clearly show that the three methods give results that are within the expected (10%) tolerance.

4. Related