When an input signal and an output signal from an amplifier are fed to an oscilloscope to determine their phase relationship, Lissajous figures are commonly used. The shape of the Lissajous figure provides direct information about the phase difference between the two signals.

Common-Base Amplifier Phase Relationship

A common-base amplifier is a type of bipolar junction transistor (BJT) amplifier configuration. One of its key characteristics is that it provides a non-inverting voltage gain. This means that the output signal (at the collector) is in phase with the input signal (at the emitter).

• The input signal applied to the emitter terminal and the output signal taken from the collector terminal of a common-base amplifier have a phase difference of approximately 0 degrees.
• Essentially, the output voltage waveform rises when the input voltage waveform rises, and falls when the input voltage waveform falls, without any significant phase shift.

Lissajous Figures Introduction

Lissajous figures are patterns that are displayed on an oscilloscope when two sinusoidal signals are applied to its horizontal (X-axis) and vertical (Y-axis) deflection plates. The shape of the Lissajous figure depends on the following factors:

• The frequency ratio of the two signals.
• The amplitude ratio of the two signals.
• The phase difference between the two signals.

In this specific scenario, the question implies that the input and output signals are of the same frequency, which is typical for amplifier analysis. Therefore, the shape of the Lissajous figure will primarily depend on the phase difference.

Lissajous Figure for In-Phase Signals

When two sinusoidal signals of the same frequency are applied to the X and Y inputs of an oscilloscope, and these signals are exactly in phase (i.e., a phase difference of 0 degrees), the resultant Lissajous figure is a straight line. Let's consider the input signal as \(X(t) = A \sin(\omega t)\) and the output signal as \(Y(t) = B \sin(\omega t + \phi)\).

For a common-base amplifier, the output is in phase with the input, meaning the phase difference \(\phi = 0^\circ\). So, the signals become:

• Input (X-axis): \(X(t) = A \sin(\omega t)\)
• Output (Y-axis): \(Y(t) = B \sin(\omega t)\)

If we relate \(X(t)\) and \(Y(t)\), we get \(Y(t) = \frac{B}{A} X(t)\). This equation represents a straight line passing through the origin with a slope of \(\frac{B}{A}\). If the phase difference were \(180^\circ\), the equation would be \(Y(t) = - \frac{B}{A} X(t)\), also a straight line but with a negative slope.

The figure below summarizes Lissajous patterns for various phase differences (assuming equal frequencies and amplitudes for simplicity):

Analyzing the Lissajous Figure Outcome

Since the input and output signals of a common-base amplifier are in phase (0° phase shift), when these are fed to an oscilloscope for a Lissajous figure display, the resulting pattern will be a straight line. This straight line will have a positive slope, reflecting the 0° phase difference. An oblique ellipse or a general ellipse would indicate phase differences other than 0°, 90°, or 180°, and a circle would specifically indicate a 90° phase difference with equal amplitudes.

Therefore, for a common-base amplifier, the Lissajous figure observed will be a straight line.