Chapter 6, Problem 6.21P

Problems 6.19 through 6.22 relate to the comparison of two sinusoidal input signals using a dual-trace oscilloscope. A schematic diagram of the measurement system is shown in Figure 6.40, in which one of the signals is assumed to be a reference standard signal, having a known frequency and amplitude. The oscilloscope trace (Input signal versus Reference signal or X versus Y) for these inputs is called a Lissajous diagram. The problems can also be worked in the laboratory.

Develop the characteristic shape of the Lissajous diagrams for two sinusoidal inputs having the same amplitude, but with the following phase relationships:

1. in phase
2. ±90 degrees out of phase
3. 180 degrees out of phase

Figure 6.40 Dual-trace oscilloscope for measuring signal characteristics by using Lissajous diagrams.

1. Show that the phase angle for two sinusoidal signals can be determined from the relationship
sin O = yjy_a
where the values of y _f and y_aare illustrated in Figure 6.40 and represent the vertical distance to they intercept and the maximumy value, respectively.

2. Draw a schematic diagram of a measurement system to determine the phase lag resulting from an electronic circuit. Your schematic diagram should include a reference signal, the electronic circuit, and the dual-trace oscilloscope. Discuss the expected result and how a quantitative estimate of the phase lag can be determined.
3. Construct Lissajous diagrams for sinusoidal inputs to a dual trace oscilloscope having the following horizontal signal to vertical signal frequency ratios: (a) 1:1, (b) 1:2, (c) 2:1, (d) 1:3, (e) 2:3, (0 5:2.
These plots can be easily developed using spreadsheet software and plotting a sufficient number of cycles of each of the input signals.