BK Precision 4011A Instrucciones de operaciones descargar pdf (Pagina 66)

Appendix D: Operating Instructions for a Typical Oscilloscope

201054

Phase and Frequency Measurement by Lissajous Patterns

The oscilloscope may be used to compare simultaneously two separate waveforms. When two

voltages of the same frequency are impressed on the oscilloscope, one on the vertical and one on

the horizontal plates, a straight line results on the screen if the voltages are in phase or 180° out

of phase. An ellipse is obtained for other phase angles. The pattern which results when two sine

waves are applied to the oscilloscope in this way are called Lissajous patterns. They can take

many forms, depending on the frequencies involved.

Phase shift (the phase angle between two waves of equal

frequency) may be calculated from the pattern on the CRT

screen. If the voltage applied to the vertical plates leads the

voltage applied to the horizontal plates by an angle



, a pat-

tern such as the one at right results. The phase difference

can be found by taking the ratio of the horizontal intercept

to the maximum horizontal deflection. However, twice the

values provide more accuracy. The phase shift is now calcu-

lated



= arcsin(a/b).

Lissajous patterns may be used to compare the frequencies

of voltages from two separate signal sources. If these are

close to the same frequency, the pattern will slowly change

back and forth from an ellipse to a straight line each half

cycle of difference in frequency. For any stationary pattern, the ratio between the two frequen-

cies may be determined by counting the number of pattern tangencies along the horizontal and

vertical axes. The ratio of vertical to horizontal frequency (Y:X) equals the number of horizontal

tangencies divided by the number of vertical tangencies. Lissajous patterns for three frequency

ratios follow.

 

sin





1 2 ... 61 62 63 64 65 66 67 68 69 70 71 72 73

Sin comentarios

BK Precision 4011A Instrucciones de operaciones Pagina 66