# Measurement of frequency phase relationship using cro and lissajous figures

### Frequency and Phase Measurement | AC Metering Circuits | Electronics Textbook

Frequency Measurements Using Lissajous Figures Lissajous We can tell that oscilloscope can measure the phase and thefrequency REFERENCE 1. . Thismode can be used to measure phase or frequency relationships. Common frequency and shape. Method: • Display similar points on the two waveforms. Figure 1. Dual-channel display. With either method, the Measuring relative phase between oscilloscope traces using the Lissajous. (ellipse) method. ○Measurement of Oscilloscope. ○Lissajous Pattern (LP) methods. OUTLINE Phase relationship Using the scale setting of the scope and the signal.

Electrical resistor Materials used in precision Resistors Lissajous pattern with equal frequency voltages and zero phase shift. This is shown in the below figure.

An ellipse is also obtained when unequal voltages of the same frequency are applied to the CRO. This textbook "Electrical and Electronics Measurements by S.

### Lissajous Patterns in CRO for Measurement of Phase & Frequency

Chand" is the best in industry. Grab it now for very less price. A number of conclusions can be drawn from the above discussions. When two sinusoidal voltages of the same frequency are applied: If the Y voltage is larger, an ellipse with vertical major axis is formed while if the X plate voltage has a greater magnitude, the major axis of the ellipse lies along the horizontal axis.

Regardless of the two amplitudes of the applied voltages, the ellipse provides a simple means of measuring phase difference between two voltages. Referring to figure, the sine of the phase angle between the voltages is given by: For convenience, the gains of the vertical and horizontal amplifiers are adjusted so that the ellipse fits exactly into a square marked by the lines on the graticule. If the major axis of the ellipse lies in the first and third quadrants i.

## Frequency and Phase Measurement

When the major axis of ellipse lies in second and fourth quadrants i. Frequency measurement of cro or cathode ray oscilloscope: Lissajous patterns may be used for accurate measurement of frequency. The signal, whose frequency is to be measured, is applied to the Y plates. An accurately calibrated standard variable frequency source is used to supply voltage to the X plates, with the internal sweep generator switched off.

The standard frequency is the adjusted unit the pattern appears as a circle or an ellipse, indicating that both signals are of the same frequency. Where it is not possible to adjust the standard signal frequency to the exact frequency of the unknown signal, the standard if adjusted to multiple or a submultiple of the frequency of the unknown source so that the pattern appears stationary.

By way of a little background reminder, phase difference, or phase angle, is the difference in phase between the same points, say a zero crossing, in two different waveforms with the same frequency.

### Lissajous Patterns of CRO or Cathode Ray Oscilloscope

A common example is the phase difference between the input signal and output signal after it passes through a circuit, cable, or PC board trace. A waveform with a leading phase has a specific point occurring earlier in time than the same point on the other signal.

That would be the case of when a signal passes through, a capacitor: Conversely, a waveform with lagging phase has a specific point occurring later in time than the other paired signal waveform. The time phase relationship between two sine waves can of course be measured from a time domain plot such as figure 1.

The software scans the waveforms looking for the time points where they cross their average value zero crossing with DC offset removed. It then uses those time points to report frequency, period, phase, delay, duty-cycle etc.

Noise and jitter will introduce errors in the results. Figure 1 Time plot of two sine waves For those old timers who have started out their careers using an analog oscilloscope, you probably remember using the classic Lissajous pattern to measure the phase difference of two sine waves.

In this figure, the waveform on channel A provides the horizontal or X displacement.

## Lissajous Patterns of CRO or Cathode Ray Oscilloscope

Channel B provides the vertical or Y deflection. The Lissajous pattern indicates the phase difference by the shape of the X-Y plot. It will only be a true circle if the amplitudes are equal.