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A Lissajous patterns on a Cathode Ray Oscilloscope (CRO) has 8 vertical maximum values and 4 horizontal maximum values. The frequency of the horizontal input is 1600 Hz. Determine the frequency of the vertical input?
800 Hz
400 Hz
200 Hz
600 Hz
800 Hz
The frequency ratio of the vertical and horizontal inputs on a CRO is determined by the ratio of the number of tangencies at the horizontal edges to those at the vertical edges of the Lissajous pattern. Given 8 vertical tangencies (NvтАЛ=8) and 4 horizontal tangencies (NhтАЛ=4), the frequency ratio is inversely proportional to these values.
The frequency ratio of the vertical and horizontal inputs on a CRO is determined by the ratio of the number of tangencies at the horizontal edges to those at the vertical edges of the Lissajous pattern. Given 8 vertical tangencies (NvтАЛ=8) and 4 horizontal tangencies (NhтАЛ=4), the frequency ratio is inversely proportional to these values.
fhтАЛfvтАЛтАЛ=NvтАЛNhтАЛтАЛ тАФ where fvтАЛ and fhтАЛ are vertical and horizontal frequencies, and NhтАЛ,NvтАЛ are the number of tangencies.
When two sinusoidal signals are applied to the vertical and horizontal deflection plates of a CRO, the resulting trace is a Lissajous figure. The frequency ratio is given by fhтАЛfvтАЛтАЛ=NvтАЛNhтАЛтАЛ, where NhтАЛ is the number of intersections with a horizontal line and NvтАЛ is the number of intersections with a vertical line.
The number of tangencies is counted by drawing a straight line that does not pass through an intersection point.
For this problem, NvтАЛ=8, NhтАЛ=4, and fhтАЛ=1600┬аHz.
Substituting the values, 1600fvтАЛтАЛ=84тАЛ=0.5, resulting in fvтАЛ=800┬аHz.
Non-contact measurement method for unknown frequencies.
Highly accurate when the ratio is an integer or simple fraction.
Becomes difficult to interpret for complex non-integer frequency ratios.
Requires stable phase relationship between input signals.
Calibration of signal generators.
Measurement of frequency ratios in communication systems.
Determination of phase shift between two identical frequency signals.
The confusion between numerator and denominator in the ratio NvтАЛNhтАЛтАЛ is the primary cause for error in this calculation.
Option B (400 Hz) would result if one erroneously inverted the ratio calculation as NhтАЛNvтАЛтАЛ.
A is correct тАФ The frequency of the vertical input is calculated as fvтАЛ=fhтАЛ├Ч(NvтАЛNhтАЛтАЛ)=1600├Ч(84тАЛ)=800┬аHz.
Always remember the simple mnemonic: the frequency ratio is the inverse of the tangency ratio, fhтАЛfvтАЛтАЛ=Vertical┬аTangenciesHorizontal┬аTangenciesтАЛ.
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