13. APPLICATION OF X-Y OPERATION* Phase MeasurementT h e X - Y operation can be used for phase measurement.Typical application covers measurement of phase distortionin circuits designed to produce a certain phase shift and au-dio amplifiers.Distortion amplitude can be measured at the same time.Phase measurement is made as follows:1) Apply sine w a v e with little distortion to the audio cir-cuit to be tested.2) Set the signal generator output to the normal operationlevel of the circuit to be tested. Observe output of thecircuit on the C R T . If e x c e s s i v e signal is input to thecircuit, the displayed waveform is clipped; reduce thesignal level in s u c h a c a s e .3) Connect the C H 1 probe to the output of the circuit tobe tested.4) Select X - Y of the H O R I Z O N T A L MODE s w i t c h e s .5) Connect the C H 2 probe to the input of the circuit tobe tested.6) Adjust channel-1 and channel-2 gains to obtain the Lis-sajous' pattern of a proper size.7) Fig. 51 s h o w s typical examples. If the t w o signals areequal in phase, the Lissajous' pattern is a straight di-agonal line. It is at 4 5 ° if the vertical and horizontalgains are set to the same level. A 9 0 ° phase shiftproduces a circular Lissajous' pattern. Phase shift moreor less than 9 0 ° produces an elliptical Lissajous' pat-tern. T h e amount of actual phase shift is calculated asfollows:Calculation of phase difference:DSin </> = Where 0 = phase angleAFig. 50Fig. 5 1 Typical Display of Phase Measurement* Frequency MeasurementIn addition to the phase measurement, frequency can bemeasured from the Lissajous' pattern.1) Apply sine w a v e of known frequency to the C H 2 inputconnector of the oscilloscope. Select X - Y of theH O R I Z O N T A L MODE s w i t c h e s .2) Connect the C H 1 probe to the unknown signal.3) Adjust the channel-1 and channel-2 gains.4) T h e resulting Lissajous' pattern s h o w s the ratio be-t w e e n the t w o frequencies.U n k n o w n f r e q u e n c y t o v e r t i c a l i n p u tR a t i o o f u n k n o w nR e f e r e n c e f r e q u e n c y t o h o r i z o n t a l i n p u tt o r e f e r e n c eFig. 5 2 Lissajous' Pattern used for FrequencyMeasurement4 0N o a m p l i t u d ed i s t o r t i o nN o p h a s ed i f f e r e n c eN o a m p l i t u d ed i s t o r t i o nW i t h p h a s ed i s t o r t i o nW i t h a m p l i t u d ed i s t o r t i o nN o p h a s ed i f f e r e n c eW i t h a m p l i t u d ed i s t o r t i o nW i t h p h a s ed i f f e r e n c eN o a m p l i t u d ed i s t o r t i o nW i t h 1 8 0 °p h a s ed i f f e r e n c eN o a m p l i t u d ed i s t o r t i o nW i t h 9 0 °p h a s ed i f f e r e n c eI : !6 : 1