14 Subject to change without noticemay result as the input range of one or both amplifiers maybe exceeded.Another precondition for obtaining true displays is the use oftwo identical probes at both inputs. But note that normal probetolerances (percent) will cause the CM rejection to be expectedto be rather moderate. In order to obtain the best possible re-sults proceed as follows: First adjust both probes as carefullyas possible, then in Add mode select the same sensitivity atboth inputs and connect both probes to the output of a pulsegenerator with sufficient amplitude to yield a good display. Re-adjust one (!) of the probe adjustment capacitors for a minimumof over or undershoot. As there is no adjustment provided withwhich the resistors can be matched a residual pulse signal willbe unavoidable. When making difference measurements it isgood practice to first connect the ground cables of the probesto the object prior to connecting the probe tips. There may behigh potentials between the object and the scope. If a probe tipis connected first there is danger of overstressing the probe or/and the scope inputs! Never perform difference measurementswithout both probe ground cables connected.XY operationThis mode is accessed by VERT/XY 32 > XY. In analog mode thetimebase will be turned off. The channel 1 signal will deflect in Xdirection (X INP. = horizontal input), hence the input attenuators,the variable and the POSITION 1 control will be operative. TheHORIZONTAL control will also remain functional.Channel 2 will deflect in Y direction.The x10 magnifier will be inoperative in XY mode. Please note thedifferences in the Y and X bandwidths, the X amplifier has a lower–3 dB frequency than the Y amplifier. Consequently the phasedifference between X and Y will increase with frequency.In XY mode the X signal (CH1 = X INP). cannot be inverted.The XY mode may generate Lissajous figures which simplifysome measuring tasks and make others possible:– Comparison of two signals of different frequency or adjust-ment of one frequency until it is equal to the other andbecomes synchronized.– This is also possible for multiples or fractions of one of thefrequencies.Phase measurements with Lissajous figuresThe following pictures show two sine waves of equal amplitudeand frequency but differing phase.Calculation of the phase angle between the X and Y signals (afterreading a and b off the screen) is possible using the followingformulas and a pocket calculator with trigonometric functions.This calculation is independent of the signal amplitudes:Please note:– As the trigonometric functions are periodic, limit the cal-culation to angles <90 degrees. This is where this functionis most useful.– Do not use too high frequencies,because, as explained above, thetwo amplifiers are not identical,their phase difference increaseswith frequency. The spec gives thefrequency at which the phase diffe-rence will stay <3 degrees.– The display will not show which of the two frequencies doeslead or lag. Use a CR combination in front of the input of thefrequency tested. As the input has a 1 MΩ resistor it will besufficient to insert a suitable capacitor in series. If the ellipseincreases with the C compared to the C short circuited thetest signal will lead and vice versa. This is only valid <90degrees. Hence C should be large and just create a barelyvisible change.If in XY mode, one or both signals may disappear, showing onlya line or a point, mostly very bright. In case of only a point thereis danger of phosphor burn, so turn the intensity down imme-diately; if only a line is shown the danger of burn will increasethe shorter the line is. Phosphor burn is permanent.Measurement of phase differences in dual channelYt modePlease note: Do not use ”alternate trigger“ because the timedifferences shown are arbitrary and depend only on the respec-tive signal shapes! Make it a rule to use alternate trigger onlyin rare special cases.The best method of measuring time or phase differences is usingthe dual channel Yt mode. Of course, only times may be read offthe screen, the phase must then be calculated as the frequencyis known. This is a much more accurate and convenient methodas the full bandwidth of the scope is used, and both amplifiersare almost identical. Trigger the time base from the signalwhich will be the reference. It is necessary to position bothtraces without signal exactly on the graticule center (POSITION1 and 2). The variables and trigger level controls may be used,this will not influence the time difference measurement. Forbest accuracy display only one period at high amplitude andobserve the zero crossings. One period equals 360 degrees.It may be advantageous to use ac coupling if there is an offsetin the signals.In this example t = 3 cm and T = 10 cm, the phase difference indegrees will result from:5 3ϕ° = — · 360° = — · 360° = 108°T 10or in angular units:t 3arc ϕ° = — · 2π = — · 2π = 1,885 radT 10Very small phase differences with moderately high frequenciesmay yield better results with Lissajous figures.However, in order to get higher precision it is possible to switchto higher sensitivities after accurately positioning at graticuleO p e r a t i n g m o d e s o f t h e v e r t i c a l a m p l i f i e rt = horizontal spacing of thezero transitions in divT= horizontal spacing for oneperiod in div0° 35° 90° 180°a basin ϕ = —bacos ϕ = 1 – (—)2baϕ = arc sin —b