MPO6002EDU Series Oscilloscope Guide

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Multiply or Divide

When you select the multiply or divide math function, the Source 1 and Source 2 values are multiplied or divided

point by point, and the result is displayed.

The divide by zero case places holes (that is, zero values) in the output waveform.

Multiply is useful for seeing power relationships when one of the channels is proportional to the current.

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FFT Operation

Using the Fast Fourier Transform (FFT), the FFT (Magnitude) math function displays the magnitudes of the

frequency content that makes up the source waveform. The FFT takes the digitized time record of the

specified source and transforms it to the frequency domain.

The source of the FFT math functions can be any analog input channels.

The horizontal axis of FFT math functions is frequency (Hertz). For the FFT (Magnitude) math function,

the vertical axis is in decibels when Logarithmic vertical units are selected or V RMS when Linear vertical

units are selected.

Use the FFT (Magnitude) function to find crosstalk problems, to find distortion problems in analog waveforms

caused by amplifier non-linearity, or for adjusting analog filters.

To display a FFT waveform:

1 Press the [Math] key. Then, press the Operator softkey and turn the V0 knob to select the math function

you want to display. Then, either push the V0 knob or press the Operator softkey again to display the selected

math function.

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* Source - selects the source for the FFT.

* Span/Center - this pair of softkeys let you define the displayed frequency range.

   Center specifies the frequency at the center vertical grid line of the display.

   Span specifies the frequency range represented by the width of the display. Divide span by 10 to calculate

             the frequency scale per division.

To set desired values, press the softkey and turn the V0 knob to adjust.

* Offset - press this softkey and turn the V0 knob to adjust the math waveform’s vertical offset.

* Scale - press the softkey and turn the V0 knob to adjust the math waveform’s vertical scale.

* Vertical Units - You can select Lograithmic (dB) or Liner (V RMS).

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* Window - selects a window to apply to your FFT input signal:

-Rectangule - good frequency resolution and amplitude accuracy, but use only where there will be no leakage

effects. Use on self-windowing waveforms such as pseudo-random noise, impulses, sine bursts, and decaying

sinusoids.

-Hanning - window for making accurate frequency measurements or for resolving two frequencies that are close

together.

-Hamming - it is a little bit better frequency resolution than Hanning. Use on transient or short pulse, the signal

levels before and after the multiplication are rather different.

-Blackman Harris - window reduces time resolution compared to a rectangle window, but improves the capacity

to detect smaller impulses due to lower secondary lobes.

-Bartlett - window is simillar to the Hanning window in that it is good for making accurate frequency measurements,

but its higher and wider secondary lobes make it not quite as good for resolving frequencies that are close together.

-Flat Top - window for making accurate amplitude measurements of frequency peaks.

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*FFT Only - when turn on, only FFT is displayed on the screen. When turn off, both FFT and its source

waveform are displayed.

*Auto Scale - sets the vertical scale and offset of the operation results to the optimal values that will cause

the entire available spectrum to be displayed.

NoteScale and offset considerations

If you do not manually change the FFT scale or offset settings, when you turn the horizontal scale knob, the

span and center frequency settings will automatically change to allow optimum viewing of the full spectrum.

If you do manually set scale or offset, turning the horizontal scale knob will not change the span or center

frequency settings, allowing you see better detail around a specific frequency.

Pressing the FFT Auto Scale softkey will automatically rescale the waveform’s vertical scale and offset.

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2 To make cursor measurements, press the [Cursors] key and set the Source softkey to Math.

Use the AX and BX cursors to measure frequency values and difference between two frequency values (ΔX).

Use the AY and BY cursors to measure amplitude in dB and difference in amplitude (ΔY).

3 To make other measurements, press the [Meas] key and set the Source softkey to Math.

You can make maximum measurements on the FFT waveform. You can also find the frequency value at the

first occurrence of the waveform maximum by using the X at Max Y measurement.

The following FFT (Magnitude) spectrum was obtained by connecting a 2.5 V, 208.5 kHz square wave to

channel 1. Set the horizontal scale to 50 ?s/div, vertical sensitivity to 2 V/div, Units/div to 20 dBV, Offset to

-20.0 dBV, Center frequency to 1.25 MHz, frequency Span to 250kHz, and window to Hanning.

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FFT Measurement Hints

When frequency span is at maximum, all points acquired for the FFT record are displayed. Once the FFT

spectrum is displayed, the frequency span and center frequency controls are used much like the controls

of a spectrum analyzer to examine the frequency of interest in greater detail. Place the desired part of the

waveform at the center of the screen and decrease frequency span to increase the display resolution.

As frequency span is decreased, the number of points shown is reduced, and the display is magnified.

While the FFT spectrum is displayed, use the [Math] and [Cursors] keys to switch between measurement

functions and frequency domain controls in FFT Menu.

Decreasing the effective sampling rate by selecting a greater time/div setting will increase the low frequency

resolution of the FFT display and also increase the chance that an alias will be displayed. The resolution of

the FFT is the effective sample rate divided by the number of points in the FFT. The actual resolution of the

display will not be this fine as the shape of the window will be the actual

limiting factor in the FFTs ability to resolve two closely space frequencies. A good way to test the ability of the

FFT to resolve two closely spaced frequencies is to examine the sidebands of an amplitude modulated sine

wave.

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FFT Aliasing

When using FFT, it is important to be aware of frequency aliasing. This requires that the operator have some

knowledge as to what the frequency domain should contain, and also consider the sampling rate, frequency

span, and oscilloscope vertical bandwidth when making FFT measurements.

Note Nyquist Frequency and Aliasing in the Frequency Domain

The Nyquist frequency is the highest frequency that any real-time digitizing oscilloscope can acquire without

aliasing. This frequency is half of the sample rate. Frequencies above the Nyquist frequency will be under

sampled, which causes aliasing. The Nyquist frequency is also called the folding frequency because aliased

frequency components fold back from that frequency when viewing the frequency domain.

Aliasing happens when there are frequency components in the signal higher than half the sample rate.

Because the FFT spectrum is limited by this frequency, any higher components are displayed at a lower

(aliased) frequency.

Because the frequency span goes from ≈ 0 to the Nyquist frequency, the best way to prevent aliasing is to make

sure that the frequency span is greater than the frequencies of significant energy present in the input signal.

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FFT DC Value

The FFT computation produces a DC value that is incorrect. It does not take the offset at center screen into

account. The DC value is not corrected in order to accurately represent frequency components near DC.

FFT Spectral Leakage

The FFT operation assumes that the time record repeats. Unless there is an integral number of cycles of the

sampled waveform in the record, a discontinuity is created at the end of the record. This is referred to as leakage.

In order to minimize spectral leakage, windows that approach zero smoothly at the beginning and end of the

signal are employed as filters to the FFT. The FFT Menu provides these windows: Rectangule, Hanning,

Hamming, Blackman-Harris, Bartlett, and Flat Top.

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Integrate

ò dt (integrate) calculates the integral of the selected source. It shows the accumulated amount of change.

You can use integrate to calculate the energy of a pulse in volt-seconds or measure the area under a waveform

by measuring the difference in the integrate function value across the pulse or waveform.

ò dt plots the integral of the source using the "Trapezoidal Rule". The equation is:

               n

In = co + Δ t ∑yi

i=0

Where:

? I = integrated waveform.

? Δt = point-to-point time difference.

? y = channel 1, 2, 3, 4, or Math (lower math function) data points.

? co = arbitrary constant.

? i = data point index.

The integrate operator provides an Offset softkey that lets you enter a DC offset correction factor for the input signal.

Small DC offset in the integrate function input (or even small oscilloscope calibration errors) can cause the integrate

function output to "ramp" up or down. This DC offset correction lets you level the integrate waveform.