# Analogue Oscilloscopes and Measurements Tutorial

MEASUREMENT PERIOD AND FREQUENCY AC WAVEFORMS

The oscilloscope is used for the measurement period(T) and the frequency(f) of an AC waveform. The period of a waveform is the time required for one complete cycle, Figure 1. Knowing the period of a signal, the frequency can be calculated using the relationship:

f = 1 / T.

The first step for the measurement of frequency is to apply the alternating waveform to the input of the oscilloscope (vertical deflection), the switch coupling entry must be set to AC, then adjust the selector scan (sweep selector) so as to obtain and display the waveform on the screen, and we calculate from the horizontal divisions the time required for a period. The frequency is calculated from the relationship

f = 1 / T.

Figure 1.

Figure 2.

Example. Figure 2 shows a waveform as illustrated in the screen of an oscilloscope, to which the selector is set to scan 10msec/div. The period is calculated by counting the number of subdivisions. In this case the number of divisions for a full period is 4, so the period is:

So the frequency is:

OSCILLOSCOPE BANDWIDTH

Figure 3.

The bandwidth of an oscilloscope determines the range of frequencies that can accurately portray on screen. As the bandwidth is greater, the greater is the range of frequencies that can be observed without distortion from the oscilloscope. Note that the bandwidth is given for sinewave signals. So a 60MHz oscilloscope will display a sinusoidal signal of 60 MHz with an attenuation of-3dB or 0.707. Oscilloscopes have zones crossing frequency range from 0Hz (DC) to a GHz or more. Figure 3 shows the bandwidth frequency of a single pulse of 20 MHz.

OSCILLOSCOPE RISE TIME

Figure 4.

The rise time it takes for an oscilloscope or a square-wave signal to rise from 10% to 90% of its maximum value, is called RISE TIME, which is shown in figure 4. The vertical amplifiers in an oscilloscope should have less rise time from the rise of the pulse we want to measure. If we know the bandwidth of an amplifier, the rise time TR is given by the relationship:

TR = 0,35/BW or

TR(nsec) = 350/BW(MHz)

The above equation gives the rise time in nsec, where BW is in MHz.
Eg the rise time of an oscilloscope (ie the rise time of the vertical amplifier) of 60 MHz is:

TR(nsec) = 350/60 = 350/60

TR(nsec) = 5,8nsec

That is a signal to rise from 10% to 90% of its maximum value at 5,8nsec. It turns out that when a signal has a certain rise time (all signals have a rise time) pass through the amplifier of the oscilloscope, the signal displayed on the screen will have a new rise time given by the relation:

Where T(signal) is the rise time of the signal applied to the input of the oscilloscope.

Where T(pulse) the rise time of the oscilloscope and TR is the rise time of the signal displayed on the screen.

Example: The signal to be measured is square with a rise time TR= 5,8nsec, and the oscilloscope used is of 60MHz, ie it has TR = 5,8nsec, then the signal displayed on the screen will have a rise time that is given by:

The signal is distorted on the screen (it has a longer rise than was the input of the oscilloscope). Note that the rise time of the signal when passed through the oscilloscope was increased by 40%. For a good illustration without much distortion the rise time of the oscilloscope should be smaller than the rise time of the signal. Eg. if the rise time of the oscilloscope is 7 times less than the time period of the upward signal to the input of the oscilloscope, then the rise time of the signal on the screen is only 1% greater than the rise time of the signal at the input.