BASIC INSTRUMENTS - oscilloscopes An oscilloscope is an instrument that allows observation of constantly varying signal voltages, usually as a two- dimensional graph of one or more electrical potential differences using the vertical or 'Y' axis, plotted as a function of time, (horizontal or 'x' axis).

TYPES OF WAVEFORMS WAVEFORM MEASUREMENTS OSCILLOSCOPE CONTROLS Vertical controls Horizontal controls X-Y Mode OSCILLOSCOPE PROBES Passive Probes Active Probes

TYPES OF WAVEFORMS Sinewave Pulses Triangular or Sawtooth Wave A sudden change in the amplitude of the signal and back to the previous value Square or Rectangular Wave

Waveform measuremens AMPLITUDE Measured from the maximum peak to the minimum peak of the voltage (peak-to-peak voltage) Can also be useful to measure the RMS voltage PERIOD AND FREQUENCY A period, T : amount of time the signal takes to complete one cycle and it is expressed in seconds A frequency: number of times the signal repeats itself in one unit of time (1/T) unit is Hertz (Hz) PHASE SHIFT When you have two similar waveforms, the oscilloscope can measure the time difference between them. This is measured in degrees or radians.

RISE TIME Time for the signal to go from 10% to 90% of its peak-to-peak voltage. But the percentage can be changed arbitrarily FALL TIME Similarly, the time for the signal to go from 90% to 10% of its peak- to-peak voltage.

Determine the pulse amplitude, frequency, rise time and fall time of the waveform in the figure below pulse amplitude = 4 x 2 V = 8V T = 5.6 x 5 μs /div = 28 μs Frequency, f = 1/T = 1/28 μs = 35.7 kHz rise time, tr = (0.5 ) x ( 5 μs /div ) = 2.5 μs

Find the phase difference between the two sine waves as shown below. From the figure, observe that 1 complete cycle takes 8 divisions = 360 One division = 45  The phase difference = 1.4 x 45  = 63

Oscilloscope controls VERTICAL CONTROLS Position: Controls vertical positioning of oscilloscope display. DC and AC Coupling: DC coupling is the most used position on a scope because it allows the scope to display both AC and DC voltage signals present in the circuit. When AC coupling is selected, a capacitor is placed into the meter lead circuit, which effectively blocks all DC voltage signals but allows the AC portion of the signal to pass and be displayed

REF: http://hackaday.com/2014/11/26/scope-noob-probing-alternating-current/

2 V DC offset 0 V DC offset

HORIZONTAL CONTROLS Position: Controls horizontal positioning of oscilloscope display. Controls the time scale and position. 50 Hz  0.02 s 0.02 / 4 = 5 ms / div 100 Hz  0.01 s 0.01 / 8 = 1.25 ms / div

X-Y MODE

X-Y Mode is generally used to find out what is the phase difference between two waveforms. This measurement technique involves in putting one signal into the vertical system as usual and then another signal into the horizontal system The waveform that results from this arrangement is called a Lissajous pattern Only focus on signals with same ratio frequency

2. At 45 1. At 0 3. At 90 4. At 135 5. At 180

Sin  = Y1 / Y2 = X1 / X2 For example, a circle shape: Y2 = Y1 Hence, sin-1 (Y1 / Y2 ) =  sin -1 (1) = 90  X2 = X1

What if the amplitude of one of the signal is higher but the frequency between them stays the same? Y2 = Y1 The phase difference is still 90 But the ratio between Y and X equal to ratio of amplitudes between the two waveforms X2 = X1 REF: http://lissajousfigures.tk/

Oscilloscope probes Test leads are likely to pick up interference or noise, so they are not suitable for low level signals. Furthermore, the leads have a high inductance, so they are not suitable for high frequencies.

So to solve this, we use coaxial cables The coaxial cable consists of an insulated central conductor surrounded by a braided circular conductor which is covered by an outer layer of insulation The central conductor carries the input signal, and the circular conductor is grounded so that it acts as a screen to help prevent unwanted signals being picked up by the oscilloscope input.

Using the coaxial cable, oscilloscope probes may be categorized into two main types, and they can fall into one of two main areas: Passive oscilloscope probes: This type of probe is the one that is in most widespread use. It only includes passive elements and may provide 1:1, i.e. straight through connectivity from the point under test, to the scope input. Other types may provide a defined degree of attenuation. 1X scope probe ( 1: 1 attenuation ratio ) The input impedance of the oscilloscope at the front panel is typically Ri in parallel with Ci. The coaxial cable connecting the probe to the oscilloscope has a capacitance (Ccc) (typically 90 -100 pF) which can overload a high-frequency signal source. Hence, this probe is suitable to be used for signals from 6 MHz to 10 MHz

The value of Ri and Ci can be found at the front panel. Value of Ri is normally 1 M and value of Ci ranges from 15 – 30 pF

At high frequency or high impedance signal, loading effect occurs At high frequency or high impedance signal, loading effect occurs. Basically what happens is that the output is no longer a correct representation of the input waveform The total impedance offered by the coaxial cable and the oscilloscope input should always be much larger than the signal source impedance. When this is not the case, the signal is attenuated and phase shifted when connected to the oscilloscope. f3db 1 Vin / Vout 0.707

10X scope probe ( 10: 1 attenuation ratio ) Hence, the 10X scope probe is introduced in order to control the attenuation factor. 12.2 pF 90 pF 20 pF Time constant, RC = C1 x 9 M 1.1 x 10-4 = C1 x 9 M C1 = 12. 2 pF Time constant, RC = (20 + 90) pF x 1 M RC = 1.1 x 10-4 = 110 ms

Example Xcc = 50  Total impedance = 450  Calculate the capacitance of the adjustable capacitor if the capacitance of the coaxial cable is 106 pF and given that the reactance is 50  Answer = 11.8 pF

It is important that every probe be correctly adjusted when it is first connected for use with a particular oscilloscope - CALIBRATION Value of adjustable capacitor is too low Value of adjustable capacitor is too high It is generally accepted that for general-purpose mid-to-low-frequency (less than around 500-MHz) measurements, the 10:1 probe is the most suitable option.

The factor of 10 loss in voltage is not a problem as long as the voltage that is being measured is not so small that dividing it by 10 makes it unreadable by the scope. This means that the scope's sensitivity and the signal voltage may be factors in deciding whether to use a 10:1 probe.