PHYS1004 S2022 Oscilloscope Experiment
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3. Oscilloscope Experiment
In this experiment, you will become familiar with the operation of function generators and digital oscilloscopes. You will learn the basics of how to obtain a measurement and how to interpret the properties of an electric circuit by analyzing the oscilloscope display. You will explore the behavior of resistors, capacitors, and diodes within an alternating current (AC) environment and study the principles of operation of a half-wave rectifier circuit to convert AC voltage to DC voltage.
An oscilloscope (Figure 1) is an instrument that measures the potential difference (voltage) across a component as a function of time. Oscilloscopes are used to record data from electrical sensors, to visualize waveforms generated by instruments and to troubleshoot and fix electronic devices. In troubleshooting devices, it is typically important to understand the concurrent behavior of multiple devices at the same time, and so modern oscilloscopes are capable of displaying and storing information for two or more signals (called channels) at the same time.
Figure 1. Rigol DS1052E digital oscilloscope.
Taking a Measurement
On an oscilloscope display, you can see a two-dimensional graph (trace). The X-axis (horizontal) represents the time and the y-axis (vertical) represents the voltage (see Figure 1). The scale of each axis can be adjusted using the vertical and horizontal controls. This means that is possible to alter what the trace on the screen looks like by ‘zooming’ in and out along both axes.
An example of this is given in Figure 2. In the left image the vertical scale is too small (500 mV), making the image too ‘zoomed in’ and not allowing us to see the full height (peak-to-peak voltage, or Vpp) of the trace. Therefore, it is necessary to ‘zoom out’ by making the scale larger (1.00 V). A similar issue can be observed on the horizontal axis. The original scale is too small (2.000 ms) and does not allow for observation of a full period (T) of the trace. Therefore, it is necessary to increase the scale (10.0ms) to ‘zoom out’ .
Figure 2. Adjustment of the oscilloscope display to show a peak-to-peak height of 1 full period of the signal trace.
Once a trace has been adjusted to display a peak-to-peak height of 1 full period (Figure 2, right) a reading can be taken from the screen by counting the divisions (div) and multiplying by the scale. The scale for each axis is given at the bottom of the display and represents the number of volts and seconds in a single division (a square) on the screen. Taking a reading means counting the number of divisions for a peak-to- peak (Vpp) voltage and number of divisions for a single period (T) and then using the scale to convert those numbers into values with appropriate units (volts and seconds, respectively). See the example below (Figure 3).
Vpp, peak-to-peak voltage
Vpp = 4 div × = 4.00 V
T = 6 div × = 60.0 mS
Figure 3. Example of obtaining a measurement from the trace displayed on the oscilloscope screen.
It is important to note however, that an oscilloscope is only a measuring tool. Therefore, adjusting the image of the trace on the screen does not change the inherent characteristics of the signal itself. The signal characteristics are determined by the source of the signal, not by the tool used to measure it.
One way to check whether an oscilloscope is functioning correctly is to compare the measurements from its display to known values. However, since the display is a two-dimensional graph, this type of verification would need to be done for both the voltage and the time axes if one wants to be sure that the oscilloscope is working properly. The most convenient way of obtaining known values with which to compare the display readings is to connect the oscilloscope to a function generator. Such a generator would allow one to have control over the frequency and the voltage of the signal that will be fed into the oscilloscope for analysis.
Properties of a sinusoidal waveform
Analyzing the resulting waveform from an oscilloscope provides useful information about the measured signal. One can determine a variety of characteristics including: minimum and maximum voltages, peak- to-peak voltage (Vpp), root mean square voltage (VRMS ), signal frequency (f), period (T), etc.
Figure 4. Characteristics of a sine waveform.
Frequency and Period
The period, T, is the time between corresponding phase points of two consecutive cycles of a periodic
waveform. The frequency, f , of the signal can be calculated as
f = (3. 1)
The oscilloscope can measure differences in time between points in an oscillating cycle or alternatively, some digital oscilloscopes allow a direct measurement of the frequency using onboard utilities.
Peak-to-peak voltage (Vpp) and Root Mean Square Voltage (VRMS)
Sinusoidal waveforms are characterized by the peak-to-peak voltage (Vpp ), which is the difference between the maximum and the minimum of the function (see Figure 3). The amplitude of the waveform is half of the peak-to-peak voltage and the voltage function is given by
V(t) = sin ( t) (3.2)
During the lowest point (trough) of the waveform, current from the power supply is traveling in the opposite direction than during the highest point (peak) of the waveform. However, power usage in any attached resistors in the circuit is being used regardless of the direction of current flow. As a result, we are generally interested in the average power (Pavg ) dissipated by the circuit with resistance (R) in terms of the time-averaged value of the voltage, known as the Root Mean Square Voltage (VRMS ). The relationship between these is:
Pavg = (3.3)
To calculate VRMS , we take the square root of the average of the square (hence: root – mean – square) of the function over a period T:
VRMS = √ ∫T (V(t))2 dt = √ ∫T ( sin ( t))2 dt
For a sinusoidal oscillating function, this reduces to a simple relationship:
Vrms is the voltage that is measured by a voltmeter (or a multimeter). For example, the standard voltage of a wall outlet is 120 Volts, this represents Vrms =120 V. Vrms is also the quantity used when you want to calculate power consumption, for which we can use P=IVrms . When a certain voltage is being set for signal from a function generator, it is the Vrms voltage that we are dealing with.
AC to DC conversion
Alternating current (AC) is the type of current coming from the power outlet, while direct current (DC) is used in most electronic devices. Alternating current (AC) forms the backbone of our technology – it is easy to produce via the electromotive force, and compared to direct current (DC), it is cheaper to transmit through power lines over great distances. However, direct current is necessary to run electronics. Thus, it is important to be able to convert between the two forms readily.
The simplest AC to DC conversion circuit is called a single-phase, half-wave rectifier. This type of rectifier requires a diode to rectify the current and a capacitor to smooth it out. In order to understand such conversion mechanism, lets review how these components behave:
A diode is an electronic component made with semiconductor materials such as silicon, germanium, or selenium which main function is to allow an electric current to flow in only one direction, the forward direction. When there is a sufficiently positive voltage source applied across the diode (typically a diode will have a 0.7 V constant load on the circuit) in the forward direction, the diode behaves like a wire with effectively zero resistance. But when the voltage applied across it is smaller than the threshold voltage (Vth), or is negative, the diode behaves like a break in the circuit, and no current can pass through it.
indicating the negative side.
In circuit diagrams, the diode is represented as a triangle followed by a vertical line (see Figure b). This triangle can be viewed as an arrow that points in the direction of the transmitted current flow. On an actual diode, there are signs indicating its directional polarity. For the diode used in this lab, a tiny dark band or dot indicates the direction of current flow.
A capacitor is an electronic component that stores electrical energy. Capacitors are made of two metallic plates separated by a dielectric (non-conductive) medium. Some of the most common dielectrics used are mica, ceramic, glass, teflon, air, etc. When the two conductors inside a capacitor experience a potential difference, an electric field builds across the dielectric, causing a net positive charge to collect on one plate and a net negative charge to collect on the other plate.
In a way, capacitors behave like a battery, as both store charge. However, the main difference between them is that a capacitor can discharge entirely in a fraction of a second, where a battery would take minutes to completely discharge. This is advantageous for a variety of applications in electronics.
Half-wave rectifier circuit
A single-phase half wave rectifier circuit is shown in Figure 6. The function generator provides a sinusoidal voltage, acting like an AC power supply. The diode blocks the lower portion of the signal, allowing only the positive portion to pass. This charges the capacitor rapidly since the resistance through the diode and the power supply is small. When the applied voltage falls below the capacitor voltage, the capacitor will discharge through the load resistor. It cannot discharge through the power source because the diode blocks current in that direction.
Figure 6. AC/DC conversion circuit (single phase half wave rectifier)
For RC circuits, the capacitor will discharge exponentially
V(t) = V0 e −t/T (3.6)
with a characteristic time constant, T = RC . If that time constant is large enough, then the exponential decay will be very slow, and a DC-like current will be maintained. For a circuit with a R=10 kQ resistor and a C=68 uF capacitor, the time constant for a discharge cycle is close to 0.68 s . This is very long
compared to the period of the 60 Hz sinusoidal voltage, T60 Hz = ≈ 0.0167 s . This means that the
voltage across the capacitor and the resistor will remain almost constant while the diode is blocking the current flow from the power source.
A plot of the voltage behaviour for the different components of the circuit is shown in Figure 7.
Figure 7. Voltage graphs for different components of the circuit during one full cycle.
When the applied voltage from the AC signal reaches the next positive peak, the voltage is momentarily more positive than the capacitor voltage. Current will then rush through the diode and into the capacitor,
quickly re-establishing a maximum peak voltage on the capacitor. Thus, a cycle starts with a fast recharge to the maximum applied voltage followed by a slow, small voltage drop until the next peak arrives. This means the voltage across the capacitor and the resistor remains almost constant while the diode is blocking the current flow from the power source.
The quality of a rectifier depends on how uniform the final output is, i.e. the amount of ripple the DC waveform contains. Ifwe measure the voltage across the capacitor and define VDC to be the average voltage and Vripple to be the peak-to-peak variance of the voltage, the qualityfactor can be defined as
VDC − Vripple
where VDC is the DC voltage (potential from ground) and Vripple is the peak-to-peak voltage of the small ripples you can see when you ‘zoom in’ on the DC waveform. Both quantities can be measured from the oscilloscope display (see Figure 8).
Figure 8. Ripple in the voltage of the AC/DC converter.
Of note, computers require a very high quality factor. Inside the computer, voltage regulator modules further reduce the ripple from the power supply. If a lower quality power supply is used in a computer – one with a larger ripple voltage – the voltage regulator modules need to work harder. This work generates heat, which burns them out faster by causing chemical changes in the components themselves. A major source of component failures in computers is due to poor power supplies.
The following instruments will be used in this experiment:
• Digital Oscilloscope (Rigol DS1052E)
• Function Generator (BK Precision 5 MHz)
• Digital Multimeter (DMM)
• Resistor (10 kQ)
• Capacitor (~50 - 70 uF)
Figure 9. Rigol DS1052E digital oscilloscope.
Several settings adjustments are necessary for ideal measurements of a waveform:
- Adjusting the POSITION of the waveform (left, right, up, down) is useful for centering or otherwise aligning waveforms. This is very important when comparing two waveforms, as all measurements require that the waveforms are aligned correctly.
- It is important that the full signal is visible and takes up the correct portion of the screen to maximize the precision of the measurements. This can be adjusted with the time (HORIZONTAL) and voltage (VERTICAL) SCALE settings.
Changing the scale or position of the waveform does not affect the voltage or time of the signal measurements; it only changes its display.
- The TRIGGER LEVEL is the minimum voltage at which the oscilloscope interprets the measurement as a signal as opposed to noise. If the value is too high or too low, the signal will never cross the trigger threshold and no waveform will be displayed. If it is too close to zero, the oscilloscope might trigger on noise and you could miss the important part of the signal. Remember that the wires in your circuit behave like antennae – you can pick up everything from radio signals to the electric lights in the room!
-If you are unable to display a waveform, make
sure that the cable is plugged in the correct
channel and that the appropriate channel button
is pressed. Pressing on the AUTO button under
RUN CONTROL will typically get a useful
measurement of the waveform, but it may not be
ideal for your purposes. (It just brings you close!).
-With a digital oscilloscope, many measurements can be done automatically. Pushing the Measure button will show you the list of possible measurements. The cursor for selecting a measurement can be controlled using the button at the left of the menu panel.
Part A. Frequency Calibration Check
In this part of the experiment, you will check the calibration of the function generator and oscilloscope by measuring the frequencies on both instruments and testing if fgen = fOSC . The frequencies on our generator extend over a range from 0 to 106 Hz. If the two frequency measurements are consistent and within experimental error, what do you expect the slope and intercept of the fOSC vS. fgen plot to be?
1. Download the Oscilloscope Logger Pro file from Brightspace.
2. Set the generator function control to SINE (~) and adjust the frequency setting to approx. 10 Hz using the COARSE and FINE dials under the FREQUENCY label.
3. Use a coax-to-coax cable to connect the output of the function generator to CH1 on the oscilloscope.
✓ On the oscilloscope display you will see a two dimensional graph. On the y-axis, you have voltage and, on the x-axis, you have time. You can zoom in or out by turning the SCALE knobs.
4. For values between 0 to 106 Hz, record the signal frequency from the generator (fgen ) and from the oscilloscope (fOSC ) with their corresponding reading errors.
✓ Perform thefrequency measurementsfor fgen ~ 100 Hz, 1000 Hz, 10 kHz, 100 kHz, 200 kHz,
400 kHz, 600 kHz, 800 kHz, 1MHz. Note that by simply pressing the next RANGE button on thefunction generator, you increase thefrequency by afactor of ~10.
✓ Press the MEASURE button on the oscilloscope MENU ,select TIME using the menu select buttons at the right of the screen, rotate the scroll dial to select FREQ, and then press it in (until it clicks) to have the measurement displayed at the bottom of the screen.
✓ As you increase thefrequency, you need to adjust the horizontal scale to properly display the waveform.
Part B. Voltage Calibration Check
In this part of the experiment, you will measure the peak-to-peak voltage and the Root Mean Square voltage of an AC signal and confirm the relationship between the two.
Analogous to Part A, if both the generator and the oscilloscope are working properly, if we measure the VrmS voltage from the oscilloscope and from the generator, we expect that Vgen = VoSC . If the two voltage measurements are consistent and within experimental error, what do you expect the slope and intercept of the VoSC vS. Vgen plot to be?
1. Place a T-connector onto the output of the function generator. Connect the DMM to one side of the T- connector using a split BNC cable. Connect a regular BNC cable to the other output of the T-connector and bring this cable to CH1 of the oscilloscope.
✓ When using the DMMfor voltage readings, the red lead of the cable should be connected to the V-Qport and the black one to the common ground (COM).
2. Set the function generator to approximately 60 Hz. Adjust the scale to properly display the waveform.
3. For VrmS values of approximately 0.7 V to 7 V, record the VrmS reading from the DMM (Vgen ) and the Vpp reading from the oscilloscope with their corresponding reading errors. To measure the peak-to- peak voltage on the oscilloscope:
a. Press the MEASURE button on the oscilloscope, and then set the SOURCE to CH1.
b. Select VOLTAGE from the on-screen menu and use the scroll dial to choose the peak-to-peak voltage (Vpp ) option. Press the scroll dial in until it clicks to confirm the selection.
c. Adjust the OUTPUT LEVEL on the function generator and record the peak-to-peak voltage, Vpp ± GVpp , from the oscilloscope.
✓ As you increase the voltage, you may need to adjust the vertical scale on the oscilloscope to properly display the waveform.
✓ Note that VoSC is a rms voltage and must be determined from the Vpp measurements using equation 3.5.
Part C. AC to DC Rectifier Circuit
In this part of the experiment, you will study a half-wave rectifier circuit to convert an AC signal into a DC signal and you will determine the quality factor of such conversion.
Figure 10. Schematics for the AC/DC rectifier circuit.
1. Assemble the circuit shown in Figure 10. The oscilloscope is connected directly to the generator on channel 1 (CH1) and to the resistor within the circuit on channel 2 (CH2).
a. Connect the coaxial T-connector to the OUTPUT ofthe function generator. One end goes to CH1 on the oscilloscope (use coax-coax cable), the other end goes to the circuit board (use coax-coax cable).
b. Connect the diode, capacitor and resistor as illustrated in Figure 10. Make sure the diode and capacitor are connected with the correct polarity.
c. Connect the BNC probe to CH2 on the oscilloscope. Connect its leads across the resistor.
d. Display both channels on the oscilloscope by making sure both CH1 and CH2 buttons are lit-up. You should now see the input sine wave on CH1 and the rectified sine wave on CH2.
2. Set the function generator to SINE (~) and adjust the frequency to approximately 60 Hz. Record the frequency value.
3. Adjust the voltage OUTPUT level on the function generator until the waveform displayed in CH1 is a sine wave with a peak-to-peak amplitude of approximately 8 volts. Record Vpp and its corresponding error.
Verify your circuit with a demonstrator before proceeding further!
Observing the effect of the diode in the circuit.
1. Disconnect the capacitor from the circuit. Figure 11 shows the resultant waveform (CH2, blue) superimposed on the original signal from the generator (CH1, yellow).
Figure 11. CH 1 and CH 2 traces superimposed when capacitor is removed from the circuit.
2. Use the VERTICAL controls on the oscilloscope (both POSITION and SCALE) to superimpose the rectified wave onto the sine wave by aligning their peaks. Make sure that the scale on CH2 is the same as on CH1.
3. Measure the diode’s threshold voltage, (Vtℎ).
a. Press the CURSOR button, set the mode to MANUAL and the TYPE to Y.
b. Use the scroll knob to move the first horizontal cursor line to the zero (arrow on the left of the oscilloscope display) of the input sine wave.
c. Press the scroll knob (until it clicks) to switch to the second horizontal cursor line.
d. Adjust the scroll knob until the second horizontal line is at the zero of the rectified wave.
e. Record the |∆Y| value shown (include correct units and error). This is the diode’s threshold voltage.
Observing the effect of the diode and capacitor in the circuit.
1. Re-connect the capacitor to the circuit. The capacitor enables the conversion of the input AC signal (CH1, yellow) to the rectified DC signal (CH2, blue). Figure 12 shows the resultant waveform superimposed on the original signal from the generator.
Figure 12. CH 1 and CH 2 traces superimposed for AC to DC conversion.
2. Press the CH1 button to turn the CH1 display off.
3. Measure VDC , the average voltage of the rectified signal (CH2). To do so,
a. Set the coupling of your rectified waveform (CH2) to DC coupling by pressing the CH2 button and selecting COUPLING > DC in the MENU.
b. Adjust the vertical scale and position so that the waveform in the oscilloscope matches Figure 13.
c. Press the MEASURE button, select CH2 as the SOURCE, clear the display and then choose the VAVG option. Record your value and its corresponding error.
4. Note that the resulting DC signal is not perfectly constant and has a small ripple on top of it. Measure Vripple , the ripple peak-to-peak amplitude relative to the DC voltage. To do so,
a. Set the coupling of your rectified waveform (CH2) to AC coupling by pressing the CH2 button and selecting COUPLING > AC in the MENU.
b. Adjust the vertical scale and position so that the waveform in the oscilloscope matches Figure 13.
c. Press the MEASURE button and select the VPP option. Record your value and its corresponding error.
5. Repeat the VDC and Vripple measurements for 5 different frequencies between 60 -300 Hz. Figure 13 shows an example of the observed traces for the 60 Hz setting.
Figure 13. Example of the trace displaying VDC and Vripple readings.
6. As part of your Observations section, include sample images of the measured waveforms. Provide an explanation of how the rectifier circuit works indicating which circuit component is responsible for each characteristic trace. Use Figures 14 – 17 to identify (and label) the waveforms.
✓ Make sure that the waveforms in the figures are numerically proportional to the on-screen oscilloscope trace.
✓ Record the zero-voltage position and the corresponding CH1 and CH2 voltage and time scales.
✓ Depict the peak-to-peak voltage Vpp in Figure 14, the diode’s threshold voltage Vth in Figure 15, and the measured VDC and Vripple voltages in Figure 16 and Figure 17