Laboratory 1 Generating and viewing signals rev. 20e. Oscilloscope Settings

1 2 Laboratory 1 Generating and viewing signals rev. 20e Purpose: Familiarization with the basic functions of an oscilloscope and of a signal generator. Adjusting and measuring specific parameters of signals. Summary of theory The oscilloscope (often abbreviated scope) is a device that allows viewing the instantaneous value of a voltage v(t) as a function of time, and quantitative measurements of voltage and time on the waveform, having broad applications in the analysis of electrical signals. In this lab we use the Tektronix TDS1001 digital scope. The description that follows corresponds to this model. The main parameters of a periodic signal - waveform (deterministic) in the time domain - period and frequency, f = 1/ T - maximum value U max - minimum value U min - peak-to-peak value, the signal range U PP = U max - U min ; - average (offset) value of the signal U avg or U DC - signal amplitude (if the signal is similar to a sine wave) U 0 = U max U DC = U DC - U min Remark: if U DC = 0, the amplitude, min and max values are equal in absolute values. - other parameters for certain waveforms, for example: - rectangular wave: duty cycle η = τ/t (τ represents the width of the high pulse, and T is the signal period), rise / fall time (t rise, t fall) - triangular wave: rising / falling slope Oscilloscope Settings Horizontally, the duration corresponding to the length of a division on the screen is adjustable from the C x knob (horizontal deflection coefficient). It is labeled in units of time per division. The following relation exists between the number of divisions N that an event occupies and its duration T x : x T x = N x C x Vertically, voltage U is applied from external input Y. Similar to the reading on the X axis, one can read the value of voltage U that occupies N y vertical divisions using the formula: U = N y C y C y is called vertical deflection coefficient and is labeled in units of volts per division. Example: A period of the sine wave in Fig. 2 occupies 7 horizontal divisions on the screen, and the time base is set at Cx=5ms/div. The signal s period is, thus, 35 ms. Vertically, the amplitude (peak value) occupies 3 divisions, which, for Cy= 2V/div, means 6V. U max τ U 0 U max t U 0 U DC U DC U min T U min T a. Sine wave b. Rectangular wave Figure 1. Periodic signals: sine, rectangular t Figure 2. Horizontal and vertical divisions

3 4 Values C x, C y are called calibrated and have standard form (1,2,5)*10 +/-K. for C y, and (1, 2.5, 5)*10 +/-K. Calibrated coefficient values for usual oscilloscopes are: Cy {5; 10; 20; 50; 100; 200; 500 mv/div; 1; 2; 5 V/div} Cx {5; 10; 25; 50; 100; 250; 500 ns/div; 1; 2,5; 5; 10; 25; 50; 100; 250; 500 μs/div; 1; 2,5; 5; 10, 25; 50; 100; 250; 500 ms/div, 1; 2,5; 5; 10 s/div} Triggering the oscilloscope: An image that is stable on the display of the oscilloscope is called triggered (synchronized). The physical meaning is the following: when 2 successive images of a periodic signal start at the same moment in time (relative to the signal period), the 2 images will overlap perfectly, and so will happen for subsequent images. Thus, the eye perceives a single stable image, although, in fact, we constantly have a new image superimposed on the previous one. An example in case of displaying a rising slope is given in Figure 3 (a). But if every display starts with some other moment of time, the images will differ, and the eye will perceive many different superposed images - Fig. 3 (b). In this case the image is called untriggered (unsynchronized) and is difficult or impossible to interpret. a) triggered image b) untriggered image Figure 3: oscilloscope triggering In order to obtain a triggered image, the operator must adjust the trigger settings. The most important are: trigger source, its level and a slope at which the displaying of the image should start. Usually, those adjustments are grouped in a trigger menu. Usually, in order for an image to be synchronized, the Trigger Level has to be between the [minimum, maximum] level of the signal. A smaller or larger level means that the Trigger Level does not intersect the signal, therefore it cannot trigger a display. In the measurements that will be performed next, the following trigger settings will especially be used: Source = CH1, slope = Rise, Mode = AUTO. For automatically adjusting the Trigger Level, the Set To 50% key has to be pushed. Generator settings The Rigol DG1022 function generator allows the generation of several waveforms (sine, rectangular, triangular etc) with different tuneable parameters. The waveform can be selected by pressing the corresponding buttons: The parameters of a certain waveform can be selected by pressing the function (unmarked) keys whose functions correspond to the indications on the display, above them: For example, in the case of pressing the Freq function key, that particular function (setting the frequency) becomes selected, and the value can be introduced either from the numerical keypad, or from the rotating knob. In the case of function keys which have a small arrow to the right side (like Freq above) successive presses of the key allow setting parameters in different variants. For instance, besides setting the amplitude (Ampl) you can also set the HiLevel value which corresponds with U max from figure 1a). After typing the numerical value, choose the desired measurement unit by pressing the function key beneath it. Pay attention! According to figure 1a), the amplitude U 0 and the value U max are equal only if U DC = 0 (null mean value). To eliminate possible confusions, this generator allows setting the amplitude in values of V PP (peak-topeak) which means that, actually, by choosing this measurement unit, the function key Ampl sets the peak-to-peak value, which is double the amplitude for signal with no DC level. For asymmetrical signals (with U DC nonzero), the peak-to-peak value stays the same, while U max and U min change (see again figure 1a).

5 6 Remark: there is no such thing as several types of volts, as the volt is uniquely defined. The optional index after the volt, like V PP, simply indicates the fact the the voltage is measured in volts between certain limits. For example, a symmetrical 2V amplitude signal is equivalent to a 4V PP signal, because the second way of expressing it explicitly signifies that it is measured between the extreme limits of the signal. The V RMS notation refers to the root mean square value which will be studied in the future lab work measuring voltages. The generator has 2 channels which can generate different waveforms. The above settings have effect on the channel that is selected using the key. Correspondingly, CH1 or CH2 will appear on the display. Moreover, the output of the respective channel is only active when the corresponding Output button is pressed and it lights up. On the scope, press CH1 MENU in order to display the settings of channel 1 (at repeated presses, channel 1 is alternatively turned on and off). Because a simple cable is used, not an attenuator probe, press the Probe soft-key until the indication is 1x (there are probes that contain a divisor that attenuates the signal 10...100 times, in which case settings 10x, 100x would be used). Set the values for the oscilloscope C X1, C Y1 (written on the blackboard). Remark: review figure 2; the oscilloscope indicates the value of C Y of channel 1 with the notation CH1, and the value of C X as M (main time base). Notice that one period of the signal is displayed on the screen. Measure the period by counting the divisions and subdivisions N x of a period and use the formula Tmeas = Cx N x. Calculate the frequency f meas =1/T meas and verify that it corresponds with the value indicated by the generator. Repeat the previous steps for the vertical adjustment. By counting the vertical divisions and subdivisions N y and applying the formula U=N y C y, measure the amplitude of the signal (peak value U P ). In the same way, measure peak-to-peak value U PP. Calculate the ratio between U P and U PP (measured values). What is the theoretical value of the ratio? Remark: for identifying settings and indications of the oscilloscope you can use annex A. 2. Computing the display settings Measurements 1. Automatic settings of the oscilloscope Using the function generator, generate a sine wave with the following parameters: - channel 1 from the key (CH1 is displayed in the upper right corner) - Sine key sine wave - frequency Freq value f 1 written on the blackboard - amplitude AMPL value A 1 written on the blackboard (pay attention to the measurement unit! An amplitude of 2V is, like previously mentioned, equivalent to 4V PP! the measurement unit eliminates all doubt regarding the limits between which the voltage is specified). - no DC level (OFFSET =0V) Press the Output key next to the CH1 output so that it is illuminated; connect the CH1 output of the generator to channel 1 of the scope using a coaxial cable (or two crocodile clips connected together). Pay attention! This exercise is only for computing the settings. You do not have to display signals on the scope! a) Compute how many divisions, NX și NY, will the amplitude and period of the signal occupy on the scope display for the following signals and settings:: a1. sine wave with amplitude UP1=4V and frequency f1=20khz. Oscilloscope settings: CX1=10μs/div and CY1=1V/div. a2. sine wave with amplitude UP2=6V and frequency f2=8khz. Oscilloscope settings: CX2=25μs/div and CY2=2V/div. Indication 1: Use the following T = NX CX and UP = NY CY. You can compute T from the frequency value. Indication 2: Use as an example the solved exercises at the end of the laboratory work. Same goes for (b) and (c). b) Compute the deflection coefficients (CXcalc, CYcalc) that should be set for displaying a sine wave with the frequency of f3=1khz and amplitude UP3 =2V, such that the amplitude occupies two divisions and the period occupies four divisions.

7 8 c) Repeat (b) for a signal with f4=500khz și UP4=8V, if the amplitude occupies four divisions, and the period 10 divisions (CXcalc, CYcalc) 3. Generating a triangular wave a) Generate a triangular wave, (Ramp button) with no DC component (OFFSET 0V), symmetry 50%, with frequency f3 and amplitude UP3 (written on the blackboard). You have to set the oscilloscope such the display looks like the next figure (in order to have the start time like in the figure, press the SET TO 50% button below the Trigger level). with U P = 2V, u(t) varies within the limits [-2V, +2V], then for a signal with a DC component, written as: u(t) = U DC + U P sin ωt [V] [2] with U P = 2V și UDC= -1V, u(t) varies within the limits [-2-1V, +2-1V] = [-3V, +1V]. The two situations are illustrated in fig. 4: Fig. 4 Signal without DC (left) and with UDC= -1V (right) a1. What is the measured period of the signal (T 3 )? Compute the necessary C X to observe exactly 2 periods on the scope. Set this value C X on the oscilloscope. How many divisions does a period occupy on the scope (N X)? a2. Compute the necessary C Y s.t. the amplitude U V3 ocuppies exactly N Y = 2 div. Set this value C Y. b) Influence of C Y on the displayed image Set C Y to the value of CY =CY / 2. How many divisions N Y does the amplitude occupy now? Compute the amplitude based on the new image: U P = N Y C Y, and compare it with U P3. Explain the relationship between U P and U P3.. c) Influence of C X on the displayed image Modify C X to the value of CX =2Cx. How many divisions N X does the period occupy now? Compute the period based on the new image: T = N X C X, and compare it with T 3. Explain the relationship between T and T 3. 4. Generating and measuring a sine wave with a DC component a) Until now the signals did not have a DC component or DC level (also named offset), being symmetrical from 0 V. If for a signal without a DC offset written as: u(t) = U P sin ωt [V] [1] Remark: the DC component is also called the average value of the signal, because it is equal to the average of u(t) over a period. Notice that in eq. [1] and [2] above, the integration over a period (equivalent to averaging) gives us the values 0 and U DC respectively. Generate a sine wave (button Sine from the generator), with the frequency of f1=20khz, amplitude UP =2V and DC component UDC1= -1V. For setting the DC component at the generator, use the OFFSET = -1V function key. For the oscilloscope, use coefficients CX1=25μs/div and CY1=1V/div. If it isn t already, adjust the 0V (Ground) level in the middle of the screen, using Vertical Position. a1. Draw the image of the scope and specify the ground level (the arrow on the left). Use CH1 MENU->Coupling ->DC. This coupling mode means the signal is applied directly, without altering the possible DC component of the signal. Write down on the graph the position of the Ground level and the C x and C y values. a2. Draw the image when using AC coupling (CH1 MENU->Coupling - >AC). This coupling mode means that a capacitor is inserted in series between the signal and the oscilloscope signal path. As you should know, capacitors do not let continuous signals to pass through, but only alternative signals. Write down on the graph the position of the Ground level and the C x and C y values.

9 10 b) How can we measure, using the oscilloscope, the DC level of a given signal? - set the oscilloscope to AC coupling: (CH1 MENU->Coupling ->AC); the DC component is blocked; therefore, the signal is symmetrical on the screen (as if OFFSET were not set from the generator) - set CH1 MENU->Coupling ->DC. At this moment, the signal will rise or fall with a number of divisions N Y. Taking as reference a point on the waveform (typically, the maximum or minimum point), count how many divisions the signal rises or falls when swtiching from AC to DC. If it rises, then the offset is positive, if it falls, the offset is negative. Count how many divisions N Y, sign included, correspond to the value of U DC, and compute U DC = N Y C Y. This value should be the same as the one generated using the OFFSET from the generator. Remark: If needed, adjust the trigger (SET TO 50%) so that the image is synchronised (it s possible that when we move the signal up or down, because of the offset, it does no longer cross the trigger level). b1. Work in a team, as follows: - Set CH1 MENU->Coupling ->AC to hise the DC level. Keep the setting of CY = 1V/div. - One of the team members will set at the generator, from the function key Offset, a DC level of U DC1set different from zero, in the interval (-2V, 2V), without telling the chosen value to the colleague. The amplitude remains 2V. - The other team member will switch from CH1 MENU->Coupling ->AC, to DC, will count how many divisions NY1 the peak of the signal rises/falls, and will compute U DC1 (value and sign): U DC1 = N Y1 C Y - Draw the image with the setting CH1 MENU->Coupling ->DC (including the 0V level indicator). b2. Switch places, and repeat b1 for a different offset value. Explain why measuring the DC level is made by switching from AC to DC coupling, and not the other way around! 5. Generating a rectangular wave Generate a rectangular wave (Square button), no DC component (OFFSET 0V), with the amplitude of UP5, frequency of f5 (written on the blackboard). Compute C X5, C Y5 s.t. exactly one period is displayed, respectively the amplitude occupies 2 divisions. View the signal with CY5, CX5 and use coupling CH1 MENU->Coupling ->DC. Adjust the duty cycle of the signal (see fig. 1b) using the functional duty cycle button DtyCyc, then the measurement unit which is % implicitly successively, to the values of η1=50%, η2=20% - Measure (in divisions) the values of T and τ for both cases (see fig 1b). - Compute the ratio τ/t - Draw the two signals. Important remark: the duty cycle is a parameter that has meaning only for a rectangular wave, according to the definition in Fig. 1b. it has no meaning for a sine or triangular wave! (you can set the symmetry of the triangle). Solved exercises 1. A sine wave with a frequency of f=2khz and amplitude of UP=4V is displayed using an oscilloscope. The settings are: C Y=1V/div, C X=250 μs/div. Determine how many divisions the amplitude and period of the signal occupy on the display of the oscilloscope. Solution: The number of divisions that the amplitude occupies on the display can be determined using UP=NY CY NY = UP/CY = 4 [V] / 1[V/div] = 4 div The period of the signal is T = 1/f = 1/2000Hz = 500 μs The number of divisions that the period of the signal occupies on the display is T = NX CX NX = T/CX = 500 10-6 [s] / 250 10-6 [s/div] = 2 div 2. A sine wave with a frequency of f=2mhz and amplitude of UP=6V is displayed using an oscilloscope. Determine the values of C X and C Y such that the amplitude occupies 3 divisions (NY=3 div), and the period occupies two divisions (NX=2div). Solution: The equations in ex. 1 can be used: The period of the signal is T = 1/f =1/2 10 6 s = 0,5 μs. CY = UP/NY = 6V / 3 div = 2 V/div CX = T/NX = 0,5 μs / 2 div = 0,25 μs/div 3. A sine wave is displayed using an oscilloscope. When the coupling is switched from AC to DC, the sine wave moves downwards by NY = 2 div. The vertical deflection coefficient is C Y=5V/div. Determine the DC level of the signal. Solution: The DC level value determines the downward movement of the signal image by a value that is equal to the value of the offset (for DC coupling). The direction of the movement determines the sign of the offset: upwards - positive; downwards - negative. Based on these observations, we can determine the DC component: UDC = - NY CY = -10V 4. A sine wave is displayed using an oscilloscope. When the coupling is switched from AC to DC, the sine wave moves downwards by NY = 4 div. The vertical deflection coefficient is CY=1V/div. Determine the DC level of the signal Solution:

11 12 The difference from ex 3 is that now we switch from DC to AC. Because, after the elimination of the DC component (AC coupling), the signal moves upwards, this means that it (the DC component) was pulling the signal downwards (in DC coupling). This means that the value of the offset is negative. UDC = - NY CY = -4V ANNEX 1. Tektronix TDS1001 Oscilloscope 1 2 3 4 5 6 Exercises 1. An oscilloscope is set to Cy=0,5V/div. The amplitude of a signal measured on the oscilloscope screen is 3.8div. What is the signal amplitude in volts? 2. An oscilloscope is set on Cx=20ms/div. The measured period of a sine wave on the screen of the oscilloscope is 5 div. Determine the frequency of the sine wave. 3. Given a sinusoidal signal of frequency 10kHz and amplitude 4V, determine the values of the horizontal and vertical deflection coefficients so that the amplitude and the period of the signal can be precisely measured on the screen. 4. A sinusoidal signal is viewed with an oscilloscope. When the coupling button is set from AC to DC position the sinusoidal signal moves on the screen, downwards by 3 divisions. Cy=1V/div. Determine the DC level of the signal. 5. A symmetrical rectangular signal, having amplitude A=1V, no DC level and frequency of 1kHz, is applied at the input of an oscilloscope. The oscilloscope has Cy=0,5V/div, Cx=0,2ms/div, trigger level Utrig=0,5V and SLOPE=falling. Draw the image. Figure A1: front panel of the oscilloscope The front panel of the oscilloscope is represented in Fig. A1. The interface of the oscilloscope contains the following elements: 1. The screen of the oscilloscope Figure A2: Informations and symbols that are displayed on the screen of the oscilloscope

13 The screen contains an area for displaying the grid of the screen, the area of the control menu (right side of the grid area) and the area for displaying parameters (above and below the grid zone). The graticule area is formed from N x =10 units horizontally and N y =8 units vertically, and it is used for displaying the image. Beside the image there are several parameters of the oscilloscope or of the waveform that are displayed according to the selected working mode. On Fig. A2, the most relevant ones are: (1) acquisition time (normal, averaging, etc) (2) Trig d = triggered = synchronized (3) Trigger moment, it can be swept using the adjustment HORIZONTAL POSITION (5) Trigger Level, it is adjusted using TRIGGER LEVEL (6) identifier of traces 1 and 2, its position is swept with VERTICAL POSITION (8) C y values of both channels (9) BW= Bandwidth Limit (it limits the maximum frequency of the oscilloscope to 20MHz) (10,11) C x values for the main time base (Main) and the secondary time base (Window) (12,13) the source and the slope of the trigger (17) the measured frequency of the signal. 14 CH1 MENU the result of pressing the button is the display in the control area of fields that allow the control of the displaying on the vertical axis, for channel 1 (CH1). The following fields will be displayed: o Coupling - it selects the coupling type AC/DC/Ground (alternating current/continuous current/zero level) o BW Limit band limiting at 20MHz instead of 40 (option ON/OFF) o Volts/Div calibrated (Coarse) or noncalibrated (Fine) adjustment. For the calibrated adjustment the vertically deflection coefficient can only have values C y={1,2,5}x10 k V/div. o Probe- the type of probe used (x1/x10/x100/x1000). The value must be the same as that used at the probe of signal. o Invert reverses the image when ON. MATH MENU allows applying some mathematical functions on signals (add, subtract, Fourier Transform). 2. Control keys - they allow changing the control fields displayed on the screen of the oscilloscope. They are called soft keys because those fields change according to the selected menu/mode. 3. Channel Y adjustments (vertical adjustments) - there is a set of adjustments for each of the two channels of the oscilloscope. 4. Digital Functions Menu the effect of pressing a button from this area is displaying on the screen a menu that contains functions which are specific to digital oscilloscopes (saving, measurement, acquisition, cursors, utilities, display). For the laboratory the menu DISPLAY is the one that is interesting. It contains the control field Format, RUN/STOP and SINGLE SEQ buttons. Figure A4: Menus for digital functions a) adjustments of the Y channel b) adjustments of the X channel Figure A3 POSITION it allows moving the image vertically VOLTS/DIV knob used for changing the vertical deflection coefficient. Its value is displayed in the bottom side of the screen (the area for displaying parameters). DISPLAY o Format selecting operating mode y(t) (YT) or x(y) (XY) RUN/STOP in RUN mode the oscilloscope acquires signal continuously. In STOP mode the acquisition is stopped, the image which is displayed being the last image before pressing the STOP button. SINGLE SEQ the oscilloscope acquires a single image (that corresponds to a single course on the screen) and it waits for a new press of the button. Pressing the button is equivalent to a RESET. 5. Adjustments for X channel of the oscilloscope (horizontal axis adjustments) SEC/DIV the adjustment of the horizontal deflection coefficient C x. Its value is displayed in the bottom side of the screen as M 10ms, which is equivalent to C x =10ms/div.

15 HORIZ MENU displays the menu for control of the displaying on horizontal axis. o MAIN- selects the display of the image for main time basis (the usual working mode). o Window zone selects the display of the image for secondary time basis (in fact, secondary time basis is the name from analogical oscilloscope. In this context it is a portion of the image that is "dilated" on horizontal axis) o Window adjustment of the temporal window for the secondary time basis. o Trigger Knob it allows selecting the function of the LEVEL button from the TRIGGER buttons area: implicitly it represents the adjustment of the trigger level; when the holdoff adjustment is selected, the LED bellow LEVEL button is on (lighting). POSITION moves the image horizontally SET TO ZERO restores the image to its original position (horizontal displacement deleted) 6. Adjustments/Settings for the synchronizing circuit (TRIGGER) For the TDS 1001 oscilloscope, the trigger moment corresponds to the middle of the screen. LEVEL it allows to set the trigger level and the holdoff time. TRIG MENU enables the menu for control of synchronization (trigger). It contains the following control fields: o Type selects the type of the trigger: Edge triggering on the slope of the signal, Video - triggering on a video signal, Pulse - triggering on pulses. o Source the source of the triggering signal (CH1, CH2, EXT, EXT/5, AC signal from the mains) o Slope type of the front: positive or negative (Rising/Falling) o Mode synchronizing mode (Auto/Normal): AUTO: if trigger conditions are not satisfied, the oscilloscope automatically generates, after a certain time, a signal to trigger the display. This way, when the input signal is not present a horizontal line can be observed on the screen. It represents the zero level. This is the default mode if not specified otherwise! Normal This time, the display is triggered only if the trigger conditions are met. Otherwise, the oscilloscope does not display any image. The trigger level can also be set outside the limits of the signal. There exists the possibility that, although on the input of the oscilloscope a signal is present, the signal is not displayed because the trigger conditions are not met. o Coupling the coupling mode of the synchronization signal: AC eliminates the DC level from the trigger signal. DC the trigger signal 16 has nonzero DC level. Noise Reject the noise is eliminated from trigger signal. HF REJ (High Frequency Reject) it eliminates high frequencies from trigger signal. LF REJ it eliminates low frequencies from trigger signal.