ET_210_Lab_01 Oscilloscope_added info(2)

QUEENSBOROUGH COMMUNITY COLLEGE Department of Engineering Technology ET 210 Lab 1: The Oscilloscope and Function Generator Objectives: 1) To become familiar with the operation of a Function Generator. 2) To become familiar with the operation of an Oscilloscope. 3) To use the Oscilloscope to display the output voltage waveform of a Function Generator. 4) To demonstrate the Thevenin Equivalent Circuit of a Function Generator. Equipment Required: Function Generator (or signal generator) with output resistance = 50 Ω Oscilloscope (with an input resistance of 1 M Ω or higher) DMM Cables: BNC to BNC coaxial cable (1), BNC to Dual Alligator Clips cable (2) Components Required: Resistors: (rated 1/2 W or above): 47 Ω, 100 Ω Theoretical Discussion: A Function Generator is a voltage source instrument, which provides output voltage signals that vary with time. The function generator output voltage is usually a periodic function of time. The Function Generator requires a source of input voltage such as the ac voltage provided at an ac outlet or the dc voltage provided by a battery in order to produce the output signal. An oscilloscope (abbreviated as scope) is a measurement instrument that displays a graph (plot) of voltage versus time. The voltage is represented on the vertical axis and time on the horizontal axis. The function generator output voltage waveform (voltage as a function of time) used in this experiment is a sinusoidal waveform, as shown in Figure-1, where the quantities are defined as follows: V P–P = Peak-to-Peak Voltage is the algebraic difference between the positive and negative peak voltages. More generally, the peak-to-peak voltage is the difference between the upper peak (highest value mathematically) and the lower trough (lowest value mathematically) of a voltage waveform. The peak-to-peak voltage always has a positive value. T = Period (time required to complete one cycle of a periodic waveform) The number of cycles that occur in one second is called the frequency (f). The frequency is expressed in Hertz (Hz). The relationship between the frequency and period is as follows: f = 1 / T or T = 1 / f (f is the frequency in Hertz and T is the period in seconds) QCC ECET John Buoncora Page 1

The Oscilloscope and Function Generator Figure-1: Sinusoidal Voltage Waveform Note : The period T can also be measured between any positive peak and the next positive peak that immediately follows it. The vertical sensitivity control (also referred to as vertical gain control) on the oscilloscope is used to select the value of the volts/div (also called volts/cm, where one major division occupies one centimeter) of the vertical axis. The horizontal sensitivity control (also referred to as the sweep time control or timebase control) on the oscilloscope is used to select the value of the time/div (in units of sec/div or with an SI prefix in front of the sec and can also be called time/cm) of the horizontal axis. The peak-to-peak voltage V P–P is found by multiplying the number of (major) vertical divisions corresponding to the peak-to-peak variation of the waveform by the vertical sensitivity setting of the oscilloscope. The period T of the waveform is found by multiplying the number of (major) horizontal divisions occupied by one complete cycle of the waveform by the horizontal sensitivity setting. For this example, refer to Figure-1 and assume the oscilloscope controls are set as follows: Vertical Sensitivity: 5 V/div Horizontal Sensivity: 100 µs/div V P–P = ( number of vertical divisions peak-to-peak ) × ( vertical sensitivity ) V P-P = 4 div × 5 V/div = 20 V (that is, the peak-to-peak voltage is 20 Volts) T = ( number of horizontal divisions for one complete waveform cycle ) × ( horizontal sensitivity ) T = 2 div × 100 µs/div = 200 µs (that is, the period is 200 microseconds) The frequency can then be found using the equation f = 1 / T as follows: f = 1 /(200 µs) = 1 /(200 × 10 – 6 sec) = 5 × 10 3 Hz = 5 k Hz (that is, the frequency is 5 kilohertz) QCC ECET John Buoncora Page 2

The Oscilloscope and Function Generator Another important aspect of the oscilloscope display is the vertical position of the 0 Volt reference line. If the input to the oscilloscope is at a fixed 0 Volt level, a line will be displayed as follows (assuming the vertical position control has been adjusted to center the 0 V reference line vertically on the display): The vertical position of the 0 V reference line can be changed (that is, the 0 V reference line can be moved up or down) by adjusting the vertical position control (also referred to as Y Position control) on the oscilloscope . The vertical position of the 0 V reference line can be set by performing the following steps: a. Set the Input Coupling Switch for the channel being used to the GROUND (GND) position. b. Adjust the vertical position (Y position) control until the 0 V reference line is located at the desired vertical position on the display. We will center the 0 V reference line vertically on the display in this lab experiment. c. Set the Input Coupling Switch to DC or AC (DC and AC coupling will be discussed in further detail later on) to display the input signal and take measurements. For this example, refer to Figure-1, and assume that we have set the oscilloscope channel for a Vertical Sensitivity of 5 V/div : In addition, assume that the 0 V reference line was vertically centered on the display (that is, the 0 V reference line was vertically positioned directly in the middle of the screen). The peak voltages are found as follows: V + PK = 2 div × 5 V/div = + 10 V (that is, the positive peak voltage is + 10 V) V – PK = – (2 div × 5 V/div) = – 10 V (that is, the negative peak voltage is – 10 V) In this example, since the positive and negative peak voltages have the same magnitude (absolute value) and the signal varies positively and negatively about the zero volt level symmetrically, the voltage is referred to as a pure AC voltage. The peak-to-peak voltage V P–P can also be found using the equation V P–P = V + PK – V – PK : V P–P = + 10 V – (– 10 V) = 20 V (as we found previously) QCC ECET John Buoncora Page 3

The Oscilloscope and Function Generator The function generator is also capable of providing voltage waveforms that contain an AC component and a DC component (or DC offset). As an example, assume that a + 5 V DC offset has been added to the waveform that was previously shown in Figure-1 (while the AC component remains the same) in order to obtain the waveform shown in Figure-2 (assume that the oscilloscope 0 V reference line was vertically centered on the display screen as indicated and the oscilloscope coupling is set to DC , as discussed below): Figure-2: Sinusoidal Voltage Waveform with an added DC Offset Voltage The Oscilloscope input coupling for each channel can be set to DC or AC (or GROUND, which was discussed previously). If the oscilloscope coupling is set to DC , then the oscilloscope will display both the DC and AC components of the voltage waveform (that is, the DC coupled mode of the oscilloscope causes the entire voltage waveform, which is the sum of the DC and AC components, to be displayed). Use of the DC coupled mode allows all of the waveform parameters (upper peak, lower trough, peak-to-peak, DC component, and period) to be measured. Note that the DC component of a voltage waveform is equal to the average value of the voltage waveform. If the oscilloscope coupling is set to AC , then the oscilloscope will display only the AC component of the voltage waveform. The AC coupled mode of the oscilloscope is implemented by internally switching a capacitor into a series connection with the oscilloscope input circuit. The internal capacitor in the oscilloscope blocks the DC component of the voltage waveform because the capacitor acts as an open circuit to DC (after if fully charges). The capacitor passes the AC component of the waveform unaltered, assuming that the capacitive reactance (X C ) of the capacitor is much less than the series resistance of the oscilloscope input circuit. Use of the AC coupled mode allows only the parameters associated with the AC component of the waveform, peak-to-peak voltage, and period to be measured. The AC coupled oscilloscope QCC ECET John Buoncora Page 4

The Oscilloscope and Function Generator mode is often used to accurately measure the parameters of the AC component of a voltage waveform if the magnitude of the AC component is much less than that of the DC component. For this example, refer to Figure-2, and assume that we have set the oscilloscope channel for a Vertical Sensitivity of 5 V/div and the oscilloscope channel coupling is set to DC (so that the the entire voltage waveform, which is the sum of the DC and AC components, is displayed as shown in Figure-2). In addition, assume that the 0 V reference line was vertically centered on the display (that is, the 0 V reference line was vertically positioned directly in the middle of the display screen as indicated in Figure-2). The U pper P eak voltage (designated V UP in Figure-2) and L ower T rough voltage (designated V LT in Figure-2) are found from the waveform displayed on the oscilloscope as follows: V UP = 3 div × 5 V/div = + 15 V V LT = – (1 div × 5 V/div) = – 5 V The peak-to-peak voltage can be found using the equation V P–P = V UP – V LT as follows: V P–P = V UP – V LT = + 15 V – (– 5 V) = 20 V We can also find the peak-to-peak voltage directly from the oscilloscope display as follows: V P-P = ( number of vertical divisions peak-to-peak ) × ( vertical sensitivity ) = 4 div × 5 V/div = 20 V The DC component or average value of a voltage waveform can be found, if the waveform is completely symmetrical about the average value (DC component) , using the following equation: V DC = V Average = (V UP + V LT ) / 2 {only for waveforms that are completely symmetrical about the average value} Note that the equation provided above can only be used for waveforms that have the symmetry mentioned above (such as an AC sine wave "riding on" a DC level). Furthermore, the symmetry about the average value involves the voltage variations, times and shape of the waveform. The DC component (average value) can be found for any waveform in general using integral calculus along with the following equation: V DC = V Average = ( algebraic sum of areas of + and – portions of waveform for one complete cycle ) / T where the T in the denominator is the period of the waveform The DC component (average value) of the voltage waveform displayed in Figure-2 can be found using the equation V DC = V Average = (V UP + V LT ) / 2 only because the waveform in Figure-2 is completely symmetrical about the average value (DC component). V DC = V Average = (V UP + V LT ) / 2 = ( +15 V + (– 5 V) ) / 2 = + 5 V (due to appropriate symmetry in Figure-2) QCC ECET John Buoncora Page 5