EXPERIMENT 12 PHYSICS 250 TRANSDUCERS: TIME RESPONSE Apparatus: Signal generator Oscilloscope Digital multimeter Microphone Photocell Hall Probe Force transducer Force generator Speaker Light sources Calibration magnet Solenoidal coil Power Voltage Introduction In previous labs you studied the steady-state response and the frequency response of transducers and generators. In this lab, you will learn about the time dependence of these devices responses. You will consider the way the varies when the changes instantaneously (or as near as we can get to instantaneous) from one constant value to another constant value. This response of a device to a rapidly changing signal is called the time response of the device. A. Time Response and Rise Time A time-response study addresses the significant question: How does the relationship between the and depend upon the rapidity with which the varies with time? Specifically, if the suddenly changes to a new value, the will not change instantaneously. The devices are made of material with mass, electrical resistance, inductance, capacitance, heat capacity, etc.; thus the cannot follow the instantaneous changes of the. If the system is not oscillatory in nature, the will eventually approach the expected that corresponds to the new value of the as determined from DC measurements. The curve illustrating the functional time variation of the following such a step change in the is called the time response for the device. If an ideal transducer or generator could be created, the would instantaneously follow the. The time response curve may be quantitatively different when the level is suddenly increased from when the level is suddenly decreased. To study the time response of a device it is common to stimulate the with a variation that alternately increases and decreases; thus, you can observe both the increasing time response and the decreasing time response in the same experiment. For many devices the gradually approaches the new stable value in a smoothly 12-1
varying manner, but for some devices the may overshoot or even have damped oscillatory variations. A typical time-variation curve that illustrates a smooth approach due to both a sudden increase and a sudden decrease in the is shown in Fig. 1. To illustrate the correspondence of the and the variations as a function of time, they are shown overlapped on the same graph. Note that the y-axes for the two graphs will have different units and different scales. If the time response curve is relatively smooth, as illustrated in Fig. 1, you can assign a numerical value to characterize the overall functional time response. It is common to define a rise time or fall time as the time required for the to rise or fall between the point where it is at 10 percent of its total magnitude (difference between its highest value and its lowest value) and the point where it is at 90 percent of its total magnitude. This numerical value represents only a qualitative estimate and should not be considered a precise measurement but is valuable in comparing various devices. B. Response of Combined Elements Figure 1. Illustration of time response to an instantaneous function. When you experimentally attempt to study the time response of a particular transducer, the problem immediately arises of producing a physical phenomenon that changes rapidly in time to produce a step function as nearly as possible. Similarly, to study a device that generates a physical quantity, you must use a transducer to detect the quantity, and you must know the time response of the transducer being used. In short, you are often forced to study a generator and transducer combination simultaneously without knowing the responses of either individually. Fig. 2 shows several examples where both the and the to the combination are s, and the physical quantity must be inferred through a knowledge of the time response of either the generator or the transducer. If you know the time response of one of the devices, you can use this information along with measurements of the s implied in Fig. 2 to determine the time response of the second device. If you do not know the time response of either device, it is difficult to get inside the combination and measure the time response of either the generator or transducer alone. By being very creative, you can devise techniques that will change a physical quantity in known ways, for example, by chopping a light beam or rotating a polarizer in the light beam or by rapidly immersing a thermocouple in a liquid of known temperature. 12-2
light bulb light photocell heater temperature thermocouple speaker sound microphone magnet coil magnetic field Hall element force generator strain gauge Figure 2. Typical generator/transducer combinations. In this experiment you will mainly study the time response of a combined system and try to reason logically which of the two parts of the system is limiting the response. Note that unless both devices have very similar time responses, the decrease in the curve in Fig. 1 will indicate basically the response of the poorest device. Because of this feature, if you have available a generator or a transducer that is known to have a very sharp time response, you can use the high performance device in conjunction with a poorer device to evaluate the inferior device. In order to make the measurements suggested for this experiment, you will have to use an electrical signal generator, s, and an oscilloscope, each of which has its own time response function that may have to be included. Fortunately, when used on DC, the oscilloscope has an excellent time response (a rise time less than 0.1 sec). A simple electronic is included in Fig. 2 as an example of a transfer device with easily measurable time response. To illustrate and bring into focus the problems involving multiple elements in an experimental setup, consider a study of the time response of one of the combinations in Fig. 2. The assembled apparatus can be represented in block diagram as shown in Fig. 3. 12-3
signal generator power magnetic coil Hall probe oscilloscope Figure 3. The train of apparatus required to measure the time response of a transducer. Note that the study of the transducer itself is the prime objective of your experiment but that all six elements are required to make the measurement. 1. The signal generator is required to generate the s. 2. The power is necessary since most physical generators require large electrical currents, and the signal generator cannot supply large currents. 3. The physical generator must generate the varying physical quantity. 4. The transducer measures the physical quantity. 5. The is often required since the from the transducer may be only a few millivolts and thus not large enough to be easily measured with an oscilloscope. 6. The oscilloscope displays the signal. The to the signal generator is the setting on the amplitude dial, and for a fixed setting, the will decrease at very high frequencies. The of the signal generator becomes the to the power and so on throughout the train of elements. The of the oscilloscope is an observed reading on the face of the scope. Since the of each element of the train is the of the previous element, the frequency or time response curve of a combination of n elements will be given by train = 1 2... 3 n (1) In the case of time response, equation (1) is a time-dependent equation. Since the oscilloscope using the DC switch is known to have a rise time of less than 0.1 sec, it is reasonably easy to check the time response of some individual elements of the train. You can directly measure the response of the signal generator alone by using the oscilloscope to measure the. You can study the two s by using the now known signal from the signal generator and measuring the. Thus, by logic you can isolate the time response of the physical generator-transducer combination. The most difficult problem is to get inside the generator and transducer combination to separate the response of these two elements. This feat is sometimes possible by recourse to a fundamental law of physics or by a separate experiment that uses a generator or transducer with known fast rise time. Hints to allow you to get inside this combinations are given in the comments section below. For example, the magnetic field of the coil is proportional at each and every time to the electrical current in the coil (Ampere's law and Biot-Savart law). Thus, by placing a small resistance in series with the coil and measuring the across the resistance with the oscilloscope you can determine the current I = V/R, which is proportional to the magnetic field at each frequency. Note that you cannot measure the current with a simple AC ammeter since you do not know the response of the ammeter. Now finally, if you know the response of all the elements except the transducer in the train of Fig. 3, you can determine the response for it. 12-4
Objective: To provide an introduction to the concept of time response in a general sense, to extend understanding of transducers and their limitations related to time response, and to give additional experience in using the oscilloscope Procedure During this lab, each group should select one of the transducer-generator systems suggested in Fig. 2 and augmented in Fig. 3 (except the temperature system) and study the time response for the system chosen with an emphasis on trying to determine the time responses for the transducer and the generator individually. You should select a system other than one used for the frequency response measurements in the previous experiment if at all possible. During the process you will, of necessity, have to study the signal generator and and understand their time response functions. In reality you will be studying the combination of several elements. You should approach this experiment as an investigation of the time characteristics of a system and make whatever measurements you feel necessary to understand the characteristics of each element in your chosen combination. The study of the response of the thermal system is inappropriate for two reasons: First, you have already studied some aspects of the thermal system, and second, the time response of thermal systems is often in minutes and not easily studied by using the oscilloscope. You must exercise a few precautions when using the s: 1. All s are limited in the magnitude of the or currents they can supply. If these values are exceeded, they will clip the signal. 2. Always begin with low amplification factors and low signals and increase these values slowly as needed. 3. Do not short the of either, especially that of the power. 4. Only very small signals (less than 0.1 volts) should be into the. You can obtain step changes in s for time response studies by using the pulse from the signal generator rather than the square-wave signal. Comments to help in choosing and characterizing your system can be found at the end of the previous lab handout (Transducers: Frequency Response). 12-5