Introduction. Objectives

Transcription

1 Experiment 8 Phase ensitive etection Objectives 1. Construct and observe the operation of a phase sensitive detector to extract a signal buried in noise. 2. Observe the operation of a commercial lock-in amplifier for detecting signals buried in noise. Equipment 1. Oscilloscope 2. Proto board Appropriate capacitors 4. Appropriate resistors 5. 1 IP W06 JFET quad analog switch 6. 2 IP 741 op amps 7. 3 function generators 8. Connecting wires 9. Commercial lock-in amplifier Introduction Phase sensitive detection Often in experimental situations, the signal of interest is smaller than the signal due to noise. Most realistic experiments involve measurements of subtle physical properties, which demand either extremely good shielding against external noise, or methods which allow extraction of the measuring signal from the noise. Phase sensitive detection is a method whereby the signal of interest is "tagged" by modulating at a frequency much higher than any normal changes which the signal might experience. This tagged signal is then later retrieved amidst the unwanted noise. Compare this to retrieving an electronically tagged porpoise amidst the "noise" of the ocean. A simple way of understanding phase sensitive operation is to study the circuit shown in figure 1. Here, the input signal is tagged with a modulating sine wave of a certain frequency. This same modulating frequency is applied to a switch which alternates from sampling the unaltered wave every odd half cycle to sampling the inverted wave every even half cycle. The input and corresponding output are shown on the same time axis. For positive going input, the switch is in position 1 and the unaltered wave is sampled. For negative going input, the switch is in position 2 and the inverted wave is sampled. Therefore, in both cases, the output is positive. 44

2 V in 1 V out modulation frequency V in t V out t Figure 1. imple phase sensitive detector circuit. Random noise interfering with this signal will, in general, be at a different frequency than the modulating frequency. Therefore, the noise will be equally likely to be sampled as an unaltered signal and as an inverted signal and over many cycles this noise will average to zero. As can be seen for the input signal, however, its output does not average to zero (since it is always positive). Therefore, the signal can be retrieved even as the noise is averaged to zero. Question 1) For an input sine wave of amplitude 10 V p-p, determine the average voltage of the rectified output. In practice, the signal averaging is done by an RC low pass filter. The RC time constant is made large to average over as many output cycles as possible. There is a limit, however. You don't want to filter out variations of the signal which occur due to changes in experimental 45

3 parameters. Therefore, the time constant must be made small enough so that experimental variations can be tracked. For example, suppose you use phase sensitive detection to measure the voltage across a temperature sensor, immersed in a bath of water. uppose you wish to measure every 10 degrees Celsius as you heat the water from 0 to 100 o C. If the water is heated at one degree per minute, you want the time constant to be small enough to track the temperature changes every 10 o C. Question 2) etermine an appropriate RC time constant which will allow you to track the changes in temperature. At the same time, you want your modulation frequency to be sufficiently high so that many output periods will occur during one time constant. This assures that many output cycles will be averaged. 3) etermine an appropriate modulation frequency for the temperature experiment. You don't have to go crazy, that is gigahertz aren't necessary. Just try to average over about 100 modulation cycles within one time constant. The whole nine yards The phase sensitive detector circuit is shown in figure 2. It involves 3 inputs, a sine wave which will serve as the noise, a triangle wave which will serve as the signal of interest, and a square wave which will serve as the modulation input. The modulation is controlled by an W06 FET analog switch. The two boxes in the diagram each represent 1/2 of the entire 16 pin IP chip. tarting at the front, the triangle wave is input into the W06 switch. Note that the two inputs (pins 3 and 14) go to the same output (pins 2 and 15 which are tied together). Note, however, that the switch is configured such that only pin 3 or pin 14 is connected to the output at any one time. The modulating signal at pin 16 switches the output from sampling the triangle wave to sampling ground. Following the first half of the W06 switch is a 741 op amp configured as a summing amplifying. It sums the modulated signal of interest and the unmodulated noise. Following this first 741 is a second 741 op amp configured as a straight inverting amplifier. Along with this is a wire which samples the non-inverted wave. Notice that the resistors here are precision 1% resistors since it is very important that the inverted wave is exactly equal in magnitude but of opposite polarity to the non-inverted wave. The output of this stage is input to the other half of the W06 switch. This half of the switch is modulated with the same frequency (and phase) as the other half switch (note the connection from pin 9 to pin 16). Therefore, the output is sampled with the same phase and frequency which has been tagged on the signal of interest. The last stage is the RC low pass filter. Here, as stated above, the RC time constant should be made small enough so that real variations in the signal of interest can be tracked. Therefore the RC time constant should be much smaller than the period of the triangle wave. The modulation frequency should be high enough to assure filtering of many cycles within one 46

4 RC time constant. Therefore, the period of modulation should be much shorter than the RC time constant. 1% A B 1% C R C V out V +15 V /2W /2W06 Figure 2. Phase sensitive dector circuit using op amps, switches and an R-C filter. Procedure Part 1, 1/2 W06 switch and summing amplifier. Construct the first two components of the phase sensitive detector circuit, the first 1/2W06 switch and the summing amplifier. For the three inputs, we will use a 60 Hz, ~ 6 V p-p sine wave for the noise input, a 50 Hz, 2 V p-p triangle wave for the signal of interest, and a 700 Hz, 0 to 5 volt square wave for the modulation input. Your signal to noise ratio is therefore 1:3. Use the same + 12 V supply voltages for the W06 switch and the 741 op amps. The data spec sheet for the WO6 switch indicates that it will operate at supply voltages down to + 12 V. To trigger the oscilloscope, use an external trigger from the triangle wave input. raw this portion of the circuit. Measure the voltages at points A and B of the circuit. ketch these voltages. Are these outputs what you would expect? HOW THEE OUTPUT TO THE INTRUCTOR BEFORE YOU CONTINUE. Part 2, remaining circuit Construct the remaining portions of the phase sensitive detector circuit, save for the RC output filter. As an initial check, make sure that the voltages you measured at points A and B in this circuit are still the same. Now, for the RC output filter, you would like to try to make the RC time constant large enough to average over many modulation cycles, but small enough to retain your original input signal. Therefore, the period of the modulation cycle << RC << the period of the input signal. This is hard to do since the input signal period and modulation period 47

5 are not that much different. Let's increase the modulation frequency to Hz. Now make RC such that 10T modulation < RC < 0.1T input signal. Record your values for R and C. Attach your RC filter to the output of the circuit. raw the entire circuit. Now, using Hz for your modulation frequency, measure points C, and finally the output of this circuit on the oscilloscope. ketch each of these outputs and make sure you understand what each component of the circuit is doing. Is your final output the triangle wave without the unwanted noise? Congratulations, you've just retrieved a signal buried in noise. Now, adjust your signal frequency and verify that you may still produce an adequate output even when the noise frequency is very close to the signal frequency. Part 3, the commercial lock in. To illustrate the effectiveness of phase sensitive detection, a circuit using a commercial lock-in amplifier is set up in the other room and diagrammed below in figure 3. A light emitting diode (LE) is powered by a function generator so that the light emitted is modulated at a frequency of about 1 khz. At the same time, a photoresistor op amp circuit is used to detect the light from this LE. The output of this circuit is monitored on both an oscilloscope and the lock-in amplifier. Also, the function generator is connected directly to the lock-in amplifier so the lock-in "knows" what signal frequency it should be looking for. Figure 3. Lock-in amplifier set up to measure the output of a light emitting diode. With the lights out in the room, draw the oscilloscope output. Label both the voltage and time axes. etermine the amplitude of the wave that corresponds to the oscillating signal. In 48

6 addition, record the output of the lock-in. Now, switch the lights on. Again draw the oscilloscope output labeling the voltage and time axes. Can you still identify the wave that corresponds to the oscillating signal? What is the signal to noise ratio? Again record the output of the lock-in. Has the lock-in's output changed appreciably due to the increased noise? Is this instrument boss or what? If you don't believe that the lock-in is really still detecting the LE, place your hand in front of the LE and see what this does to the signal. Write the most profound conclusion you can muster and thank you for taking Physics 304L! References Richard Wolfson, "The lock-in amplifier: A student experiment", Am. J. Phys. 59, (1991). 49

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