Electronics. RC Filter, DC Supply, and 555

Transcription

1 Electronics RC Filter, DC Supply, and Lab Ticket Each individual will write up his or her own Lab Report for this two-week experiment. You must also submit Lab Tickets individually. You are expected to discuss the plans for the lab with your partner, but we require that all written work to be done on your own. Week 1: A nicely polished, typed, rough draft of the Introduction, Experimental Design and Procedure sections of your lab report. We will grade these and get them back to you during week 2 of the extended projects. Week 2: No lab ticket. Use your spare time to work on writing your lab report. Feel free to meet with me to discuss what you have written. 1 Introduction In this extended project we will continue our study of a variety of electrical circuits. First we ll revisit our RC filter circuits by designing a filter to separate out signal from noise. Then we ll extend our study of diodes to include a full-wave rectifier. After that we ll see how to improve the quality of our DC power supply output and then, finally, take a look at an interesting integrated circuit, the 555 timer. 2 RC Filter Application In this part of the lab we ll generate a waveform that is a combination of a high frequency sine wave and a lower frequency sine wave and then build a filter to separate them. 1 This type of situation is common and can occur 1 Adapted from Hayes and Horowitz, The Student Manual for the Art of Electronics. 1

2 when high frequency noise contaminates the signal in power outlets. We d like to separate out this noise, as shown in Fig. 1, from our lower frequency signal and can do so with a simple RC filter. V Figure 1: Voltage versus time snapshot of a sine wave contaminated with high frequency noise. Our goal here is to design a filter to allow the signal, a 60 Hz sine wave, to pass, and to stop the noise, a much higher frequency sine wave. We ll be using some fancy Agilent arbitrary waveform generators to make our noisy waveform. We ve borrowed them from the Junior Laboratory so please be careful with them. You ll only be using these waveform generators for the first part of the experiment so we ve pre-configured them with a 60Hz sine wave with 1000Hz noise on it, similar to that in Fig. 1. Just turn them on using the power button in the lower left-hand corner of the front panel and you should be ready to go. t Agilent Waveform Generator Your RC Filter V out Figure 2: Block diagram of circuit used for testing your filter design. 2

3 We need to design a filter to separate out the high frequency noise from the signal we want, the 60 Hz sine wave. Your task is to choose which type of RC filter to use, high-pass or low-pass, and then to choose the appropriate components to retain the signal we want and to remove the noise we don t want. In other words you have to choose R and C for your filter such that f 3db is between the signal and noise. This may seem relatively arbitrary since you could choose it to occur anywhere, however keep in mind the shape of the gain curves you measured for RC filters in Lab 5. Select f 3db so that you retain most of the signal while removing as much noise as possible. Choose your filter components and then build your filter. Hook up your noisy waveform to your RC filter and then observe how well your filter performs by viewing both Vin (the noisy waveform), and Vout (the output of your filter) on the DataStudio oscilloscope. Is the 60 Hz sine wave reduced in voltage at all as it passes through your filter? If so, could you have chosen an f 3db so that the 60 Hz signal would pass through unchanged? How reduced is the 1k Hz noise? Is there a choice of f 3db that would lead to an even greater reduction in the amplitude of the noise? Reduce your f 3db by half and note the change in the output of the filter. Then double your original f 3db and note the change in the output of the filter. Given our limited selection of capacitors you ll likely have to change the R in your filter to change f 3db to the value you want. As you have likely observed, there are tradeoffs when choosing f 3db for a filter. If you choose it close to the noise in order to preserve the signal we want then the noise isn t reduced by much. If you choose it closer to the signal then the signal itself is reduced significantly by the filter. The latter is the best choice when designing a filter since it s easy to amplify the post-filtered signal again once you ve removed the noise. 3 Full-wave Rectifier In Lab 6 we took a quick look at a diode circuit, the half-wave rectifier. Using it we were able to build a reasonable approximation of a DC power supply by adding a capacitor at the output of the rectifier. Many of you noted, however, that we were just throwing away the negative portion of our input sine wave, a good consideration when designing a power supply to operate efficiently. A similar but slightly more complex circuit, the full-wave rectifier, uses a total of 4 diodes to make use of the negative portion of the input sine wave. Fig. 3 shows the half wave rectifier circuit you built in Lab 6. Build 3

4 Pasco Power Amp 4.7kΩ V out Figure 3: Half-wave rectifier circuit. that circuit again on your breadboard and observe the output of the circuit when driven with the output from the DataStudio Power Amplifier set to provide a 60 Hz sine wave at 10V amplitude. Now construct the full-wave rectifier shown in Fig. 4 on your breadboard as well and drive it with the same input signal. Try to construct the circuit similar to how it appears in Fig. 4 so that you ll have an easier time troubleshooting if necessary. Observe both outputs using two Voltage Sensors. You should see that the full-wave rectifier circuit does a much better job at turning the oscillating AC signal into a positive signal with a frequency twice that of the original. Pasco Power Amp 4.7kΩ V out Figure 4: Full-wave rectifier circuit. Note, also, the voltage differences between the outputs of the two rectifiers. The full wave rectifier will have an output slightly smaller than that of the half-wave. Can you trace the current through the full-wave rectifier circuit to see why the output is two diode drops below the input for a full-wave rectifier instead of just one diode drop as with the half-wave rectifier? Recall that current can t just stop but must flow in a complete loop. 4

5 4 DC Power Supply Now, as we did in Lab 6 with the half-wave rectifier, add a 22 microfarad capacitor across the output of your full-wave rectifier (in parallel with the resistor). These capacitors are known as electrolytic capacitors and have a polarity that must be observed. Make sure that the arrow on the white band points to the lower voltage part of your circuit. Observe the output in the DataStudio oscilloscope. We hope that you ll find a reasonable approximation of a DC voltage as your output. In fact, it ought to have half the ripple, or variation in the output waveform, as the half-wave rectifier from Lab 6. So, aside from the additional diode drop we ve managed to get a much better DC voltage using a full-wave rectifier than we got with a half-wave rectifier. I Zener Voltage V Figure 5: Current versus voltage curve for a typical Zener diode. As you can see, though, the output from the full-wave rectifier still isn t that great of a DC voltage. It s not flat at all compared to the DC voltages output by the Pasco Power Amplifier you ve been using in previous labs. With the addition of a single component, a Zener diode, you can turn your passable DC voltage into a reasonably stable DC voltage. A Zener diode is a special type of diode that is made to have a specific breakdown voltage. Fig. 5 shows an I-V curve for a Zener diode. You can tell that, at a particular reverse-bias voltage (the cathode voltage higher than the anode voltage) the diode starts to conduct. We can use this to 5

6 our advantage with our full-wave rectifier as shown in the circuit in Fig. 6. By adding a resistor in series (Why do you think we need to do this?) and the Zener diode in parallel to the output we will effectively short the output that is greater than the Zener breakdown voltage to ground which will hold our output constant at the Zener diode voltage, in other words, we ve regulated the output voltage. Pasco Power Amp + 220Ω 4.7kΩ V out Zener Diode Figure 6: Basic regulated DC Power Supply using Zener Diode as regulator. Build the circuit in Fig. 6 and look at the output on your Datastudio oscilloscope. Note that the output is both a bit flatter and lower in voltage than without the Zener in place. We ve chosen a Zener diode with a 5.1V breakdown voltage and, we hope, your circuit reflects this. You may be wondering why we still aren t achieving a really flat output. It s a very reasonable question and has to do with the variable resistance in the breakdown region on the Zener diode. Our Zener diode I-V curve was a little optimistic about the shape of the curve after the diode breaks down in reverse-bias and it s less vertical than we portrayed. If the Zener diode circuit leaves you unsatisfied with the flatness of your DC voltage then we have one more circuit that might appease you. It s called, unsurprisingly, a voltage regulator. It s a three-terminal integrated circuit (IC) that does just that using a lot of transistors (more on those in Physics 202) and a cool circuit feature called feedback. It s far more complex than we re going to go into now, but we want to introduce you to them since they re super easy to use and work really well. Fig. 7 shows the voltage regulator we ll be using, the It s got three terminals: input, ground, and output from left to right if you re viewing it from the front (where the writing is). The pins on the 7805 should fit into the holes on your breadboard but make sure that the pins are electrically isolated from each other when you insert it. Note that we ve added capacitors to the input and output of the

7 7805 Input Output Ground Figure 7: Pinout of a three-terminal voltage regulator, the regulator. Since the circuit uses feedback these are required to prevent noise oscillations that can form. Capacitors are used in this capacity throughout most commercially produced circuits (not only on regulators) to prevent oscillations and noise from dominating circuit performance. Also note that we no longer need the two resistors that we used in the Zener diode circuit; the 7805 takes care of all of that for us! Pasco Power Amp + In 7805 Ground Out V out 22µF 0.22µF Figure 8: DC power supply circuit using a 7805 voltage regulator. Build the circuit shown in Fig. 8 and apply the same 10V, 60 Hz. sine wave you ve been using to the input. Look at both the input and output on the Datastudio oscilloscope. We hope that you now see a very nicely regulated 5V DC output and are beginning to see the power of integrated circuits to simplify circuit building. Voltage regulator ICs are about as simple as ICs come but, as you can see, they do a great job with a rather complex task. We now move on to discuss a more complex, but also very common, IC, the 555 Timer. 7

8 5 555 Timer The 555 timer is a cheap, important and relatively simple integrated circuit (IC) that produces very accurate sequences of digital signals 2, called pulse trains (for example, a square wave is an example of a periodic pulse train). Among their many uses, 555 timers can be used to control everything from simple robotic motors called servos to complex electrical circuits operation Figure 9: a) The 555 timer chip with pin numbers and names. b) The pin configuration of the 555. Note that Pin 3 is the output, Pin 5 is not connected, and Pin 1 is connected to ground. The 555 is relatively simple...for an IC. To describe exactly why the 555 works the way it does is beyond the scope of this lab and so we ll only focus on the basic ideas and rules regarding it s function here. The most important aspect of the 555, the way we ll be using it, is that it takes in a DC voltage (5V DC in our case) and outputs a pulse train (think square wave). It s also sometimes known as an oscillator chip because of just this feature. 2 Digital signals, unlike analog signals, can have only one of two voltage values, in this case zero and five volts. In general, the lower voltage signal is called low or off and the high voltage signal is called high or on. While not all digital signals operate on the same voltages, they all operate on this same basic principle. 8

9 As shown in Fig. 9, the 555 has 8 pins which link the internal circuitry to the outside. The second diagram in Fig. 9 shows the manner in which the 555 should be setup. This configuration of the 555 is called the astable mode and, configured this way, it will generate a periodic pulse train, such as a square wave. Output (Pin 3) Pin 6 Figure 10: The output signal of a 555 timer when the input signal comes from an RC circuit in which the capacitor continually charges through both resistors and discharges through R B to Pin 7, jumping back and forth from 2/3 V cc to 1/3 V cc. When the capacitor is charging, the output of the 555 (Pin 3) is a digital high signal, when it is discharging, the output is a digital low signal. The 555 functions in the following manner. Refer to Fig. 9 and Fig. 10 for clarification. 1. When the power is first turned on (V cc = 5V DC is applied to the circuit) the output pin (Pin 3) is low (zero volts). 2. The capacitor charges through the combined resistance of R A and R B. This forms a simple RC charging circuit with time constant, τ = (R A + R B ) C. 3. When the capacitor charges to a value of 1/3 V cc, Pin 2 is triggered, causing the output (Pin 3) of the 555 to go high (five volts). 9

10 4. The capacitor continues to charge until the voltage across it reaches 2/3 V cc, at which point Pin 6 causes the output (Pin 3) go low (zero volts) and the discharge (Pin 7) to connect to ground. With the discharge (Pin 7) connected to ground the capacitor discharges through R B to ground with time constant τ = R B C. 5. The capacitor continues to discharge until the voltage across the capacitor reaches 1/3 V cc, at which point Pin 2 causes the output to go high again the discharge Pin 7 to close (no longer connected to ground). Now the capacitor begins to charge again through the combined resistance of R A and R B. 6. This charging and discharging continues indefinitely (as long as power is supplied) and the output (Pin 3) continues to flip-flop between zero and five volts. The 555 turns an analog timing signal (the RC charging and discharging curve shown as Input in Fig. 10) into a digital, pulsed timing signal. The time the output is high, T H (also called the pulse width ), is controlled by the values of R A, R B, and C. The pulse width is given by the time it takes the capacitor to charge from 1/3 to 2/3 Vcc. The time the output is low T L is controlled by the value of R B and C, and is equivalent to the time it takes the capacitor to discharge from 2/3 to 1/3 Vcc through R B. T H and T L are given by T H = Cln(2)(R A + R B ) (1) T L = Cln(2)R B (2) Note that T H must always be greater than T L (since R A 0), which we can express this in terms of duty cycle. Duty cycle is the percentage of time the circuit spends high during one period of operation. T H Duty Cycle = = R A + R B (3) T H + T L R A + 2R B In other words, the duty cycle can never be less than 50 percent. This is unfortunate since there are many times when it is desirable to have short pulse widths and low duty cycles, such as when controlling a servo! To get around this we can simply add a basic digital integrated circuit called a NOT gate (Fig. 11) which inverts the input. If the input to the NOT gate is low, the output will be high and If the input to the NOT gate is high, the output will be low. 10

11 Figure 11: This chip contains six NOT gates, each one indicated by a triangle/circle symbol. The lead going into the triangle is the input to the gate and the lead coming from the circle is the output. V cc for the chip should be 5 volts DC Experiment Now that you ve got a basic understanding of the 555 timer IC set it up on your breadboard as described below. 1. Hook up the 555 on your breadboard as shown in Fig. 9. It s best if you orient your breadboard horizontally and then place the 555 timer IC so that the legs span the large trough down the center of the breadboard with the scalloped end of the chip oriented to the left. Some chips may have a spot on them instead of the scallop shown in Fig. 9, just orient them with the spot to the left. Using your DataStudio Power Amplifier supply 5V DC to Pins 4 and 8 (V cc ). Also don t forget to connect Pin 1 to ground. Hook up the remainder of the pins as shown in Fig Use values for the resistors of between 5kΩ and 10kΩ for R A and R B and a value between 0.1 and 1 µf for the capacitor, C. Use values which give the circuit a duty cycle between 50 and 80 percent. 3. Use two voltage sensors to help analyze the circuit. Place one across the capacitor (from Pin 6 to ground) and hook the other one up to the output of the 555 timer, Pin 3 (Fig. 9). View both outputs on a single oscilloscope using DataStudio. 11

12 4. If you re interested you may hook up a variable resistor (also called a potentiometer) in place of R B to vary the pulse width. How close are T H and T L, for both the RC circuit charging/discharging and the digital output, to what is predicted by (1) and (2). Is the duty cycle what you expected it to be? Are these values within uncertainty of the components used (Resistors are ±5% and the capacitor is ±10%)? Does the potential on the capacitor jump back and forth from 1/3 Vcc to 2/3 Vcc continually? Now, choose values for the resistors which make the duty rate around 90 percent. Now that you ve achieved a duty cycle of 90% we ll use a NOT gate to invert it to obtain a duty cycle of 10%, not possible with just the 555 timer alone. Set-up one of the NOT gates from the 7404 IC chip by applying 5V DC to Pin 14 (V cc ) and ground to Pin 7. Note that the long rectangular chip has 6 NOT gates as shown in Fig. 11, but we ll only use one. Now attach the output of the 555 timer (Pin 3) to the input of one of the NOT gates (such as Pin 1 on the NOT gate chip). Now, using two Voltage Sensors and the DataStudio oscilloscope, observe the output of the 555 timer (Pin 3) and the output of the NOT gate (if you used Pin 1 on the NOT gate as your input, then observe Pin 2 on the NOT gate using your second Voltage Sensor). Is the NOT gate acting like an inverter, changing the duty cycle from about 90% to about 10%? to control servo motor Using the circuit we ve built with the 555 timer and NOT gate we can now drive a servo motor. The angular position of the shaft on servo motors is controlled by the spacing between pulses applied to the input. By varying the time between pulses we can vary the position of the shaft. This particular servo, called an HS-303 and used in many robotic applications, is controlled by a signal of a periodic pulse train with a pulse width from one to two milliseconds with a time between pulses of 20 to 30 milliseconds. The time between pulses controls the position of the servo. For example, it might be the case that with a time between pulses of 20 milliseconds the servo is at an angular position of zero degrees, while with a time between pulses of 30 milliseconds the servo is at an angular position of 180 degrees. Of the three wires coming out of the servo the black wire should be grounded, the red wire should be hooked up to a voltage source (the 5V DC 12

13 supply you re powering your 555 and NOT gate with should work fine) and the yellow wire is where the controlling signal (output of the NOT gate) is attached. Choose R A = 10kΩ and R B to be a 10kΩ variable resistor, which will allow you to easily control the servo. For C use a 1µF capacitor. Set up your 555 timer with the resistor and potentiometer as described and view the output of the NOT gate on the oscilloscope. Can you see the time between pulses change when you turn the dial of the potentiometer? If so then go ahead and hook up the output to the servo motor. Now the servo motor should move as you turn the potentiometer. 13