by Earl Boysen
B. 7.7 kΩ (approximately).
C. The number of turns in the coil and the position of the tap are not known.
Figure 9.28 shows a Hartley oscillator with the parallel LC circuit connected between the collector and the supply voltage. As with the circuit shown in Figure 9.27, this circuit provides a feedback signal to the emitter from a tap in the coil, in the correct phase to provide positive feedback.
Figure 9.28
Project 9.2: The Hartley Oscillator
Objective
The objective of this project is to demonstrate a Hartley oscillator using two inductors in series.
General Instructions
After the Hartley oscillator circuit is set up, you use your oscilloscope to measure the period of the waveform, from which you can calculate the frequency of the oscillator. You also calculate the frequency from the inductance and capacitance used in the parallel LC circuit. Note that when two inductors in series are used, rather than a tapped coil, the total inductance is found by adding the individual inductance values, using the following equation:
LT = L1 + L2
Parts List
You need the following equipment and supplies:
One 10 k, 0.25-watt resistor.
One 510 , 0.25-watt resistor.
One 82 k, 0.25-watt resistor.
One 8.2 k, 0.25-watt resistor.
Three 1 μF capacitors. (This value of capacitor is available in either polarizied or unpolarized versions.You should get unpolarized capacitors for this application.)
One 0.01 μF capacitor.
One 6.8 mH inductor.
One 3.1 mH inductor.
One 9-volt battery pack.
One breadboard.
One oscilloscope.
One PN2222 transistor. Figure 9.29 shows the pinout diagram for PN2222 transistors.
Figure 9.29
Step-by-Step Instructions
Set up the Hartley oscillator circuit shown in Figure 9.30. If you have some experience in building circuits, this schematic (along with the previous parts list) should provide all the information you need to build the circuit. If you need a bit more help building the circuit, look at the photos of the completed circuit in the “Expected Results” section.
Figure 9.30
Carefully check your circuit against the diagram.
When you have checked your circuit, follow these steps.
1. Connect the oscilloscope probe for Channel 1 to a jumper wire connected to Vout. Connect the ground clip to a jumper wire attached to the ground bus.
2. Measure and record the period of the sine wave.
Period = _____
3. Calculate the frequency of the sine wave.
Frequency = _____
4. Calculate the expected resonance frequency from the value of the capacitor and inductors used in the parallel LC circuit using the following equation:
fr = _____
Expected Results
Figure 9.31 shows the breadboarded Hartley oscillator.
Figure 9.31
Figure 9.32 shows an oscilloscope attached to the circuit.
Figure 9.32
Figure 9.33 shows the sine wave generated by the Hartley oscillator. You can determine the period of this waveform by counting the number of horizontal divisions the waveform takes to complete one cycle, and then multiplying the number of divisions by the TIME/DIV setting.
Figure 9.33
As you measure the period, you may need to adjust the TIME/DIV, the horizontal POSITION, and the vertical POSITION controls on the oscilloscope. The controls shown in Figure 9.34 are adjusted to measure the period for the Hartley oscillator.
Your values should be close to those shown here:
Period = 74 μsec
Frequency = 13.5 kHz
This measured frequency is close to the calculated resonance frequency of 15.8 kHz.
Figure 9.34
The Armstrong Oscillator
The Armstrong oscillator shown in Figure 9.35 is somewhat more difficult to design and build. Here, the oscillations depend more on the extra winding on the coil than on any other factor.
Figure 9.35
Because of the large variety of transformers and coils available, it is almost impossible to give you a simple procedure for designing an Armstrong oscillator. Instead, the manufacturer specifies the number of turns required on the coils, which guarantees that the oscillator will work in its most common operation, at high radio frequencies.
Because of the practical difficulties, the Armstrong oscillator and its variations are not explored any further.
Practical Oscillator Design
26 This section briefly covers some practical problems with oscillators.
Before you proceed, review the important points of this chapter by answering the following questions.
Questions
A. What three elements must an oscillator have present to work? _____
B. What determines the frequency of an oscillator's output signal?
C. What provides the feedback?
D. How many feedback methods for oscillators have been discussed?
E. What do you need to start the oscillations once the circuit has been built?
Answers
A. An amplifier, a resonant LC circuit (or some other frequency determining components), and feedback.
B. The frequency of the output signal is the same as the resonance frequency.
C. A voltage divider on the resonant circuit.
D. Three: the Colpitts, Hartley, and the Armstrong.
E. Nothing: The oscillations should start spontaneously if the component values in the circuit are correct.
The main practical problem with building oscillators is selecting the coil. For mass production, a manufacturer can specify and purchase the exact coil required. But in a lab or workshop (where you are building only a single circuit), it is often difficult or impossible to find the exact inductor specified in a circuit design. What usually happens is that you use the most readily available coil, and design the rest of the circuit around it. This presents three possible problems:
You may not know the exact value of the inductance.
The inductance value may not be the best for the wanted frequency range.
The coil may or may not have tap points or extra windings, and this may cause a change in the circuit design. For example, if there are no taps, then you cannot build a Hartley oscillator.
Because Colpitts is the easiest oscillator to make work in practice, and provides an easy way around some of the practical difficulties, you can focus on that oscillator.
You can use almost any coil when building a Colpitts oscillator, provided it is suitable for the frequency range you want. For example, a coil from the tuner section of a television set would not be suitable for a 1-kHz audio oscillator because its inductance value is outside the range best suited to a low-frequency audio circuit.
Simple Oscillator Design Procedure
27 Following is a simple step-by-step procedure for the design of a Colpitts oscillator. The Colpitts can work over a wide frequency range. (A Hartley can be designed using a similar set of steps.)
By following this procedure, you can design an oscillator that works in the majority of cases. There is a procedure you can use that guarantees that the oscillator will work, but it is far more complex.
Follow these steps:
1. Choose the frequency of the oscillator output signal.
2. Choose a suitable coil. This step presents the greatest practical difficulty. Some values of coil are often not available, so you must use whatever is readily available. Fortunately, you can use a wide range of inductance values and still obtain the desired resonance frequency by adjusting the value of the capacitor.
3. If you know the value of the inductance, calculate the capacitor value using this formula:
Use this value of capacitor for C1 in the next steps.
4. If you don't know the inductance value, choose any value
of capacitance and call this C1. This may produce a frequency considerably different from what you require. However, at this stage, the main thing is to get the circuit oscillating. You can adjust values later.
5. Choose a capacitor C2 that is between 3 and 10 times the value of C1. Figure 9.36 shows the two capacitors and the coil connected in a parallel circuit, with the two capacitors acting as a voltage divider.
Figure 9.36
At this point, stop and make some assumptions. Suppose you need a frequency of 10 kHz and have a coil with a 16 mH inductance.
Questions
A. What approximate value of C1 do you need?_____
B. What value of C2 do you need?_____
Answers
A. C1 = 0.016 μF
B. C2 = 0.048 μF to 0.16 μF
28 Now, continue with the design procedure by following the next steps.
6. Design an amplifier with a common emitter gain of about 20. Choose a collector DC voltage that is about half the supply voltage. The main point to keep in mind here is that the collector resistor RC should be about one-tenth the value of the impedance of the LC circuit at the resonance frequency. This is often a difficult choice to make, especially if you don't know the coil value. Usually, you have to make an assumption, so RC is an arbitrary choice. 7. Draw the circuit.
8. Calculate the value of CC. Do this by making XC 160 ohms at the desired frequency. This is another “rule of thumb” that happens to work, and you can justify it mathematically. Use the following formula:
Question
Substitute the values given so far into the formula to calculate CC._____
Answer
29 Now, complete one last step.
9. Calculate the value of CB. Again, choose a value so that XC is 160 ohms at the desired frequency.
Question
What is the value of CB?_____
Answer
30 Continue the design procedure steps.
10. After you build an oscillator, apply power to the circuit and look at the output signal on an oscilloscope. If the output signal is oscillating, check the frequency. If the frequency varies significantly from the desired frequency, then change C1 until you get the wanted frequency. Change C2 to keep the ratio of the capacitance values about the same as discussed in step 5. C2 affects the output level.
11. If the circuit does not oscillate, go through the steps outlined in the troubleshooting checklist that follows.
Oscillator Troubleshooting Checklist
If an oscillator does not work, most often the trouble is with the feedback connections. A little experimenting (as outlined in steps 2 through 6 of the following checklist) should produce the right results. This is especially true when you use an unknown coil that may have several taps or windings. However, you should try each of the following steps if you have trouble.
1. Ensure that CB, CC, and CE are all large enough to have a reactance value less than 160 ohms. Ensure that CE is less than one-tenth of RE.
2. Check the C1/C2 ratio. It should be between 3:1 and 10:1.
3. Swap out C1 and C2. They may be connected to the wrong end of the LC circuit.
4. Check that you made the feedback connection to and from the correct place.
5. Check both ends of the LC circuit to see that they are connected to the correct place.
6. Check the DC voltage level of the collector, base, and emitter.
7. Check the capacitor values of the LC circuit. If necessary, try some other values until the circuit oscillates.
8. If none of the previous actions produce oscillations, check to see if any of the components are defective. The coil may be opened or shorted. The capacitor may be shorted. The transistor may be dead, or its β may be too low. Check the circuit wiring carefully.
In most cases, one or more of these steps produces oscillations.
When an oscillator works, it may still have one or two main faults, including the following:
Distorted output waveform—This can happen when CB, CC, or CE are not low enough in value, or when an output amplitude is too high.
Output level too low—When this happens, the sine wave is usually “clean” and “pure.” In a Colpitts oscillator, changing the ratio of C1 and C2 often helps raise the output level. If not, you can use another transistor as an amplifier after the oscillator, as discussed in Chapter 8, problem 21.
31 Now, work through a design example. Design an oscillator with an output frequency of 25 kHz using a coil with a value of 4 mH, and address each of the steps in problems 27–30 as described in these questions.
Questions
1. The value of fr is given as 25 kHz.
2. L is given as 4 mH.
3. Use the formula to find C1.
C1 = _____
4. You do not need this step.
5. Choose C2.
C2 = _____
6. The procedure to design amplifiers is shown in Chapter 8.
7. The circuit is shown in Figure 9.37.
8. Find CC.
CC = _____
9. Find CB.
CB = _____
Figure 9.37
Answers
C1 = 0.01 μF
C2 = 0.1 μF
CC = 0.047 μF (use 0.1 μF)
CB = 0.047 μF (use 0.1 μF)
Steps 10–11 are the procedure you use to ensure that the oscillator works. If you built this circuit, go through steps 10–11. You don't need to do them if you didn't actually build the circuit.
32 Figure 9.37 shows the circuit designed in problem 31.
Measurements of the output signal of this oscillator confirm a frequency close to 25 kHz.
Question
Find the impedance of the LC circuit at resonance. Note that r (the DC resistance of the inductor) is 12 ohms._____
Answer
This is about three times the value used for RC, instead of being 10 times the value of RC, as suggested in step 6 of problem 28.
33 If you want, work through this second oscillator design example. Design an oscillator with an output frequency of 250 kHz using a coil with a value of 500 μH.
Questions
1. fr = 250 kHz
2. L = 500 μH = 0.5 mH
3. Find C1.
C1 = _____
4. You do not need this step.
5. Find C2.
C2 = _____
6. Use the same amplifier as in the last example.
7. The circuit is shown in Figure 9.38.
8. Find CC.
CC = _____
9. Find CB.
CB = _____
Answer
C1 = 0.0008 μF; therefore, choose a standard value of 0.001 μF.
C2 = 0.0047 μF, which is a standard value.
CB = CC = 0.004 μF (minimum).
34 The circuit you designed in problem 33 is shown in Figure 9.38.
Figure 9.38
Measurements of the output signal of this oscillator confirm a frequency close to 250 kHz.
Question
Find the impedance of the LC circuit at resonance. Note that r (the DC resistance of the inductor) is 20 ohms._____
Answer
Z = 30 kΩ
This is about 3 times the value of RC, rather than 10 times the value of RC, as suggested in step 6 of problem 28.
35 Figure 9.39 shows several other oscillator circuits. Calculate the expected output frequency for each circuit and build as many as you want. Check the measured oscillator output frequency against the calculated values for each circuit you build.
Figure 9.39
Questions
What is the output frequency for each circuit?
A. f = _____
B. f = _____
C. f = _____
D. f = _____
Answers
A. 8.8 kHz
B. 10 kHz
C. 3 kHz
D. 1 kHz
Summary and Applications
This chapter covered the following topics related to oscillators:
The main elements that make up an oscillator
How to differentiate between positive and negative feedback
The type of feedback that causes a circuit to oscillate
Two methods to obtain feedback in an oscillator circuit
How resonant LC circuits set the frequency of an oscillator
You also practiced designing a simple oscillator circuit to solidify your understanding of its elements and operation.
Self-Test
These questions test your understanding of the concepts and equations presented in this chapter. Use a separate sheet of paper for your diagrams or calculations. Compare your answers with the answers provided following the test.
1. What are the three sections necessary in an oscillator?_____
2. What is the difference between positive and negative feedback?_____
3. What type of feedback is required in an oscillator?_____
4. What is the formula for the frequency of an oscillator?_____
5. Draw the circuit for a Colpitts oscillator.
6. Draw the circuit for a Hartley oscillator.
7. Draw the circuit for an Armstrong oscillator.
8. Problems 27–30 give a design procedure for oscillators. How well do the circuits in problem 35 fulfill the criteria for that procedure? In other words, check the values of Vf, AV (for a common emitter amplifier), C1/C2 ratio, RC/Z ratio, and the frequency.
A. _____
B. _____
C. _____
D. _____
9. For the circuit shown in Figure 9.38, calculate the values of C1, C2, CC, and CB for an oscillator with an output frequency of 10 kHz using a 100 mH coil.