### Project I - A Wien-Bridge Oscillator

The object of this experiment is to assemble, evaluate, and simulate a Wien-bridge oscillator circuit. You can read the textbook's treatment of the circuit here. The items to be performed in the lab are described in the following.

For all of the circuits, you should have 100 μF decoupling capacitors from each power supply rail to circuit ground. You should be aware that these capacitors are polar electrolytics which can explode if they are put in with the wrong polarity.

Op amps can oscillate when equipment such as an oscilloscope is connected to a circuit. This is caused by the shunt capacitance of the connecting leads and the input capacitance of the test equipment. To minimize these problems, clip a 100 Ω resistor in series with the signal lead to the oscilloscope. Use the other end of the resistor to connect to the proto board.

You should never turn on a circuit without the oscilloscope connected to its output. Not doing this is like driving on a highway blindfolded. Connect the oscilloscope and adjust it so that it displays a trace before applying power to any circuit. Observe the scope to verify that the circuit is operating before taking any measurements.

An analysis of the Wien-bridge oscillator from my ECE 3050 notes is here. This page shows the circuit diagram of the vacuum tube oscillator built by Hewlett and Packard when they were seniors at Stanford in the 1930s. Their circuit became the first product of Hewlett-Packard Corp.

#### Part A

1. Assemble the circuit in Fig. 10.2(a) of the text. Pick a convenient value for C, e.g. you might choose C = 0.01 μF. Calculate R for an oscillation frequency f0 = 5 kHz. Use R1 = 10 kΩ and R2 = 20 kΩ. This combination gives a gain from Vp to Vo of 3. This is the theoretical gain for stable oscillations.
2. Disconnect the upper right resistor labeled R in Figure 10.2 from the Vo node. Connect the output of the function generator to the unconnected side of R. Set the output resistance of the function generator to low, ideally zero. Set the generator amplitude to a convenient value, e.g. this might be 1 V peak. Connect Channel 1 of the oscilloscope to the function generator output and Channel 2 to the Vo node. Manually sweep the generator frequency and use the oscilloscope to verify that the gain around the loop at f0 is 1 at an angle of 0 degrees. Check your circuit if it is not.
3. Connect the x channel of the osciloscope to the function generator output and the y channel to the Vo node. Display the Lissajous figure on the oscilloscope. Manually vary the frequency of the function generator and note that the Lissajous figure collapses to a straight line of slope +1 at the frequency f0. This means that the loop-gain is 1 at angle 0 degrees at that frequency. Observe the shape of the Lissajous figure for frequencies not equal to f0.
4. Use the automated measurement capabilities of the lab equipment to measure the Bode magnitude and phase plots shown in Fig. 10.2(b) of the text.
5. Remove the function generator and connect resistor R to the Vo node. The circuit should oscillate and put out a sine wave at the frequency f0. The amplitude of the oscillations cannot be predicted at this point in the procedure. If the circuit does not oscillate, it might be that the gain of the op amp, set by R1 and R2, is less than 3. You should be able to tweak the circuit to make it oscillate, but the amplitude will be unpredictable.
6. Replace resistor R2 to the diode circuit shown in Fig. 10.2(a). Use Use a 22 k&Omega resistor in place of the 22.1 k&Omega resistor shown in the text. Use 1N4148 diodes. When the two diodes are non conducting, the gain of the op amp is 3.2. When either diode is conducting, the gain reduces to 2.8. The op amp must have a gain of 3 for stable oscillations. Thus the diodes should act to stabilize the amplitude of the output voltage so that the peaks of the sine wave just cause one of the diodes to conduct.
7. The circuit should oscillate when power is applied. If we assume a diode threshold of 0.5 V, the amplitude of the oscillations should be about 1.4 V peak. You should derive this in your report. Use the available equipment in the laboratory to measure the spectrum of the output signal. Use this to calculate the % distortion in the waveform.
8. A better limiter circuit is shown in Fig. 10.5 of the text. The amplitude of the output signal is set by the supply voltage and the ratio of R4 to R3. For the values given in the figure, the amplitude of the output signal should be approximately 4.6 V peak when the diodes turn on.
9. Assemble the circuit. The circuit should oscillate. Use the equipment available in the laboratory to measure the spectrum of the output signal. Use this to calculate the % distortion in the waveform.
10. This experiment will be continued in the second week of the lab. The object will be to assemble a circuit similar to the one in Fig. 10.3(b) which uses a JFET as a variable resistor. This circuit should exhibit a lower distortion that what can be obtained with the diode limiter circuits.

#### Part B

This circuit diagram shows a better version of the Wien Bridge Oscillator. (The polarity of the 1 μF capacitor is backward in the circuit.) Instead of a diode limiter circuit to set the amplitude, the circuit uses a JFET operated in its triode region as a linear resistor to vary the resistor R3 (R1 in the original circuit in the textbook). The JFET is in series with a 3.3 kΩ resistor. This combination replaces R1 of the original circuit. Note that the 20 kΩ resistor of the orignal circuit is now 10 kΩ. The values of the elements that you used for the resistors and capacitors that set the oscillation frequency are not to be changed from those used in Part One. An explanation of how this circuit works is at http://hobby_elec.piclist.com/e_ckt18_2.htm.

The first step is to measure the threshold voltage VTO and transconductance parameter β of the JFET. The JFET type is to be a 2N5457. Put the JFET in some vacant area on your protoboard. Use jumper wires to connect the gate and the source to ground. Apply a dc voltage to the drain of 10 V in series with a 100 Ω resistor. The resistor is to limit the current in case something is not connected right. Measure the drain current and record it as the drain-source saturation current IDSS. Replace the jumper connected to the source with a potentiometer connected as a variable resistor. Leave the gate connected to ground. With the 10 V applied to the drain, adjust the resistor until the drain current is 1/4 the value obtained without the potentiometer. If the current is very sensitive to the setting on the potentiometer, use a smaller value potentiometer or add a resistor (maybe 1 kΩ) in parallel with the potentiometer. Measure the gate to source voltage and record the value as VGS1. This voltage should be negative. Calculate the transconductance parameter and threshold voltage as follows:

VTO = 2VGS1

β = 0.25IDSS/VGS12

After you make these calculations, you may use the curve tracer to measure the parameters to check your results. For the 2N5457, IDSS typically falls in the range of 2 mA to 3 mA and VTO falls in the range of -2 V to -3 V.

The two 100 kΩ resistors that connect to the JFET are used to linearize its small-signal resistance. They do this by feeding back one-half of the ac drain-source voltage into the gate of the JFET. Note that C3 and C4 are short circuits for this calculation. Because C3 is an are open circuit for dc, it follows that the dc voltage at the JFET gate is equal to the voltage across C4. When the two resistors and the 10 μF capacitor are added to the circuit, the small-signal resistance seen looking into the drain is given by

rds = [2β(VC - VTO)]-1

where VC is the voltage across the 1 μF capacitor.

The gain of the op amp from Vp to Vo must be exactly +3 for stable oscillations. Using the resistor subscripts in the new figure, this gain is given by

Av = 3 = 1 + R4/(R3 + rds)

This can be solved for the required value of R3 to obtain

R3 = 5 kΩ - rds

To solve for R3, we need the value of rds. But this depends on the value of VC. I recommend choosing VC = VTO/2 for this calculation. In this case, rds and R3 are given by

rds = -[βVTO]-1

R3 = 5 kΩ - rds

Because VTO is negative, rds is positive and R3 is less than 5 kΩ.

After you calculate the required value of R3, assemble the circuit using 2N4148 diodes and turn the dc power supplies on. You should observe a clean sine wave at the output. Measure the voltage across the 1 µF capacitor. It should be approximately VTO/2. The amplitude of the oscillations should be approximately 2VD - VTO/2, where VD is the diode threshold voltage, which should be approximately 0.6 V. (Remember that VTO is negative, so that -VTO is positive.)

Measure the distortion of the circuit. It should be lower than that of the circuits with the diode limiters. A truly low-distortion audio oscillator can have a percent distortion as low as 0.001%.

The harmonic distortion content is calculated as the square root of the sum of the squares of all harmonics. When this is divided by the fundamental and multiplied by 100%, you obtain the percent distortion.