Laboratory Design Project I

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 capacitance on the connecting leads. 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.

Part One

1. Assemble the circuit in Fig. 10.2(a). Let C = 0.01 μF, or any convenient value. Calculate R for an oscillation frequency f₀ = 2 kHz. Use R₁ = 10 kΩ and R₂ = 20 kΩ.
2. Disconnect the upper right resistor labeled R from the V_o node. Connect the function generator to the unconnected side of R. 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 and Channel 2 to the V_o 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 V_o 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. 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 V_o 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 1. You should be able to tweak the circuit to make it oscillate, but the amplitude will be unpredictable.
6. Change the resistor R₂ to the circuit shown in Fig. 10.2(a). when the two diodes are non conducting, the gain of the op amp was shown in class to be 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. Before closing the loop, display the Lissajous figure as explained above. Manually set the frequency of the function generator so that the figure collapses to a straight line. Increase the amplitude of the signal and observe the effect of the diodes. You should observe the characteristic of what is called a "soft limiter." That is, when either diode conducts, the +1 slope of of the figure is reduced. The small-signal gain of the op amp is equal to the slope of this curve. Thus the soft limiter acts to reduce the gain of the op amp when either diode conducts. Because the limiting of this circuit is very soft, it might not be noticeable on the oscilloscope. It should be much more noticeable if the 100 kΩ resistor is reduced to 10 kΩ. However, the 100 kΩ value gives a lower distortion in the output signal and should be used when measuring the harmonic distortion content of the output.
7. Remove the function generator and close the loop. The circuit should oscillate. In class, it was shown that the amplitude of the oscillations should be approximately 1.5 V peak. 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. 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, it was shown in class that the amplitude of the output signal should be approximately 4.6 V peak when the diodes turn on.
9. Assemble the circuit. With the loop open, use the x and y inputs of the oscilloscope to observe the Lissajous figure that was observed with the first diode circuit. You should notice a harder limiting characteristic with this circuit.
10. Remove the function generator and close the loop. 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.
11. 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 Two

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 V_TO 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 I_DSS. 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 V_GS1. This voltage should be negative. Calculate the transconductance parameter and threshold voltage as follows:

V_TO = 2V_GS1

β = 0.25I_DSS/V_GS1²

After you make these calculations, you may use the curve tracer to measure the parameters to check your results. For the 2N5457, I_DSS typically falls in the range of 2 mA to 3 mA and V_TO 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, it was shown in class that the small-signal resistance seen looking into the drain is given by

r_ds = [2β(V_C - V_TO)]^-1

where V_C is the voltage across the 1 μF capacitor.

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

A_v = 3 = 1 + R₄/(R₃ + r_ds)

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

R₃ = 5 kΩ - r_ds

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

r_ds = -[βV_TO]^-1

R₃ = 5 kΩ - r_ds

Because V_TO is negative, r_ds 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 V_TO/2. The amplitude of the oscillations should be approximately 2V_D - V_TO/2, where V_D is the diode threshold voltage, which should be approximately 0.6 V. (Remember that V_TO is negative, so that -V_TO 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.