# Perfect Sine Waves At Particular Frequencies example essay topic

The results we got were very sound. We were able to generate all of the minimum requirements (a square wave and ramp wave). Also, we were able to generate the waves that would give us extra credit (a triangle wave and approximations to a sine wave). We also discovered a way to easily vary frequency and amplitude.

2. Introduction This experiment uses four operational amplifier's (op amps) to deliver these waveforms in the 6 Hz to 7000 Hz range. The sine wave is a pseudo sine wave produces by a very simple wave Shaping circuit. A digital counter can be used along with a DAC to generate analog voltage functions of time such as square wave and ramp wave. In this lab, we were to design and build a circuit that generates an analog square wave and a saw-tooth (ramp) wave of voltage, using a counter and DAC/.

3. Design Process While working on this project, we thought of alternatives that would increase efficiency. An alternative we considered was to switch to a different project. This was thought about when we were having trouble with the implementation of the circuit.

However, we decided to stick with this project. We decided this because we had already put in much thought and work into this particular project. Also, we decided to use flip-flops to simplify the circuit. 4. Implementation CIRCUIT DESCRIPTION Square, sine and triangle waves are produced using an LM 348 and passive components. The LM 348 is a quad operational amplifier IC package; that is, it contains four separate op amps all in the one IC.

They are marked A, B, C & D in the schematic diagram. Square Wave. One op amp (LM 348: D) is used. The voltage level to pin 13 is set by the resistor divider pair R 1 and R 2. The input to pin 12 depends on two things; firstly the potential of pin 14, and secondly, the voltage output of op amp C at pin 8. When the input at pin 13 is higher than the input at pin 12 the output goes low.

If it is lower then the output goes high. Switching back and forth between the two states causes a square wave to be produced. The time constant (R 4+R 5) C 2 determines the frequency. Triangle Wave. You can also consider that op amp D is set up as a bi-directional threshold detector with positive feedback provided by R 3. R 3 also gives hysteresis.

The output provides a bias, which tends to keep it in its existing state before allowing switching to take place. The inverting input is set up at about half the op amp output swing voltage by resistors R 1 andR 2. Accordingly the signal required from op amp C to cause switching is offset from this midpoint voltage by R 11/ (R 11+R 3), which is approximately 2/3 the voltage from midpoint to swing limit, and is symmetrical above and below the switching point. Op amp C is set up as an integrator. It performs the mathematical operation of integration with respect to time.

For a constant input the output is a constant multiplied by the elapsed time, that is, the output is a ramp. Since the input signal goes to the inverting input, a high input will produce a ramp down and a low input will produce a ramp up. The input signal is a square wave symmetrical about the midpoint potential. The current this potential produces through R 4 and R 5 is constant so the up and down ramps are of equal gradient and the resultant triangular wave is symmetrical.

Any increase in the trim pot R 5 reduces the current and the integration constant which lowers the gradient of the ramp. The switching levels have not changed so the frequency reduces while the amplitude remains constant. In a similar way the current depends on the value of integration capacitor. Accordingly the integration constant and hence the frequency vary with the value of the capacitor.

(Higher value, lower frequency since the capacitor takes longer to charge.) If C 2, for example, is increased to say 680 nF then the minimum frequency will be less than 1 Hz. The output triangle wave does not require amplification but it does require buffering so that that loading does not affect the waveform generator circuit. It is buffered here with op amp A connected as a unity gain buffer. Unity gain is achieved by directly coupling back the output to the inverting input. Sine Wave. A pseudo or imitation sine wave is produced by a wave shaping circuit.

A diode is a non-linear device. As the potential difference across it increases the current rises in the characteristic way published in all textbooks. This circuit 'joins together' this characteristic curve to produce an approximation to a sine wave. Two diodes have been joined together as a series pair in order to provide higher amplitude than would be obtained using only a single diode. The shape of the pseudo sine wave could be improved at any particular frequency by filtering, but filtering will cause distortion at lower frequencies and loss of amplitude at higher frequencies. You can have perfect sine waves at particular frequencies by switching inappropriate filters at those frequencies.

The sine wave is sensitive to loading and must be buffered. It is also low in amplitude and needs amplification. R 9 & R 10 set the gain of op amp B by forming a voltage divider between the source and the output. If the wave shaper voltage is 1 volt higher than the reference (at the non-inverting input) the op amp reduces the output voltage until the inverting input voltage set by the divider is equal to the non-inverting voltage.

The ratio of the values of R 10 to R 9 gives the gain. The gain here is about 2.5. Testing 6. Evaluation Overall, we were very successful in completing the objectives set forth by the project description. We worked very well together to finish this project, and the following write-up.

Initially, we encountered a problem with developing the square wave. However, this problem was solved with the proper logic techniques. We were surprised to find that adding a flip-flop changed the signal to a sine wave. 7.

Summary This project, in particular, is well designed. We learned much information about flip-flops, frequency control and counters. We would recommend this project to any incoming students taking this class. If we were to do a redesign, we would draw the schematic before the actual construction of the circuit. This is very efficient and saves much needed time, as well as improves organization. ASSEMBLY INSTRUCTIONS Identify all the components supplied in the kit against the Components listing.

Make sure you get the 4 diodes and the integrated circuit (IC) around the correct way. Match the bar on the diodes with the bar shown on the PCB overlay. WHAT TO DO IF IT DOES NOT WORK Poor soldering is the most likely reason that the circuit does not work. Check all solder joints carefully under a good light. Next check that the four diodes and the IC are in their correct orientation on the PCB. Is the battery flat?

A cathode ray oscilloscope (CRO) is the ideal test instrument to check the operation of the Kit.