Derivative Action on Analog Signals

In this project, the analog waveform are generated through the integrated circuits, which generates Sine, Triangular and Square wave and further this signal is passed to the differentiator, and the output is observed accordingly.

Operational Amplifier:

An operational amplifier, also known as OpAmp, is an IC chip which works as a voltage amplifier, giving output in much amplified range, and this output can be set by setting or adjusting the gain of the OpAmp. It has got two differential inputs, that is, inputs of reverse polarity and a single output.

Differentiator:

A differentiator is nothing but an OpAmp, which gives the differentiated output of the respective input, just like the mathematical operation on a respective input.

A basic and ideal differentiator has a resistor in the feedback path and the negative input of the OpAmp has the capacitor while the reverse polarity is grounded.

The project:

There are two IC chips used in this respective project, and they are namely:

1.      LM741- A normal OpAmp which can be used as a differentiator.

2.    XR2206- A function generator IC which gives output as three waveforms, depending on the connections.

LM741 :

It is an 8 pin IC, having two inputs of opposite polarities, one output, two power supply pins (+Vcc and GND), two offset null pins and a no connection pin.

Figure 1.1: LM341 Pin configuration

Figure 1.2: LM341 operational amplifier pin connection at non-inverting end.

Connecting a resistor in the feedback path and a capacitor at the inverting input, makes up a differentiator circuit.

     Differentiator using LM741:

In this project,  we have generated three wave forms, namely:

• Sinusoidal Wave, whose differentiation is a Cosine Wave.
• Triangular Wave, whose differentiation  is Square Wave.
• Square Wave, whose differentiation is Impulse peaks.

The circuit diagram of the differentiator circuit is as follows:

Figure 1.3: Differentiator circuit

where, Vin is the input to the Op-Amp

            R is the equivalent resistance

                      f is the frequency of the input signal

C is the capacitance.

Here the values of the components are:

1.      C = 33 pF

2.      R1= 470 Ω

3.      R2= 6.10 kΩ

 XR2206:

The wave forms are generated through XR2206, which is a function generator, and is a 16pin IC.

The pin diagram of XR2206 is:

Figure 1.4: XR2206 pin configuration

The pin description is as follows:

1.      AMSI- Amplitude Modulating Sinusoidal Input.

2.      STO- Sinusoidal or Triangular Output.

3.      MO- Multiplying Output, that is, 60mV for Sinusoidal wave and 160mV for Triangular Wave.

4.      Vcc- Power supply, which can be varied in the range from +12Volts to 24Volts.

5.      TC1 & TC2- A capacitor is connected between these two pins.

6.   TR1 & TR2- A resistor Rt1 or Rt2, has to be connected at this pin for generating the required frequency. Hence, a potentiometer is connected at TR2 in our circuit.

7.      FSK- Frequency Shift Key, used for selecting either Rt1 or Rt2.

8.      BIAS- A external capacitor of 10µF is grounded from this pin.

9.    SYNC- An open collector pin, tied to Vcc through a resistor. The square output is generated at this pin.

10.  GND

11. WAVEA1 & WAVEA2- Used for selection of output wave, by using a switch and a resistor connected in series.

     For the purpose of this project, the circuit that we have used is directly taken from the datasheet. The specifications are as follows:

   

Figure 1.5: XR2206 Connections circuit

   

Here,

·         R2= 10kΩ Potentiometer.

·         C= 1nF

  Final Circuit Diagram:

    

Figure 1.6:  Final circuit (output of XR2206 to the input of the LM741 differentiator)

For the signal verification, we have used a DSO for displaying the output for the various signals hereby, concerned with this project. DSO is an oscilloscope which stores and analyses the signal digitally rather than using analog techniques. It is now the most common type of oscilloscope in use because of the advanced trigger, storage, display and measurement features which it typically provides.

Understanding the output:

1. Triangular Wave: Since, a triangular wave is increasing and decreasing ramp signal, that is, 

r(t)=t or r(t)= - t

for some fixed interval, hence derivation of ramp signal is or ,

d r(t)/ dt = 1 or d r(-t)/dt = -1

hence the output will be a square wave or unit step wave.

2. Sine Wave: The derivation of sine wave is cosine wave with a phase shift of 90 degrees.

3. Square Wave: The derivation of square wave is impulse, that is , or , hence the output would be

      δ(t)  = 1;  for t=0;

       = 0; else

FINAL	OUTPUTS
Input Waveform	Output Waveform
1. Square Wave:	1. Impulse peaks:

      

2. Triangular Wave:

2. Square Wave(approx.):

3. Sinusoidal Wave:

3. Cosine Wave:

FINAL

OUTPUTS

Input Waveform

Output Waveform

1. Square Wave:

1. Impulse peaks:

2. Triangular Wave:

2. Square Wave(approx.):

3. Sinusoidal Wave:

3. Cosine Wave:

Here, in the wave forms the Cosine and square wave is clipped due to value of the potentiometer. and also due to noise interference.

Final Circuit:

Find the following documents attached with this mail:

1. LM341 Datasheet:  https://www.sparkfun.com/datasheets/Kits/XR2206_104_020808.pdf
2. XR2206 Datasheet: http://www.ti.com/lit/ds/symlink/lm341.pdf