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:
|
|