Experiment 17
Two Differentiators Circuit
Analog Computing
• Analog computers
– First were mechanical systems. Electrical analog
computers were developed in the early 1940’s and
used extensively.
• Maximum speed of response was limited to less than
10 MHz.
• Analog controllers
– PID (proportional-integral-derivative) controllers
• Thermostats
Capacitors
dvC
iC (t )  C
dt
t1
1
vC (t )   iC (t )dt  vC (to )
C to
iR + iC + i =0
where i = 0mA
iR
iC
iC =C1 dVin/dt
i=0
iR = [0V – Vo]/R1
Vo = -R1C1 dVin/dt
If Vin = 0.5V sin(wt), then Vo =[ -R1C1 w cos(wt)] x 0.5V
where -R1C1 w is the maximum gain of the differentiator.
Conversions for Sinusoids
A sin(wt +f)
- A sin(wt +f)
- A cos(wt +f)
A sin(wt +f)
A cos(wt +f)
A cos(wt + f - 90o)
A sin(wt + f + 180o )
Or
A sin(wt + f - 180o )
A cos(wt + f + 180o )
Or
A cos(wt + f - 180o )
A sin (wt + f - 360o)
Or
A sin (wt + f + 360o)
A cos (wt + f - 360o)
Or
A cos (wt + f + 360o)
Sine – Cosine Conversion
• Vin = sin(wt)
•
•
•
•
Vo = -R1C1 w cos(wt)
Vo = R1C1 w cos(wt – 180o)
Vo = R1C1 w sin(wt – 180o + 90o)
Vo = R1C1 w sin(wt – 90o)
When the input voltage is sinusoidal, the output
voltage has a phase shift of 90o with respect to
the input voltage.
Limitation of Ideal Differentiator
• If the input contains electronic noise with high
frequency components, the magnitude of the
high frequency components will be amplified
significantly over the signal of interest and the
system could become unstable.
– It is necessary to modify the circuit to reduce or
eliminate such effects (see Practical Differentiator
circuit in Experiment 16 of the lab manual).
Circuit to be constructed
Velleman Function
Generator
Circuit Construction
• Position of the two switches changes the maximum
gain of the differentiator.
– R1 is determined by setting w R1 C1 = 1 when f is 7.23
kHz. Use 0.1 µF for C1.
– R2 is determined by setting w R2 C1 = 1 when f is 723 Hz.
• Use two of the three slide switches in the parts kit
– Three pin black rectangle with knob
• Middle pin should be connected to the circuit
• Either one of the outer two pins should be connected to the
other portion of the circuit
– Sliding the knob from right to left changes which outer pin is
shorted to the middle pin
Phase Shift
--Dt --
d sin( wt )
 w cos(wt )  w sin( wt  90 o )  w sin( wt  f ) where f is the phase angle.
dt
Dt
1 2
f  -360 degrees where the period of the sine wave is T  
T
f
w
Phase Shift as a Function of Frequency
• The phase shift between the input voltage and
the output voltage of the op amp will change
from 90o to 180o.
Caution:
PSpice Transient Analysis Issue
Information in first half cycle is incorrect because
the initial charge on the capacitor is zero.
Measurement of Phase Angle
• There are two sets of instructions in the Week 11
Module.
– Phase Delay.pdf, which explains how to make a phase
angle calculation using the information displayed
when the Oscilloscope function of the Velleman
oscilloscope is used.
• You should become familiar with this technique.
– Magnitude and Phase.pdf, which explains how to use
the automated measurement tools on the Velleman
scope to obtain the magnitude and phase of a signal
at a single frequency and over a range of frequencies.
dB
• dB is an abbreviation for decibels
 Pout 

dB  10 log 
 Pin 
 Pout  1
 
- 3dB occurs when 
 Pin  2
 Vout 

dB  20 log 
 Vin 
 Vout 
2


- 3dB occurs when 

 0.707

 Vin  2