Wave Function Generation
Microelectronics
Objectives and outlines:
1. Op-amp as a comparator
2. Square wave generator (SQW)
3.Traingular wave generator (TRW)
4. Linear Voltage Controlled Oscillator
(VCO)
Chapter 4:
( Lecture 5 )
Wave Function Generation
Winter 2010
1
1. Op-amp as a comparator
In Open loop
Configuration
The basic op-amp can
be considered as a
comparator if the
voltage gain is very
high, therefore the
transition region is
very small.
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Electronics and Electrical Engineering Department
Prof. Dr. Soliman Mahmoud & Dr. Ahmed Madian
Electronics and Electrical Engineering Department
1. Op-amp as a comparator
In order to improve
the effect of the
transition region a
positive feedback to
the high gain op-amp
connected to obtain
Schmitt trigger
Comparator.
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Vin
Vout
+
R1
R2
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1
1. Op-amp as a comparator
1. Op-amp as a comparator
Therefore, as long as
Vin < V+, the o/p is constant
at + Vcc, As Vin increases,
the o/p remains constant
until Vin reaches to:
The Voltage
Transfer
Characteristic (VTC)
1. Assume the o/p
voltage of Schmitt
trigger is + Vcc,
Therefore :
V+ = VCC
VTH = VCC
Due to the positive FB
action, the o/p is switched to
- Vcc
R2
R1 + R2
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VCC
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R2
R1 + R2
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1. Op-amp as a comparator
1. Op-amp as a comparator
From 1 and 2 , the VTC of the Schmitt trigger
comparator is shown:
2. Similarly, the o/p
remains at – Vcc until
Vin becomes less
than :
VTL = −VCC
R2
R1 + R2
V+ = −VCC
R2
R1 + R2
R2
R1 + R2
Then the o/p switch to
+ VCC
− VCC
− VCC
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R2
R1 + R2
VCC
R2
R1 + R2
R2
R1 + R2
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2
Op-amp as a comparator
Effect of using comparator Schmitt trigger circuit
2. Square wave Generator
SQW can be
designed
using RC
circuit with a
comparator.
R
V- = Vc
+
Vc
-
Vout
C
+
R1
V+
R2
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Electronics and Electrical Engineering Department
Steps of solution
1. Assume Vout = Vcc,
the capacitor will
charge through a time
constant RC to Vcc,
however when the
voltage across the
capacitor reaches to:
VC = VCC
R2
R1 + R2
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Steps of solution
2. When Vout = - Vcc, the
capacitor will discharge
through a time constant
RC to -Vcc, however
when the voltage across
the capacitor reaches to:
V+ = VCC
R2
R1 + R2
VC = −VCC
V+ = −VCC
R2
R1 + R2
The o/p switches to Vcc
The o/p switches to - Vcc
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R2
R1 + R2
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3
Steps of solution
Steps of solution
3. Drawing
the o/p
waveform
and
calculating
the oscillation
frequency
The oscillation frequency fosc can be calculated as follows:
f osc =
1
(T1 + T2 )
Where T1 and T2 are calculated from the exponential equation of
charging and discharging of a Capacitor by a time constant RC as
follow:
T1( or 2 ) = RC ln
R2
VC = VCC
R1 + R2
VC = −VCC
Where VSS is the steady state value of the capacitor.
Vini is the initial value of the capacitor.
And
Vf is the finial vaue.
R2
R1 + R2
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(Vss − Vini )
(Vss − VF )
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Steps of solution
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Notes:
1. T1=T2 Symmetrical SQW
Therefore:
R2
)
R
R2 + R1
T1 = RC ln(
) = RC ln(1 + 2 2 )
R2
R1
Vcc − Vcc
R2 + R1
2. f osc =
R2
R2 + R1
R
T2 = RC ln(
) = RC ln(1 + 2 2 )
R2
R1
− Vcc − (−Vcc
)
R2 + R1
3. Peak to peak value of the o/p waveform
is 2 Vcc
Vcc − ( −Vcc
And similarly
− Vcc − Vcc
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1
2 RC ln(1 + 2
R2
)
R1
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4
Note: Asymmetrical SQW
Asymmetrical SQW
cab be designed by
making the time
constants of charging
and discharging are
different using the
shown circuit:
Report: Find T1 and
T2 and show the o/p
waveform is
asymmetrical SQW
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Note: Asymmetric SQW with limited
output voltage
To limit the output
voltage to a
specific values two
Zener diodes are
used back to back
to limit the output to
+ Vz and –Vz
instead of + Vcc
and –Vcc, as
shown:
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3.Triangular wave generator (TRW)
TRW can be designed using a comparator and an integrator as
shown:
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Analysis
1. let the output of the comparator is –VCC:
Therefore,
R2
R1
V+ = −VCC
+ Vout
R1 + R2
R1 + R2
And the capacitor charge with a constant current and the
output
of the integrator will increase linearly with time.
Therefore, V+ will increase with time until V+ = VR, then the
o/p
of the comparator switch to +VCC and the maximum value
of
R2
R2
Vout is given by: Vout. max = VR (1 + ) + VCC
R1
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R1
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5
Analysis
o/p waveform
2. When the output of the comparator is +VCC:
Therefore,
R2
R1
V+ = VCC
+ Vout
R1 + R2
R1 + R2
(Vout ,max − Vout ,min ) / T1 = (
2VCC R2
(Vcc + Vs )
)=
T1 R1
RC
Therefore T1 is given by: T1 = 2
Similarly T2 is given by: T2 = 2
R2 RC
R1 (1 + Vs )
Vcc
R2 RC
R1 (1 − Vs )
Vcc
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Electronics and Electrical Engineering Department
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g
arg
in
ch
gin
g
ar
ch
g
1. Calculating T1 and T2:
The slope of the output waveform during T1
is given by:
gin
The oscillation frequency
ar
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cg
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Vout ,max
dis
And the capacitor discharge with a constant current and the
Output of the integrator will decrease linearly with time.
Therefore, V+ will increase with time until V+ = VR, then the
o/p of the comparator switch to -VCC and the minimum
value of Vout is given by:
R
R
Vout.min = VR (1 + 2 ) − VCC 2
R1
R1
Vout ,min
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The oscillation frequency
Therefore the oscillation frequency is given by:
f osc =
R 1
Vs 2
1
= 1
[1 − (
) ]
(T1 + T2 ) 4 R2 RC
Vcc
Note that, the voltage Vs can be used to control
the frequency of operation Voltage controlled
Oscillator (VCO)
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6
4. Linear Voltage Controlled
Oscillator (VCO)
4. Linear Voltage Controlled
Oscillator (VCO)
The previous circuit is a simple VCO, but the
disadvantage of this circuit is the nonlinear
relation between frequency and voltage.
The following circuit is used as a linear voltage
control oscillator and its consists of:
- Comparator
- CMOS inverter
- Voltage buffer
- Integrator
As shown in the following figure:
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Analysis
Analysis
1. Consider the output of the comparator =Vcc,
R2
therefore: V = V
2. When the output of the comparator =- Vcc, therefore:
+
CC
R1 + R2
The o/p of the CMOS inverter = -VCTR, the o/p
of the buffer = - VCTR, and the o/p (Vout)
increases linearly with time with slope
(VCTR/RC) until reaches to its maximum value:
R2
Vout ,max = VCC
R1 + R2
at which the o/p of the compartor switch to -Vcc
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V+ = −VCC
R2
R1 + R2
The o/p of the CMOS inverter = VCTR, the o/p of the
buffer = VCTR, and the o/p (Vout) decreases linearly with
time with slope (VCTR/RC) until reaches to its minimum
value:
Vout ,min = −VCC
R2
R1 + R2
at which the o/p of the compartor switch to Vcc and so on
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7
o/p waveform
The oscillation frequency
During T1, the slope is given by:
VccR2
V
R2
V
2
= CTR ⇒ T1 = 2
( CC ) RC
( R1 + R2 )T1 RC
( R1 + R2 ) VCTR
Similarly T2 = T1, and the oscillation
Frequency is given by:
Vout ,max
f osc =
Note that the oscillation frequency is linearly proportional
to the control voltage VCTR .
Vout ,min
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( R1 + R2 ) VCTR
4 R2 RC Vcc
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Wave Function Generation
END of Chapter 4
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