Download 8.4. Practice Problems

CAPÍTULO 8. OSCILADORES SENOSOIDALES
Since
is real,for
to be real
90
must be real. This is satisfied for a frequency
At this frequency,
and
. Thus the magnitude of the loop gain is
, which should be greater than 1 for sustained oscilations, and
Since we neglected
, another condition the must be satisfied is that
8.4. Practice Problems
From chapter 12: problems 3, 9, 10, 13, 14, 21 and 22.
8.4.1. Extra Practice Problems
1. The following diagram shows a Wein-Bridge oscillator using an amplifoer with a nonzero output resistance
. The opamp is ideal. Derive expresions for the frequency of
oscillation and the conditions that
must satisfy for sustained oscillations.
R1
R2
Rout
−
vout
+
R
C
R
C
2. The following circuit is used as the phase-shifting network for a two-stage FET oscilla. Determine the frequency of oscillation and the gain
tor. Find the circuit’s beta,
required from the amplifier. (30 points)
R
+
vo
-
C
C
R
+
vf
-
CAPÍTULO 8. OSCILADORES SENOSOIDALES
91
3. Design a 680kHz Wein-bridge oscillator. Use an ideal op-amp as your active element.
4. For the oscilator circuit shown below, the two transistors have
below is 5 points.
. Each part
a) Draw a diagram of the phase shift network.
b) Find
from the diagram drawn in part (a).
c) Determine the loop gain,
SHIFT NETWORK.
. HINT: THE GAIN WILL DEPEND ON THE PHASE
d) Apply the Barkhausen Criterion to find the frequency of oscillation.
e) Find the minimum value of
that would satisfy the Barkhausen Criterion.
VCC
RD
RD
vO
vi
M1
M2
L=25mH
C=0.1µF
R=1MΩ
5. For the oscillator shown below, derive an expression for the frequency of oscillation in
is required for oscillations to be maintained?
terms of and . What minimum value of
R1
R2
−
vO
+
C
R
R
C
6. For the Colpitts oscillator shown below, find values for
duce sustained oscillations at
if
. Use
,
and
.
appropriate to pro-
CAPÍTULO 8. OSCILADORES SENOSOIDALES
92
vO
L2
C1
RD
C3
CAPÍTULO 8. OSCILADORES SENOSOIDALES
Solutions
1.
93
CAPÍTULO 8. OSCILADORES SENOSOIDALES
2. Let
be defined as follows
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CAPÍTULO 8. OSCILADORES SENOSOIDALES
R
95
VA
C
+
vo
-
+
C
R
vf
-
Zeq
Then
Applying the voltage divider rule,
To satisfy the Barkhausen Criterion,
or
At
,
; thus the amplifier gain should be grater or equal than 3.
3. From your lecture notes,
and
and
. You can set the gain to
.
The resulting circuit is the following:
. So for
by selecting
, select
, or
and
CAPÍTULO 8. OSCILADORES SENOSOIDALES
96
1k
9k
−
vOUT
+
234nF 1k
234nF
4.
1k
a) The phase-shift network is
0.1µF
vo
vf
25mH
b) Find
1MΩ
from the diagram drawn in part (a).
c) The impedance seen looking into the phase-shift network is
so that the impedance connected to the drain is
d) The frequency of oscillation is
CAPÍTULO 8. OSCILADORES SENOSOIDALES
97
e) The minimum value of
that would satisfy the Barkhausen Criterion should be
found from the gain at . For minimum
,
From this the second order equation
is obtained. The solution is
.
5. The feedback network is identical to the one shown in problem 1. Thus
6. The phase-shift network
is
The impedance at the drain is
The Barkhausen Criterion requires that
which leads to the following expression for the frequency of oscillation:
CAPÍTULO 8. OSCILADORES SENOSOIDALES
Selecting
and
leads to
or
To select
, apply the magnitude criterion which requires that
For the component values chosen,
A good selection would be
.
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