CAP´ITULO 8. OSCILADORES SENOSOIDALES
Since is real,for to be real 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
90
From chapter 12: problems 3, 9, 10, 13, 14, 21 and 22.
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.
R
1
R
2
R out
−
+ v out
R
R C
C
2. The following circuit is used as the phase-shifting network for a two-stage FET oscillator. Find the circuit’s beta, . Determine the frequency of oscillation and the gain required from the amplifier. (30 points)
R
-
+ v o C
C
R
-
+ v f

CAP´ITULO 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.
v i
R
D
M
1
R
D
V
CC v
O
M
2
L=25mH
R=1M Ω
C=0.1
µ F
5. For the oscillator shown below, derive an expression for the frequency of oscillation in terms of and . What minimum value of is required for oscillations to be maintained?
R
1
R
C
−
+
R
2
C
R v
O
6. For the Colpitts oscillator shown below, find values for , and duce sustained oscillations at if . Use .
appropriate to pro-

CAP´ITULO 8. OSCILADORES SENOSOIDALES
L
2
C
1
C
3
R
D v
O
92

CAP´ITULO 8. OSCILADORES SENOSOIDALES
Solutions
93
1.

CAP´ITULO 8. OSCILADORES SENOSOIDALES 94
2. Let be defined as follows

CAP´ITULO 8. OSCILADORES SENOSOIDALES
+ v o
-
R V
A
C
C
R
+
v f
Z eq
Then
Applying the voltage divider rule,
95
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
The resulting circuit is the following:
. So for
. You can set the gain to by selecting , or
, select and

CAP´ITULO 8. OSCILADORES SENOSOIDALES
1k 9k
−
+
234nF 1k
234nF
1k v
OUT
4.
a ) The phase-shift network is v o
0.1
µ F
25mH v f
1M Ω b ) Find 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
96 d ) The frequency of oscillation is

CAP´ITULO 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:

CAP´ITULO 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 .
98