oscillators oscillators with lc feedback circuits
TRANSCRIPT
Oscillators
Oscillators with LC Feedback Circuits
Oscillators
Oscillators With LC Feedback Circuits
•For frequencies above 1 MHz, LC feedback oscillators are used.
•LC feedback oscillators use resonant circuits in the feedback path.
•We will discuss the Colpitts, Hartley and crystal-controlled oscillators.
•Transistors are used as the active device in these types.
LC Oscillators – Colpitts
The Colpitts
oscillator utilizes a
tank circuit (LC) in
the feedback loop
to provide the
necessary phase
shift and to act as
a resonant filter
that passes only
the desired
frequency of
oscillation.
R 2 R 4 C 4
C 3
LC 1 C 2
R 1 R 3 C 5 V out
Amplifier
Feedbackcircuit
V CC
A popular LC oscillator is the Colpitts oscillator. It uses two series capacitors in the resonant circuit. The feedback voltage is developed across C1.
In
L
Vf Vout
AvVf
Vout
IC1 C2
Out
The effect is that the tank circuit is “tapped”. Usually C1 is the larger capacitor because it develops the smaller voltage.
LC Oscillators – Colpitts
LC Oscillators – Colpitts
The resonant frequency can be determined by the formula below.
T
rLC
f2
1
L
Zin
C1 C2
Vout2
2T
1
12πr
Qf
QLC
• Figure below shows the input impedance of the amplifier acts as a load on the resonant feedback circuit and reduces the Q of the circuit.
• The resonant frequency of a parallel resonant circuit depends on the Q, according to the formula below:
LC Oscillators – Colpitts
LC Oscillators – Hartley
C 1
C 2 C 4
C 3
C 5
R 1 R 3
R 2 R 4
L 1 L 2
VCC
V out
Amplifier
Feedbackcircuit
The Hartley oscillator is similar to the Colpitts except that the feedback circuit consists of two series inductors and a parallel capacitor.
The frequency of oscillation for Q > 10 is:
In
AvVf
Vout
Out L1 L2
C
One advantage of a Hartley oscillator is that it can be tuned by using a variable capacitor in the resonant circuit.
T 1 2
1 1
2π 2πrf
L C L L C
LC Oscillators – Hartley
where LT = L1 + L2
LC Oscillators – Crystal-Controlled
The crystal-controlled oscillator is the most stable and
accurate of all oscillators. A crystal has a natural
frequency of resonance. Quartz material can be cut or
shaped to have a certain frequency.
Quartzwafer
XTAL
(a) Typical packaged crystal
(b) Basic construction (without case)
(b) Symbol (b) Electrical equivalent
L sC s
R s
C m
Since crystal has natural resonant frequencies of 20 MHz or less, generation of higher frequencies is attained by operating the crystal in what is called the overtone mode
LC Oscillators – Crystal-Controlled
XTAL
C 1
V out
V CC
R 2 R 4
C C
R 1 R 3 C 2
Oscillators
Relaxation Oscillators
Oscillators – Relaxation
Relaxation oscillators make use of an RC timing and a device that changes states to generate a periodic waveform (non-sinusoidal).
1. Triangular-wave
2. Square-wave
3. Sawtooth
Oscillators – Relaxation
Triangular-wave oscillator
Triangular-wave oscillator circuit is a combination of a comparator and integrator circuit.
Comparator
IntegratorV out
C
R 1
R 3
R 2
A square wave can be taken as an output here.
Oscillators – Relaxation
Triangular-wave oscillator
• Assume that the output voltage of the comparator is at its maximum negative level.
• This output is connected to the inverting input of the integrator through R1, producing a positive-going ramp on the output of the integrator.
• When the ramp voltage reaches the UTP, the comparator switches to its maximum positive level.
•This positive level causes the integrator ramp to change to a negative-going direction.
•The ramp continues in this direction until the LTP of the comparator is reached and the cycle repeats.
Oscillators – Relaxation
Triangular-wave oscillator
Comparator output
+Vmax
V out
- Vmax
V UTP
V LTP
Oscillators – Relaxation
Triangular-wave oscillator
3
2
14
1
R
R
CRfr
2
3max R
RVVUTP
-
2
3max R
RVVLTP
Amplitude of the triangular output is set by establishing the UTP and LTP voltages according to the following formulas:
The frequency of both waveforms depends on the R1C time constant as well as the amplitude-setting resistors, R2 and R3. By varying R1, the fr can be adjusted without changing the output amplitude.
Determine the frequency of oscillation of the circuit in figure below. To what value must R1 be changed to make the frequency 20 kHz?
Oscillators – Relaxation - EXAMPLE
Answer: fr = 8.25 kHz, R1 = 4.13 kOhm
Oscillators – Square-wave
A square wave relaxation oscillator is like the
Schmitt trigger or Comparator circuit.
The charging and discharging of the capacitor
cause the op-amp to switch states rapidly and
produce a square wave.
The RC time constant determines the frequency.
Oscillators – Square-wave
C
R 1
R 3
R 2
V C
V fV out
Oscillators – Square-wave
Oscillators – Sawtooth voltage controlled oscillator (VCO)
R i
V IN
0 V
PUTV G
V out
V p
I
+-
Sawtooth VCO circuit is a combination of a Programmable Unijunction Transistor (PUT) and integrator circuit.
Oscillators – Sawtooth VCO
OPERATION
Initially, dc input = -VIN
• Vout = 0V, Vanode < VG
• The circuit is like an integrator.
• Capacitor is charging.
• Output is increasing positive going ramp.
Oscillators – Sawtooth VCO
OPERATION
R i
V IN
0 V
PUTV G
V out
V p
I
+-
0
Oscillators – Sawtooth VCO
OPERATION
When Vout = VP
• Vanode > VG , PUT turns ‘ON’
• The capacitor rapidly discharges.
• Vout drop until Vout = VF.
• Vanode < VG , PUT turns ‘OFF’
VP – maximum peak value
VF – minimum peak value
Oscillators – Sawtooth VCO
OPERATION
Oscillation frequency
-
FPi
IN
VVCR
Vf
1
Oscillators – Sawtooth VCO
EXAMPLE
In the following circuit, let VF = 1V.
a) Find;
(i) amplitude;
(ii) frequency;
b) Sketch the output waveform
Oscillators – Sawtooth VCO
EXAMPLE (cont’d)
Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (i) Amplitude
V 5.7151010
10
43
4
VRR
RVG
V 5.7 GP VV V 1FVand
So, the peak-to-peak amplitude is;
V 5.615.7 -- FP VV
Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (ii) Frequency
-
FPi
IN
VVCR
Vf
1
V 92.121
2 --
VRR
RVIN
Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (ii) Frequency
Hz 628
V1V5.7
1
μ0047.0k100
92.1
-f
Oscillators – Sawtooth VCO
EXAMPLE – Solution
b) Output waveform
2 ms
V out
1 V
7.5 V
t
ms 2628
11
fT
OscillatorsThe 555 timer as an oscillator
OscillatorsThe 555 Timer As An Oscillator
The 555 timer is an integrated circuit that can be
used in many applications. The frequency of
output is determined by the external components
R1, R2, and C. The formula below shows the
relationship.
extr CRRf
21 2
144
OscillatorsThe 555 Timer As An Oscillator
Duty cycles can be adjusted by values of R1 and R2. The duty cycle is limited to 50% with this arrangement. To have duty cycles less than 50%, a diode is placed across R2. The two formulas show the relationship;
Duty Cycle > 50 %
%1002
cycleDuty 21
21
RR
RR
OscillatorsThe 555 Timer As An Oscillator
Duty Cycle < 50 %
%100cycleDuty 21
1
RR
R
OscillatorsThe 555 Timer As An Oscillator
OscillatorsThe 555 Timer As An Oscillator
The 555 timer may be operated as a VCO with a control voltage applied to the CONT input (pin 5).
END CHAPTER 5